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py-why/dowhy

Functional api/estimate effect function

#### Estimate Effect function * Refactors the estimate effect into a separate function to keep backwards compatibility #### TODO (future PRs): * Add `fit(...)` method to estimators - Move data related parameters from the constructor to the `fit(...)` method * Refactor code to avoid `**kwargs` in `__init__(...)` constructors

2022-10-18 15:49:21+00:00

2022-10-25 17:02:02+00:00

dowhy/causal_estimator.py

import logging from collections import namedtuple import numpy as np import pandas as pd import sympy as sp from sklearn.utils import resample import dowhy.interpreters as interpreters from dowhy.utils.api import parse_state class CausalEstimator: """Base class for an estimator of causal effect. Subclasses implement different estimation methods. All estimation methods are in the package "dowhy.causal_estimators" """ # The default number of simulations for statistical testing DEFAULT_NUMBER_OF_SIMULATIONS_STAT_TEST = 1000 # The default number of simulations to obtain confidence intervals DEFAULT_NUMBER_OF_SIMULATIONS_CI = 100 # The portion of the total size that should be taken each time to find the confidence intervals # 1 is the recommended value # https://ocw.mit.edu/courses/mathematics/18-05-introduction-to-probability-and-statistics-spring-2014/readings/MIT18_05S14_Reading24.pdf # https://projecteuclid.org/download/pdf_1/euclid.ss/1032280214 DEFAULT_SAMPLE_SIZE_FRACTION = 1 # The default Confidence Level DEFAULT_CONFIDENCE_LEVEL = 0.95 # Number of quantiles to discretize continuous columns, for applying groupby NUM_QUANTILES_TO_DISCRETIZE_CONT_COLS = 5 # Prefix to add to temporary categorical variables created after discretization TEMP_CAT_COLUMN_PREFIX = "__categorical__" DEFAULT_NOTIMPLEMENTEDERROR_MSG = "not yet implemented for {0}. If you would this to be implemented in the next version, please raise an issue at https://github.com/microsoft/dowhy/issues" BootstrapEstimates = namedtuple("BootstrapEstimates", ["estimates", "params"]) DEFAULT_INTERPRET_METHOD = ["textual_effect_interpreter"] # std args to be removed from locals() before being passed to args_dict _STD_INIT_ARGS = ("self", "__class__", "args", "kwargs") def __init__( self, data, identified_estimand, treatment, outcome, control_value=0, treatment_value=1, test_significance=False, evaluate_effect_strength=False, confidence_intervals=False, target_units=None, effect_modifiers=None, num_null_simulations=DEFAULT_NUMBER_OF_SIMULATIONS_STAT_TEST, num_simulations=DEFAULT_NUMBER_OF_SIMULATIONS_CI, sample_size_fraction=DEFAULT_SAMPLE_SIZE_FRACTION, confidence_level=DEFAULT_CONFIDENCE_LEVEL, need_conditional_estimates="auto", num_quantiles_to_discretize_cont_cols=NUM_QUANTILES_TO_DISCRETIZE_CONT_COLS, **kwargs, ): """Initializes an estimator with data and names of relevant variables. This method is called from the constructors of its child classes. :param data: data frame containing the data :param identified_estimand: probability expression representing the target identified estimand to estimate. :param treatment: name of the treatment variable :param outcome: name of the outcome variable :param control_value: Value of the treatment in the control group, for effect estimation. If treatment is multi-variate, this can be a list. :param treatment_value: Value of the treatment in the treated group, for effect estimation. If treatment is multi-variate, this can be a list. :param test_significance: Binary flag or a string indicating whether to test significance and by which method. All estimators support test_significance="bootstrap" that estimates a p-value for the obtained estimate using the bootstrap method. Individual estimators can override this to support custom testing methods. The bootstrap method supports an optional parameter, num_null_simulations. If False, no testing is done. If True, significance of the estimate is tested using the custom method if available, otherwise by bootstrap. :param evaluate_effect_strength: (Experimental) whether to evaluate the strength of effect :param confidence_intervals: Binary flag or a string indicating whether the confidence intervals should be computed and which method should be used. All methods support estimation of confidence intervals using the bootstrap method by using the parameter confidence_intervals="bootstrap". The bootstrap method takes in two arguments (num_simulations and sample_size_fraction) that can be optionally specified in the params dictionary. Estimators may also override this to implement their own confidence interval method. If this parameter is False, no confidence intervals are computed. If True, confidence intervals are computed by the estimator's specific method if available, otherwise through bootstrap. :param target_units: The units for which the treatment effect should be estimated. This can be a string for common specifications of target units (namely, "ate", "att" and "atc"). It can also be a lambda function that can be used as an index for the data (pandas DataFrame). Alternatively, it can be a new DataFrame that contains values of the effect_modifiers and effect will be estimated only for this new data. :param effect_modifiers: Variables on which to compute separate effects, or return a heterogeneous effect function. Not all methods support this currently. :param num_null_simulations: The number of simulations for testing the statistical significance of the estimator :param num_simulations: The number of simulations for finding the confidence interval (and/or standard error) for a estimate :param sample_size_fraction: The size of the sample for the bootstrap estimator :param confidence_level: The confidence level of the confidence interval estimate :param need_conditional_estimates: Boolean flag indicating whether conditional estimates should be computed. Defaults to True if there are effect modifiers in the graph :param num_quantiles_to_discretize_cont_cols: The number of quantiles into which a numeric effect modifier is split, to enable estimation of conditional treatment effect over it. :param kwargs: (optional) Additional estimator-specific parameters :returns: an instance of the estimator class. """ self._data = data self._target_estimand = identified_estimand # Currently estimation methods only support univariate treatment and outcome self._treatment_name = treatment self._outcome_name = outcome[0] # assuming one-dimensional outcome self._control_value = control_value self._treatment_value = treatment_value self._significance_test = test_significance self._effect_strength_eval = evaluate_effect_strength self._target_units = target_units self._effect_modifier_names = effect_modifiers self._confidence_intervals = confidence_intervals self._bootstrap_estimates = None # for confidence intervals and std error self._bootstrap_null_estimates = None # for significance test self._effect_modifiers = None self.method_params = kwargs # Setting the default interpret method self.interpret_method = CausalEstimator.DEFAULT_INTERPRET_METHOD self.logger = logging.getLogger(__name__) # Setting treatment and outcome values if self._data is not None: self._treatment = self._data[self._treatment_name] self._outcome = self._data[self._outcome_name] # Now saving the effect modifiers if self._effect_modifier_names: # only add the observed nodes self._effect_modifier_names = [ cname for cname in self._effect_modifier_names if cname in self._data.columns ] if len(self._effect_modifier_names) > 0: self._effect_modifiers = self._data[self._effect_modifier_names] self._effect_modifiers = pd.get_dummies(self._effect_modifiers, drop_first=True) self.logger.debug("Effect modifiers: " + ",".join(self._effect_modifier_names)) else: self._effect_modifier_names = None # Check if some parameters were set, otherwise set to default values self.num_null_simulations = num_null_simulations self.num_simulations = num_simulations self.sample_size_fraction = sample_size_fraction self.confidence_level = confidence_level self.num_quantiles_to_discretize_cont_cols = num_quantiles_to_discretize_cont_cols # Estimate conditional estimates by default self.need_conditional_estimates = ( need_conditional_estimates if need_conditional_estimates != "auto" else bool(self._effect_modifier_names) ) @staticmethod def get_estimator_object(new_data, identified_estimand, estimate): """Create a new estimator of the same type as the one passed in the estimate argument. Creates a new object with new_data and the identified_estimand :param new_data: np.ndarray, pd.Series, pd.DataFrame The newly assigned data on which the estimator should run :param identified_estimand: IdentifiedEstimand An instance of the identified estimand class that provides the information with respect to which causal pathways are employed when the treatment effects the outcome :param estimate: CausalEstimate It is an already existing estimate whose properties we wish to replicate :returns: An instance of the same estimator class that had generated the given estimate. """ estimator_class = estimate.params["estimator_class"] new_estimator = estimator_class( new_data, identified_estimand, identified_estimand.treatment_variable, identified_estimand.outcome_variable, # names of treatment and outcome control_value=estimate.control_value, treatment_value=estimate.treatment_value, test_significance=False, evaluate_effect_strength=False, confidence_intervals=estimate.params["confidence_intervals"], target_units=estimate.params["target_units"], effect_modifiers=estimate.params["effect_modifiers"], **estimate.params["method_params"], ) return new_estimator def _estimate_effect(self): """This method is to be overriden by the child classes, so that they can run the estimation technique of their choice""" raise NotImplementedError( ("Main estimation method is " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG).format(self.__class__) ) def estimate_effect(self): """Base estimation method that calls the estimate_effect method of its calling subclass. Can optionally also test significance and estimate effect strength for any returned estimate. :param self: object instance of class Estimator :returns: A CausalEstimate instance that contains point estimates of average and conditional effects. Based on the parameters provided, it optionally includes confidence intervals, standard errors,statistical significance and other statistical parameters. """ est = self._estimate_effect() est.add_estimator(self) if self._significance_test: self.test_significance(est.value, method=self._significance_test) if self._confidence_intervals: self.estimate_confidence_intervals( est.value, confidence_level=self.confidence_level, method=self._confidence_intervals ) if self._effect_strength_eval: effect_strength_dict = self.evaluate_effect_strength(est) est.add_effect_strength(effect_strength_dict) return est def estimate_effect_naive(self): # TODO Only works for binary treatment df_withtreatment = self._data.loc[self._data[self._treatment_name] == 1] df_notreatment = self._data.loc[self._data[self._treatment_name] == 0] est = np.mean(df_withtreatment[self._outcome_name]) - np.mean(df_notreatment[self._outcome_name]) return CausalEstimate(est, None, None, control_value=0, treatment_value=1) def _estimate_effect_fn(self, data_df): """Function used in conditional effect estimation. This function is to be overridden by each child estimator. The overridden function should take in a dataframe as input and return the estimate for that data. """ raise NotImplementedError( ("Conditional treatment effects are " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG).format( self.__class__ ) ) def _estimate_conditional_effects(self, estimate_effect_fn, effect_modifier_names=None, num_quantiles=None): """Estimate conditional treatment effects. Common method for all estimators that utilizes a specific estimate_effect_fn implemented by each child estimator. If a numeric effect modifier is provided, it is discretized into quantile bins. If you would like a custom discretization, you can do so yourself: create a new column containing the discretized effect modifier and then include that column's name in the effect_modifier_names argument. :param estimate_effect_fn: Function that has a single parameter (a data frame) and returns the treatment effect estimate on that data. :param effect_modifier_names: Names of effect modifier variables over which the conditional effects will be estimated. If not provided, defaults to the effect modifiers specified during creation of the CausalEstimator object. :param num_quantiles: The number of quantiles into which a numeric effect modifier variable is discretized. Does not affect any categorical effect modifiers. :returns: A (multi-index) dataframe that provides separate effects for each value of the (discretized) effect modifiers. """ # Defaulting to class default values if parameters are not provided if effect_modifier_names is None: effect_modifier_names = self._effect_modifier_names if num_quantiles is None: num_quantiles = self.num_quantiles_to_discretize_cont_cols # Checking that there is at least one effect modifier if not effect_modifier_names: raise ValueError("At least one effect modifier should be specified to compute conditional effects.") # Making sure that effect_modifier_names is a list effect_modifier_names = parse_state(effect_modifier_names) if not all(em in self._effect_modifier_names for em in effect_modifier_names): self.logger.warn( "At least one of the provided effect modifiers was not included while fitting the estimator. You may get incorrect results. To resolve, fit the estimator again by providing the updated effect modifiers in estimate_effect()." ) # Making a copy since we are going to be changing effect modifier names effect_modifier_names = effect_modifier_names.copy() prefix = CausalEstimator.TEMP_CAT_COLUMN_PREFIX # For every numeric effect modifier, adding a temp categorical column for i in range(len(effect_modifier_names)): em = effect_modifier_names[i] if pd.api.types.is_numeric_dtype(self._data[em].dtypes): self._data[prefix + str(em)] = pd.qcut(self._data[em], num_quantiles, duplicates="drop") effect_modifier_names[i] = prefix + str(em) # Grouping by effect modifiers and computing effect separately by_effect_mods = self._data.groupby(effect_modifier_names) cond_est_fn = lambda x: self._do(self._treatment_value, x) - self._do(self._control_value, x) conditional_estimates = by_effect_mods.apply(estimate_effect_fn) # Deleting the temporary categorical columns for em in effect_modifier_names: if em.startswith(prefix): self._data.pop(em) return conditional_estimates def _do(self, x, data_df=None): raise NotImplementedError( ("Do-operator is " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG).format(self.__class__) ) def do(self, x, data_df=None): """Method that implements the do-operator. Given a value x for the treatment, returns the expected value of the outcome when the treatment is intervened to a value x. :param x: Value of the treatment :param data_df: Data on which the do-operator is to be applied. :returns: Value of the outcome when treatment is intervened/set to x. """ est = self._do(x, data_df) return est def construct_symbolic_estimator(self, estimand): raise NotImplementedError(("Symbolic estimator string is ").format(self.__class__)) def _generate_bootstrap_estimates(self, num_bootstrap_simulations, sample_size_fraction): """Helper function to generate causal estimates over bootstrapped samples. :param num_bootstrap_simulations: Number of simulations for the bootstrap method. :param sample_size_fraction: Fraction of the dataset to be resampled. :returns: A collections.namedtuple containing a list of bootstrapped estimates and a dictionary containing parameters used for the bootstrap. """ # The array that stores the results of all estimations simulation_results = np.zeros(num_bootstrap_simulations) # Find the sample size the proportion with the population size sample_size = int(sample_size_fraction * len(self._data)) if sample_size > len(self._data): self.logger.warning("WARN: The sample size is greater than the data being sampled") self.logger.info("INFO: The sample size: {}".format(sample_size)) self.logger.info("INFO: The number of simulations: {}".format(num_bootstrap_simulations)) # Perform the set number of simulations for index in range(num_bootstrap_simulations): new_data = resample(self._data, n_samples=sample_size) new_estimator = type(self)( new_data, self._target_estimand, self._target_estimand.treatment_variable, self._target_estimand.outcome_variable, # names of treatment and outcome treatment_value=self._treatment_value, control_value=self._control_value, test_significance=False, evaluate_effect_strength=False, confidence_intervals=False, target_units=self._target_units, effect_modifiers=self._effect_modifier_names, **self.method_params, ) new_effect = new_estimator.estimate_effect() simulation_results[index] = new_effect.value estimates = CausalEstimator.BootstrapEstimates( simulation_results, {"num_simulations": num_bootstrap_simulations, "sample_size_fraction": sample_size_fraction}, ) return estimates def _estimate_confidence_intervals_with_bootstrap( self, estimate_value, confidence_level=None, num_simulations=None, sample_size_fraction=None ): """ Method to compute confidence interval using bootstrapped sampling. :param estimate_value: obtained estimate's value :param confidence_level: The level for which to compute CI (e.g., 95% confidence level translates to confidence_level=0.95) :param num_simulations: The number of simulations to be performed to get the bootstrap confidence intervals. :param sample_size_fraction: The fraction of the dataset to be resampled. :returns: confidence interval at the specified level. For more details on bootstrap or resampling statistics, refer to the following links: https://ocw.mit.edu/courses/mathematics/18-05-introduction-to-probability-and-statistics-spring-2014/readings/MIT18_05S14_Reading24.pdf https://projecteuclid.org/download/pdf_1/euclid.ss/1032280214 """ # Using class default parameters if not specified if num_simulations is None: num_simulations = self.num_simulations if sample_size_fraction is None: sample_size_fraction = self.sample_size_fraction # Checking if bootstrap_estimates are already computed if self._bootstrap_estimates is None: self._bootstrap_estimates = self._generate_bootstrap_estimates(num_simulations, sample_size_fraction) elif CausalEstimator.is_bootstrap_parameter_changed(self._bootstrap_estimates.params, locals()): # Checked if any parameter is changed from the previous std error estimate self._bootstrap_estimates = self._generate_bootstrap_estimates(num_simulations, sample_size_fraction) # Now use the data obtained from the simulations to get the value of the confidence estimates bootstrap_estimates = self._bootstrap_estimates.estimates # Get the variations of each bootstrap estimate and sort bootstrap_variations = [bootstrap_estimate - estimate_value for bootstrap_estimate in bootstrap_estimates] sorted_bootstrap_variations = np.sort(bootstrap_variations) # Now we take the (1- p)th and the (p)th variations, where p is the chosen confidence level upper_bound_index = int((1 - confidence_level) * len(sorted_bootstrap_variations)) lower_bound_index = int(confidence_level * len(sorted_bootstrap_variations)) # Get the lower and upper bounds by subtracting the variations from the estimate lower_bound = estimate_value - sorted_bootstrap_variations[lower_bound_index] upper_bound = estimate_value - sorted_bootstrap_variations[upper_bound_index] return lower_bound, upper_bound def _estimate_confidence_intervals(self, confidence_level=None, method=None, **kwargs): """ This method is to be overriden by the child classes, so that they can run a confidence interval estimation method suited to the specific causal estimator. """ raise NotImplementedError( ( "This method for estimating confidence intervals is " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG + " Meanwhile, you can try the bootstrap method (method='bootstrap') to estimate confidence intervals." ).format(self.__class__) ) def estimate_confidence_intervals(self, estimate_value, confidence_level=None, method=None, **kwargs): """Find the confidence intervals corresponding to any estimator By default, this is done with the help of bootstrapped confidence intervals but can be overridden if the specific estimator implements other methods of estimating confidence intervals. If the method provided is not bootstrap, this function calls the implementation of the specific estimator. :param estimate_value: obtained estimate's value :param method: Method for estimating confidence intervals. :param confidence_level: The confidence level of the confidence intervals of the estimate. :param kwargs: Other optional args to be passed to the CI method. :returns: The obtained confidence interval. """ if method is None: if self._confidence_intervals: method = self._confidence_intervals # this is either True or methodname else: method = "default" confidence_intervals = None if confidence_level is None: confidence_level = self.confidence_level if method == "default" or method is True: # user has not provided any method try: confidence_intervals = self._estimate_confidence_intervals(confidence_level, method=method, **kwargs) except NotImplementedError: confidence_intervals = self._estimate_confidence_intervals_with_bootstrap( estimate_value, confidence_level, **kwargs ) else: if method == "bootstrap": confidence_intervals = self._estimate_confidence_intervals_with_bootstrap( estimate_value, confidence_level, **kwargs ) else: confidence_intervals = self._estimate_confidence_intervals(confidence_level, method=method, **kwargs) return confidence_intervals def _estimate_std_error_with_bootstrap(self, num_simulations=None, sample_size_fraction=None): """Compute standard error using the bootstrap method. Standard error and confidence intervals use the same parameter num_simulations for the number of bootstrap simulations. :param num_simulations: Number of bootstrapped samples. :param sample_size_fraction: Fraction of data to be resampled. :returns: Standard error of the obtained estimate. """ # Use existing params, if new user defined params are not present if num_simulations is None: num_simulations = self.num_simulations if sample_size_fraction is None: sample_size_fraction = self.sample_size_fraction # Checking if bootstrap_estimates are already computed if self._bootstrap_estimates is None: self._bootstrap_estimates = self._generate_bootstrap_estimates(num_simulations, sample_size_fraction) elif CausalEstimator.is_bootstrap_parameter_changed(self._bootstrap_estimates.params, locals()): # Check if any parameter is changed from the previous std error estimate self._bootstrap_estimates = self._generate_bootstrap_estimates(num_simulations, sample_size_fraction) std_error = np.std(self._bootstrap_estimates.estimates) return std_error def _estimate_std_error(self, method=None, **kwargs): """ This method is to be overriden by the child classes, so that they can run a standard error estimation method suited to the specific causal estimator. """ raise NotImplementedError( ( "This method for estimating standard errors is " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG + " Meanwhile, you can try the bootstrap method (method='bootstrap') to estimate standard errors." ).format(self.__class__) ) def estimate_std_error(self, method=None, **kwargs): """Compute standard error of an obtained causal estimate. :param method: Method for computing the standard error. :param kwargs: Other optional parameters to be passed to the estimating method. :returns: Standard error of the causal estimate. """ if method is None: if self._confidence_intervals: method = self._confidence_intervals else: method = "default" std_error = None if method == "default" or method is True: # user has not provided any method try: std_error = self._estimate_std_error(method, **kwargs) except NotImplementedError: std_error = self._estimate_std_error_with_bootstrap(**kwargs) else: if method == "bootstrap": std_error = self._estimate_std_error_with_bootstrap(**kwargs) else: std_error = self._estimate_std_error(method, **kwargs) return std_error def _test_significance_with_bootstrap(self, estimate_value, num_null_simulations=None): """Test statistical significance of an estimate using the bootstrap method. :param estimate_value: Obtained estimate's value :param num_null_simulations: Number of simulations for the null hypothesis :returns: p-value of the statistical significance test. """ # Use existing params, if new user defined params are not present if num_null_simulations is None: num_null_simulations = self.num_null_simulations do_retest = self._bootstrap_null_estimates is None or CausalEstimator.is_bootstrap_parameter_changed( self._bootstrap_null_estimates.params, locals() ) if do_retest: null_estimates = np.zeros(num_null_simulations) for i in range(num_null_simulations): new_outcome = np.random.permutation(self._outcome) new_data = self._data.assign(dummy_outcome=new_outcome) # self._outcome = self._data["dummy_outcome"] new_estimator = type(self)( new_data, self._target_estimand, self._target_estimand.treatment_variable, ("dummy_outcome",), test_significance=False, evaluate_effect_strength=False, confidence_intervals=False, target_units=self._target_units, effect_modifiers=self._effect_modifier_names, **self.method_params, ) new_effect = new_estimator.estimate_effect() null_estimates[i] = new_effect.value self._bootstrap_null_estimates = CausalEstimator.BootstrapEstimates( null_estimates, {"num_null_simulations": num_null_simulations, "sample_size_fraction": 1} ) # Processing the null hypothesis estimates sorted_null_estimates = np.sort(self._bootstrap_null_estimates.estimates) self.logger.debug("Null estimates: {0}".format(sorted_null_estimates)) median_estimate = sorted_null_estimates[int(num_null_simulations / 2)] # Doing a two-sided test if estimate_value > median_estimate: # Being conservative with the p-value reported estimate_index = np.searchsorted(sorted_null_estimates, estimate_value, side="left") p_value = 1 - (estimate_index / num_null_simulations) if estimate_value <= median_estimate: # Being conservative with the p-value reported estimate_index = np.searchsorted(sorted_null_estimates, estimate_value, side="right") p_value = estimate_index / num_null_simulations # If the estimate_index is 0, it depends on the number of simulations if p_value == 0: p_value = (0, 1 / len(sorted_null_estimates)) # a tuple determining the range. elif p_value == 1: p_value = (1 - 1 / len(sorted_null_estimates), 1) signif_dict = {"p_value": p_value} return signif_dict def _test_significance(self, estimate_value, method=None, **kwargs): """ This method is to be overriden by the child classes, so that they can run a significance test suited to the specific causal estimator. """ raise NotImplementedError( ( "This method for testing statistical significance is " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG + " Meanwhile, you can try the bootstrap method (method='bootstrap') to test statistical significance." ).format(self.__class__) ) def test_significance(self, estimate_value, method=None, **kwargs): """Test statistical significance of obtained estimate. By default, uses resampling to create a non-parametric significance test. A general procedure. Individual child estimators can implement different methods. If the method name is different from "bootstrap", this function calls the implementation of the child estimator. :param self: object instance of class Estimator :param estimate_value: obtained estimate's value :param method: Method for checking statistical significance :returns: p-value from the significance test """ if method is None: if self._significance_test: method = self._significance_test # this is either True or methodname else: method = "default" signif_dict = None if method == "default" or method is True: # user has not provided any method try: signif_dict = self._test_significance(estimate_value, method, **kwargs) except NotImplementedError: signif_dict = self._test_significance_with_bootstrap(estimate_value, **kwargs) else: if method == "bootstrap": signif_dict = self._test_significance_with_bootstrap(estimate_value, **kwargs) else: signif_dict = self._test_significance(estimate_value, method, **kwargs) return signif_dict def evaluate_effect_strength(self, estimate): fraction_effect_explained = self._evaluate_effect_strength(estimate, method="fraction-effect") # Need to test r-squared before supporting # effect_r_squared = self._evaluate_effect_strength(estimate, method="r-squared") strength_dict = { "fraction-effect": fraction_effect_explained # 'r-squared': effect_r_squared } return strength_dict def _evaluate_effect_strength(self, estimate, method="fraction-effect"): supported_methods = ["fraction-effect"] if method not in supported_methods: raise NotImplementedError("This method is not supported for evaluating effect strength") if method == "fraction-effect": naive_obs_estimate = self.estimate_effect_naive() self.logger.debug(estimate.value, naive_obs_estimate.value) fraction_effect_explained = estimate.value / naive_obs_estimate.value return fraction_effect_explained # elif method == "r-squared": # outcome_mean = np.mean(self._outcome) # total_variance = np.sum(np.square(self._outcome - outcome_mean)) # Assuming a linear model with one variable: the treatment # Currently only works for continuous y # causal_model = outcome_mean + estimate.value*self._treatment # squared_residual = np.sum(np.square(self._outcome - causal_model)) # r_squared = 1 - (squared_residual/total_variance) # return r_squared else: return None def update_input(self, treatment_value, control_value, target_units): self._control_value = control_value self._treatment_value = treatment_value self._target_units = target_units @staticmethod def is_bootstrap_parameter_changed(bootstrap_estimates_params, given_params): """Check whether parameters of the bootstrap have changed. This is an efficiency method that checks if fresh resampling of the bootstrap samples is required. Returns True if parameters have changed and resampling should be done again. :param bootstrap_estimates_params: A dictionary of parameters for the current bootstrap samples :param given_params: A dictionary of parameters passed by the user :returns: A binary flag denoting whether the parameters are different. """ is_any_parameter_changed = False for prm, val in bootstrap_estimates_params.items(): given_val = given_params.get(prm, None) if given_val is not None and given_val != val: is_any_parameter_changed = True break return is_any_parameter_changed def target_units_tostr(self): s = "" if type(self._target_units) is str: s += self._target_units elif callable(self._target_units): s += "Data subset defined by a function" elif isinstance(self._target_units, pd.DataFrame): s += "Data subset provided as a data frame" return s def signif_results_tostr(self, signif_results): s = "" pval = signif_results["p_value"] if type(pval) is tuple: s += "[{0}, {1}]".format(pval[0], pval[1]) else: s += "{0}".format(pval) return s class CausalEstimate: """Class for the estimate object that every causal estimator returns""" def __init__( self, estimate, target_estimand, realized_estimand_expr, control_value, treatment_value, conditional_estimates=None, **kwargs, ): self.value = estimate self.target_estimand = target_estimand self.realized_estimand_expr = realized_estimand_expr self.control_value = control_value self.treatment_value = treatment_value self.conditional_estimates = conditional_estimates self.params = kwargs if self.params is not None: for key, value in self.params.items(): setattr(self, key, value) self.effect_strength = None def add_estimator(self, estimator_instance): self.estimator = estimator_instance def add_effect_strength(self, strength_dict): self.effect_strength = strength_dict def add_params(self, **kwargs): self.params.update(kwargs) def get_confidence_intervals(self, confidence_level=None, method=None, **kwargs): """Get confidence intervals of the obtained estimate. By default, this is done with the help of bootstrapped confidence intervals but can be overridden if the specific estimator implements other methods of estimating confidence intervals. If the method provided is not bootstrap, this function calls the implementation of the specific estimator. :param method: Method for estimating confidence intervals. :param confidence_level: The confidence level of the confidence intervals of the estimate. :param kwargs: Other optional args to be passed to the CI method. :returns: The obtained confidence interval. """ confidence_intervals = self.estimator.estimate_confidence_intervals( estimate_value=self.value, confidence_level=confidence_level, method=method, **kwargs ) return confidence_intervals def get_standard_error(self, method=None, **kwargs): """Get standard error of the obtained estimate. By default, this is done with the help of bootstrapped standard errors but can be overridden if the specific estimator implements other methods of estimating standard error. If the method provided is not bootstrap, this function calls the implementation of the specific estimator. :param method: Method for computing the standard error. :param kwargs: Other optional parameters to be passed to the estimating method. :returns: Standard error of the causal estimate. """ std_error = self.estimator.estimate_std_error(method=method, **kwargs) return std_error def test_stat_significance(self, method=None, **kwargs): """Test statistical significance of the estimate obtained. By default, uses resampling to create a non-parametric significance test. Individual child estimators can implement different methods. If the method name is different from "bootstrap", this function calls the implementation of the child estimator. :param method: Method for checking statistical significance :param kwargs: Other optional parameters to be passed to the estimating method. :returns: p-value from the significance test """ signif_results = self.estimator.test_significance(self.value, method=method, **kwargs) return {"p_value": signif_results["p_value"]} def estimate_conditional_effects( self, effect_modifiers=None, num_quantiles=CausalEstimator.NUM_QUANTILES_TO_DISCRETIZE_CONT_COLS ): """Estimate treatment effect conditioned on given variables. If a numeric effect modifier is provided, it is discretized into quantile bins. If you would like a custom discretization, you can do so yourself: create a new column containing the discretized effect modifier and then include that column's name in the effect_modifier_names argument. :param effect_modifiers: Names of effect modifier variables over which the conditional effects will be estimated. If not provided, defaults to the effect modifiers specified during creation of the CausalEstimator object. :param num_quantiles: The number of quantiles into which a numeric effect modifier variable is discretized. Does not affect any categorical effect modifiers. :returns: A (multi-index) dataframe that provides separate effects for each value of the (discretized) effect modifiers. """ return self.estimator._estimate_conditional_effects( self.estimator._estimate_effect_fn, effect_modifiers, num_quantiles ) def interpret(self, method_name=None, **kwargs): """Interpret the causal estimate. :param method_name: Method used (string) or a list of methods. If None, then the default for the specific estimator is used. :param kwargs:: Optional parameters that are directly passed to the interpreter method. :returns: None """ if method_name is None: method_name = self.estimator.interpret_method method_name_arr = parse_state(method_name) for method in method_name_arr: interpreter = interpreters.get_class_object(method) interpreter(self, **kwargs).interpret() def __str__(self): s = "*** Causal Estimate ***\n" # No estimand was identified (identification failed) if self.target_estimand is None: return "Estimation failed! No relevant identified estimand available for this estimation method." s += "\n## Identified estimand\n{0}".format(self.target_estimand.__str__(only_target_estimand=True)) s += "\n## Realized estimand\n{0}".format(self.realized_estimand_expr) if hasattr(self, "estimator"): s += "\nTarget units: {0}\n".format(self.estimator.target_units_tostr()) s += "\n## Estimate\n" s += "Mean value: {0}\n".format(self.value) s += "" if hasattr(self, "cate_estimates"): s += "Effect estimates: {0}\n".format(self.cate_estimates) if hasattr(self, "estimator"): if self.estimator._significance_test: s += "p-value: {0}\n".format(self.estimator.signif_results_tostr(self.test_stat_significance())) if self.estimator._confidence_intervals: s += "{0}% confidence interval: {1}\n".format( 100 * self.estimator.confidence_level, self.get_confidence_intervals() ) if self.conditional_estimates is not None: s += "### Conditional Estimates\n" s += str(self.conditional_estimates) if self.effect_strength is not None: s += "\n## Effect Strength\n" s += "Change in outcome attributable to treatment: {}\n".format(self.effect_strength["fraction-effect"]) # s += "Variance in outcome explained by treatment: {}\n".format(self.effect_strength["r-squared"]) return s class RealizedEstimand(object): def __init__(self, identified_estimand, estimator_name): self.treatment_variable = identified_estimand.treatment_variable self.outcome_variable = identified_estimand.outcome_variable self.backdoor_variables = identified_estimand.get_backdoor_variables() self.instrumental_variables = identified_estimand.instrumental_variables self.estimand_type = identified_estimand.estimand_type self.estimand_expression = None self.assumptions = None self.estimator_name = estimator_name def update_assumptions(self, estimator_assumptions): self.assumptions = estimator_assumptions def update_estimand_expression(self, estimand_expression): self.estimand_expression = estimand_expression def __str__(self): s = "Realized estimand: {0}\n".format(self.estimator_name) s += "Realized estimand type: {0}\n".format(self.estimand_type) s += "Estimand expression:\n{0}\n".format(sp.pretty(self.estimand_expression)) j = 1 for ass_name, ass_str in self.assumptions.items(): s += "Estimand assumption {0}, {1}: {2}\n".format(j, ass_name, ass_str) j += 1 return s

import logging from collections import namedtuple from typing import Dict, List, Optional, Union import numpy as np import pandas as pd import sympy as sp from sklearn.utils import resample import dowhy.interpreters as interpreters from dowhy import causal_estimators from dowhy.causal_graph import CausalGraph from dowhy.causal_identifier.identified_estimand import IdentifiedEstimand from dowhy.utils.api import parse_state logger = logging.getLogger(__name__) class CausalEstimator: """Base class for an estimator of causal effect. Subclasses implement different estimation methods. All estimation methods are in the package "dowhy.causal_estimators" """ # The default number of simulations for statistical testing DEFAULT_NUMBER_OF_SIMULATIONS_STAT_TEST = 1000 # The default number of simulations to obtain confidence intervals DEFAULT_NUMBER_OF_SIMULATIONS_CI = 100 # The portion of the total size that should be taken each time to find the confidence intervals # 1 is the recommended value # https://ocw.mit.edu/courses/mathematics/18-05-introduction-to-probability-and-statistics-spring-2014/readings/MIT18_05S14_Reading24.pdf # https://projecteuclid.org/download/pdf_1/euclid.ss/1032280214 DEFAULT_SAMPLE_SIZE_FRACTION = 1 # The default Confidence Level DEFAULT_CONFIDENCE_LEVEL = 0.95 # Number of quantiles to discretize continuous columns, for applying groupby NUM_QUANTILES_TO_DISCRETIZE_CONT_COLS = 5 # Prefix to add to temporary categorical variables created after discretization TEMP_CAT_COLUMN_PREFIX = "__categorical__" DEFAULT_NOTIMPLEMENTEDERROR_MSG = "not yet implemented for {0}. If you would this to be implemented in the next version, please raise an issue at https://github.com/microsoft/dowhy/issues" BootstrapEstimates = namedtuple("BootstrapEstimates", ["estimates", "params"]) DEFAULT_INTERPRET_METHOD = ["textual_effect_interpreter"] # std args to be removed from locals() before being passed to args_dict _STD_INIT_ARGS = ("self", "__class__", "args", "kwargs") def __init__( self, data, identified_estimand, treatment, outcome, control_value=0, treatment_value=1, test_significance=False, evaluate_effect_strength=False, confidence_intervals=False, target_units=None, effect_modifiers=None, num_null_simulations=DEFAULT_NUMBER_OF_SIMULATIONS_STAT_TEST, num_simulations=DEFAULT_NUMBER_OF_SIMULATIONS_CI, sample_size_fraction=DEFAULT_SAMPLE_SIZE_FRACTION, confidence_level=DEFAULT_CONFIDENCE_LEVEL, need_conditional_estimates="auto", num_quantiles_to_discretize_cont_cols=NUM_QUANTILES_TO_DISCRETIZE_CONT_COLS, **kwargs, ): """Initializes an estimator with data and names of relevant variables. This method is called from the constructors of its child classes. :param data: data frame containing the data :param identified_estimand: probability expression representing the target identified estimand to estimate. :param treatment: name of the treatment variable :param outcome: name of the outcome variable :param control_value: Value of the treatment in the control group, for effect estimation. If treatment is multi-variate, this can be a list. :param treatment_value: Value of the treatment in the treated group, for effect estimation. If treatment is multi-variate, this can be a list. :param test_significance: Binary flag or a string indicating whether to test significance and by which method. All estimators support test_significance="bootstrap" that estimates a p-value for the obtained estimate using the bootstrap method. Individual estimators can override this to support custom testing methods. The bootstrap method supports an optional parameter, num_null_simulations. If False, no testing is done. If True, significance of the estimate is tested using the custom method if available, otherwise by bootstrap. :param evaluate_effect_strength: (Experimental) whether to evaluate the strength of effect :param confidence_intervals: Binary flag or a string indicating whether the confidence intervals should be computed and which method should be used. All methods support estimation of confidence intervals using the bootstrap method by using the parameter confidence_intervals="bootstrap". The bootstrap method takes in two arguments (num_simulations and sample_size_fraction) that can be optionally specified in the params dictionary. Estimators may also override this to implement their own confidence interval method. If this parameter is False, no confidence intervals are computed. If True, confidence intervals are computed by the estimator's specific method if available, otherwise through bootstrap. :param target_units: The units for which the treatment effect should be estimated. This can be a string for common specifications of target units (namely, "ate", "att" and "atc"). It can also be a lambda function that can be used as an index for the data (pandas DataFrame). Alternatively, it can be a new DataFrame that contains values of the effect_modifiers and effect will be estimated only for this new data. :param effect_modifiers: Variables on which to compute separate effects, or return a heterogeneous effect function. Not all methods support this currently. :param num_null_simulations: The number of simulations for testing the statistical significance of the estimator :param num_simulations: The number of simulations for finding the confidence interval (and/or standard error) for a estimate :param sample_size_fraction: The size of the sample for the bootstrap estimator :param confidence_level: The confidence level of the confidence interval estimate :param need_conditional_estimates: Boolean flag indicating whether conditional estimates should be computed. Defaults to True if there are effect modifiers in the graph :param num_quantiles_to_discretize_cont_cols: The number of quantiles into which a numeric effect modifier is split, to enable estimation of conditional treatment effect over it. :param kwargs: (optional) Additional estimator-specific parameters :returns: an instance of the estimator class. """ self._data = data self._target_estimand = identified_estimand # Currently estimation methods only support univariate treatment and outcome self._treatment_name = treatment self._outcome_name = outcome[0] # assuming one-dimensional outcome self._control_value = control_value self._treatment_value = treatment_value self._significance_test = test_significance self._effect_strength_eval = evaluate_effect_strength self._target_units = target_units self._effect_modifier_names = effect_modifiers self._confidence_intervals = confidence_intervals self._bootstrap_estimates = None # for confidence intervals and std error self._bootstrap_null_estimates = None # for significance test self._effect_modifiers = None self.method_params = kwargs # Setting the default interpret method self.interpret_method = CausalEstimator.DEFAULT_INTERPRET_METHOD self.logger = logging.getLogger(__name__) # Setting treatment and outcome values if self._data is not None: self._treatment = self._data[self._treatment_name] self._outcome = self._data[self._outcome_name] if self._effect_modifier_names: # only add the observed nodes self._effect_modifier_names = [ cname for cname in self._effect_modifier_names if cname in self._data.columns ] if len(self._effect_modifier_names) > 0: self._effect_modifiers = self._data[self._effect_modifier_names] self._effect_modifiers = pd.get_dummies(self._effect_modifiers, drop_first=True) self.logger.debug("Effect modifiers: " + ",".join(self._effect_modifier_names)) else: self._effect_modifier_names = None # Check if some parameters were set, otherwise set to default values self.num_null_simulations = num_null_simulations self.num_simulations = num_simulations self.sample_size_fraction = sample_size_fraction self.confidence_level = confidence_level self.num_quantiles_to_discretize_cont_cols = num_quantiles_to_discretize_cont_cols # Estimate conditional estimates by default self.need_conditional_estimates = ( need_conditional_estimates if need_conditional_estimates != "auto" else bool(self._effect_modifier_names) ) @staticmethod def get_estimator_object(new_data, identified_estimand, estimate): """Create a new estimator of the same type as the one passed in the estimate argument. Creates a new object with new_data and the identified_estimand :param new_data: np.ndarray, pd.Series, pd.DataFrame The newly assigned data on which the estimator should run :param identified_estimand: IdentifiedEstimand An instance of the identified estimand class that provides the information with respect to which causal pathways are employed when the treatment effects the outcome :param estimate: CausalEstimate It is an already existing estimate whose properties we wish to replicate :returns: An instance of the same estimator class that had generated the given estimate. """ estimator_class = estimate.params["estimator_class"] new_estimator = estimator_class( new_data, identified_estimand, identified_estimand.treatment_variable, identified_estimand.outcome_variable, # names of treatment and outcome control_value=estimate.control_value, treatment_value=estimate.treatment_value, test_significance=False, evaluate_effect_strength=False, confidence_intervals=estimate.params["confidence_intervals"], target_units=estimate.params["target_units"], effect_modifiers=estimate.params["effect_modifiers"], **estimate.params["method_params"] if estimate.params["method_params"] is not None else {}, ) return new_estimator def _estimate_effect(self): """This method is to be overriden by the child classes, so that they can run the estimation technique of their choice""" raise NotImplementedError( ("Main estimation method is " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG).format(self.__class__) ) def estimate_effect(self): """Base estimation method that calls the estimate_effect method of its calling subclass. Can optionally also test significance and estimate effect strength for any returned estimate. :param self: object instance of class Estimator :returns: A CausalEstimate instance that contains point estimates of average and conditional effects. Based on the parameters provided, it optionally includes confidence intervals, standard errors,statistical significance and other statistical parameters. """ est = self._estimate_effect() est.add_estimator(self) if self._significance_test: self.test_significance(est.value, method=self._significance_test) if self._confidence_intervals: self.estimate_confidence_intervals( est.value, confidence_level=self.confidence_level, method=self._confidence_intervals ) if self._effect_strength_eval: effect_strength_dict = self.evaluate_effect_strength(est) est.add_effect_strength(effect_strength_dict) return est def estimate_effect_naive(self): # TODO Only works for binary treatment df_withtreatment = self._data.loc[self._data[self._treatment_name] == 1] df_notreatment = self._data.loc[self._data[self._treatment_name] == 0] est = np.mean(df_withtreatment[self._outcome_name]) - np.mean(df_notreatment[self._outcome_name]) return CausalEstimate(est, None, None, control_value=0, treatment_value=1) def _estimate_effect_fn(self, data_df): """Function used in conditional effect estimation. This function is to be overridden by each child estimator. The overridden function should take in a dataframe as input and return the estimate for that data. """ raise NotImplementedError( ("Conditional treatment effects are " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG).format( self.__class__ ) ) def _estimate_conditional_effects(self, estimate_effect_fn, effect_modifier_names=None, num_quantiles=None): """Estimate conditional treatment effects. Common method for all estimators that utilizes a specific estimate_effect_fn implemented by each child estimator. If a numeric effect modifier is provided, it is discretized into quantile bins. If you would like a custom discretization, you can do so yourself: create a new column containing the discretized effect modifier and then include that column's name in the effect_modifier_names argument. :param estimate_effect_fn: Function that has a single parameter (a data frame) and returns the treatment effect estimate on that data. :param effect_modifier_names: Names of effect modifier variables over which the conditional effects will be estimated. If not provided, defaults to the effect modifiers specified during creation of the CausalEstimator object. :param num_quantiles: The number of quantiles into which a numeric effect modifier variable is discretized. Does not affect any categorical effect modifiers. :returns: A (multi-index) dataframe that provides separate effects for each value of the (discretized) effect modifiers. """ # Defaulting to class default values if parameters are not provided if effect_modifier_names is None: effect_modifier_names = self._effect_modifier_names if num_quantiles is None: num_quantiles = self.num_quantiles_to_discretize_cont_cols # Checking that there is at least one effect modifier if not effect_modifier_names: raise ValueError("At least one effect modifier should be specified to compute conditional effects.") # Making sure that effect_modifier_names is a list effect_modifier_names = parse_state(effect_modifier_names) if not all(em in self._effect_modifier_names for em in effect_modifier_names): self.logger.warn( "At least one of the provided effect modifiers was not included while fitting the estimator. You may get incorrect results. To resolve, fit the estimator again by providing the updated effect modifiers in estimate_effect()." ) # Making a copy since we are going to be changing effect modifier names effect_modifier_names = effect_modifier_names.copy() prefix = CausalEstimator.TEMP_CAT_COLUMN_PREFIX # For every numeric effect modifier, adding a temp categorical column for i in range(len(effect_modifier_names)): em = effect_modifier_names[i] if pd.api.types.is_numeric_dtype(self._data[em].dtypes): self._data[prefix + str(em)] = pd.qcut(self._data[em], num_quantiles, duplicates="drop") effect_modifier_names[i] = prefix + str(em) # Grouping by effect modifiers and computing effect separately by_effect_mods = self._data.groupby(effect_modifier_names) cond_est_fn = lambda x: self._do(self._treatment_value, x) - self._do(self._control_value, x) conditional_estimates = by_effect_mods.apply(estimate_effect_fn) # Deleting the temporary categorical columns for em in effect_modifier_names: if em.startswith(prefix): self._data.pop(em) return conditional_estimates def _do(self, x, data_df=None): raise NotImplementedError( ("Do-operator is " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG).format(self.__class__) ) def do(self, x, data_df=None): """Method that implements the do-operator. Given a value x for the treatment, returns the expected value of the outcome when the treatment is intervened to a value x. :param x: Value of the treatment :param data_df: Data on which the do-operator is to be applied. :returns: Value of the outcome when treatment is intervened/set to x. """ est = self._do(x, data_df) return est def construct_symbolic_estimator(self, estimand): raise NotImplementedError(("Symbolic estimator string is ").format(self.__class__)) def _generate_bootstrap_estimates(self, num_bootstrap_simulations, sample_size_fraction): """Helper function to generate causal estimates over bootstrapped samples. :param num_bootstrap_simulations: Number of simulations for the bootstrap method. :param sample_size_fraction: Fraction of the dataset to be resampled. :returns: A collections.namedtuple containing a list of bootstrapped estimates and a dictionary containing parameters used for the bootstrap. """ # The array that stores the results of all estimations simulation_results = np.zeros(num_bootstrap_simulations) # Find the sample size the proportion with the population size sample_size = int(sample_size_fraction * len(self._data)) if sample_size > len(self._data): self.logger.warning("WARN: The sample size is greater than the data being sampled") self.logger.info("INFO: The sample size: {}".format(sample_size)) self.logger.info("INFO: The number of simulations: {}".format(num_bootstrap_simulations)) # Perform the set number of simulations for index in range(num_bootstrap_simulations): new_data = resample(self._data, n_samples=sample_size) new_estimator = type(self)( new_data, self._target_estimand, self._target_estimand.treatment_variable, self._target_estimand.outcome_variable, # names of treatment and outcome treatment_value=self._treatment_value, control_value=self._control_value, test_significance=False, evaluate_effect_strength=False, confidence_intervals=False, target_units=self._target_units, effect_modifiers=self._effect_modifier_names, **self.method_params, ) new_effect = new_estimator.estimate_effect() simulation_results[index] = new_effect.value estimates = CausalEstimator.BootstrapEstimates( simulation_results, {"num_simulations": num_bootstrap_simulations, "sample_size_fraction": sample_size_fraction}, ) return estimates def _estimate_confidence_intervals_with_bootstrap( self, estimate_value, confidence_level=None, num_simulations=None, sample_size_fraction=None ): """ Method to compute confidence interval using bootstrapped sampling. :param estimate_value: obtained estimate's value :param confidence_level: The level for which to compute CI (e.g., 95% confidence level translates to confidence_level=0.95) :param num_simulations: The number of simulations to be performed to get the bootstrap confidence intervals. :param sample_size_fraction: The fraction of the dataset to be resampled. :returns: confidence interval at the specified level. For more details on bootstrap or resampling statistics, refer to the following links: https://ocw.mit.edu/courses/mathematics/18-05-introduction-to-probability-and-statistics-spring-2014/readings/MIT18_05S14_Reading24.pdf https://projecteuclid.org/download/pdf_1/euclid.ss/1032280214 """ # Using class default parameters if not specified if num_simulations is None: num_simulations = self.num_simulations if sample_size_fraction is None: sample_size_fraction = self.sample_size_fraction # Checking if bootstrap_estimates are already computed if self._bootstrap_estimates is None: self._bootstrap_estimates = self._generate_bootstrap_estimates(num_simulations, sample_size_fraction) elif CausalEstimator.is_bootstrap_parameter_changed(self._bootstrap_estimates.params, locals()): # Checked if any parameter is changed from the previous std error estimate self._bootstrap_estimates = self._generate_bootstrap_estimates(num_simulations, sample_size_fraction) # Now use the data obtained from the simulations to get the value of the confidence estimates bootstrap_estimates = self._bootstrap_estimates.estimates # Get the variations of each bootstrap estimate and sort bootstrap_variations = [bootstrap_estimate - estimate_value for bootstrap_estimate in bootstrap_estimates] sorted_bootstrap_variations = np.sort(bootstrap_variations) # Now we take the (1- p)th and the (p)th variations, where p is the chosen confidence level upper_bound_index = int((1 - confidence_level) * len(sorted_bootstrap_variations)) lower_bound_index = int(confidence_level * len(sorted_bootstrap_variations)) # Get the lower and upper bounds by subtracting the variations from the estimate lower_bound = estimate_value - sorted_bootstrap_variations[lower_bound_index] upper_bound = estimate_value - sorted_bootstrap_variations[upper_bound_index] return lower_bound, upper_bound def _estimate_confidence_intervals(self, confidence_level=None, method=None, **kwargs): """ This method is to be overriden by the child classes, so that they can run a confidence interval estimation method suited to the specific causal estimator. """ raise NotImplementedError( ( "This method for estimating confidence intervals is " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG + " Meanwhile, you can try the bootstrap method (method='bootstrap') to estimate confidence intervals." ).format(self.__class__) ) def estimate_confidence_intervals(self, estimate_value, confidence_level=None, method=None, **kwargs): """Find the confidence intervals corresponding to any estimator By default, this is done with the help of bootstrapped confidence intervals but can be overridden if the specific estimator implements other methods of estimating confidence intervals. If the method provided is not bootstrap, this function calls the implementation of the specific estimator. :param estimate_value: obtained estimate's value :param method: Method for estimating confidence intervals. :param confidence_level: The confidence level of the confidence intervals of the estimate. :param kwargs: Other optional args to be passed to the CI method. :returns: The obtained confidence interval. """ if method is None: if self._confidence_intervals: method = self._confidence_intervals # this is either True or methodname else: method = "default" confidence_intervals = None if confidence_level is None: confidence_level = self.confidence_level if method == "default" or method is True: # user has not provided any method try: confidence_intervals = self._estimate_confidence_intervals(confidence_level, method=method, **kwargs) except NotImplementedError: confidence_intervals = self._estimate_confidence_intervals_with_bootstrap( estimate_value, confidence_level, **kwargs ) else: if method == "bootstrap": confidence_intervals = self._estimate_confidence_intervals_with_bootstrap( estimate_value, confidence_level, **kwargs ) else: confidence_intervals = self._estimate_confidence_intervals(confidence_level, method=method, **kwargs) return confidence_intervals def _estimate_std_error_with_bootstrap(self, num_simulations=None, sample_size_fraction=None): """Compute standard error using the bootstrap method. Standard error and confidence intervals use the same parameter num_simulations for the number of bootstrap simulations. :param num_simulations: Number of bootstrapped samples. :param sample_size_fraction: Fraction of data to be resampled. :returns: Standard error of the obtained estimate. """ # Use existing params, if new user defined params are not present if num_simulations is None: num_simulations = self.num_simulations if sample_size_fraction is None: sample_size_fraction = self.sample_size_fraction # Checking if bootstrap_estimates are already computed if self._bootstrap_estimates is None: self._bootstrap_estimates = self._generate_bootstrap_estimates(num_simulations, sample_size_fraction) elif CausalEstimator.is_bootstrap_parameter_changed(self._bootstrap_estimates.params, locals()): # Check if any parameter is changed from the previous std error estimate self._bootstrap_estimates = self._generate_bootstrap_estimates(num_simulations, sample_size_fraction) std_error = np.std(self._bootstrap_estimates.estimates) return std_error def _estimate_std_error(self, method=None, **kwargs): """ This method is to be overriden by the child classes, so that they can run a standard error estimation method suited to the specific causal estimator. """ raise NotImplementedError( ( "This method for estimating standard errors is " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG + " Meanwhile, you can try the bootstrap method (method='bootstrap') to estimate standard errors." ).format(self.__class__) ) def estimate_std_error(self, method=None, **kwargs): """Compute standard error of an obtained causal estimate. :param method: Method for computing the standard error. :param kwargs: Other optional parameters to be passed to the estimating method. :returns: Standard error of the causal estimate. """ if method is None: if self._confidence_intervals: method = self._confidence_intervals else: method = "default" std_error = None if method == "default" or method is True: # user has not provided any method try: std_error = self._estimate_std_error(method, **kwargs) except NotImplementedError: std_error = self._estimate_std_error_with_bootstrap(**kwargs) else: if method == "bootstrap": std_error = self._estimate_std_error_with_bootstrap(**kwargs) else: std_error = self._estimate_std_error(method, **kwargs) return std_error def _test_significance_with_bootstrap(self, estimate_value, num_null_simulations=None): """Test statistical significance of an estimate using the bootstrap method. :param estimate_value: Obtained estimate's value :param num_null_simulations: Number of simulations for the null hypothesis :returns: p-value of the statistical significance test. """ # Use existing params, if new user defined params are not present if num_null_simulations is None: num_null_simulations = self.num_null_simulations do_retest = self._bootstrap_null_estimates is None or CausalEstimator.is_bootstrap_parameter_changed( self._bootstrap_null_estimates.params, locals() ) if do_retest: null_estimates = np.zeros(num_null_simulations) for i in range(num_null_simulations): new_outcome = np.random.permutation(self._outcome) new_data = self._data.assign(dummy_outcome=new_outcome) # self._outcome = self._data["dummy_outcome"] new_estimator = type(self)( new_data, self._target_estimand, self._target_estimand.treatment_variable, ("dummy_outcome",), test_significance=False, evaluate_effect_strength=False, confidence_intervals=False, target_units=self._target_units, effect_modifiers=self._effect_modifier_names, **self.method_params, ) new_effect = new_estimator.estimate_effect() null_estimates[i] = new_effect.value self._bootstrap_null_estimates = CausalEstimator.BootstrapEstimates( null_estimates, {"num_null_simulations": num_null_simulations, "sample_size_fraction": 1} ) # Processing the null hypothesis estimates sorted_null_estimates = np.sort(self._bootstrap_null_estimates.estimates) self.logger.debug("Null estimates: {0}".format(sorted_null_estimates)) median_estimate = sorted_null_estimates[int(num_null_simulations / 2)] # Doing a two-sided test if estimate_value > median_estimate: # Being conservative with the p-value reported estimate_index = np.searchsorted(sorted_null_estimates, estimate_value, side="left") p_value = 1 - (estimate_index / num_null_simulations) if estimate_value <= median_estimate: # Being conservative with the p-value reported estimate_index = np.searchsorted(sorted_null_estimates, estimate_value, side="right") p_value = estimate_index / num_null_simulations # If the estimate_index is 0, it depends on the number of simulations if p_value == 0: p_value = (0, 1 / len(sorted_null_estimates)) # a tuple determining the range. elif p_value == 1: p_value = (1 - 1 / len(sorted_null_estimates), 1) signif_dict = {"p_value": p_value} return signif_dict def _test_significance(self, estimate_value, method=None, **kwargs): """ This method is to be overriden by the child classes, so that they can run a significance test suited to the specific causal estimator. """ raise NotImplementedError( ( "This method for testing statistical significance is " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG + " Meanwhile, you can try the bootstrap method (method='bootstrap') to test statistical significance." ).format(self.__class__) ) def test_significance(self, estimate_value, method=None, **kwargs): """Test statistical significance of obtained estimate. By default, uses resampling to create a non-parametric significance test. A general procedure. Individual child estimators can implement different methods. If the method name is different from "bootstrap", this function calls the implementation of the child estimator. :param self: object instance of class Estimator :param estimate_value: obtained estimate's value :param method: Method for checking statistical significance :returns: p-value from the significance test """ if method is None: if self._significance_test: method = self._significance_test # this is either True or methodname else: method = "default" signif_dict = None if method == "default" or method is True: # user has not provided any method try: signif_dict = self._test_significance(estimate_value, method, **kwargs) except NotImplementedError: signif_dict = self._test_significance_with_bootstrap(estimate_value, **kwargs) else: if method == "bootstrap": signif_dict = self._test_significance_with_bootstrap(estimate_value, **kwargs) else: signif_dict = self._test_significance(estimate_value, method, **kwargs) return signif_dict def evaluate_effect_strength(self, estimate): fraction_effect_explained = self._evaluate_effect_strength(estimate, method="fraction-effect") # Need to test r-squared before supporting # effect_r_squared = self._evaluate_effect_strength(estimate, method="r-squared") strength_dict = { "fraction-effect": fraction_effect_explained # 'r-squared': effect_r_squared } return strength_dict def _evaluate_effect_strength(self, estimate, method="fraction-effect"): supported_methods = ["fraction-effect"] if method not in supported_methods: raise NotImplementedError("This method is not supported for evaluating effect strength") if method == "fraction-effect": naive_obs_estimate = self.estimate_effect_naive() self.logger.debug(estimate.value, naive_obs_estimate.value) fraction_effect_explained = estimate.value / naive_obs_estimate.value return fraction_effect_explained # elif method == "r-squared": # outcome_mean = np.mean(self._outcome) # total_variance = np.sum(np.square(self._outcome - outcome_mean)) # Assuming a linear model with one variable: the treatment # Currently only works for continuous y # causal_model = outcome_mean + estimate.value*self._treatment # squared_residual = np.sum(np.square(self._outcome - causal_model)) # r_squared = 1 - (squared_residual/total_variance) # return r_squared else: return None def update_input(self, treatment_value, control_value, target_units): self._control_value = control_value self._treatment_value = treatment_value self._target_units = target_units @staticmethod def is_bootstrap_parameter_changed(bootstrap_estimates_params, given_params): """Check whether parameters of the bootstrap have changed. This is an efficiency method that checks if fresh resampling of the bootstrap samples is required. Returns True if parameters have changed and resampling should be done again. :param bootstrap_estimates_params: A dictionary of parameters for the current bootstrap samples :param given_params: A dictionary of parameters passed by the user :returns: A binary flag denoting whether the parameters are different. """ is_any_parameter_changed = False for prm, val in bootstrap_estimates_params.items(): given_val = given_params.get(prm, None) if given_val is not None and given_val != val: is_any_parameter_changed = True break return is_any_parameter_changed def target_units_tostr(self): s = "" if type(self._target_units) is str: s += self._target_units elif callable(self._target_units): s += "Data subset defined by a function" elif isinstance(self._target_units, pd.DataFrame): s += "Data subset provided as a data frame" return s def signif_results_tostr(self, signif_results): s = "" pval = signif_results["p_value"] if type(pval) is tuple: s += "[{0}, {1}]".format(pval[0], pval[1]) else: s += "{0}".format(pval) return s def estimate_effect( treatment: Union[str, List[str]], outcome: Union[str, List[str]], identified_estimand: IdentifiedEstimand, identifier_name: str, method: CausalEstimator, control_value: int = 0, treatment_value: int = 1, test_significance: Optional[bool] = None, evaluate_effect_strength: bool = False, confidence_intervals: bool = False, target_units: str = "ate", effect_modifiers: List[str] = [], fit_estimator: bool = True, method_params: Optional[Dict] = None, ): """Estimate the identified causal effect. Currently requires an explicit method name to be specified. Method names follow the convention of identification method followed by the specific estimation method: "[backdoor/iv].estimation_method_name". Following methods are supported. * Propensity Score Matching: "backdoor.propensity_score_matching" * Propensity Score Stratification: "backdoor.propensity_score_stratification" * Propensity Score-based Inverse Weighting: "backdoor.propensity_score_weighting" * Linear Regression: "backdoor.linear_regression" * Generalized Linear Models (e.g., logistic regression): "backdoor.generalized_linear_model" * Instrumental Variables: "iv.instrumental_variable" * Regression Discontinuity: "iv.regression_discontinuity" In addition, you can directly call any of the EconML estimation methods. The convention is "backdoor.econml.path-to-estimator-class". For example, for the double machine learning estimator ("DML" class) that is located inside "dml" module of EconML, you can use the method name, "backdoor.econml.dml.DML". CausalML estimators can also be called. See `this demo notebook <https://py-why.github.io/dowhy/example_notebooks/dowhy-conditional-treatment-effects.html>`_. :param treatment: Name of the treatment :param outcome: Name of the outcome :param identified_estimand: a probability expression that represents the effect to be estimated. Output of CausalModel.identify_effect method :param method_name: name of the estimation method to be used. :param control_value: Value of the treatment in the control group, for effect estimation. If treatment is multi-variate, this can be a list. :param treatment_value: Value of the treatment in the treated group, for effect estimation. If treatment is multi-variate, this can be a list. :param test_significance: Binary flag on whether to additionally do a statistical signficance test for the estimate. :param evaluate_effect_strength: (Experimental) Binary flag on whether to estimate the relative strength of the treatment's effect. This measure can be used to compare different treatments for the same outcome (by running this method with different treatments sequentially). :param confidence_intervals: (Experimental) Binary flag indicating whether confidence intervals should be computed. :param target_units: (Experimental) The units for which the treatment effect should be estimated. This can be of three types. (1) a string for common specifications of target units (namely, "ate", "att" and "atc"), (2) a lambda function that can be used as an index for the data (pandas DataFrame), or (3) a new DataFrame that contains values of the effect_modifiers and effect will be estimated only for this new data. :param effect_modifiers: Names of effect modifier variables can be (optionally) specified here too, since they do not affect identification. If None, the effect_modifiers from the CausalModel are used. :param fit_estimator: Boolean flag on whether to fit the estimator. Setting it to False is useful to estimate the effect on new data using a previously fitted estimator. :param method_params: Dictionary containing any method-specific parameters. These are passed directly to the estimating method. See the docs for each estimation method for allowed method-specific params. :returns: An instance of the CausalEstimate class, containing the causal effect estimate and other method-dependent information """ treatment = parse_state(treatment) outcome = parse_state(outcome) causal_estimator_class = method.__class__ identified_estimand.set_identifier_method(identifier_name) if identified_estimand.no_directed_path: logger.warning("No directed path from {0} to {1}.".format(treatment, outcome)) return CausalEstimate( 0, identified_estimand, None, control_value=control_value, treatment_value=treatment_value ) # Check if estimator's target estimand is identified elif identified_estimand.estimands[identifier_name] is None: logger.error("No valid identified estimand available.") return CausalEstimate(None, None, None, control_value=control_value, treatment_value=treatment_value) method.update_input(treatment_value, control_value, target_units) estimate = method.estimate_effect() # Store parameters inside estimate object for refutation methods # TODO: This add_params needs to move to the estimator class # inside estimate_effect and estimate_conditional_effect estimate.add_params( estimand_type=identified_estimand.estimand_type, estimator_class=causal_estimator_class, test_significance=test_significance, evaluate_effect_strength=evaluate_effect_strength, confidence_intervals=confidence_intervals, target_units=target_units, effect_modifiers=effect_modifiers, method_params=method_params, ) return estimate class CausalEstimate: """Class for the estimate object that every causal estimator returns""" def __init__( self, estimate, target_estimand, realized_estimand_expr, control_value, treatment_value, conditional_estimates=None, **kwargs, ): self.value = estimate self.target_estimand = target_estimand self.realized_estimand_expr = realized_estimand_expr self.control_value = control_value self.treatment_value = treatment_value self.conditional_estimates = conditional_estimates self.params = kwargs if self.params is not None: for key, value in self.params.items(): setattr(self, key, value) self.effect_strength = None def add_estimator(self, estimator_instance): self.estimator = estimator_instance def add_effect_strength(self, strength_dict): self.effect_strength = strength_dict def add_params(self, **kwargs): self.params.update(kwargs) def get_confidence_intervals(self, confidence_level=None, method=None, **kwargs): """Get confidence intervals of the obtained estimate. By default, this is done with the help of bootstrapped confidence intervals but can be overridden if the specific estimator implements other methods of estimating confidence intervals. If the method provided is not bootstrap, this function calls the implementation of the specific estimator. :param method: Method for estimating confidence intervals. :param confidence_level: The confidence level of the confidence intervals of the estimate. :param kwargs: Other optional args to be passed to the CI method. :returns: The obtained confidence interval. """ confidence_intervals = self.estimator.estimate_confidence_intervals( estimate_value=self.value, confidence_level=confidence_level, method=method, **kwargs ) return confidence_intervals def get_standard_error(self, method=None, **kwargs): """Get standard error of the obtained estimate. By default, this is done with the help of bootstrapped standard errors but can be overridden if the specific estimator implements other methods of estimating standard error. If the method provided is not bootstrap, this function calls the implementation of the specific estimator. :param method: Method for computing the standard error. :param kwargs: Other optional parameters to be passed to the estimating method. :returns: Standard error of the causal estimate. """ std_error = self.estimator.estimate_std_error(method=method, **kwargs) return std_error def test_stat_significance(self, method=None, **kwargs): """Test statistical significance of the estimate obtained. By default, uses resampling to create a non-parametric significance test. Individual child estimators can implement different methods. If the method name is different from "bootstrap", this function calls the implementation of the child estimator. :param method: Method for checking statistical significance :param kwargs: Other optional parameters to be passed to the estimating method. :returns: p-value from the significance test """ signif_results = self.estimator.test_significance(self.value, method=method, **kwargs) return {"p_value": signif_results["p_value"]} def estimate_conditional_effects( self, effect_modifiers=None, num_quantiles=CausalEstimator.NUM_QUANTILES_TO_DISCRETIZE_CONT_COLS ): """Estimate treatment effect conditioned on given variables. If a numeric effect modifier is provided, it is discretized into quantile bins. If you would like a custom discretization, you can do so yourself: create a new column containing the discretized effect modifier and then include that column's name in the effect_modifier_names argument. :param effect_modifiers: Names of effect modifier variables over which the conditional effects will be estimated. If not provided, defaults to the effect modifiers specified during creation of the CausalEstimator object. :param num_quantiles: The number of quantiles into which a numeric effect modifier variable is discretized. Does not affect any categorical effect modifiers. :returns: A (multi-index) dataframe that provides separate effects for each value of the (discretized) effect modifiers. """ return self.estimator._estimate_conditional_effects( self.estimator._estimate_effect_fn, effect_modifiers, num_quantiles ) def interpret(self, method_name=None, **kwargs): """Interpret the causal estimate. :param method_name: Method used (string) or a list of methods. If None, then the default for the specific estimator is used. :param kwargs:: Optional parameters that are directly passed to the interpreter method. :returns: None """ if method_name is None: method_name = self.estimator.interpret_method method_name_arr = parse_state(method_name) for method in method_name_arr: interpreter = interpreters.get_class_object(method) interpreter(self, **kwargs).interpret() def __str__(self): s = "*** Causal Estimate ***\n" # No estimand was identified (identification failed) if self.target_estimand is None: return "Estimation failed! No relevant identified estimand available for this estimation method." s += "\n## Identified estimand\n{0}".format(self.target_estimand.__str__(only_target_estimand=True)) s += "\n## Realized estimand\n{0}".format(self.realized_estimand_expr) if hasattr(self, "estimator"): s += "\nTarget units: {0}\n".format(self.estimator.target_units_tostr()) s += "\n## Estimate\n" s += "Mean value: {0}\n".format(self.value) s += "" if hasattr(self, "cate_estimates"): s += "Effect estimates: {0}\n".format(self.cate_estimates) if hasattr(self, "estimator"): if self.estimator._significance_test: s += "p-value: {0}\n".format(self.estimator.signif_results_tostr(self.test_stat_significance())) if self.estimator._confidence_intervals: s += "{0}% confidence interval: {1}\n".format( 100 * self.estimator.confidence_level, self.get_confidence_intervals() ) if self.conditional_estimates is not None: s += "### Conditional Estimates\n" s += str(self.conditional_estimates) if self.effect_strength is not None: s += "\n## Effect Strength\n" s += "Change in outcome attributable to treatment: {}\n".format(self.effect_strength["fraction-effect"]) # s += "Variance in outcome explained by treatment: {}\n".format(self.effect_strength["r-squared"]) return s class RealizedEstimand(object): def __init__(self, identified_estimand, estimator_name): self.treatment_variable = identified_estimand.treatment_variable self.outcome_variable = identified_estimand.outcome_variable self.backdoor_variables = identified_estimand.get_backdoor_variables() self.instrumental_variables = identified_estimand.instrumental_variables self.estimand_type = identified_estimand.estimand_type self.estimand_expression = None self.assumptions = None self.estimator_name = estimator_name def update_assumptions(self, estimator_assumptions): self.assumptions = estimator_assumptions def update_estimand_expression(self, estimand_expression): self.estimand_expression = estimand_expression def __str__(self): s = "Realized estimand: {0}\n".format(self.estimator_name) s += "Realized estimand type: {0}\n".format(self.estimand_type) s += "Estimand expression:\n{0}\n".format(sp.pretty(self.estimand_expression)) j = 1 for ass_name, ass_str in self.assumptions.items(): s += "Estimand assumption {0}, {1}: {2}\n".format(j, ass_name, ass_str) j += 1 return s

andresmor-ms

2044d216c322a4b32c6eadce5da7d83463f19c2f

05bfa49dacf0061988c96c6f3e3756219df5422a

Right... that was confusing for me, I don't like the fit_estimator flag as that seems to be a functionality of the estimator instead of this function. I'll change the input parameter to be an object so that we can keep that functionality for this PR and modify this method in future PRs to add the `fit()` call

andresmor-ms

py-why/dowhy

Functional api/estimate effect function

#### Estimate Effect function * Refactors the estimate effect into a separate function to keep backwards compatibility #### TODO (future PRs): * Add `fit(...)` method to estimators - Move data related parameters from the constructor to the `fit(...)` method * Refactor code to avoid `**kwargs` in `__init__(...)` constructors

2022-10-18 15:49:21+00:00

2022-10-25 17:02:02+00:00

dowhy/causal_estimator.py

import logging from collections import namedtuple import numpy as np import pandas as pd import sympy as sp from sklearn.utils import resample import dowhy.interpreters as interpreters from dowhy.utils.api import parse_state class CausalEstimator: """Base class for an estimator of causal effect. Subclasses implement different estimation methods. All estimation methods are in the package "dowhy.causal_estimators" """ # The default number of simulations for statistical testing DEFAULT_NUMBER_OF_SIMULATIONS_STAT_TEST = 1000 # The default number of simulations to obtain confidence intervals DEFAULT_NUMBER_OF_SIMULATIONS_CI = 100 # The portion of the total size that should be taken each time to find the confidence intervals # 1 is the recommended value # https://ocw.mit.edu/courses/mathematics/18-05-introduction-to-probability-and-statistics-spring-2014/readings/MIT18_05S14_Reading24.pdf # https://projecteuclid.org/download/pdf_1/euclid.ss/1032280214 DEFAULT_SAMPLE_SIZE_FRACTION = 1 # The default Confidence Level DEFAULT_CONFIDENCE_LEVEL = 0.95 # Number of quantiles to discretize continuous columns, for applying groupby NUM_QUANTILES_TO_DISCRETIZE_CONT_COLS = 5 # Prefix to add to temporary categorical variables created after discretization TEMP_CAT_COLUMN_PREFIX = "__categorical__" DEFAULT_NOTIMPLEMENTEDERROR_MSG = "not yet implemented for {0}. If you would this to be implemented in the next version, please raise an issue at https://github.com/microsoft/dowhy/issues" BootstrapEstimates = namedtuple("BootstrapEstimates", ["estimates", "params"]) DEFAULT_INTERPRET_METHOD = ["textual_effect_interpreter"] # std args to be removed from locals() before being passed to args_dict _STD_INIT_ARGS = ("self", "__class__", "args", "kwargs") def __init__( self, data, identified_estimand, treatment, outcome, control_value=0, treatment_value=1, test_significance=False, evaluate_effect_strength=False, confidence_intervals=False, target_units=None, effect_modifiers=None, num_null_simulations=DEFAULT_NUMBER_OF_SIMULATIONS_STAT_TEST, num_simulations=DEFAULT_NUMBER_OF_SIMULATIONS_CI, sample_size_fraction=DEFAULT_SAMPLE_SIZE_FRACTION, confidence_level=DEFAULT_CONFIDENCE_LEVEL, need_conditional_estimates="auto", num_quantiles_to_discretize_cont_cols=NUM_QUANTILES_TO_DISCRETIZE_CONT_COLS, **kwargs, ): """Initializes an estimator with data and names of relevant variables. This method is called from the constructors of its child classes. :param data: data frame containing the data :param identified_estimand: probability expression representing the target identified estimand to estimate. :param treatment: name of the treatment variable :param outcome: name of the outcome variable :param control_value: Value of the treatment in the control group, for effect estimation. If treatment is multi-variate, this can be a list. :param treatment_value: Value of the treatment in the treated group, for effect estimation. If treatment is multi-variate, this can be a list. :param test_significance: Binary flag or a string indicating whether to test significance and by which method. All estimators support test_significance="bootstrap" that estimates a p-value for the obtained estimate using the bootstrap method. Individual estimators can override this to support custom testing methods. The bootstrap method supports an optional parameter, num_null_simulations. If False, no testing is done. If True, significance of the estimate is tested using the custom method if available, otherwise by bootstrap. :param evaluate_effect_strength: (Experimental) whether to evaluate the strength of effect :param confidence_intervals: Binary flag or a string indicating whether the confidence intervals should be computed and which method should be used. All methods support estimation of confidence intervals using the bootstrap method by using the parameter confidence_intervals="bootstrap". The bootstrap method takes in two arguments (num_simulations and sample_size_fraction) that can be optionally specified in the params dictionary. Estimators may also override this to implement their own confidence interval method. If this parameter is False, no confidence intervals are computed. If True, confidence intervals are computed by the estimator's specific method if available, otherwise through bootstrap. :param target_units: The units for which the treatment effect should be estimated. This can be a string for common specifications of target units (namely, "ate", "att" and "atc"). It can also be a lambda function that can be used as an index for the data (pandas DataFrame). Alternatively, it can be a new DataFrame that contains values of the effect_modifiers and effect will be estimated only for this new data. :param effect_modifiers: Variables on which to compute separate effects, or return a heterogeneous effect function. Not all methods support this currently. :param num_null_simulations: The number of simulations for testing the statistical significance of the estimator :param num_simulations: The number of simulations for finding the confidence interval (and/or standard error) for a estimate :param sample_size_fraction: The size of the sample for the bootstrap estimator :param confidence_level: The confidence level of the confidence interval estimate :param need_conditional_estimates: Boolean flag indicating whether conditional estimates should be computed. Defaults to True if there are effect modifiers in the graph :param num_quantiles_to_discretize_cont_cols: The number of quantiles into which a numeric effect modifier is split, to enable estimation of conditional treatment effect over it. :param kwargs: (optional) Additional estimator-specific parameters :returns: an instance of the estimator class. """ self._data = data self._target_estimand = identified_estimand # Currently estimation methods only support univariate treatment and outcome self._treatment_name = treatment self._outcome_name = outcome[0] # assuming one-dimensional outcome self._control_value = control_value self._treatment_value = treatment_value self._significance_test = test_significance self._effect_strength_eval = evaluate_effect_strength self._target_units = target_units self._effect_modifier_names = effect_modifiers self._confidence_intervals = confidence_intervals self._bootstrap_estimates = None # for confidence intervals and std error self._bootstrap_null_estimates = None # for significance test self._effect_modifiers = None self.method_params = kwargs # Setting the default interpret method self.interpret_method = CausalEstimator.DEFAULT_INTERPRET_METHOD self.logger = logging.getLogger(__name__) # Setting treatment and outcome values if self._data is not None: self._treatment = self._data[self._treatment_name] self._outcome = self._data[self._outcome_name] # Now saving the effect modifiers if self._effect_modifier_names: # only add the observed nodes self._effect_modifier_names = [ cname for cname in self._effect_modifier_names if cname in self._data.columns ] if len(self._effect_modifier_names) > 0: self._effect_modifiers = self._data[self._effect_modifier_names] self._effect_modifiers = pd.get_dummies(self._effect_modifiers, drop_first=True) self.logger.debug("Effect modifiers: " + ",".join(self._effect_modifier_names)) else: self._effect_modifier_names = None # Check if some parameters were set, otherwise set to default values self.num_null_simulations = num_null_simulations self.num_simulations = num_simulations self.sample_size_fraction = sample_size_fraction self.confidence_level = confidence_level self.num_quantiles_to_discretize_cont_cols = num_quantiles_to_discretize_cont_cols # Estimate conditional estimates by default self.need_conditional_estimates = ( need_conditional_estimates if need_conditional_estimates != "auto" else bool(self._effect_modifier_names) ) @staticmethod def get_estimator_object(new_data, identified_estimand, estimate): """Create a new estimator of the same type as the one passed in the estimate argument. Creates a new object with new_data and the identified_estimand :param new_data: np.ndarray, pd.Series, pd.DataFrame The newly assigned data on which the estimator should run :param identified_estimand: IdentifiedEstimand An instance of the identified estimand class that provides the information with respect to which causal pathways are employed when the treatment effects the outcome :param estimate: CausalEstimate It is an already existing estimate whose properties we wish to replicate :returns: An instance of the same estimator class that had generated the given estimate. """ estimator_class = estimate.params["estimator_class"] new_estimator = estimator_class( new_data, identified_estimand, identified_estimand.treatment_variable, identified_estimand.outcome_variable, # names of treatment and outcome control_value=estimate.control_value, treatment_value=estimate.treatment_value, test_significance=False, evaluate_effect_strength=False, confidence_intervals=estimate.params["confidence_intervals"], target_units=estimate.params["target_units"], effect_modifiers=estimate.params["effect_modifiers"], **estimate.params["method_params"], ) return new_estimator def _estimate_effect(self): """This method is to be overriden by the child classes, so that they can run the estimation technique of their choice""" raise NotImplementedError( ("Main estimation method is " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG).format(self.__class__) ) def estimate_effect(self): """Base estimation method that calls the estimate_effect method of its calling subclass. Can optionally also test significance and estimate effect strength for any returned estimate. :param self: object instance of class Estimator :returns: A CausalEstimate instance that contains point estimates of average and conditional effects. Based on the parameters provided, it optionally includes confidence intervals, standard errors,statistical significance and other statistical parameters. """ est = self._estimate_effect() est.add_estimator(self) if self._significance_test: self.test_significance(est.value, method=self._significance_test) if self._confidence_intervals: self.estimate_confidence_intervals( est.value, confidence_level=self.confidence_level, method=self._confidence_intervals ) if self._effect_strength_eval: effect_strength_dict = self.evaluate_effect_strength(est) est.add_effect_strength(effect_strength_dict) return est def estimate_effect_naive(self): # TODO Only works for binary treatment df_withtreatment = self._data.loc[self._data[self._treatment_name] == 1] df_notreatment = self._data.loc[self._data[self._treatment_name] == 0] est = np.mean(df_withtreatment[self._outcome_name]) - np.mean(df_notreatment[self._outcome_name]) return CausalEstimate(est, None, None, control_value=0, treatment_value=1) def _estimate_effect_fn(self, data_df): """Function used in conditional effect estimation. This function is to be overridden by each child estimator. The overridden function should take in a dataframe as input and return the estimate for that data. """ raise NotImplementedError( ("Conditional treatment effects are " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG).format( self.__class__ ) ) def _estimate_conditional_effects(self, estimate_effect_fn, effect_modifier_names=None, num_quantiles=None): """Estimate conditional treatment effects. Common method for all estimators that utilizes a specific estimate_effect_fn implemented by each child estimator. If a numeric effect modifier is provided, it is discretized into quantile bins. If you would like a custom discretization, you can do so yourself: create a new column containing the discretized effect modifier and then include that column's name in the effect_modifier_names argument. :param estimate_effect_fn: Function that has a single parameter (a data frame) and returns the treatment effect estimate on that data. :param effect_modifier_names: Names of effect modifier variables over which the conditional effects will be estimated. If not provided, defaults to the effect modifiers specified during creation of the CausalEstimator object. :param num_quantiles: The number of quantiles into which a numeric effect modifier variable is discretized. Does not affect any categorical effect modifiers. :returns: A (multi-index) dataframe that provides separate effects for each value of the (discretized) effect modifiers. """ # Defaulting to class default values if parameters are not provided if effect_modifier_names is None: effect_modifier_names = self._effect_modifier_names if num_quantiles is None: num_quantiles = self.num_quantiles_to_discretize_cont_cols # Checking that there is at least one effect modifier if not effect_modifier_names: raise ValueError("At least one effect modifier should be specified to compute conditional effects.") # Making sure that effect_modifier_names is a list effect_modifier_names = parse_state(effect_modifier_names) if not all(em in self._effect_modifier_names for em in effect_modifier_names): self.logger.warn( "At least one of the provided effect modifiers was not included while fitting the estimator. You may get incorrect results. To resolve, fit the estimator again by providing the updated effect modifiers in estimate_effect()." ) # Making a copy since we are going to be changing effect modifier names effect_modifier_names = effect_modifier_names.copy() prefix = CausalEstimator.TEMP_CAT_COLUMN_PREFIX # For every numeric effect modifier, adding a temp categorical column for i in range(len(effect_modifier_names)): em = effect_modifier_names[i] if pd.api.types.is_numeric_dtype(self._data[em].dtypes): self._data[prefix + str(em)] = pd.qcut(self._data[em], num_quantiles, duplicates="drop") effect_modifier_names[i] = prefix + str(em) # Grouping by effect modifiers and computing effect separately by_effect_mods = self._data.groupby(effect_modifier_names) cond_est_fn = lambda x: self._do(self._treatment_value, x) - self._do(self._control_value, x) conditional_estimates = by_effect_mods.apply(estimate_effect_fn) # Deleting the temporary categorical columns for em in effect_modifier_names: if em.startswith(prefix): self._data.pop(em) return conditional_estimates def _do(self, x, data_df=None): raise NotImplementedError( ("Do-operator is " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG).format(self.__class__) ) def do(self, x, data_df=None): """Method that implements the do-operator. Given a value x for the treatment, returns the expected value of the outcome when the treatment is intervened to a value x. :param x: Value of the treatment :param data_df: Data on which the do-operator is to be applied. :returns: Value of the outcome when treatment is intervened/set to x. """ est = self._do(x, data_df) return est def construct_symbolic_estimator(self, estimand): raise NotImplementedError(("Symbolic estimator string is ").format(self.__class__)) def _generate_bootstrap_estimates(self, num_bootstrap_simulations, sample_size_fraction): """Helper function to generate causal estimates over bootstrapped samples. :param num_bootstrap_simulations: Number of simulations for the bootstrap method. :param sample_size_fraction: Fraction of the dataset to be resampled. :returns: A collections.namedtuple containing a list of bootstrapped estimates and a dictionary containing parameters used for the bootstrap. """ # The array that stores the results of all estimations simulation_results = np.zeros(num_bootstrap_simulations) # Find the sample size the proportion with the population size sample_size = int(sample_size_fraction * len(self._data)) if sample_size > len(self._data): self.logger.warning("WARN: The sample size is greater than the data being sampled") self.logger.info("INFO: The sample size: {}".format(sample_size)) self.logger.info("INFO: The number of simulations: {}".format(num_bootstrap_simulations)) # Perform the set number of simulations for index in range(num_bootstrap_simulations): new_data = resample(self._data, n_samples=sample_size) new_estimator = type(self)( new_data, self._target_estimand, self._target_estimand.treatment_variable, self._target_estimand.outcome_variable, # names of treatment and outcome treatment_value=self._treatment_value, control_value=self._control_value, test_significance=False, evaluate_effect_strength=False, confidence_intervals=False, target_units=self._target_units, effect_modifiers=self._effect_modifier_names, **self.method_params, ) new_effect = new_estimator.estimate_effect() simulation_results[index] = new_effect.value estimates = CausalEstimator.BootstrapEstimates( simulation_results, {"num_simulations": num_bootstrap_simulations, "sample_size_fraction": sample_size_fraction}, ) return estimates def _estimate_confidence_intervals_with_bootstrap( self, estimate_value, confidence_level=None, num_simulations=None, sample_size_fraction=None ): """ Method to compute confidence interval using bootstrapped sampling. :param estimate_value: obtained estimate's value :param confidence_level: The level for which to compute CI (e.g., 95% confidence level translates to confidence_level=0.95) :param num_simulations: The number of simulations to be performed to get the bootstrap confidence intervals. :param sample_size_fraction: The fraction of the dataset to be resampled. :returns: confidence interval at the specified level. For more details on bootstrap or resampling statistics, refer to the following links: https://ocw.mit.edu/courses/mathematics/18-05-introduction-to-probability-and-statistics-spring-2014/readings/MIT18_05S14_Reading24.pdf https://projecteuclid.org/download/pdf_1/euclid.ss/1032280214 """ # Using class default parameters if not specified if num_simulations is None: num_simulations = self.num_simulations if sample_size_fraction is None: sample_size_fraction = self.sample_size_fraction # Checking if bootstrap_estimates are already computed if self._bootstrap_estimates is None: self._bootstrap_estimates = self._generate_bootstrap_estimates(num_simulations, sample_size_fraction) elif CausalEstimator.is_bootstrap_parameter_changed(self._bootstrap_estimates.params, locals()): # Checked if any parameter is changed from the previous std error estimate self._bootstrap_estimates = self._generate_bootstrap_estimates(num_simulations, sample_size_fraction) # Now use the data obtained from the simulations to get the value of the confidence estimates bootstrap_estimates = self._bootstrap_estimates.estimates # Get the variations of each bootstrap estimate and sort bootstrap_variations = [bootstrap_estimate - estimate_value for bootstrap_estimate in bootstrap_estimates] sorted_bootstrap_variations = np.sort(bootstrap_variations) # Now we take the (1- p)th and the (p)th variations, where p is the chosen confidence level upper_bound_index = int((1 - confidence_level) * len(sorted_bootstrap_variations)) lower_bound_index = int(confidence_level * len(sorted_bootstrap_variations)) # Get the lower and upper bounds by subtracting the variations from the estimate lower_bound = estimate_value - sorted_bootstrap_variations[lower_bound_index] upper_bound = estimate_value - sorted_bootstrap_variations[upper_bound_index] return lower_bound, upper_bound def _estimate_confidence_intervals(self, confidence_level=None, method=None, **kwargs): """ This method is to be overriden by the child classes, so that they can run a confidence interval estimation method suited to the specific causal estimator. """ raise NotImplementedError( ( "This method for estimating confidence intervals is " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG + " Meanwhile, you can try the bootstrap method (method='bootstrap') to estimate confidence intervals." ).format(self.__class__) ) def estimate_confidence_intervals(self, estimate_value, confidence_level=None, method=None, **kwargs): """Find the confidence intervals corresponding to any estimator By default, this is done with the help of bootstrapped confidence intervals but can be overridden if the specific estimator implements other methods of estimating confidence intervals. If the method provided is not bootstrap, this function calls the implementation of the specific estimator. :param estimate_value: obtained estimate's value :param method: Method for estimating confidence intervals. :param confidence_level: The confidence level of the confidence intervals of the estimate. :param kwargs: Other optional args to be passed to the CI method. :returns: The obtained confidence interval. """ if method is None: if self._confidence_intervals: method = self._confidence_intervals # this is either True or methodname else: method = "default" confidence_intervals = None if confidence_level is None: confidence_level = self.confidence_level if method == "default" or method is True: # user has not provided any method try: confidence_intervals = self._estimate_confidence_intervals(confidence_level, method=method, **kwargs) except NotImplementedError: confidence_intervals = self._estimate_confidence_intervals_with_bootstrap( estimate_value, confidence_level, **kwargs ) else: if method == "bootstrap": confidence_intervals = self._estimate_confidence_intervals_with_bootstrap( estimate_value, confidence_level, **kwargs ) else: confidence_intervals = self._estimate_confidence_intervals(confidence_level, method=method, **kwargs) return confidence_intervals def _estimate_std_error_with_bootstrap(self, num_simulations=None, sample_size_fraction=None): """Compute standard error using the bootstrap method. Standard error and confidence intervals use the same parameter num_simulations for the number of bootstrap simulations. :param num_simulations: Number of bootstrapped samples. :param sample_size_fraction: Fraction of data to be resampled. :returns: Standard error of the obtained estimate. """ # Use existing params, if new user defined params are not present if num_simulations is None: num_simulations = self.num_simulations if sample_size_fraction is None: sample_size_fraction = self.sample_size_fraction # Checking if bootstrap_estimates are already computed if self._bootstrap_estimates is None: self._bootstrap_estimates = self._generate_bootstrap_estimates(num_simulations, sample_size_fraction) elif CausalEstimator.is_bootstrap_parameter_changed(self._bootstrap_estimates.params, locals()): # Check if any parameter is changed from the previous std error estimate self._bootstrap_estimates = self._generate_bootstrap_estimates(num_simulations, sample_size_fraction) std_error = np.std(self._bootstrap_estimates.estimates) return std_error def _estimate_std_error(self, method=None, **kwargs): """ This method is to be overriden by the child classes, so that they can run a standard error estimation method suited to the specific causal estimator. """ raise NotImplementedError( ( "This method for estimating standard errors is " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG + " Meanwhile, you can try the bootstrap method (method='bootstrap') to estimate standard errors." ).format(self.__class__) ) def estimate_std_error(self, method=None, **kwargs): """Compute standard error of an obtained causal estimate. :param method: Method for computing the standard error. :param kwargs: Other optional parameters to be passed to the estimating method. :returns: Standard error of the causal estimate. """ if method is None: if self._confidence_intervals: method = self._confidence_intervals else: method = "default" std_error = None if method == "default" or method is True: # user has not provided any method try: std_error = self._estimate_std_error(method, **kwargs) except NotImplementedError: std_error = self._estimate_std_error_with_bootstrap(**kwargs) else: if method == "bootstrap": std_error = self._estimate_std_error_with_bootstrap(**kwargs) else: std_error = self._estimate_std_error(method, **kwargs) return std_error def _test_significance_with_bootstrap(self, estimate_value, num_null_simulations=None): """Test statistical significance of an estimate using the bootstrap method. :param estimate_value: Obtained estimate's value :param num_null_simulations: Number of simulations for the null hypothesis :returns: p-value of the statistical significance test. """ # Use existing params, if new user defined params are not present if num_null_simulations is None: num_null_simulations = self.num_null_simulations do_retest = self._bootstrap_null_estimates is None or CausalEstimator.is_bootstrap_parameter_changed( self._bootstrap_null_estimates.params, locals() ) if do_retest: null_estimates = np.zeros(num_null_simulations) for i in range(num_null_simulations): new_outcome = np.random.permutation(self._outcome) new_data = self._data.assign(dummy_outcome=new_outcome) # self._outcome = self._data["dummy_outcome"] new_estimator = type(self)( new_data, self._target_estimand, self._target_estimand.treatment_variable, ("dummy_outcome",), test_significance=False, evaluate_effect_strength=False, confidence_intervals=False, target_units=self._target_units, effect_modifiers=self._effect_modifier_names, **self.method_params, ) new_effect = new_estimator.estimate_effect() null_estimates[i] = new_effect.value self._bootstrap_null_estimates = CausalEstimator.BootstrapEstimates( null_estimates, {"num_null_simulations": num_null_simulations, "sample_size_fraction": 1} ) # Processing the null hypothesis estimates sorted_null_estimates = np.sort(self._bootstrap_null_estimates.estimates) self.logger.debug("Null estimates: {0}".format(sorted_null_estimates)) median_estimate = sorted_null_estimates[int(num_null_simulations / 2)] # Doing a two-sided test if estimate_value > median_estimate: # Being conservative with the p-value reported estimate_index = np.searchsorted(sorted_null_estimates, estimate_value, side="left") p_value = 1 - (estimate_index / num_null_simulations) if estimate_value <= median_estimate: # Being conservative with the p-value reported estimate_index = np.searchsorted(sorted_null_estimates, estimate_value, side="right") p_value = estimate_index / num_null_simulations # If the estimate_index is 0, it depends on the number of simulations if p_value == 0: p_value = (0, 1 / len(sorted_null_estimates)) # a tuple determining the range. elif p_value == 1: p_value = (1 - 1 / len(sorted_null_estimates), 1) signif_dict = {"p_value": p_value} return signif_dict def _test_significance(self, estimate_value, method=None, **kwargs): """ This method is to be overriden by the child classes, so that they can run a significance test suited to the specific causal estimator. """ raise NotImplementedError( ( "This method for testing statistical significance is " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG + " Meanwhile, you can try the bootstrap method (method='bootstrap') to test statistical significance." ).format(self.__class__) ) def test_significance(self, estimate_value, method=None, **kwargs): """Test statistical significance of obtained estimate. By default, uses resampling to create a non-parametric significance test. A general procedure. Individual child estimators can implement different methods. If the method name is different from "bootstrap", this function calls the implementation of the child estimator. :param self: object instance of class Estimator :param estimate_value: obtained estimate's value :param method: Method for checking statistical significance :returns: p-value from the significance test """ if method is None: if self._significance_test: method = self._significance_test # this is either True or methodname else: method = "default" signif_dict = None if method == "default" or method is True: # user has not provided any method try: signif_dict = self._test_significance(estimate_value, method, **kwargs) except NotImplementedError: signif_dict = self._test_significance_with_bootstrap(estimate_value, **kwargs) else: if method == "bootstrap": signif_dict = self._test_significance_with_bootstrap(estimate_value, **kwargs) else: signif_dict = self._test_significance(estimate_value, method, **kwargs) return signif_dict def evaluate_effect_strength(self, estimate): fraction_effect_explained = self._evaluate_effect_strength(estimate, method="fraction-effect") # Need to test r-squared before supporting # effect_r_squared = self._evaluate_effect_strength(estimate, method="r-squared") strength_dict = { "fraction-effect": fraction_effect_explained # 'r-squared': effect_r_squared } return strength_dict def _evaluate_effect_strength(self, estimate, method="fraction-effect"): supported_methods = ["fraction-effect"] if method not in supported_methods: raise NotImplementedError("This method is not supported for evaluating effect strength") if method == "fraction-effect": naive_obs_estimate = self.estimate_effect_naive() self.logger.debug(estimate.value, naive_obs_estimate.value) fraction_effect_explained = estimate.value / naive_obs_estimate.value return fraction_effect_explained # elif method == "r-squared": # outcome_mean = np.mean(self._outcome) # total_variance = np.sum(np.square(self._outcome - outcome_mean)) # Assuming a linear model with one variable: the treatment # Currently only works for continuous y # causal_model = outcome_mean + estimate.value*self._treatment # squared_residual = np.sum(np.square(self._outcome - causal_model)) # r_squared = 1 - (squared_residual/total_variance) # return r_squared else: return None def update_input(self, treatment_value, control_value, target_units): self._control_value = control_value self._treatment_value = treatment_value self._target_units = target_units @staticmethod def is_bootstrap_parameter_changed(bootstrap_estimates_params, given_params): """Check whether parameters of the bootstrap have changed. This is an efficiency method that checks if fresh resampling of the bootstrap samples is required. Returns True if parameters have changed and resampling should be done again. :param bootstrap_estimates_params: A dictionary of parameters for the current bootstrap samples :param given_params: A dictionary of parameters passed by the user :returns: A binary flag denoting whether the parameters are different. """ is_any_parameter_changed = False for prm, val in bootstrap_estimates_params.items(): given_val = given_params.get(prm, None) if given_val is not None and given_val != val: is_any_parameter_changed = True break return is_any_parameter_changed def target_units_tostr(self): s = "" if type(self._target_units) is str: s += self._target_units elif callable(self._target_units): s += "Data subset defined by a function" elif isinstance(self._target_units, pd.DataFrame): s += "Data subset provided as a data frame" return s def signif_results_tostr(self, signif_results): s = "" pval = signif_results["p_value"] if type(pval) is tuple: s += "[{0}, {1}]".format(pval[0], pval[1]) else: s += "{0}".format(pval) return s class CausalEstimate: """Class for the estimate object that every causal estimator returns""" def __init__( self, estimate, target_estimand, realized_estimand_expr, control_value, treatment_value, conditional_estimates=None, **kwargs, ): self.value = estimate self.target_estimand = target_estimand self.realized_estimand_expr = realized_estimand_expr self.control_value = control_value self.treatment_value = treatment_value self.conditional_estimates = conditional_estimates self.params = kwargs if self.params is not None: for key, value in self.params.items(): setattr(self, key, value) self.effect_strength = None def add_estimator(self, estimator_instance): self.estimator = estimator_instance def add_effect_strength(self, strength_dict): self.effect_strength = strength_dict def add_params(self, **kwargs): self.params.update(kwargs) def get_confidence_intervals(self, confidence_level=None, method=None, **kwargs): """Get confidence intervals of the obtained estimate. By default, this is done with the help of bootstrapped confidence intervals but can be overridden if the specific estimator implements other methods of estimating confidence intervals. If the method provided is not bootstrap, this function calls the implementation of the specific estimator. :param method: Method for estimating confidence intervals. :param confidence_level: The confidence level of the confidence intervals of the estimate. :param kwargs: Other optional args to be passed to the CI method. :returns: The obtained confidence interval. """ confidence_intervals = self.estimator.estimate_confidence_intervals( estimate_value=self.value, confidence_level=confidence_level, method=method, **kwargs ) return confidence_intervals def get_standard_error(self, method=None, **kwargs): """Get standard error of the obtained estimate. By default, this is done with the help of bootstrapped standard errors but can be overridden if the specific estimator implements other methods of estimating standard error. If the method provided is not bootstrap, this function calls the implementation of the specific estimator. :param method: Method for computing the standard error. :param kwargs: Other optional parameters to be passed to the estimating method. :returns: Standard error of the causal estimate. """ std_error = self.estimator.estimate_std_error(method=method, **kwargs) return std_error def test_stat_significance(self, method=None, **kwargs): """Test statistical significance of the estimate obtained. By default, uses resampling to create a non-parametric significance test. Individual child estimators can implement different methods. If the method name is different from "bootstrap", this function calls the implementation of the child estimator. :param method: Method for checking statistical significance :param kwargs: Other optional parameters to be passed to the estimating method. :returns: p-value from the significance test """ signif_results = self.estimator.test_significance(self.value, method=method, **kwargs) return {"p_value": signif_results["p_value"]} def estimate_conditional_effects( self, effect_modifiers=None, num_quantiles=CausalEstimator.NUM_QUANTILES_TO_DISCRETIZE_CONT_COLS ): """Estimate treatment effect conditioned on given variables. If a numeric effect modifier is provided, it is discretized into quantile bins. If you would like a custom discretization, you can do so yourself: create a new column containing the discretized effect modifier and then include that column's name in the effect_modifier_names argument. :param effect_modifiers: Names of effect modifier variables over which the conditional effects will be estimated. If not provided, defaults to the effect modifiers specified during creation of the CausalEstimator object. :param num_quantiles: The number of quantiles into which a numeric effect modifier variable is discretized. Does not affect any categorical effect modifiers. :returns: A (multi-index) dataframe that provides separate effects for each value of the (discretized) effect modifiers. """ return self.estimator._estimate_conditional_effects( self.estimator._estimate_effect_fn, effect_modifiers, num_quantiles ) def interpret(self, method_name=None, **kwargs): """Interpret the causal estimate. :param method_name: Method used (string) or a list of methods. If None, then the default for the specific estimator is used. :param kwargs:: Optional parameters that are directly passed to the interpreter method. :returns: None """ if method_name is None: method_name = self.estimator.interpret_method method_name_arr = parse_state(method_name) for method in method_name_arr: interpreter = interpreters.get_class_object(method) interpreter(self, **kwargs).interpret() def __str__(self): s = "*** Causal Estimate ***\n" # No estimand was identified (identification failed) if self.target_estimand is None: return "Estimation failed! No relevant identified estimand available for this estimation method." s += "\n## Identified estimand\n{0}".format(self.target_estimand.__str__(only_target_estimand=True)) s += "\n## Realized estimand\n{0}".format(self.realized_estimand_expr) if hasattr(self, "estimator"): s += "\nTarget units: {0}\n".format(self.estimator.target_units_tostr()) s += "\n## Estimate\n" s += "Mean value: {0}\n".format(self.value) s += "" if hasattr(self, "cate_estimates"): s += "Effect estimates: {0}\n".format(self.cate_estimates) if hasattr(self, "estimator"): if self.estimator._significance_test: s += "p-value: {0}\n".format(self.estimator.signif_results_tostr(self.test_stat_significance())) if self.estimator._confidence_intervals: s += "{0}% confidence interval: {1}\n".format( 100 * self.estimator.confidence_level, self.get_confidence_intervals() ) if self.conditional_estimates is not None: s += "### Conditional Estimates\n" s += str(self.conditional_estimates) if self.effect_strength is not None: s += "\n## Effect Strength\n" s += "Change in outcome attributable to treatment: {}\n".format(self.effect_strength["fraction-effect"]) # s += "Variance in outcome explained by treatment: {}\n".format(self.effect_strength["r-squared"]) return s class RealizedEstimand(object): def __init__(self, identified_estimand, estimator_name): self.treatment_variable = identified_estimand.treatment_variable self.outcome_variable = identified_estimand.outcome_variable self.backdoor_variables = identified_estimand.get_backdoor_variables() self.instrumental_variables = identified_estimand.instrumental_variables self.estimand_type = identified_estimand.estimand_type self.estimand_expression = None self.assumptions = None self.estimator_name = estimator_name def update_assumptions(self, estimator_assumptions): self.assumptions = estimator_assumptions def update_estimand_expression(self, estimand_expression): self.estimand_expression = estimand_expression def __str__(self): s = "Realized estimand: {0}\n".format(self.estimator_name) s += "Realized estimand type: {0}\n".format(self.estimand_type) s += "Estimand expression:\n{0}\n".format(sp.pretty(self.estimand_expression)) j = 1 for ass_name, ass_str in self.assumptions.items(): s += "Estimand assumption {0}, {1}: {2}\n".format(j, ass_name, ass_str) j += 1 return s

import logging from collections import namedtuple from typing import Dict, List, Optional, Union import numpy as np import pandas as pd import sympy as sp from sklearn.utils import resample import dowhy.interpreters as interpreters from dowhy import causal_estimators from dowhy.causal_graph import CausalGraph from dowhy.causal_identifier.identified_estimand import IdentifiedEstimand from dowhy.utils.api import parse_state logger = logging.getLogger(__name__) class CausalEstimator: """Base class for an estimator of causal effect. Subclasses implement different estimation methods. All estimation methods are in the package "dowhy.causal_estimators" """ # The default number of simulations for statistical testing DEFAULT_NUMBER_OF_SIMULATIONS_STAT_TEST = 1000 # The default number of simulations to obtain confidence intervals DEFAULT_NUMBER_OF_SIMULATIONS_CI = 100 # The portion of the total size that should be taken each time to find the confidence intervals # 1 is the recommended value # https://ocw.mit.edu/courses/mathematics/18-05-introduction-to-probability-and-statistics-spring-2014/readings/MIT18_05S14_Reading24.pdf # https://projecteuclid.org/download/pdf_1/euclid.ss/1032280214 DEFAULT_SAMPLE_SIZE_FRACTION = 1 # The default Confidence Level DEFAULT_CONFIDENCE_LEVEL = 0.95 # Number of quantiles to discretize continuous columns, for applying groupby NUM_QUANTILES_TO_DISCRETIZE_CONT_COLS = 5 # Prefix to add to temporary categorical variables created after discretization TEMP_CAT_COLUMN_PREFIX = "__categorical__" DEFAULT_NOTIMPLEMENTEDERROR_MSG = "not yet implemented for {0}. If you would this to be implemented in the next version, please raise an issue at https://github.com/microsoft/dowhy/issues" BootstrapEstimates = namedtuple("BootstrapEstimates", ["estimates", "params"]) DEFAULT_INTERPRET_METHOD = ["textual_effect_interpreter"] # std args to be removed from locals() before being passed to args_dict _STD_INIT_ARGS = ("self", "__class__", "args", "kwargs") def __init__( self, data, identified_estimand, treatment, outcome, control_value=0, treatment_value=1, test_significance=False, evaluate_effect_strength=False, confidence_intervals=False, target_units=None, effect_modifiers=None, num_null_simulations=DEFAULT_NUMBER_OF_SIMULATIONS_STAT_TEST, num_simulations=DEFAULT_NUMBER_OF_SIMULATIONS_CI, sample_size_fraction=DEFAULT_SAMPLE_SIZE_FRACTION, confidence_level=DEFAULT_CONFIDENCE_LEVEL, need_conditional_estimates="auto", num_quantiles_to_discretize_cont_cols=NUM_QUANTILES_TO_DISCRETIZE_CONT_COLS, **kwargs, ): """Initializes an estimator with data and names of relevant variables. This method is called from the constructors of its child classes. :param data: data frame containing the data :param identified_estimand: probability expression representing the target identified estimand to estimate. :param treatment: name of the treatment variable :param outcome: name of the outcome variable :param control_value: Value of the treatment in the control group, for effect estimation. If treatment is multi-variate, this can be a list. :param treatment_value: Value of the treatment in the treated group, for effect estimation. If treatment is multi-variate, this can be a list. :param test_significance: Binary flag or a string indicating whether to test significance and by which method. All estimators support test_significance="bootstrap" that estimates a p-value for the obtained estimate using the bootstrap method. Individual estimators can override this to support custom testing methods. The bootstrap method supports an optional parameter, num_null_simulations. If False, no testing is done. If True, significance of the estimate is tested using the custom method if available, otherwise by bootstrap. :param evaluate_effect_strength: (Experimental) whether to evaluate the strength of effect :param confidence_intervals: Binary flag or a string indicating whether the confidence intervals should be computed and which method should be used. All methods support estimation of confidence intervals using the bootstrap method by using the parameter confidence_intervals="bootstrap". The bootstrap method takes in two arguments (num_simulations and sample_size_fraction) that can be optionally specified in the params dictionary. Estimators may also override this to implement their own confidence interval method. If this parameter is False, no confidence intervals are computed. If True, confidence intervals are computed by the estimator's specific method if available, otherwise through bootstrap. :param target_units: The units for which the treatment effect should be estimated. This can be a string for common specifications of target units (namely, "ate", "att" and "atc"). It can also be a lambda function that can be used as an index for the data (pandas DataFrame). Alternatively, it can be a new DataFrame that contains values of the effect_modifiers and effect will be estimated only for this new data. :param effect_modifiers: Variables on which to compute separate effects, or return a heterogeneous effect function. Not all methods support this currently. :param num_null_simulations: The number of simulations for testing the statistical significance of the estimator :param num_simulations: The number of simulations for finding the confidence interval (and/or standard error) for a estimate :param sample_size_fraction: The size of the sample for the bootstrap estimator :param confidence_level: The confidence level of the confidence interval estimate :param need_conditional_estimates: Boolean flag indicating whether conditional estimates should be computed. Defaults to True if there are effect modifiers in the graph :param num_quantiles_to_discretize_cont_cols: The number of quantiles into which a numeric effect modifier is split, to enable estimation of conditional treatment effect over it. :param kwargs: (optional) Additional estimator-specific parameters :returns: an instance of the estimator class. """ self._data = data self._target_estimand = identified_estimand # Currently estimation methods only support univariate treatment and outcome self._treatment_name = treatment self._outcome_name = outcome[0] # assuming one-dimensional outcome self._control_value = control_value self._treatment_value = treatment_value self._significance_test = test_significance self._effect_strength_eval = evaluate_effect_strength self._target_units = target_units self._effect_modifier_names = effect_modifiers self._confidence_intervals = confidence_intervals self._bootstrap_estimates = None # for confidence intervals and std error self._bootstrap_null_estimates = None # for significance test self._effect_modifiers = None self.method_params = kwargs # Setting the default interpret method self.interpret_method = CausalEstimator.DEFAULT_INTERPRET_METHOD self.logger = logging.getLogger(__name__) # Setting treatment and outcome values if self._data is not None: self._treatment = self._data[self._treatment_name] self._outcome = self._data[self._outcome_name] if self._effect_modifier_names: # only add the observed nodes self._effect_modifier_names = [ cname for cname in self._effect_modifier_names if cname in self._data.columns ] if len(self._effect_modifier_names) > 0: self._effect_modifiers = self._data[self._effect_modifier_names] self._effect_modifiers = pd.get_dummies(self._effect_modifiers, drop_first=True) self.logger.debug("Effect modifiers: " + ",".join(self._effect_modifier_names)) else: self._effect_modifier_names = None # Check if some parameters were set, otherwise set to default values self.num_null_simulations = num_null_simulations self.num_simulations = num_simulations self.sample_size_fraction = sample_size_fraction self.confidence_level = confidence_level self.num_quantiles_to_discretize_cont_cols = num_quantiles_to_discretize_cont_cols # Estimate conditional estimates by default self.need_conditional_estimates = ( need_conditional_estimates if need_conditional_estimates != "auto" else bool(self._effect_modifier_names) ) @staticmethod def get_estimator_object(new_data, identified_estimand, estimate): """Create a new estimator of the same type as the one passed in the estimate argument. Creates a new object with new_data and the identified_estimand :param new_data: np.ndarray, pd.Series, pd.DataFrame The newly assigned data on which the estimator should run :param identified_estimand: IdentifiedEstimand An instance of the identified estimand class that provides the information with respect to which causal pathways are employed when the treatment effects the outcome :param estimate: CausalEstimate It is an already existing estimate whose properties we wish to replicate :returns: An instance of the same estimator class that had generated the given estimate. """ estimator_class = estimate.params["estimator_class"] new_estimator = estimator_class( new_data, identified_estimand, identified_estimand.treatment_variable, identified_estimand.outcome_variable, # names of treatment and outcome control_value=estimate.control_value, treatment_value=estimate.treatment_value, test_significance=False, evaluate_effect_strength=False, confidence_intervals=estimate.params["confidence_intervals"], target_units=estimate.params["target_units"], effect_modifiers=estimate.params["effect_modifiers"], **estimate.params["method_params"] if estimate.params["method_params"] is not None else {}, ) return new_estimator def _estimate_effect(self): """This method is to be overriden by the child classes, so that they can run the estimation technique of their choice""" raise NotImplementedError( ("Main estimation method is " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG).format(self.__class__) ) def estimate_effect(self): """Base estimation method that calls the estimate_effect method of its calling subclass. Can optionally also test significance and estimate effect strength for any returned estimate. :param self: object instance of class Estimator :returns: A CausalEstimate instance that contains point estimates of average and conditional effects. Based on the parameters provided, it optionally includes confidence intervals, standard errors,statistical significance and other statistical parameters. """ est = self._estimate_effect() est.add_estimator(self) if self._significance_test: self.test_significance(est.value, method=self._significance_test) if self._confidence_intervals: self.estimate_confidence_intervals( est.value, confidence_level=self.confidence_level, method=self._confidence_intervals ) if self._effect_strength_eval: effect_strength_dict = self.evaluate_effect_strength(est) est.add_effect_strength(effect_strength_dict) return est def estimate_effect_naive(self): # TODO Only works for binary treatment df_withtreatment = self._data.loc[self._data[self._treatment_name] == 1] df_notreatment = self._data.loc[self._data[self._treatment_name] == 0] est = np.mean(df_withtreatment[self._outcome_name]) - np.mean(df_notreatment[self._outcome_name]) return CausalEstimate(est, None, None, control_value=0, treatment_value=1) def _estimate_effect_fn(self, data_df): """Function used in conditional effect estimation. This function is to be overridden by each child estimator. The overridden function should take in a dataframe as input and return the estimate for that data. """ raise NotImplementedError( ("Conditional treatment effects are " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG).format( self.__class__ ) ) def _estimate_conditional_effects(self, estimate_effect_fn, effect_modifier_names=None, num_quantiles=None): """Estimate conditional treatment effects. Common method for all estimators that utilizes a specific estimate_effect_fn implemented by each child estimator. If a numeric effect modifier is provided, it is discretized into quantile bins. If you would like a custom discretization, you can do so yourself: create a new column containing the discretized effect modifier and then include that column's name in the effect_modifier_names argument. :param estimate_effect_fn: Function that has a single parameter (a data frame) and returns the treatment effect estimate on that data. :param effect_modifier_names: Names of effect modifier variables over which the conditional effects will be estimated. If not provided, defaults to the effect modifiers specified during creation of the CausalEstimator object. :param num_quantiles: The number of quantiles into which a numeric effect modifier variable is discretized. Does not affect any categorical effect modifiers. :returns: A (multi-index) dataframe that provides separate effects for each value of the (discretized) effect modifiers. """ # Defaulting to class default values if parameters are not provided if effect_modifier_names is None: effect_modifier_names = self._effect_modifier_names if num_quantiles is None: num_quantiles = self.num_quantiles_to_discretize_cont_cols # Checking that there is at least one effect modifier if not effect_modifier_names: raise ValueError("At least one effect modifier should be specified to compute conditional effects.") # Making sure that effect_modifier_names is a list effect_modifier_names = parse_state(effect_modifier_names) if not all(em in self._effect_modifier_names for em in effect_modifier_names): self.logger.warn( "At least one of the provided effect modifiers was not included while fitting the estimator. You may get incorrect results. To resolve, fit the estimator again by providing the updated effect modifiers in estimate_effect()." ) # Making a copy since we are going to be changing effect modifier names effect_modifier_names = effect_modifier_names.copy() prefix = CausalEstimator.TEMP_CAT_COLUMN_PREFIX # For every numeric effect modifier, adding a temp categorical column for i in range(len(effect_modifier_names)): em = effect_modifier_names[i] if pd.api.types.is_numeric_dtype(self._data[em].dtypes): self._data[prefix + str(em)] = pd.qcut(self._data[em], num_quantiles, duplicates="drop") effect_modifier_names[i] = prefix + str(em) # Grouping by effect modifiers and computing effect separately by_effect_mods = self._data.groupby(effect_modifier_names) cond_est_fn = lambda x: self._do(self._treatment_value, x) - self._do(self._control_value, x) conditional_estimates = by_effect_mods.apply(estimate_effect_fn) # Deleting the temporary categorical columns for em in effect_modifier_names: if em.startswith(prefix): self._data.pop(em) return conditional_estimates def _do(self, x, data_df=None): raise NotImplementedError( ("Do-operator is " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG).format(self.__class__) ) def do(self, x, data_df=None): """Method that implements the do-operator. Given a value x for the treatment, returns the expected value of the outcome when the treatment is intervened to a value x. :param x: Value of the treatment :param data_df: Data on which the do-operator is to be applied. :returns: Value of the outcome when treatment is intervened/set to x. """ est = self._do(x, data_df) return est def construct_symbolic_estimator(self, estimand): raise NotImplementedError(("Symbolic estimator string is ").format(self.__class__)) def _generate_bootstrap_estimates(self, num_bootstrap_simulations, sample_size_fraction): """Helper function to generate causal estimates over bootstrapped samples. :param num_bootstrap_simulations: Number of simulations for the bootstrap method. :param sample_size_fraction: Fraction of the dataset to be resampled. :returns: A collections.namedtuple containing a list of bootstrapped estimates and a dictionary containing parameters used for the bootstrap. """ # The array that stores the results of all estimations simulation_results = np.zeros(num_bootstrap_simulations) # Find the sample size the proportion with the population size sample_size = int(sample_size_fraction * len(self._data)) if sample_size > len(self._data): self.logger.warning("WARN: The sample size is greater than the data being sampled") self.logger.info("INFO: The sample size: {}".format(sample_size)) self.logger.info("INFO: The number of simulations: {}".format(num_bootstrap_simulations)) # Perform the set number of simulations for index in range(num_bootstrap_simulations): new_data = resample(self._data, n_samples=sample_size) new_estimator = type(self)( new_data, self._target_estimand, self._target_estimand.treatment_variable, self._target_estimand.outcome_variable, # names of treatment and outcome treatment_value=self._treatment_value, control_value=self._control_value, test_significance=False, evaluate_effect_strength=False, confidence_intervals=False, target_units=self._target_units, effect_modifiers=self._effect_modifier_names, **self.method_params, ) new_effect = new_estimator.estimate_effect() simulation_results[index] = new_effect.value estimates = CausalEstimator.BootstrapEstimates( simulation_results, {"num_simulations": num_bootstrap_simulations, "sample_size_fraction": sample_size_fraction}, ) return estimates def _estimate_confidence_intervals_with_bootstrap( self, estimate_value, confidence_level=None, num_simulations=None, sample_size_fraction=None ): """ Method to compute confidence interval using bootstrapped sampling. :param estimate_value: obtained estimate's value :param confidence_level: The level for which to compute CI (e.g., 95% confidence level translates to confidence_level=0.95) :param num_simulations: The number of simulations to be performed to get the bootstrap confidence intervals. :param sample_size_fraction: The fraction of the dataset to be resampled. :returns: confidence interval at the specified level. For more details on bootstrap or resampling statistics, refer to the following links: https://ocw.mit.edu/courses/mathematics/18-05-introduction-to-probability-and-statistics-spring-2014/readings/MIT18_05S14_Reading24.pdf https://projecteuclid.org/download/pdf_1/euclid.ss/1032280214 """ # Using class default parameters if not specified if num_simulations is None: num_simulations = self.num_simulations if sample_size_fraction is None: sample_size_fraction = self.sample_size_fraction # Checking if bootstrap_estimates are already computed if self._bootstrap_estimates is None: self._bootstrap_estimates = self._generate_bootstrap_estimates(num_simulations, sample_size_fraction) elif CausalEstimator.is_bootstrap_parameter_changed(self._bootstrap_estimates.params, locals()): # Checked if any parameter is changed from the previous std error estimate self._bootstrap_estimates = self._generate_bootstrap_estimates(num_simulations, sample_size_fraction) # Now use the data obtained from the simulations to get the value of the confidence estimates bootstrap_estimates = self._bootstrap_estimates.estimates # Get the variations of each bootstrap estimate and sort bootstrap_variations = [bootstrap_estimate - estimate_value for bootstrap_estimate in bootstrap_estimates] sorted_bootstrap_variations = np.sort(bootstrap_variations) # Now we take the (1- p)th and the (p)th variations, where p is the chosen confidence level upper_bound_index = int((1 - confidence_level) * len(sorted_bootstrap_variations)) lower_bound_index = int(confidence_level * len(sorted_bootstrap_variations)) # Get the lower and upper bounds by subtracting the variations from the estimate lower_bound = estimate_value - sorted_bootstrap_variations[lower_bound_index] upper_bound = estimate_value - sorted_bootstrap_variations[upper_bound_index] return lower_bound, upper_bound def _estimate_confidence_intervals(self, confidence_level=None, method=None, **kwargs): """ This method is to be overriden by the child classes, so that they can run a confidence interval estimation method suited to the specific causal estimator. """ raise NotImplementedError( ( "This method for estimating confidence intervals is " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG + " Meanwhile, you can try the bootstrap method (method='bootstrap') to estimate confidence intervals." ).format(self.__class__) ) def estimate_confidence_intervals(self, estimate_value, confidence_level=None, method=None, **kwargs): """Find the confidence intervals corresponding to any estimator By default, this is done with the help of bootstrapped confidence intervals but can be overridden if the specific estimator implements other methods of estimating confidence intervals. If the method provided is not bootstrap, this function calls the implementation of the specific estimator. :param estimate_value: obtained estimate's value :param method: Method for estimating confidence intervals. :param confidence_level: The confidence level of the confidence intervals of the estimate. :param kwargs: Other optional args to be passed to the CI method. :returns: The obtained confidence interval. """ if method is None: if self._confidence_intervals: method = self._confidence_intervals # this is either True or methodname else: method = "default" confidence_intervals = None if confidence_level is None: confidence_level = self.confidence_level if method == "default" or method is True: # user has not provided any method try: confidence_intervals = self._estimate_confidence_intervals(confidence_level, method=method, **kwargs) except NotImplementedError: confidence_intervals = self._estimate_confidence_intervals_with_bootstrap( estimate_value, confidence_level, **kwargs ) else: if method == "bootstrap": confidence_intervals = self._estimate_confidence_intervals_with_bootstrap( estimate_value, confidence_level, **kwargs ) else: confidence_intervals = self._estimate_confidence_intervals(confidence_level, method=method, **kwargs) return confidence_intervals def _estimate_std_error_with_bootstrap(self, num_simulations=None, sample_size_fraction=None): """Compute standard error using the bootstrap method. Standard error and confidence intervals use the same parameter num_simulations for the number of bootstrap simulations. :param num_simulations: Number of bootstrapped samples. :param sample_size_fraction: Fraction of data to be resampled. :returns: Standard error of the obtained estimate. """ # Use existing params, if new user defined params are not present if num_simulations is None: num_simulations = self.num_simulations if sample_size_fraction is None: sample_size_fraction = self.sample_size_fraction # Checking if bootstrap_estimates are already computed if self._bootstrap_estimates is None: self._bootstrap_estimates = self._generate_bootstrap_estimates(num_simulations, sample_size_fraction) elif CausalEstimator.is_bootstrap_parameter_changed(self._bootstrap_estimates.params, locals()): # Check if any parameter is changed from the previous std error estimate self._bootstrap_estimates = self._generate_bootstrap_estimates(num_simulations, sample_size_fraction) std_error = np.std(self._bootstrap_estimates.estimates) return std_error def _estimate_std_error(self, method=None, **kwargs): """ This method is to be overriden by the child classes, so that they can run a standard error estimation method suited to the specific causal estimator. """ raise NotImplementedError( ( "This method for estimating standard errors is " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG + " Meanwhile, you can try the bootstrap method (method='bootstrap') to estimate standard errors." ).format(self.__class__) ) def estimate_std_error(self, method=None, **kwargs): """Compute standard error of an obtained causal estimate. :param method: Method for computing the standard error. :param kwargs: Other optional parameters to be passed to the estimating method. :returns: Standard error of the causal estimate. """ if method is None: if self._confidence_intervals: method = self._confidence_intervals else: method = "default" std_error = None if method == "default" or method is True: # user has not provided any method try: std_error = self._estimate_std_error(method, **kwargs) except NotImplementedError: std_error = self._estimate_std_error_with_bootstrap(**kwargs) else: if method == "bootstrap": std_error = self._estimate_std_error_with_bootstrap(**kwargs) else: std_error = self._estimate_std_error(method, **kwargs) return std_error def _test_significance_with_bootstrap(self, estimate_value, num_null_simulations=None): """Test statistical significance of an estimate using the bootstrap method. :param estimate_value: Obtained estimate's value :param num_null_simulations: Number of simulations for the null hypothesis :returns: p-value of the statistical significance test. """ # Use existing params, if new user defined params are not present if num_null_simulations is None: num_null_simulations = self.num_null_simulations do_retest = self._bootstrap_null_estimates is None or CausalEstimator.is_bootstrap_parameter_changed( self._bootstrap_null_estimates.params, locals() ) if do_retest: null_estimates = np.zeros(num_null_simulations) for i in range(num_null_simulations): new_outcome = np.random.permutation(self._outcome) new_data = self._data.assign(dummy_outcome=new_outcome) # self._outcome = self._data["dummy_outcome"] new_estimator = type(self)( new_data, self._target_estimand, self._target_estimand.treatment_variable, ("dummy_outcome",), test_significance=False, evaluate_effect_strength=False, confidence_intervals=False, target_units=self._target_units, effect_modifiers=self._effect_modifier_names, **self.method_params, ) new_effect = new_estimator.estimate_effect() null_estimates[i] = new_effect.value self._bootstrap_null_estimates = CausalEstimator.BootstrapEstimates( null_estimates, {"num_null_simulations": num_null_simulations, "sample_size_fraction": 1} ) # Processing the null hypothesis estimates sorted_null_estimates = np.sort(self._bootstrap_null_estimates.estimates) self.logger.debug("Null estimates: {0}".format(sorted_null_estimates)) median_estimate = sorted_null_estimates[int(num_null_simulations / 2)] # Doing a two-sided test if estimate_value > median_estimate: # Being conservative with the p-value reported estimate_index = np.searchsorted(sorted_null_estimates, estimate_value, side="left") p_value = 1 - (estimate_index / num_null_simulations) if estimate_value <= median_estimate: # Being conservative with the p-value reported estimate_index = np.searchsorted(sorted_null_estimates, estimate_value, side="right") p_value = estimate_index / num_null_simulations # If the estimate_index is 0, it depends on the number of simulations if p_value == 0: p_value = (0, 1 / len(sorted_null_estimates)) # a tuple determining the range. elif p_value == 1: p_value = (1 - 1 / len(sorted_null_estimates), 1) signif_dict = {"p_value": p_value} return signif_dict def _test_significance(self, estimate_value, method=None, **kwargs): """ This method is to be overriden by the child classes, so that they can run a significance test suited to the specific causal estimator. """ raise NotImplementedError( ( "This method for testing statistical significance is " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG + " Meanwhile, you can try the bootstrap method (method='bootstrap') to test statistical significance." ).format(self.__class__) ) def test_significance(self, estimate_value, method=None, **kwargs): """Test statistical significance of obtained estimate. By default, uses resampling to create a non-parametric significance test. A general procedure. Individual child estimators can implement different methods. If the method name is different from "bootstrap", this function calls the implementation of the child estimator. :param self: object instance of class Estimator :param estimate_value: obtained estimate's value :param method: Method for checking statistical significance :returns: p-value from the significance test """ if method is None: if self._significance_test: method = self._significance_test # this is either True or methodname else: method = "default" signif_dict = None if method == "default" or method is True: # user has not provided any method try: signif_dict = self._test_significance(estimate_value, method, **kwargs) except NotImplementedError: signif_dict = self._test_significance_with_bootstrap(estimate_value, **kwargs) else: if method == "bootstrap": signif_dict = self._test_significance_with_bootstrap(estimate_value, **kwargs) else: signif_dict = self._test_significance(estimate_value, method, **kwargs) return signif_dict def evaluate_effect_strength(self, estimate): fraction_effect_explained = self._evaluate_effect_strength(estimate, method="fraction-effect") # Need to test r-squared before supporting # effect_r_squared = self._evaluate_effect_strength(estimate, method="r-squared") strength_dict = { "fraction-effect": fraction_effect_explained # 'r-squared': effect_r_squared } return strength_dict def _evaluate_effect_strength(self, estimate, method="fraction-effect"): supported_methods = ["fraction-effect"] if method not in supported_methods: raise NotImplementedError("This method is not supported for evaluating effect strength") if method == "fraction-effect": naive_obs_estimate = self.estimate_effect_naive() self.logger.debug(estimate.value, naive_obs_estimate.value) fraction_effect_explained = estimate.value / naive_obs_estimate.value return fraction_effect_explained # elif method == "r-squared": # outcome_mean = np.mean(self._outcome) # total_variance = np.sum(np.square(self._outcome - outcome_mean)) # Assuming a linear model with one variable: the treatment # Currently only works for continuous y # causal_model = outcome_mean + estimate.value*self._treatment # squared_residual = np.sum(np.square(self._outcome - causal_model)) # r_squared = 1 - (squared_residual/total_variance) # return r_squared else: return None def update_input(self, treatment_value, control_value, target_units): self._control_value = control_value self._treatment_value = treatment_value self._target_units = target_units @staticmethod def is_bootstrap_parameter_changed(bootstrap_estimates_params, given_params): """Check whether parameters of the bootstrap have changed. This is an efficiency method that checks if fresh resampling of the bootstrap samples is required. Returns True if parameters have changed and resampling should be done again. :param bootstrap_estimates_params: A dictionary of parameters for the current bootstrap samples :param given_params: A dictionary of parameters passed by the user :returns: A binary flag denoting whether the parameters are different. """ is_any_parameter_changed = False for prm, val in bootstrap_estimates_params.items(): given_val = given_params.get(prm, None) if given_val is not None and given_val != val: is_any_parameter_changed = True break return is_any_parameter_changed def target_units_tostr(self): s = "" if type(self._target_units) is str: s += self._target_units elif callable(self._target_units): s += "Data subset defined by a function" elif isinstance(self._target_units, pd.DataFrame): s += "Data subset provided as a data frame" return s def signif_results_tostr(self, signif_results): s = "" pval = signif_results["p_value"] if type(pval) is tuple: s += "[{0}, {1}]".format(pval[0], pval[1]) else: s += "{0}".format(pval) return s def estimate_effect( treatment: Union[str, List[str]], outcome: Union[str, List[str]], identified_estimand: IdentifiedEstimand, identifier_name: str, method: CausalEstimator, control_value: int = 0, treatment_value: int = 1, test_significance: Optional[bool] = None, evaluate_effect_strength: bool = False, confidence_intervals: bool = False, target_units: str = "ate", effect_modifiers: List[str] = [], fit_estimator: bool = True, method_params: Optional[Dict] = None, ): """Estimate the identified causal effect. Currently requires an explicit method name to be specified. Method names follow the convention of identification method followed by the specific estimation method: "[backdoor/iv].estimation_method_name". Following methods are supported. * Propensity Score Matching: "backdoor.propensity_score_matching" * Propensity Score Stratification: "backdoor.propensity_score_stratification" * Propensity Score-based Inverse Weighting: "backdoor.propensity_score_weighting" * Linear Regression: "backdoor.linear_regression" * Generalized Linear Models (e.g., logistic regression): "backdoor.generalized_linear_model" * Instrumental Variables: "iv.instrumental_variable" * Regression Discontinuity: "iv.regression_discontinuity" In addition, you can directly call any of the EconML estimation methods. The convention is "backdoor.econml.path-to-estimator-class". For example, for the double machine learning estimator ("DML" class) that is located inside "dml" module of EconML, you can use the method name, "backdoor.econml.dml.DML". CausalML estimators can also be called. See `this demo notebook <https://py-why.github.io/dowhy/example_notebooks/dowhy-conditional-treatment-effects.html>`_. :param treatment: Name of the treatment :param outcome: Name of the outcome :param identified_estimand: a probability expression that represents the effect to be estimated. Output of CausalModel.identify_effect method :param method_name: name of the estimation method to be used. :param control_value: Value of the treatment in the control group, for effect estimation. If treatment is multi-variate, this can be a list. :param treatment_value: Value of the treatment in the treated group, for effect estimation. If treatment is multi-variate, this can be a list. :param test_significance: Binary flag on whether to additionally do a statistical signficance test for the estimate. :param evaluate_effect_strength: (Experimental) Binary flag on whether to estimate the relative strength of the treatment's effect. This measure can be used to compare different treatments for the same outcome (by running this method with different treatments sequentially). :param confidence_intervals: (Experimental) Binary flag indicating whether confidence intervals should be computed. :param target_units: (Experimental) The units for which the treatment effect should be estimated. This can be of three types. (1) a string for common specifications of target units (namely, "ate", "att" and "atc"), (2) a lambda function that can be used as an index for the data (pandas DataFrame), or (3) a new DataFrame that contains values of the effect_modifiers and effect will be estimated only for this new data. :param effect_modifiers: Names of effect modifier variables can be (optionally) specified here too, since they do not affect identification. If None, the effect_modifiers from the CausalModel are used. :param fit_estimator: Boolean flag on whether to fit the estimator. Setting it to False is useful to estimate the effect on new data using a previously fitted estimator. :param method_params: Dictionary containing any method-specific parameters. These are passed directly to the estimating method. See the docs for each estimation method for allowed method-specific params. :returns: An instance of the CausalEstimate class, containing the causal effect estimate and other method-dependent information """ treatment = parse_state(treatment) outcome = parse_state(outcome) causal_estimator_class = method.__class__ identified_estimand.set_identifier_method(identifier_name) if identified_estimand.no_directed_path: logger.warning("No directed path from {0} to {1}.".format(treatment, outcome)) return CausalEstimate( 0, identified_estimand, None, control_value=control_value, treatment_value=treatment_value ) # Check if estimator's target estimand is identified elif identified_estimand.estimands[identifier_name] is None: logger.error("No valid identified estimand available.") return CausalEstimate(None, None, None, control_value=control_value, treatment_value=treatment_value) method.update_input(treatment_value, control_value, target_units) estimate = method.estimate_effect() # Store parameters inside estimate object for refutation methods # TODO: This add_params needs to move to the estimator class # inside estimate_effect and estimate_conditional_effect estimate.add_params( estimand_type=identified_estimand.estimand_type, estimator_class=causal_estimator_class, test_significance=test_significance, evaluate_effect_strength=evaluate_effect_strength, confidence_intervals=confidence_intervals, target_units=target_units, effect_modifiers=effect_modifiers, method_params=method_params, ) return estimate class CausalEstimate: """Class for the estimate object that every causal estimator returns""" def __init__( self, estimate, target_estimand, realized_estimand_expr, control_value, treatment_value, conditional_estimates=None, **kwargs, ): self.value = estimate self.target_estimand = target_estimand self.realized_estimand_expr = realized_estimand_expr self.control_value = control_value self.treatment_value = treatment_value self.conditional_estimates = conditional_estimates self.params = kwargs if self.params is not None: for key, value in self.params.items(): setattr(self, key, value) self.effect_strength = None def add_estimator(self, estimator_instance): self.estimator = estimator_instance def add_effect_strength(self, strength_dict): self.effect_strength = strength_dict def add_params(self, **kwargs): self.params.update(kwargs) def get_confidence_intervals(self, confidence_level=None, method=None, **kwargs): """Get confidence intervals of the obtained estimate. By default, this is done with the help of bootstrapped confidence intervals but can be overridden if the specific estimator implements other methods of estimating confidence intervals. If the method provided is not bootstrap, this function calls the implementation of the specific estimator. :param method: Method for estimating confidence intervals. :param confidence_level: The confidence level of the confidence intervals of the estimate. :param kwargs: Other optional args to be passed to the CI method. :returns: The obtained confidence interval. """ confidence_intervals = self.estimator.estimate_confidence_intervals( estimate_value=self.value, confidence_level=confidence_level, method=method, **kwargs ) return confidence_intervals def get_standard_error(self, method=None, **kwargs): """Get standard error of the obtained estimate. By default, this is done with the help of bootstrapped standard errors but can be overridden if the specific estimator implements other methods of estimating standard error. If the method provided is not bootstrap, this function calls the implementation of the specific estimator. :param method: Method for computing the standard error. :param kwargs: Other optional parameters to be passed to the estimating method. :returns: Standard error of the causal estimate. """ std_error = self.estimator.estimate_std_error(method=method, **kwargs) return std_error def test_stat_significance(self, method=None, **kwargs): """Test statistical significance of the estimate obtained. By default, uses resampling to create a non-parametric significance test. Individual child estimators can implement different methods. If the method name is different from "bootstrap", this function calls the implementation of the child estimator. :param method: Method for checking statistical significance :param kwargs: Other optional parameters to be passed to the estimating method. :returns: p-value from the significance test """ signif_results = self.estimator.test_significance(self.value, method=method, **kwargs) return {"p_value": signif_results["p_value"]} def estimate_conditional_effects( self, effect_modifiers=None, num_quantiles=CausalEstimator.NUM_QUANTILES_TO_DISCRETIZE_CONT_COLS ): """Estimate treatment effect conditioned on given variables. If a numeric effect modifier is provided, it is discretized into quantile bins. If you would like a custom discretization, you can do so yourself: create a new column containing the discretized effect modifier and then include that column's name in the effect_modifier_names argument. :param effect_modifiers: Names of effect modifier variables over which the conditional effects will be estimated. If not provided, defaults to the effect modifiers specified during creation of the CausalEstimator object. :param num_quantiles: The number of quantiles into which a numeric effect modifier variable is discretized. Does not affect any categorical effect modifiers. :returns: A (multi-index) dataframe that provides separate effects for each value of the (discretized) effect modifiers. """ return self.estimator._estimate_conditional_effects( self.estimator._estimate_effect_fn, effect_modifiers, num_quantiles ) def interpret(self, method_name=None, **kwargs): """Interpret the causal estimate. :param method_name: Method used (string) or a list of methods. If None, then the default for the specific estimator is used. :param kwargs:: Optional parameters that are directly passed to the interpreter method. :returns: None """ if method_name is None: method_name = self.estimator.interpret_method method_name_arr = parse_state(method_name) for method in method_name_arr: interpreter = interpreters.get_class_object(method) interpreter(self, **kwargs).interpret() def __str__(self): s = "*** Causal Estimate ***\n" # No estimand was identified (identification failed) if self.target_estimand is None: return "Estimation failed! No relevant identified estimand available for this estimation method." s += "\n## Identified estimand\n{0}".format(self.target_estimand.__str__(only_target_estimand=True)) s += "\n## Realized estimand\n{0}".format(self.realized_estimand_expr) if hasattr(self, "estimator"): s += "\nTarget units: {0}\n".format(self.estimator.target_units_tostr()) s += "\n## Estimate\n" s += "Mean value: {0}\n".format(self.value) s += "" if hasattr(self, "cate_estimates"): s += "Effect estimates: {0}\n".format(self.cate_estimates) if hasattr(self, "estimator"): if self.estimator._significance_test: s += "p-value: {0}\n".format(self.estimator.signif_results_tostr(self.test_stat_significance())) if self.estimator._confidence_intervals: s += "{0}% confidence interval: {1}\n".format( 100 * self.estimator.confidence_level, self.get_confidence_intervals() ) if self.conditional_estimates is not None: s += "### Conditional Estimates\n" s += str(self.conditional_estimates) if self.effect_strength is not None: s += "\n## Effect Strength\n" s += "Change in outcome attributable to treatment: {}\n".format(self.effect_strength["fraction-effect"]) # s += "Variance in outcome explained by treatment: {}\n".format(self.effect_strength["r-squared"]) return s class RealizedEstimand(object): def __init__(self, identified_estimand, estimator_name): self.treatment_variable = identified_estimand.treatment_variable self.outcome_variable = identified_estimand.outcome_variable self.backdoor_variables = identified_estimand.get_backdoor_variables() self.instrumental_variables = identified_estimand.instrumental_variables self.estimand_type = identified_estimand.estimand_type self.estimand_expression = None self.assumptions = None self.estimator_name = estimator_name def update_assumptions(self, estimator_assumptions): self.assumptions = estimator_assumptions def update_estimand_expression(self, estimand_expression): self.estimand_expression = estimand_expression def __str__(self): s = "Realized estimand: {0}\n".format(self.estimator_name) s += "Realized estimand type: {0}\n".format(self.estimand_type) s += "Estimand expression:\n{0}\n".format(sp.pretty(self.estimand_expression)) j = 1 for ass_name, ass_str in self.assumptions.items(): s += "Estimand assumption {0}, {1}: {2}\n".format(j, ass_name, ass_str) j += 1 return s

andresmor-ms

2044d216c322a4b32c6eadce5da7d83463f19c2f

05bfa49dacf0061988c96c6f3e3756219df5422a

moved the code into causal_model (for compatibility and removed the param from this function :)

andresmor-ms

py-why/dowhy

Functional api/estimate effect function

#### Estimate Effect function * Refactors the estimate effect into a separate function to keep backwards compatibility #### TODO (future PRs): * Add `fit(...)` method to estimators - Move data related parameters from the constructor to the `fit(...)` method * Refactor code to avoid `**kwargs` in `__init__(...)` constructors

2022-10-18 15:49:21+00:00

2022-10-25 17:02:02+00:00

dowhy/causal_estimator.py

import logging from collections import namedtuple import numpy as np import pandas as pd import sympy as sp from sklearn.utils import resample import dowhy.interpreters as interpreters from dowhy.utils.api import parse_state class CausalEstimator: """Base class for an estimator of causal effect. Subclasses implement different estimation methods. All estimation methods are in the package "dowhy.causal_estimators" """ # The default number of simulations for statistical testing DEFAULT_NUMBER_OF_SIMULATIONS_STAT_TEST = 1000 # The default number of simulations to obtain confidence intervals DEFAULT_NUMBER_OF_SIMULATIONS_CI = 100 # The portion of the total size that should be taken each time to find the confidence intervals # 1 is the recommended value # https://ocw.mit.edu/courses/mathematics/18-05-introduction-to-probability-and-statistics-spring-2014/readings/MIT18_05S14_Reading24.pdf # https://projecteuclid.org/download/pdf_1/euclid.ss/1032280214 DEFAULT_SAMPLE_SIZE_FRACTION = 1 # The default Confidence Level DEFAULT_CONFIDENCE_LEVEL = 0.95 # Number of quantiles to discretize continuous columns, for applying groupby NUM_QUANTILES_TO_DISCRETIZE_CONT_COLS = 5 # Prefix to add to temporary categorical variables created after discretization TEMP_CAT_COLUMN_PREFIX = "__categorical__" DEFAULT_NOTIMPLEMENTEDERROR_MSG = "not yet implemented for {0}. If you would this to be implemented in the next version, please raise an issue at https://github.com/microsoft/dowhy/issues" BootstrapEstimates = namedtuple("BootstrapEstimates", ["estimates", "params"]) DEFAULT_INTERPRET_METHOD = ["textual_effect_interpreter"] # std args to be removed from locals() before being passed to args_dict _STD_INIT_ARGS = ("self", "__class__", "args", "kwargs") def __init__( self, data, identified_estimand, treatment, outcome, control_value=0, treatment_value=1, test_significance=False, evaluate_effect_strength=False, confidence_intervals=False, target_units=None, effect_modifiers=None, num_null_simulations=DEFAULT_NUMBER_OF_SIMULATIONS_STAT_TEST, num_simulations=DEFAULT_NUMBER_OF_SIMULATIONS_CI, sample_size_fraction=DEFAULT_SAMPLE_SIZE_FRACTION, confidence_level=DEFAULT_CONFIDENCE_LEVEL, need_conditional_estimates="auto", num_quantiles_to_discretize_cont_cols=NUM_QUANTILES_TO_DISCRETIZE_CONT_COLS, **kwargs, ): """Initializes an estimator with data and names of relevant variables. This method is called from the constructors of its child classes. :param data: data frame containing the data :param identified_estimand: probability expression representing the target identified estimand to estimate. :param treatment: name of the treatment variable :param outcome: name of the outcome variable :param control_value: Value of the treatment in the control group, for effect estimation. If treatment is multi-variate, this can be a list. :param treatment_value: Value of the treatment in the treated group, for effect estimation. If treatment is multi-variate, this can be a list. :param test_significance: Binary flag or a string indicating whether to test significance and by which method. All estimators support test_significance="bootstrap" that estimates a p-value for the obtained estimate using the bootstrap method. Individual estimators can override this to support custom testing methods. The bootstrap method supports an optional parameter, num_null_simulations. If False, no testing is done. If True, significance of the estimate is tested using the custom method if available, otherwise by bootstrap. :param evaluate_effect_strength: (Experimental) whether to evaluate the strength of effect :param confidence_intervals: Binary flag or a string indicating whether the confidence intervals should be computed and which method should be used. All methods support estimation of confidence intervals using the bootstrap method by using the parameter confidence_intervals="bootstrap". The bootstrap method takes in two arguments (num_simulations and sample_size_fraction) that can be optionally specified in the params dictionary. Estimators may also override this to implement their own confidence interval method. If this parameter is False, no confidence intervals are computed. If True, confidence intervals are computed by the estimator's specific method if available, otherwise through bootstrap. :param target_units: The units for which the treatment effect should be estimated. This can be a string for common specifications of target units (namely, "ate", "att" and "atc"). It can also be a lambda function that can be used as an index for the data (pandas DataFrame). Alternatively, it can be a new DataFrame that contains values of the effect_modifiers and effect will be estimated only for this new data. :param effect_modifiers: Variables on which to compute separate effects, or return a heterogeneous effect function. Not all methods support this currently. :param num_null_simulations: The number of simulations for testing the statistical significance of the estimator :param num_simulations: The number of simulations for finding the confidence interval (and/or standard error) for a estimate :param sample_size_fraction: The size of the sample for the bootstrap estimator :param confidence_level: The confidence level of the confidence interval estimate :param need_conditional_estimates: Boolean flag indicating whether conditional estimates should be computed. Defaults to True if there are effect modifiers in the graph :param num_quantiles_to_discretize_cont_cols: The number of quantiles into which a numeric effect modifier is split, to enable estimation of conditional treatment effect over it. :param kwargs: (optional) Additional estimator-specific parameters :returns: an instance of the estimator class. """ self._data = data self._target_estimand = identified_estimand # Currently estimation methods only support univariate treatment and outcome self._treatment_name = treatment self._outcome_name = outcome[0] # assuming one-dimensional outcome self._control_value = control_value self._treatment_value = treatment_value self._significance_test = test_significance self._effect_strength_eval = evaluate_effect_strength self._target_units = target_units self._effect_modifier_names = effect_modifiers self._confidence_intervals = confidence_intervals self._bootstrap_estimates = None # for confidence intervals and std error self._bootstrap_null_estimates = None # for significance test self._effect_modifiers = None self.method_params = kwargs # Setting the default interpret method self.interpret_method = CausalEstimator.DEFAULT_INTERPRET_METHOD self.logger = logging.getLogger(__name__) # Setting treatment and outcome values if self._data is not None: self._treatment = self._data[self._treatment_name] self._outcome = self._data[self._outcome_name] # Now saving the effect modifiers if self._effect_modifier_names: # only add the observed nodes self._effect_modifier_names = [ cname for cname in self._effect_modifier_names if cname in self._data.columns ] if len(self._effect_modifier_names) > 0: self._effect_modifiers = self._data[self._effect_modifier_names] self._effect_modifiers = pd.get_dummies(self._effect_modifiers, drop_first=True) self.logger.debug("Effect modifiers: " + ",".join(self._effect_modifier_names)) else: self._effect_modifier_names = None # Check if some parameters were set, otherwise set to default values self.num_null_simulations = num_null_simulations self.num_simulations = num_simulations self.sample_size_fraction = sample_size_fraction self.confidence_level = confidence_level self.num_quantiles_to_discretize_cont_cols = num_quantiles_to_discretize_cont_cols # Estimate conditional estimates by default self.need_conditional_estimates = ( need_conditional_estimates if need_conditional_estimates != "auto" else bool(self._effect_modifier_names) ) @staticmethod def get_estimator_object(new_data, identified_estimand, estimate): """Create a new estimator of the same type as the one passed in the estimate argument. Creates a new object with new_data and the identified_estimand :param new_data: np.ndarray, pd.Series, pd.DataFrame The newly assigned data on which the estimator should run :param identified_estimand: IdentifiedEstimand An instance of the identified estimand class that provides the information with respect to which causal pathways are employed when the treatment effects the outcome :param estimate: CausalEstimate It is an already existing estimate whose properties we wish to replicate :returns: An instance of the same estimator class that had generated the given estimate. """ estimator_class = estimate.params["estimator_class"] new_estimator = estimator_class( new_data, identified_estimand, identified_estimand.treatment_variable, identified_estimand.outcome_variable, # names of treatment and outcome control_value=estimate.control_value, treatment_value=estimate.treatment_value, test_significance=False, evaluate_effect_strength=False, confidence_intervals=estimate.params["confidence_intervals"], target_units=estimate.params["target_units"], effect_modifiers=estimate.params["effect_modifiers"], **estimate.params["method_params"], ) return new_estimator def _estimate_effect(self): """This method is to be overriden by the child classes, so that they can run the estimation technique of their choice""" raise NotImplementedError( ("Main estimation method is " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG).format(self.__class__) ) def estimate_effect(self): """Base estimation method that calls the estimate_effect method of its calling subclass. Can optionally also test significance and estimate effect strength for any returned estimate. :param self: object instance of class Estimator :returns: A CausalEstimate instance that contains point estimates of average and conditional effects. Based on the parameters provided, it optionally includes confidence intervals, standard errors,statistical significance and other statistical parameters. """ est = self._estimate_effect() est.add_estimator(self) if self._significance_test: self.test_significance(est.value, method=self._significance_test) if self._confidence_intervals: self.estimate_confidence_intervals( est.value, confidence_level=self.confidence_level, method=self._confidence_intervals ) if self._effect_strength_eval: effect_strength_dict = self.evaluate_effect_strength(est) est.add_effect_strength(effect_strength_dict) return est def estimate_effect_naive(self): # TODO Only works for binary treatment df_withtreatment = self._data.loc[self._data[self._treatment_name] == 1] df_notreatment = self._data.loc[self._data[self._treatment_name] == 0] est = np.mean(df_withtreatment[self._outcome_name]) - np.mean(df_notreatment[self._outcome_name]) return CausalEstimate(est, None, None, control_value=0, treatment_value=1) def _estimate_effect_fn(self, data_df): """Function used in conditional effect estimation. This function is to be overridden by each child estimator. The overridden function should take in a dataframe as input and return the estimate for that data. """ raise NotImplementedError( ("Conditional treatment effects are " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG).format( self.__class__ ) ) def _estimate_conditional_effects(self, estimate_effect_fn, effect_modifier_names=None, num_quantiles=None): """Estimate conditional treatment effects. Common method for all estimators that utilizes a specific estimate_effect_fn implemented by each child estimator. If a numeric effect modifier is provided, it is discretized into quantile bins. If you would like a custom discretization, you can do so yourself: create a new column containing the discretized effect modifier and then include that column's name in the effect_modifier_names argument. :param estimate_effect_fn: Function that has a single parameter (a data frame) and returns the treatment effect estimate on that data. :param effect_modifier_names: Names of effect modifier variables over which the conditional effects will be estimated. If not provided, defaults to the effect modifiers specified during creation of the CausalEstimator object. :param num_quantiles: The number of quantiles into which a numeric effect modifier variable is discretized. Does not affect any categorical effect modifiers. :returns: A (multi-index) dataframe that provides separate effects for each value of the (discretized) effect modifiers. """ # Defaulting to class default values if parameters are not provided if effect_modifier_names is None: effect_modifier_names = self._effect_modifier_names if num_quantiles is None: num_quantiles = self.num_quantiles_to_discretize_cont_cols # Checking that there is at least one effect modifier if not effect_modifier_names: raise ValueError("At least one effect modifier should be specified to compute conditional effects.") # Making sure that effect_modifier_names is a list effect_modifier_names = parse_state(effect_modifier_names) if not all(em in self._effect_modifier_names for em in effect_modifier_names): self.logger.warn( "At least one of the provided effect modifiers was not included while fitting the estimator. You may get incorrect results. To resolve, fit the estimator again by providing the updated effect modifiers in estimate_effect()." ) # Making a copy since we are going to be changing effect modifier names effect_modifier_names = effect_modifier_names.copy() prefix = CausalEstimator.TEMP_CAT_COLUMN_PREFIX # For every numeric effect modifier, adding a temp categorical column for i in range(len(effect_modifier_names)): em = effect_modifier_names[i] if pd.api.types.is_numeric_dtype(self._data[em].dtypes): self._data[prefix + str(em)] = pd.qcut(self._data[em], num_quantiles, duplicates="drop") effect_modifier_names[i] = prefix + str(em) # Grouping by effect modifiers and computing effect separately by_effect_mods = self._data.groupby(effect_modifier_names) cond_est_fn = lambda x: self._do(self._treatment_value, x) - self._do(self._control_value, x) conditional_estimates = by_effect_mods.apply(estimate_effect_fn) # Deleting the temporary categorical columns for em in effect_modifier_names: if em.startswith(prefix): self._data.pop(em) return conditional_estimates def _do(self, x, data_df=None): raise NotImplementedError( ("Do-operator is " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG).format(self.__class__) ) def do(self, x, data_df=None): """Method that implements the do-operator. Given a value x for the treatment, returns the expected value of the outcome when the treatment is intervened to a value x. :param x: Value of the treatment :param data_df: Data on which the do-operator is to be applied. :returns: Value of the outcome when treatment is intervened/set to x. """ est = self._do(x, data_df) return est def construct_symbolic_estimator(self, estimand): raise NotImplementedError(("Symbolic estimator string is ").format(self.__class__)) def _generate_bootstrap_estimates(self, num_bootstrap_simulations, sample_size_fraction): """Helper function to generate causal estimates over bootstrapped samples. :param num_bootstrap_simulations: Number of simulations for the bootstrap method. :param sample_size_fraction: Fraction of the dataset to be resampled. :returns: A collections.namedtuple containing a list of bootstrapped estimates and a dictionary containing parameters used for the bootstrap. """ # The array that stores the results of all estimations simulation_results = np.zeros(num_bootstrap_simulations) # Find the sample size the proportion with the population size sample_size = int(sample_size_fraction * len(self._data)) if sample_size > len(self._data): self.logger.warning("WARN: The sample size is greater than the data being sampled") self.logger.info("INFO: The sample size: {}".format(sample_size)) self.logger.info("INFO: The number of simulations: {}".format(num_bootstrap_simulations)) # Perform the set number of simulations for index in range(num_bootstrap_simulations): new_data = resample(self._data, n_samples=sample_size) new_estimator = type(self)( new_data, self._target_estimand, self._target_estimand.treatment_variable, self._target_estimand.outcome_variable, # names of treatment and outcome treatment_value=self._treatment_value, control_value=self._control_value, test_significance=False, evaluate_effect_strength=False, confidence_intervals=False, target_units=self._target_units, effect_modifiers=self._effect_modifier_names, **self.method_params, ) new_effect = new_estimator.estimate_effect() simulation_results[index] = new_effect.value estimates = CausalEstimator.BootstrapEstimates( simulation_results, {"num_simulations": num_bootstrap_simulations, "sample_size_fraction": sample_size_fraction}, ) return estimates def _estimate_confidence_intervals_with_bootstrap( self, estimate_value, confidence_level=None, num_simulations=None, sample_size_fraction=None ): """ Method to compute confidence interval using bootstrapped sampling. :param estimate_value: obtained estimate's value :param confidence_level: The level for which to compute CI (e.g., 95% confidence level translates to confidence_level=0.95) :param num_simulations: The number of simulations to be performed to get the bootstrap confidence intervals. :param sample_size_fraction: The fraction of the dataset to be resampled. :returns: confidence interval at the specified level. For more details on bootstrap or resampling statistics, refer to the following links: https://ocw.mit.edu/courses/mathematics/18-05-introduction-to-probability-and-statistics-spring-2014/readings/MIT18_05S14_Reading24.pdf https://projecteuclid.org/download/pdf_1/euclid.ss/1032280214 """ # Using class default parameters if not specified if num_simulations is None: num_simulations = self.num_simulations if sample_size_fraction is None: sample_size_fraction = self.sample_size_fraction # Checking if bootstrap_estimates are already computed if self._bootstrap_estimates is None: self._bootstrap_estimates = self._generate_bootstrap_estimates(num_simulations, sample_size_fraction) elif CausalEstimator.is_bootstrap_parameter_changed(self._bootstrap_estimates.params, locals()): # Checked if any parameter is changed from the previous std error estimate self._bootstrap_estimates = self._generate_bootstrap_estimates(num_simulations, sample_size_fraction) # Now use the data obtained from the simulations to get the value of the confidence estimates bootstrap_estimates = self._bootstrap_estimates.estimates # Get the variations of each bootstrap estimate and sort bootstrap_variations = [bootstrap_estimate - estimate_value for bootstrap_estimate in bootstrap_estimates] sorted_bootstrap_variations = np.sort(bootstrap_variations) # Now we take the (1- p)th and the (p)th variations, where p is the chosen confidence level upper_bound_index = int((1 - confidence_level) * len(sorted_bootstrap_variations)) lower_bound_index = int(confidence_level * len(sorted_bootstrap_variations)) # Get the lower and upper bounds by subtracting the variations from the estimate lower_bound = estimate_value - sorted_bootstrap_variations[lower_bound_index] upper_bound = estimate_value - sorted_bootstrap_variations[upper_bound_index] return lower_bound, upper_bound def _estimate_confidence_intervals(self, confidence_level=None, method=None, **kwargs): """ This method is to be overriden by the child classes, so that they can run a confidence interval estimation method suited to the specific causal estimator. """ raise NotImplementedError( ( "This method for estimating confidence intervals is " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG + " Meanwhile, you can try the bootstrap method (method='bootstrap') to estimate confidence intervals." ).format(self.__class__) ) def estimate_confidence_intervals(self, estimate_value, confidence_level=None, method=None, **kwargs): """Find the confidence intervals corresponding to any estimator By default, this is done with the help of bootstrapped confidence intervals but can be overridden if the specific estimator implements other methods of estimating confidence intervals. If the method provided is not bootstrap, this function calls the implementation of the specific estimator. :param estimate_value: obtained estimate's value :param method: Method for estimating confidence intervals. :param confidence_level: The confidence level of the confidence intervals of the estimate. :param kwargs: Other optional args to be passed to the CI method. :returns: The obtained confidence interval. """ if method is None: if self._confidence_intervals: method = self._confidence_intervals # this is either True or methodname else: method = "default" confidence_intervals = None if confidence_level is None: confidence_level = self.confidence_level if method == "default" or method is True: # user has not provided any method try: confidence_intervals = self._estimate_confidence_intervals(confidence_level, method=method, **kwargs) except NotImplementedError: confidence_intervals = self._estimate_confidence_intervals_with_bootstrap( estimate_value, confidence_level, **kwargs ) else: if method == "bootstrap": confidence_intervals = self._estimate_confidence_intervals_with_bootstrap( estimate_value, confidence_level, **kwargs ) else: confidence_intervals = self._estimate_confidence_intervals(confidence_level, method=method, **kwargs) return confidence_intervals def _estimate_std_error_with_bootstrap(self, num_simulations=None, sample_size_fraction=None): """Compute standard error using the bootstrap method. Standard error and confidence intervals use the same parameter num_simulations for the number of bootstrap simulations. :param num_simulations: Number of bootstrapped samples. :param sample_size_fraction: Fraction of data to be resampled. :returns: Standard error of the obtained estimate. """ # Use existing params, if new user defined params are not present if num_simulations is None: num_simulations = self.num_simulations if sample_size_fraction is None: sample_size_fraction = self.sample_size_fraction # Checking if bootstrap_estimates are already computed if self._bootstrap_estimates is None: self._bootstrap_estimates = self._generate_bootstrap_estimates(num_simulations, sample_size_fraction) elif CausalEstimator.is_bootstrap_parameter_changed(self._bootstrap_estimates.params, locals()): # Check if any parameter is changed from the previous std error estimate self._bootstrap_estimates = self._generate_bootstrap_estimates(num_simulations, sample_size_fraction) std_error = np.std(self._bootstrap_estimates.estimates) return std_error def _estimate_std_error(self, method=None, **kwargs): """ This method is to be overriden by the child classes, so that they can run a standard error estimation method suited to the specific causal estimator. """ raise NotImplementedError( ( "This method for estimating standard errors is " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG + " Meanwhile, you can try the bootstrap method (method='bootstrap') to estimate standard errors." ).format(self.__class__) ) def estimate_std_error(self, method=None, **kwargs): """Compute standard error of an obtained causal estimate. :param method: Method for computing the standard error. :param kwargs: Other optional parameters to be passed to the estimating method. :returns: Standard error of the causal estimate. """ if method is None: if self._confidence_intervals: method = self._confidence_intervals else: method = "default" std_error = None if method == "default" or method is True: # user has not provided any method try: std_error = self._estimate_std_error(method, **kwargs) except NotImplementedError: std_error = self._estimate_std_error_with_bootstrap(**kwargs) else: if method == "bootstrap": std_error = self._estimate_std_error_with_bootstrap(**kwargs) else: std_error = self._estimate_std_error(method, **kwargs) return std_error def _test_significance_with_bootstrap(self, estimate_value, num_null_simulations=None): """Test statistical significance of an estimate using the bootstrap method. :param estimate_value: Obtained estimate's value :param num_null_simulations: Number of simulations for the null hypothesis :returns: p-value of the statistical significance test. """ # Use existing params, if new user defined params are not present if num_null_simulations is None: num_null_simulations = self.num_null_simulations do_retest = self._bootstrap_null_estimates is None or CausalEstimator.is_bootstrap_parameter_changed( self._bootstrap_null_estimates.params, locals() ) if do_retest: null_estimates = np.zeros(num_null_simulations) for i in range(num_null_simulations): new_outcome = np.random.permutation(self._outcome) new_data = self._data.assign(dummy_outcome=new_outcome) # self._outcome = self._data["dummy_outcome"] new_estimator = type(self)( new_data, self._target_estimand, self._target_estimand.treatment_variable, ("dummy_outcome",), test_significance=False, evaluate_effect_strength=False, confidence_intervals=False, target_units=self._target_units, effect_modifiers=self._effect_modifier_names, **self.method_params, ) new_effect = new_estimator.estimate_effect() null_estimates[i] = new_effect.value self._bootstrap_null_estimates = CausalEstimator.BootstrapEstimates( null_estimates, {"num_null_simulations": num_null_simulations, "sample_size_fraction": 1} ) # Processing the null hypothesis estimates sorted_null_estimates = np.sort(self._bootstrap_null_estimates.estimates) self.logger.debug("Null estimates: {0}".format(sorted_null_estimates)) median_estimate = sorted_null_estimates[int(num_null_simulations / 2)] # Doing a two-sided test if estimate_value > median_estimate: # Being conservative with the p-value reported estimate_index = np.searchsorted(sorted_null_estimates, estimate_value, side="left") p_value = 1 - (estimate_index / num_null_simulations) if estimate_value <= median_estimate: # Being conservative with the p-value reported estimate_index = np.searchsorted(sorted_null_estimates, estimate_value, side="right") p_value = estimate_index / num_null_simulations # If the estimate_index is 0, it depends on the number of simulations if p_value == 0: p_value = (0, 1 / len(sorted_null_estimates)) # a tuple determining the range. elif p_value == 1: p_value = (1 - 1 / len(sorted_null_estimates), 1) signif_dict = {"p_value": p_value} return signif_dict def _test_significance(self, estimate_value, method=None, **kwargs): """ This method is to be overriden by the child classes, so that they can run a significance test suited to the specific causal estimator. """ raise NotImplementedError( ( "This method for testing statistical significance is " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG + " Meanwhile, you can try the bootstrap method (method='bootstrap') to test statistical significance." ).format(self.__class__) ) def test_significance(self, estimate_value, method=None, **kwargs): """Test statistical significance of obtained estimate. By default, uses resampling to create a non-parametric significance test. A general procedure. Individual child estimators can implement different methods. If the method name is different from "bootstrap", this function calls the implementation of the child estimator. :param self: object instance of class Estimator :param estimate_value: obtained estimate's value :param method: Method for checking statistical significance :returns: p-value from the significance test """ if method is None: if self._significance_test: method = self._significance_test # this is either True or methodname else: method = "default" signif_dict = None if method == "default" or method is True: # user has not provided any method try: signif_dict = self._test_significance(estimate_value, method, **kwargs) except NotImplementedError: signif_dict = self._test_significance_with_bootstrap(estimate_value, **kwargs) else: if method == "bootstrap": signif_dict = self._test_significance_with_bootstrap(estimate_value, **kwargs) else: signif_dict = self._test_significance(estimate_value, method, **kwargs) return signif_dict def evaluate_effect_strength(self, estimate): fraction_effect_explained = self._evaluate_effect_strength(estimate, method="fraction-effect") # Need to test r-squared before supporting # effect_r_squared = self._evaluate_effect_strength(estimate, method="r-squared") strength_dict = { "fraction-effect": fraction_effect_explained # 'r-squared': effect_r_squared } return strength_dict def _evaluate_effect_strength(self, estimate, method="fraction-effect"): supported_methods = ["fraction-effect"] if method not in supported_methods: raise NotImplementedError("This method is not supported for evaluating effect strength") if method == "fraction-effect": naive_obs_estimate = self.estimate_effect_naive() self.logger.debug(estimate.value, naive_obs_estimate.value) fraction_effect_explained = estimate.value / naive_obs_estimate.value return fraction_effect_explained # elif method == "r-squared": # outcome_mean = np.mean(self._outcome) # total_variance = np.sum(np.square(self._outcome - outcome_mean)) # Assuming a linear model with one variable: the treatment # Currently only works for continuous y # causal_model = outcome_mean + estimate.value*self._treatment # squared_residual = np.sum(np.square(self._outcome - causal_model)) # r_squared = 1 - (squared_residual/total_variance) # return r_squared else: return None def update_input(self, treatment_value, control_value, target_units): self._control_value = control_value self._treatment_value = treatment_value self._target_units = target_units @staticmethod def is_bootstrap_parameter_changed(bootstrap_estimates_params, given_params): """Check whether parameters of the bootstrap have changed. This is an efficiency method that checks if fresh resampling of the bootstrap samples is required. Returns True if parameters have changed and resampling should be done again. :param bootstrap_estimates_params: A dictionary of parameters for the current bootstrap samples :param given_params: A dictionary of parameters passed by the user :returns: A binary flag denoting whether the parameters are different. """ is_any_parameter_changed = False for prm, val in bootstrap_estimates_params.items(): given_val = given_params.get(prm, None) if given_val is not None and given_val != val: is_any_parameter_changed = True break return is_any_parameter_changed def target_units_tostr(self): s = "" if type(self._target_units) is str: s += self._target_units elif callable(self._target_units): s += "Data subset defined by a function" elif isinstance(self._target_units, pd.DataFrame): s += "Data subset provided as a data frame" return s def signif_results_tostr(self, signif_results): s = "" pval = signif_results["p_value"] if type(pval) is tuple: s += "[{0}, {1}]".format(pval[0], pval[1]) else: s += "{0}".format(pval) return s class CausalEstimate: """Class for the estimate object that every causal estimator returns""" def __init__( self, estimate, target_estimand, realized_estimand_expr, control_value, treatment_value, conditional_estimates=None, **kwargs, ): self.value = estimate self.target_estimand = target_estimand self.realized_estimand_expr = realized_estimand_expr self.control_value = control_value self.treatment_value = treatment_value self.conditional_estimates = conditional_estimates self.params = kwargs if self.params is not None: for key, value in self.params.items(): setattr(self, key, value) self.effect_strength = None def add_estimator(self, estimator_instance): self.estimator = estimator_instance def add_effect_strength(self, strength_dict): self.effect_strength = strength_dict def add_params(self, **kwargs): self.params.update(kwargs) def get_confidence_intervals(self, confidence_level=None, method=None, **kwargs): """Get confidence intervals of the obtained estimate. By default, this is done with the help of bootstrapped confidence intervals but can be overridden if the specific estimator implements other methods of estimating confidence intervals. If the method provided is not bootstrap, this function calls the implementation of the specific estimator. :param method: Method for estimating confidence intervals. :param confidence_level: The confidence level of the confidence intervals of the estimate. :param kwargs: Other optional args to be passed to the CI method. :returns: The obtained confidence interval. """ confidence_intervals = self.estimator.estimate_confidence_intervals( estimate_value=self.value, confidence_level=confidence_level, method=method, **kwargs ) return confidence_intervals def get_standard_error(self, method=None, **kwargs): """Get standard error of the obtained estimate. By default, this is done with the help of bootstrapped standard errors but can be overridden if the specific estimator implements other methods of estimating standard error. If the method provided is not bootstrap, this function calls the implementation of the specific estimator. :param method: Method for computing the standard error. :param kwargs: Other optional parameters to be passed to the estimating method. :returns: Standard error of the causal estimate. """ std_error = self.estimator.estimate_std_error(method=method, **kwargs) return std_error def test_stat_significance(self, method=None, **kwargs): """Test statistical significance of the estimate obtained. By default, uses resampling to create a non-parametric significance test. Individual child estimators can implement different methods. If the method name is different from "bootstrap", this function calls the implementation of the child estimator. :param method: Method for checking statistical significance :param kwargs: Other optional parameters to be passed to the estimating method. :returns: p-value from the significance test """ signif_results = self.estimator.test_significance(self.value, method=method, **kwargs) return {"p_value": signif_results["p_value"]} def estimate_conditional_effects( self, effect_modifiers=None, num_quantiles=CausalEstimator.NUM_QUANTILES_TO_DISCRETIZE_CONT_COLS ): """Estimate treatment effect conditioned on given variables. If a numeric effect modifier is provided, it is discretized into quantile bins. If you would like a custom discretization, you can do so yourself: create a new column containing the discretized effect modifier and then include that column's name in the effect_modifier_names argument. :param effect_modifiers: Names of effect modifier variables over which the conditional effects will be estimated. If not provided, defaults to the effect modifiers specified during creation of the CausalEstimator object. :param num_quantiles: The number of quantiles into which a numeric effect modifier variable is discretized. Does not affect any categorical effect modifiers. :returns: A (multi-index) dataframe that provides separate effects for each value of the (discretized) effect modifiers. """ return self.estimator._estimate_conditional_effects( self.estimator._estimate_effect_fn, effect_modifiers, num_quantiles ) def interpret(self, method_name=None, **kwargs): """Interpret the causal estimate. :param method_name: Method used (string) or a list of methods. If None, then the default for the specific estimator is used. :param kwargs:: Optional parameters that are directly passed to the interpreter method. :returns: None """ if method_name is None: method_name = self.estimator.interpret_method method_name_arr = parse_state(method_name) for method in method_name_arr: interpreter = interpreters.get_class_object(method) interpreter(self, **kwargs).interpret() def __str__(self): s = "*** Causal Estimate ***\n" # No estimand was identified (identification failed) if self.target_estimand is None: return "Estimation failed! No relevant identified estimand available for this estimation method." s += "\n## Identified estimand\n{0}".format(self.target_estimand.__str__(only_target_estimand=True)) s += "\n## Realized estimand\n{0}".format(self.realized_estimand_expr) if hasattr(self, "estimator"): s += "\nTarget units: {0}\n".format(self.estimator.target_units_tostr()) s += "\n## Estimate\n" s += "Mean value: {0}\n".format(self.value) s += "" if hasattr(self, "cate_estimates"): s += "Effect estimates: {0}\n".format(self.cate_estimates) if hasattr(self, "estimator"): if self.estimator._significance_test: s += "p-value: {0}\n".format(self.estimator.signif_results_tostr(self.test_stat_significance())) if self.estimator._confidence_intervals: s += "{0}% confidence interval: {1}\n".format( 100 * self.estimator.confidence_level, self.get_confidence_intervals() ) if self.conditional_estimates is not None: s += "### Conditional Estimates\n" s += str(self.conditional_estimates) if self.effect_strength is not None: s += "\n## Effect Strength\n" s += "Change in outcome attributable to treatment: {}\n".format(self.effect_strength["fraction-effect"]) # s += "Variance in outcome explained by treatment: {}\n".format(self.effect_strength["r-squared"]) return s class RealizedEstimand(object): def __init__(self, identified_estimand, estimator_name): self.treatment_variable = identified_estimand.treatment_variable self.outcome_variable = identified_estimand.outcome_variable self.backdoor_variables = identified_estimand.get_backdoor_variables() self.instrumental_variables = identified_estimand.instrumental_variables self.estimand_type = identified_estimand.estimand_type self.estimand_expression = None self.assumptions = None self.estimator_name = estimator_name def update_assumptions(self, estimator_assumptions): self.assumptions = estimator_assumptions def update_estimand_expression(self, estimand_expression): self.estimand_expression = estimand_expression def __str__(self): s = "Realized estimand: {0}\n".format(self.estimator_name) s += "Realized estimand type: {0}\n".format(self.estimand_type) s += "Estimand expression:\n{0}\n".format(sp.pretty(self.estimand_expression)) j = 1 for ass_name, ass_str in self.assumptions.items(): s += "Estimand assumption {0}, {1}: {2}\n".format(j, ass_name, ass_str) j += 1 return s

import logging from collections import namedtuple from typing import Dict, List, Optional, Union import numpy as np import pandas as pd import sympy as sp from sklearn.utils import resample import dowhy.interpreters as interpreters from dowhy import causal_estimators from dowhy.causal_graph import CausalGraph from dowhy.causal_identifier.identified_estimand import IdentifiedEstimand from dowhy.utils.api import parse_state logger = logging.getLogger(__name__) class CausalEstimator: """Base class for an estimator of causal effect. Subclasses implement different estimation methods. All estimation methods are in the package "dowhy.causal_estimators" """ # The default number of simulations for statistical testing DEFAULT_NUMBER_OF_SIMULATIONS_STAT_TEST = 1000 # The default number of simulations to obtain confidence intervals DEFAULT_NUMBER_OF_SIMULATIONS_CI = 100 # The portion of the total size that should be taken each time to find the confidence intervals # 1 is the recommended value # https://ocw.mit.edu/courses/mathematics/18-05-introduction-to-probability-and-statistics-spring-2014/readings/MIT18_05S14_Reading24.pdf # https://projecteuclid.org/download/pdf_1/euclid.ss/1032280214 DEFAULT_SAMPLE_SIZE_FRACTION = 1 # The default Confidence Level DEFAULT_CONFIDENCE_LEVEL = 0.95 # Number of quantiles to discretize continuous columns, for applying groupby NUM_QUANTILES_TO_DISCRETIZE_CONT_COLS = 5 # Prefix to add to temporary categorical variables created after discretization TEMP_CAT_COLUMN_PREFIX = "__categorical__" DEFAULT_NOTIMPLEMENTEDERROR_MSG = "not yet implemented for {0}. If you would this to be implemented in the next version, please raise an issue at https://github.com/microsoft/dowhy/issues" BootstrapEstimates = namedtuple("BootstrapEstimates", ["estimates", "params"]) DEFAULT_INTERPRET_METHOD = ["textual_effect_interpreter"] # std args to be removed from locals() before being passed to args_dict _STD_INIT_ARGS = ("self", "__class__", "args", "kwargs") def __init__( self, data, identified_estimand, treatment, outcome, control_value=0, treatment_value=1, test_significance=False, evaluate_effect_strength=False, confidence_intervals=False, target_units=None, effect_modifiers=None, num_null_simulations=DEFAULT_NUMBER_OF_SIMULATIONS_STAT_TEST, num_simulations=DEFAULT_NUMBER_OF_SIMULATIONS_CI, sample_size_fraction=DEFAULT_SAMPLE_SIZE_FRACTION, confidence_level=DEFAULT_CONFIDENCE_LEVEL, need_conditional_estimates="auto", num_quantiles_to_discretize_cont_cols=NUM_QUANTILES_TO_DISCRETIZE_CONT_COLS, **kwargs, ): """Initializes an estimator with data and names of relevant variables. This method is called from the constructors of its child classes. :param data: data frame containing the data :param identified_estimand: probability expression representing the target identified estimand to estimate. :param treatment: name of the treatment variable :param outcome: name of the outcome variable :param control_value: Value of the treatment in the control group, for effect estimation. If treatment is multi-variate, this can be a list. :param treatment_value: Value of the treatment in the treated group, for effect estimation. If treatment is multi-variate, this can be a list. :param test_significance: Binary flag or a string indicating whether to test significance and by which method. All estimators support test_significance="bootstrap" that estimates a p-value for the obtained estimate using the bootstrap method. Individual estimators can override this to support custom testing methods. The bootstrap method supports an optional parameter, num_null_simulations. If False, no testing is done. If True, significance of the estimate is tested using the custom method if available, otherwise by bootstrap. :param evaluate_effect_strength: (Experimental) whether to evaluate the strength of effect :param confidence_intervals: Binary flag or a string indicating whether the confidence intervals should be computed and which method should be used. All methods support estimation of confidence intervals using the bootstrap method by using the parameter confidence_intervals="bootstrap". The bootstrap method takes in two arguments (num_simulations and sample_size_fraction) that can be optionally specified in the params dictionary. Estimators may also override this to implement their own confidence interval method. If this parameter is False, no confidence intervals are computed. If True, confidence intervals are computed by the estimator's specific method if available, otherwise through bootstrap. :param target_units: The units for which the treatment effect should be estimated. This can be a string for common specifications of target units (namely, "ate", "att" and "atc"). It can also be a lambda function that can be used as an index for the data (pandas DataFrame). Alternatively, it can be a new DataFrame that contains values of the effect_modifiers and effect will be estimated only for this new data. :param effect_modifiers: Variables on which to compute separate effects, or return a heterogeneous effect function. Not all methods support this currently. :param num_null_simulations: The number of simulations for testing the statistical significance of the estimator :param num_simulations: The number of simulations for finding the confidence interval (and/or standard error) for a estimate :param sample_size_fraction: The size of the sample for the bootstrap estimator :param confidence_level: The confidence level of the confidence interval estimate :param need_conditional_estimates: Boolean flag indicating whether conditional estimates should be computed. Defaults to True if there are effect modifiers in the graph :param num_quantiles_to_discretize_cont_cols: The number of quantiles into which a numeric effect modifier is split, to enable estimation of conditional treatment effect over it. :param kwargs: (optional) Additional estimator-specific parameters :returns: an instance of the estimator class. """ self._data = data self._target_estimand = identified_estimand # Currently estimation methods only support univariate treatment and outcome self._treatment_name = treatment self._outcome_name = outcome[0] # assuming one-dimensional outcome self._control_value = control_value self._treatment_value = treatment_value self._significance_test = test_significance self._effect_strength_eval = evaluate_effect_strength self._target_units = target_units self._effect_modifier_names = effect_modifiers self._confidence_intervals = confidence_intervals self._bootstrap_estimates = None # for confidence intervals and std error self._bootstrap_null_estimates = None # for significance test self._effect_modifiers = None self.method_params = kwargs # Setting the default interpret method self.interpret_method = CausalEstimator.DEFAULT_INTERPRET_METHOD self.logger = logging.getLogger(__name__) # Setting treatment and outcome values if self._data is not None: self._treatment = self._data[self._treatment_name] self._outcome = self._data[self._outcome_name] if self._effect_modifier_names: # only add the observed nodes self._effect_modifier_names = [ cname for cname in self._effect_modifier_names if cname in self._data.columns ] if len(self._effect_modifier_names) > 0: self._effect_modifiers = self._data[self._effect_modifier_names] self._effect_modifiers = pd.get_dummies(self._effect_modifiers, drop_first=True) self.logger.debug("Effect modifiers: " + ",".join(self._effect_modifier_names)) else: self._effect_modifier_names = None # Check if some parameters were set, otherwise set to default values self.num_null_simulations = num_null_simulations self.num_simulations = num_simulations self.sample_size_fraction = sample_size_fraction self.confidence_level = confidence_level self.num_quantiles_to_discretize_cont_cols = num_quantiles_to_discretize_cont_cols # Estimate conditional estimates by default self.need_conditional_estimates = ( need_conditional_estimates if need_conditional_estimates != "auto" else bool(self._effect_modifier_names) ) @staticmethod def get_estimator_object(new_data, identified_estimand, estimate): """Create a new estimator of the same type as the one passed in the estimate argument. Creates a new object with new_data and the identified_estimand :param new_data: np.ndarray, pd.Series, pd.DataFrame The newly assigned data on which the estimator should run :param identified_estimand: IdentifiedEstimand An instance of the identified estimand class that provides the information with respect to which causal pathways are employed when the treatment effects the outcome :param estimate: CausalEstimate It is an already existing estimate whose properties we wish to replicate :returns: An instance of the same estimator class that had generated the given estimate. """ estimator_class = estimate.params["estimator_class"] new_estimator = estimator_class( new_data, identified_estimand, identified_estimand.treatment_variable, identified_estimand.outcome_variable, # names of treatment and outcome control_value=estimate.control_value, treatment_value=estimate.treatment_value, test_significance=False, evaluate_effect_strength=False, confidence_intervals=estimate.params["confidence_intervals"], target_units=estimate.params["target_units"], effect_modifiers=estimate.params["effect_modifiers"], **estimate.params["method_params"] if estimate.params["method_params"] is not None else {}, ) return new_estimator def _estimate_effect(self): """This method is to be overriden by the child classes, so that they can run the estimation technique of their choice""" raise NotImplementedError( ("Main estimation method is " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG).format(self.__class__) ) def estimate_effect(self): """Base estimation method that calls the estimate_effect method of its calling subclass. Can optionally also test significance and estimate effect strength for any returned estimate. :param self: object instance of class Estimator :returns: A CausalEstimate instance that contains point estimates of average and conditional effects. Based on the parameters provided, it optionally includes confidence intervals, standard errors,statistical significance and other statistical parameters. """ est = self._estimate_effect() est.add_estimator(self) if self._significance_test: self.test_significance(est.value, method=self._significance_test) if self._confidence_intervals: self.estimate_confidence_intervals( est.value, confidence_level=self.confidence_level, method=self._confidence_intervals ) if self._effect_strength_eval: effect_strength_dict = self.evaluate_effect_strength(est) est.add_effect_strength(effect_strength_dict) return est def estimate_effect_naive(self): # TODO Only works for binary treatment df_withtreatment = self._data.loc[self._data[self._treatment_name] == 1] df_notreatment = self._data.loc[self._data[self._treatment_name] == 0] est = np.mean(df_withtreatment[self._outcome_name]) - np.mean(df_notreatment[self._outcome_name]) return CausalEstimate(est, None, None, control_value=0, treatment_value=1) def _estimate_effect_fn(self, data_df): """Function used in conditional effect estimation. This function is to be overridden by each child estimator. The overridden function should take in a dataframe as input and return the estimate for that data. """ raise NotImplementedError( ("Conditional treatment effects are " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG).format( self.__class__ ) ) def _estimate_conditional_effects(self, estimate_effect_fn, effect_modifier_names=None, num_quantiles=None): """Estimate conditional treatment effects. Common method for all estimators that utilizes a specific estimate_effect_fn implemented by each child estimator. If a numeric effect modifier is provided, it is discretized into quantile bins. If you would like a custom discretization, you can do so yourself: create a new column containing the discretized effect modifier and then include that column's name in the effect_modifier_names argument. :param estimate_effect_fn: Function that has a single parameter (a data frame) and returns the treatment effect estimate on that data. :param effect_modifier_names: Names of effect modifier variables over which the conditional effects will be estimated. If not provided, defaults to the effect modifiers specified during creation of the CausalEstimator object. :param num_quantiles: The number of quantiles into which a numeric effect modifier variable is discretized. Does not affect any categorical effect modifiers. :returns: A (multi-index) dataframe that provides separate effects for each value of the (discretized) effect modifiers. """ # Defaulting to class default values if parameters are not provided if effect_modifier_names is None: effect_modifier_names = self._effect_modifier_names if num_quantiles is None: num_quantiles = self.num_quantiles_to_discretize_cont_cols # Checking that there is at least one effect modifier if not effect_modifier_names: raise ValueError("At least one effect modifier should be specified to compute conditional effects.") # Making sure that effect_modifier_names is a list effect_modifier_names = parse_state(effect_modifier_names) if not all(em in self._effect_modifier_names for em in effect_modifier_names): self.logger.warn( "At least one of the provided effect modifiers was not included while fitting the estimator. You may get incorrect results. To resolve, fit the estimator again by providing the updated effect modifiers in estimate_effect()." ) # Making a copy since we are going to be changing effect modifier names effect_modifier_names = effect_modifier_names.copy() prefix = CausalEstimator.TEMP_CAT_COLUMN_PREFIX # For every numeric effect modifier, adding a temp categorical column for i in range(len(effect_modifier_names)): em = effect_modifier_names[i] if pd.api.types.is_numeric_dtype(self._data[em].dtypes): self._data[prefix + str(em)] = pd.qcut(self._data[em], num_quantiles, duplicates="drop") effect_modifier_names[i] = prefix + str(em) # Grouping by effect modifiers and computing effect separately by_effect_mods = self._data.groupby(effect_modifier_names) cond_est_fn = lambda x: self._do(self._treatment_value, x) - self._do(self._control_value, x) conditional_estimates = by_effect_mods.apply(estimate_effect_fn) # Deleting the temporary categorical columns for em in effect_modifier_names: if em.startswith(prefix): self._data.pop(em) return conditional_estimates def _do(self, x, data_df=None): raise NotImplementedError( ("Do-operator is " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG).format(self.__class__) ) def do(self, x, data_df=None): """Method that implements the do-operator. Given a value x for the treatment, returns the expected value of the outcome when the treatment is intervened to a value x. :param x: Value of the treatment :param data_df: Data on which the do-operator is to be applied. :returns: Value of the outcome when treatment is intervened/set to x. """ est = self._do(x, data_df) return est def construct_symbolic_estimator(self, estimand): raise NotImplementedError(("Symbolic estimator string is ").format(self.__class__)) def _generate_bootstrap_estimates(self, num_bootstrap_simulations, sample_size_fraction): """Helper function to generate causal estimates over bootstrapped samples. :param num_bootstrap_simulations: Number of simulations for the bootstrap method. :param sample_size_fraction: Fraction of the dataset to be resampled. :returns: A collections.namedtuple containing a list of bootstrapped estimates and a dictionary containing parameters used for the bootstrap. """ # The array that stores the results of all estimations simulation_results = np.zeros(num_bootstrap_simulations) # Find the sample size the proportion with the population size sample_size = int(sample_size_fraction * len(self._data)) if sample_size > len(self._data): self.logger.warning("WARN: The sample size is greater than the data being sampled") self.logger.info("INFO: The sample size: {}".format(sample_size)) self.logger.info("INFO: The number of simulations: {}".format(num_bootstrap_simulations)) # Perform the set number of simulations for index in range(num_bootstrap_simulations): new_data = resample(self._data, n_samples=sample_size) new_estimator = type(self)( new_data, self._target_estimand, self._target_estimand.treatment_variable, self._target_estimand.outcome_variable, # names of treatment and outcome treatment_value=self._treatment_value, control_value=self._control_value, test_significance=False, evaluate_effect_strength=False, confidence_intervals=False, target_units=self._target_units, effect_modifiers=self._effect_modifier_names, **self.method_params, ) new_effect = new_estimator.estimate_effect() simulation_results[index] = new_effect.value estimates = CausalEstimator.BootstrapEstimates( simulation_results, {"num_simulations": num_bootstrap_simulations, "sample_size_fraction": sample_size_fraction}, ) return estimates def _estimate_confidence_intervals_with_bootstrap( self, estimate_value, confidence_level=None, num_simulations=None, sample_size_fraction=None ): """ Method to compute confidence interval using bootstrapped sampling. :param estimate_value: obtained estimate's value :param confidence_level: The level for which to compute CI (e.g., 95% confidence level translates to confidence_level=0.95) :param num_simulations: The number of simulations to be performed to get the bootstrap confidence intervals. :param sample_size_fraction: The fraction of the dataset to be resampled. :returns: confidence interval at the specified level. For more details on bootstrap or resampling statistics, refer to the following links: https://ocw.mit.edu/courses/mathematics/18-05-introduction-to-probability-and-statistics-spring-2014/readings/MIT18_05S14_Reading24.pdf https://projecteuclid.org/download/pdf_1/euclid.ss/1032280214 """ # Using class default parameters if not specified if num_simulations is None: num_simulations = self.num_simulations if sample_size_fraction is None: sample_size_fraction = self.sample_size_fraction # Checking if bootstrap_estimates are already computed if self._bootstrap_estimates is None: self._bootstrap_estimates = self._generate_bootstrap_estimates(num_simulations, sample_size_fraction) elif CausalEstimator.is_bootstrap_parameter_changed(self._bootstrap_estimates.params, locals()): # Checked if any parameter is changed from the previous std error estimate self._bootstrap_estimates = self._generate_bootstrap_estimates(num_simulations, sample_size_fraction) # Now use the data obtained from the simulations to get the value of the confidence estimates bootstrap_estimates = self._bootstrap_estimates.estimates # Get the variations of each bootstrap estimate and sort bootstrap_variations = [bootstrap_estimate - estimate_value for bootstrap_estimate in bootstrap_estimates] sorted_bootstrap_variations = np.sort(bootstrap_variations) # Now we take the (1- p)th and the (p)th variations, where p is the chosen confidence level upper_bound_index = int((1 - confidence_level) * len(sorted_bootstrap_variations)) lower_bound_index = int(confidence_level * len(sorted_bootstrap_variations)) # Get the lower and upper bounds by subtracting the variations from the estimate lower_bound = estimate_value - sorted_bootstrap_variations[lower_bound_index] upper_bound = estimate_value - sorted_bootstrap_variations[upper_bound_index] return lower_bound, upper_bound def _estimate_confidence_intervals(self, confidence_level=None, method=None, **kwargs): """ This method is to be overriden by the child classes, so that they can run a confidence interval estimation method suited to the specific causal estimator. """ raise NotImplementedError( ( "This method for estimating confidence intervals is " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG + " Meanwhile, you can try the bootstrap method (method='bootstrap') to estimate confidence intervals." ).format(self.__class__) ) def estimate_confidence_intervals(self, estimate_value, confidence_level=None, method=None, **kwargs): """Find the confidence intervals corresponding to any estimator By default, this is done with the help of bootstrapped confidence intervals but can be overridden if the specific estimator implements other methods of estimating confidence intervals. If the method provided is not bootstrap, this function calls the implementation of the specific estimator. :param estimate_value: obtained estimate's value :param method: Method for estimating confidence intervals. :param confidence_level: The confidence level of the confidence intervals of the estimate. :param kwargs: Other optional args to be passed to the CI method. :returns: The obtained confidence interval. """ if method is None: if self._confidence_intervals: method = self._confidence_intervals # this is either True or methodname else: method = "default" confidence_intervals = None if confidence_level is None: confidence_level = self.confidence_level if method == "default" or method is True: # user has not provided any method try: confidence_intervals = self._estimate_confidence_intervals(confidence_level, method=method, **kwargs) except NotImplementedError: confidence_intervals = self._estimate_confidence_intervals_with_bootstrap( estimate_value, confidence_level, **kwargs ) else: if method == "bootstrap": confidence_intervals = self._estimate_confidence_intervals_with_bootstrap( estimate_value, confidence_level, **kwargs ) else: confidence_intervals = self._estimate_confidence_intervals(confidence_level, method=method, **kwargs) return confidence_intervals def _estimate_std_error_with_bootstrap(self, num_simulations=None, sample_size_fraction=None): """Compute standard error using the bootstrap method. Standard error and confidence intervals use the same parameter num_simulations for the number of bootstrap simulations. :param num_simulations: Number of bootstrapped samples. :param sample_size_fraction: Fraction of data to be resampled. :returns: Standard error of the obtained estimate. """ # Use existing params, if new user defined params are not present if num_simulations is None: num_simulations = self.num_simulations if sample_size_fraction is None: sample_size_fraction = self.sample_size_fraction # Checking if bootstrap_estimates are already computed if self._bootstrap_estimates is None: self._bootstrap_estimates = self._generate_bootstrap_estimates(num_simulations, sample_size_fraction) elif CausalEstimator.is_bootstrap_parameter_changed(self._bootstrap_estimates.params, locals()): # Check if any parameter is changed from the previous std error estimate self._bootstrap_estimates = self._generate_bootstrap_estimates(num_simulations, sample_size_fraction) std_error = np.std(self._bootstrap_estimates.estimates) return std_error def _estimate_std_error(self, method=None, **kwargs): """ This method is to be overriden by the child classes, so that they can run a standard error estimation method suited to the specific causal estimator. """ raise NotImplementedError( ( "This method for estimating standard errors is " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG + " Meanwhile, you can try the bootstrap method (method='bootstrap') to estimate standard errors." ).format(self.__class__) ) def estimate_std_error(self, method=None, **kwargs): """Compute standard error of an obtained causal estimate. :param method: Method for computing the standard error. :param kwargs: Other optional parameters to be passed to the estimating method. :returns: Standard error of the causal estimate. """ if method is None: if self._confidence_intervals: method = self._confidence_intervals else: method = "default" std_error = None if method == "default" or method is True: # user has not provided any method try: std_error = self._estimate_std_error(method, **kwargs) except NotImplementedError: std_error = self._estimate_std_error_with_bootstrap(**kwargs) else: if method == "bootstrap": std_error = self._estimate_std_error_with_bootstrap(**kwargs) else: std_error = self._estimate_std_error(method, **kwargs) return std_error def _test_significance_with_bootstrap(self, estimate_value, num_null_simulations=None): """Test statistical significance of an estimate using the bootstrap method. :param estimate_value: Obtained estimate's value :param num_null_simulations: Number of simulations for the null hypothesis :returns: p-value of the statistical significance test. """ # Use existing params, if new user defined params are not present if num_null_simulations is None: num_null_simulations = self.num_null_simulations do_retest = self._bootstrap_null_estimates is None or CausalEstimator.is_bootstrap_parameter_changed( self._bootstrap_null_estimates.params, locals() ) if do_retest: null_estimates = np.zeros(num_null_simulations) for i in range(num_null_simulations): new_outcome = np.random.permutation(self._outcome) new_data = self._data.assign(dummy_outcome=new_outcome) # self._outcome = self._data["dummy_outcome"] new_estimator = type(self)( new_data, self._target_estimand, self._target_estimand.treatment_variable, ("dummy_outcome",), test_significance=False, evaluate_effect_strength=False, confidence_intervals=False, target_units=self._target_units, effect_modifiers=self._effect_modifier_names, **self.method_params, ) new_effect = new_estimator.estimate_effect() null_estimates[i] = new_effect.value self._bootstrap_null_estimates = CausalEstimator.BootstrapEstimates( null_estimates, {"num_null_simulations": num_null_simulations, "sample_size_fraction": 1} ) # Processing the null hypothesis estimates sorted_null_estimates = np.sort(self._bootstrap_null_estimates.estimates) self.logger.debug("Null estimates: {0}".format(sorted_null_estimates)) median_estimate = sorted_null_estimates[int(num_null_simulations / 2)] # Doing a two-sided test if estimate_value > median_estimate: # Being conservative with the p-value reported estimate_index = np.searchsorted(sorted_null_estimates, estimate_value, side="left") p_value = 1 - (estimate_index / num_null_simulations) if estimate_value <= median_estimate: # Being conservative with the p-value reported estimate_index = np.searchsorted(sorted_null_estimates, estimate_value, side="right") p_value = estimate_index / num_null_simulations # If the estimate_index is 0, it depends on the number of simulations if p_value == 0: p_value = (0, 1 / len(sorted_null_estimates)) # a tuple determining the range. elif p_value == 1: p_value = (1 - 1 / len(sorted_null_estimates), 1) signif_dict = {"p_value": p_value} return signif_dict def _test_significance(self, estimate_value, method=None, **kwargs): """ This method is to be overriden by the child classes, so that they can run a significance test suited to the specific causal estimator. """ raise NotImplementedError( ( "This method for testing statistical significance is " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG + " Meanwhile, you can try the bootstrap method (method='bootstrap') to test statistical significance." ).format(self.__class__) ) def test_significance(self, estimate_value, method=None, **kwargs): """Test statistical significance of obtained estimate. By default, uses resampling to create a non-parametric significance test. A general procedure. Individual child estimators can implement different methods. If the method name is different from "bootstrap", this function calls the implementation of the child estimator. :param self: object instance of class Estimator :param estimate_value: obtained estimate's value :param method: Method for checking statistical significance :returns: p-value from the significance test """ if method is None: if self._significance_test: method = self._significance_test # this is either True or methodname else: method = "default" signif_dict = None if method == "default" or method is True: # user has not provided any method try: signif_dict = self._test_significance(estimate_value, method, **kwargs) except NotImplementedError: signif_dict = self._test_significance_with_bootstrap(estimate_value, **kwargs) else: if method == "bootstrap": signif_dict = self._test_significance_with_bootstrap(estimate_value, **kwargs) else: signif_dict = self._test_significance(estimate_value, method, **kwargs) return signif_dict def evaluate_effect_strength(self, estimate): fraction_effect_explained = self._evaluate_effect_strength(estimate, method="fraction-effect") # Need to test r-squared before supporting # effect_r_squared = self._evaluate_effect_strength(estimate, method="r-squared") strength_dict = { "fraction-effect": fraction_effect_explained # 'r-squared': effect_r_squared } return strength_dict def _evaluate_effect_strength(self, estimate, method="fraction-effect"): supported_methods = ["fraction-effect"] if method not in supported_methods: raise NotImplementedError("This method is not supported for evaluating effect strength") if method == "fraction-effect": naive_obs_estimate = self.estimate_effect_naive() self.logger.debug(estimate.value, naive_obs_estimate.value) fraction_effect_explained = estimate.value / naive_obs_estimate.value return fraction_effect_explained # elif method == "r-squared": # outcome_mean = np.mean(self._outcome) # total_variance = np.sum(np.square(self._outcome - outcome_mean)) # Assuming a linear model with one variable: the treatment # Currently only works for continuous y # causal_model = outcome_mean + estimate.value*self._treatment # squared_residual = np.sum(np.square(self._outcome - causal_model)) # r_squared = 1 - (squared_residual/total_variance) # return r_squared else: return None def update_input(self, treatment_value, control_value, target_units): self._control_value = control_value self._treatment_value = treatment_value self._target_units = target_units @staticmethod def is_bootstrap_parameter_changed(bootstrap_estimates_params, given_params): """Check whether parameters of the bootstrap have changed. This is an efficiency method that checks if fresh resampling of the bootstrap samples is required. Returns True if parameters have changed and resampling should be done again. :param bootstrap_estimates_params: A dictionary of parameters for the current bootstrap samples :param given_params: A dictionary of parameters passed by the user :returns: A binary flag denoting whether the parameters are different. """ is_any_parameter_changed = False for prm, val in bootstrap_estimates_params.items(): given_val = given_params.get(prm, None) if given_val is not None and given_val != val: is_any_parameter_changed = True break return is_any_parameter_changed def target_units_tostr(self): s = "" if type(self._target_units) is str: s += self._target_units elif callable(self._target_units): s += "Data subset defined by a function" elif isinstance(self._target_units, pd.DataFrame): s += "Data subset provided as a data frame" return s def signif_results_tostr(self, signif_results): s = "" pval = signif_results["p_value"] if type(pval) is tuple: s += "[{0}, {1}]".format(pval[0], pval[1]) else: s += "{0}".format(pval) return s def estimate_effect( treatment: Union[str, List[str]], outcome: Union[str, List[str]], identified_estimand: IdentifiedEstimand, identifier_name: str, method: CausalEstimator, control_value: int = 0, treatment_value: int = 1, test_significance: Optional[bool] = None, evaluate_effect_strength: bool = False, confidence_intervals: bool = False, target_units: str = "ate", effect_modifiers: List[str] = [], fit_estimator: bool = True, method_params: Optional[Dict] = None, ): """Estimate the identified causal effect. Currently requires an explicit method name to be specified. Method names follow the convention of identification method followed by the specific estimation method: "[backdoor/iv].estimation_method_name". Following methods are supported. * Propensity Score Matching: "backdoor.propensity_score_matching" * Propensity Score Stratification: "backdoor.propensity_score_stratification" * Propensity Score-based Inverse Weighting: "backdoor.propensity_score_weighting" * Linear Regression: "backdoor.linear_regression" * Generalized Linear Models (e.g., logistic regression): "backdoor.generalized_linear_model" * Instrumental Variables: "iv.instrumental_variable" * Regression Discontinuity: "iv.regression_discontinuity" In addition, you can directly call any of the EconML estimation methods. The convention is "backdoor.econml.path-to-estimator-class". For example, for the double machine learning estimator ("DML" class) that is located inside "dml" module of EconML, you can use the method name, "backdoor.econml.dml.DML". CausalML estimators can also be called. See `this demo notebook <https://py-why.github.io/dowhy/example_notebooks/dowhy-conditional-treatment-effects.html>`_. :param treatment: Name of the treatment :param outcome: Name of the outcome :param identified_estimand: a probability expression that represents the effect to be estimated. Output of CausalModel.identify_effect method :param method_name: name of the estimation method to be used. :param control_value: Value of the treatment in the control group, for effect estimation. If treatment is multi-variate, this can be a list. :param treatment_value: Value of the treatment in the treated group, for effect estimation. If treatment is multi-variate, this can be a list. :param test_significance: Binary flag on whether to additionally do a statistical signficance test for the estimate. :param evaluate_effect_strength: (Experimental) Binary flag on whether to estimate the relative strength of the treatment's effect. This measure can be used to compare different treatments for the same outcome (by running this method with different treatments sequentially). :param confidence_intervals: (Experimental) Binary flag indicating whether confidence intervals should be computed. :param target_units: (Experimental) The units for which the treatment effect should be estimated. This can be of three types. (1) a string for common specifications of target units (namely, "ate", "att" and "atc"), (2) a lambda function that can be used as an index for the data (pandas DataFrame), or (3) a new DataFrame that contains values of the effect_modifiers and effect will be estimated only for this new data. :param effect_modifiers: Names of effect modifier variables can be (optionally) specified here too, since they do not affect identification. If None, the effect_modifiers from the CausalModel are used. :param fit_estimator: Boolean flag on whether to fit the estimator. Setting it to False is useful to estimate the effect on new data using a previously fitted estimator. :param method_params: Dictionary containing any method-specific parameters. These are passed directly to the estimating method. See the docs for each estimation method for allowed method-specific params. :returns: An instance of the CausalEstimate class, containing the causal effect estimate and other method-dependent information """ treatment = parse_state(treatment) outcome = parse_state(outcome) causal_estimator_class = method.__class__ identified_estimand.set_identifier_method(identifier_name) if identified_estimand.no_directed_path: logger.warning("No directed path from {0} to {1}.".format(treatment, outcome)) return CausalEstimate( 0, identified_estimand, None, control_value=control_value, treatment_value=treatment_value ) # Check if estimator's target estimand is identified elif identified_estimand.estimands[identifier_name] is None: logger.error("No valid identified estimand available.") return CausalEstimate(None, None, None, control_value=control_value, treatment_value=treatment_value) method.update_input(treatment_value, control_value, target_units) estimate = method.estimate_effect() # Store parameters inside estimate object for refutation methods # TODO: This add_params needs to move to the estimator class # inside estimate_effect and estimate_conditional_effect estimate.add_params( estimand_type=identified_estimand.estimand_type, estimator_class=causal_estimator_class, test_significance=test_significance, evaluate_effect_strength=evaluate_effect_strength, confidence_intervals=confidence_intervals, target_units=target_units, effect_modifiers=effect_modifiers, method_params=method_params, ) return estimate class CausalEstimate: """Class for the estimate object that every causal estimator returns""" def __init__( self, estimate, target_estimand, realized_estimand_expr, control_value, treatment_value, conditional_estimates=None, **kwargs, ): self.value = estimate self.target_estimand = target_estimand self.realized_estimand_expr = realized_estimand_expr self.control_value = control_value self.treatment_value = treatment_value self.conditional_estimates = conditional_estimates self.params = kwargs if self.params is not None: for key, value in self.params.items(): setattr(self, key, value) self.effect_strength = None def add_estimator(self, estimator_instance): self.estimator = estimator_instance def add_effect_strength(self, strength_dict): self.effect_strength = strength_dict def add_params(self, **kwargs): self.params.update(kwargs) def get_confidence_intervals(self, confidence_level=None, method=None, **kwargs): """Get confidence intervals of the obtained estimate. By default, this is done with the help of bootstrapped confidence intervals but can be overridden if the specific estimator implements other methods of estimating confidence intervals. If the method provided is not bootstrap, this function calls the implementation of the specific estimator. :param method: Method for estimating confidence intervals. :param confidence_level: The confidence level of the confidence intervals of the estimate. :param kwargs: Other optional args to be passed to the CI method. :returns: The obtained confidence interval. """ confidence_intervals = self.estimator.estimate_confidence_intervals( estimate_value=self.value, confidence_level=confidence_level, method=method, **kwargs ) return confidence_intervals def get_standard_error(self, method=None, **kwargs): """Get standard error of the obtained estimate. By default, this is done with the help of bootstrapped standard errors but can be overridden if the specific estimator implements other methods of estimating standard error. If the method provided is not bootstrap, this function calls the implementation of the specific estimator. :param method: Method for computing the standard error. :param kwargs: Other optional parameters to be passed to the estimating method. :returns: Standard error of the causal estimate. """ std_error = self.estimator.estimate_std_error(method=method, **kwargs) return std_error def test_stat_significance(self, method=None, **kwargs): """Test statistical significance of the estimate obtained. By default, uses resampling to create a non-parametric significance test. Individual child estimators can implement different methods. If the method name is different from "bootstrap", this function calls the implementation of the child estimator. :param method: Method for checking statistical significance :param kwargs: Other optional parameters to be passed to the estimating method. :returns: p-value from the significance test """ signif_results = self.estimator.test_significance(self.value, method=method, **kwargs) return {"p_value": signif_results["p_value"]} def estimate_conditional_effects( self, effect_modifiers=None, num_quantiles=CausalEstimator.NUM_QUANTILES_TO_DISCRETIZE_CONT_COLS ): """Estimate treatment effect conditioned on given variables. If a numeric effect modifier is provided, it is discretized into quantile bins. If you would like a custom discretization, you can do so yourself: create a new column containing the discretized effect modifier and then include that column's name in the effect_modifier_names argument. :param effect_modifiers: Names of effect modifier variables over which the conditional effects will be estimated. If not provided, defaults to the effect modifiers specified during creation of the CausalEstimator object. :param num_quantiles: The number of quantiles into which a numeric effect modifier variable is discretized. Does not affect any categorical effect modifiers. :returns: A (multi-index) dataframe that provides separate effects for each value of the (discretized) effect modifiers. """ return self.estimator._estimate_conditional_effects( self.estimator._estimate_effect_fn, effect_modifiers, num_quantiles ) def interpret(self, method_name=None, **kwargs): """Interpret the causal estimate. :param method_name: Method used (string) or a list of methods. If None, then the default for the specific estimator is used. :param kwargs:: Optional parameters that are directly passed to the interpreter method. :returns: None """ if method_name is None: method_name = self.estimator.interpret_method method_name_arr = parse_state(method_name) for method in method_name_arr: interpreter = interpreters.get_class_object(method) interpreter(self, **kwargs).interpret() def __str__(self): s = "*** Causal Estimate ***\n" # No estimand was identified (identification failed) if self.target_estimand is None: return "Estimation failed! No relevant identified estimand available for this estimation method." s += "\n## Identified estimand\n{0}".format(self.target_estimand.__str__(only_target_estimand=True)) s += "\n## Realized estimand\n{0}".format(self.realized_estimand_expr) if hasattr(self, "estimator"): s += "\nTarget units: {0}\n".format(self.estimator.target_units_tostr()) s += "\n## Estimate\n" s += "Mean value: {0}\n".format(self.value) s += "" if hasattr(self, "cate_estimates"): s += "Effect estimates: {0}\n".format(self.cate_estimates) if hasattr(self, "estimator"): if self.estimator._significance_test: s += "p-value: {0}\n".format(self.estimator.signif_results_tostr(self.test_stat_significance())) if self.estimator._confidence_intervals: s += "{0}% confidence interval: {1}\n".format( 100 * self.estimator.confidence_level, self.get_confidence_intervals() ) if self.conditional_estimates is not None: s += "### Conditional Estimates\n" s += str(self.conditional_estimates) if self.effect_strength is not None: s += "\n## Effect Strength\n" s += "Change in outcome attributable to treatment: {}\n".format(self.effect_strength["fraction-effect"]) # s += "Variance in outcome explained by treatment: {}\n".format(self.effect_strength["r-squared"]) return s class RealizedEstimand(object): def __init__(self, identified_estimand, estimator_name): self.treatment_variable = identified_estimand.treatment_variable self.outcome_variable = identified_estimand.outcome_variable self.backdoor_variables = identified_estimand.get_backdoor_variables() self.instrumental_variables = identified_estimand.instrumental_variables self.estimand_type = identified_estimand.estimand_type self.estimand_expression = None self.assumptions = None self.estimator_name = estimator_name def update_assumptions(self, estimator_assumptions): self.assumptions = estimator_assumptions def update_estimand_expression(self, estimand_expression): self.estimand_expression = estimand_expression def __str__(self): s = "Realized estimand: {0}\n".format(self.estimator_name) s += "Realized estimand type: {0}\n".format(self.estimand_type) s += "Estimand expression:\n{0}\n".format(sp.pretty(self.estimand_expression)) j = 1 for ass_name, ass_str in self.assumptions.items(): s += "Estimand assumption {0}, {1}: {2}\n".format(j, ass_name, ass_str) j += 1 return s

andresmor-ms

2044d216c322a4b32c6eadce5da7d83463f19c2f

05bfa49dacf0061988c96c6f3e3756219df5422a

I moved all the code to initialize the estimator into the causal_model (for compatibility) and made the function accept the object as parameter, so that it works the way you suggest

andresmor-ms

py-why/dowhy

Functional api/estimate effect function

#### Estimate Effect function * Refactors the estimate effect into a separate function to keep backwards compatibility #### TODO (future PRs): * Add `fit(...)` method to estimators - Move data related parameters from the constructor to the `fit(...)` method * Refactor code to avoid `**kwargs` in `__init__(...)` constructors

2022-10-18 15:49:21+00:00

2022-10-25 17:02:02+00:00

dowhy/causal_estimator.py

import logging from collections import namedtuple import numpy as np import pandas as pd import sympy as sp from sklearn.utils import resample import dowhy.interpreters as interpreters from dowhy.utils.api import parse_state class CausalEstimator: """Base class for an estimator of causal effect. Subclasses implement different estimation methods. All estimation methods are in the package "dowhy.causal_estimators" """ # The default number of simulations for statistical testing DEFAULT_NUMBER_OF_SIMULATIONS_STAT_TEST = 1000 # The default number of simulations to obtain confidence intervals DEFAULT_NUMBER_OF_SIMULATIONS_CI = 100 # The portion of the total size that should be taken each time to find the confidence intervals # 1 is the recommended value # https://ocw.mit.edu/courses/mathematics/18-05-introduction-to-probability-and-statistics-spring-2014/readings/MIT18_05S14_Reading24.pdf # https://projecteuclid.org/download/pdf_1/euclid.ss/1032280214 DEFAULT_SAMPLE_SIZE_FRACTION = 1 # The default Confidence Level DEFAULT_CONFIDENCE_LEVEL = 0.95 # Number of quantiles to discretize continuous columns, for applying groupby NUM_QUANTILES_TO_DISCRETIZE_CONT_COLS = 5 # Prefix to add to temporary categorical variables created after discretization TEMP_CAT_COLUMN_PREFIX = "__categorical__" DEFAULT_NOTIMPLEMENTEDERROR_MSG = "not yet implemented for {0}. If you would this to be implemented in the next version, please raise an issue at https://github.com/microsoft/dowhy/issues" BootstrapEstimates = namedtuple("BootstrapEstimates", ["estimates", "params"]) DEFAULT_INTERPRET_METHOD = ["textual_effect_interpreter"] # std args to be removed from locals() before being passed to args_dict _STD_INIT_ARGS = ("self", "__class__", "args", "kwargs") def __init__( self, data, identified_estimand, treatment, outcome, control_value=0, treatment_value=1, test_significance=False, evaluate_effect_strength=False, confidence_intervals=False, target_units=None, effect_modifiers=None, num_null_simulations=DEFAULT_NUMBER_OF_SIMULATIONS_STAT_TEST, num_simulations=DEFAULT_NUMBER_OF_SIMULATIONS_CI, sample_size_fraction=DEFAULT_SAMPLE_SIZE_FRACTION, confidence_level=DEFAULT_CONFIDENCE_LEVEL, need_conditional_estimates="auto", num_quantiles_to_discretize_cont_cols=NUM_QUANTILES_TO_DISCRETIZE_CONT_COLS, **kwargs, ): """Initializes an estimator with data and names of relevant variables. This method is called from the constructors of its child classes. :param data: data frame containing the data :param identified_estimand: probability expression representing the target identified estimand to estimate. :param treatment: name of the treatment variable :param outcome: name of the outcome variable :param control_value: Value of the treatment in the control group, for effect estimation. If treatment is multi-variate, this can be a list. :param treatment_value: Value of the treatment in the treated group, for effect estimation. If treatment is multi-variate, this can be a list. :param test_significance: Binary flag or a string indicating whether to test significance and by which method. All estimators support test_significance="bootstrap" that estimates a p-value for the obtained estimate using the bootstrap method. Individual estimators can override this to support custom testing methods. The bootstrap method supports an optional parameter, num_null_simulations. If False, no testing is done. If True, significance of the estimate is tested using the custom method if available, otherwise by bootstrap. :param evaluate_effect_strength: (Experimental) whether to evaluate the strength of effect :param confidence_intervals: Binary flag or a string indicating whether the confidence intervals should be computed and which method should be used. All methods support estimation of confidence intervals using the bootstrap method by using the parameter confidence_intervals="bootstrap". The bootstrap method takes in two arguments (num_simulations and sample_size_fraction) that can be optionally specified in the params dictionary. Estimators may also override this to implement their own confidence interval method. If this parameter is False, no confidence intervals are computed. If True, confidence intervals are computed by the estimator's specific method if available, otherwise through bootstrap. :param target_units: The units for which the treatment effect should be estimated. This can be a string for common specifications of target units (namely, "ate", "att" and "atc"). It can also be a lambda function that can be used as an index for the data (pandas DataFrame). Alternatively, it can be a new DataFrame that contains values of the effect_modifiers and effect will be estimated only for this new data. :param effect_modifiers: Variables on which to compute separate effects, or return a heterogeneous effect function. Not all methods support this currently. :param num_null_simulations: The number of simulations for testing the statistical significance of the estimator :param num_simulations: The number of simulations for finding the confidence interval (and/or standard error) for a estimate :param sample_size_fraction: The size of the sample for the bootstrap estimator :param confidence_level: The confidence level of the confidence interval estimate :param need_conditional_estimates: Boolean flag indicating whether conditional estimates should be computed. Defaults to True if there are effect modifiers in the graph :param num_quantiles_to_discretize_cont_cols: The number of quantiles into which a numeric effect modifier is split, to enable estimation of conditional treatment effect over it. :param kwargs: (optional) Additional estimator-specific parameters :returns: an instance of the estimator class. """ self._data = data self._target_estimand = identified_estimand # Currently estimation methods only support univariate treatment and outcome self._treatment_name = treatment self._outcome_name = outcome[0] # assuming one-dimensional outcome self._control_value = control_value self._treatment_value = treatment_value self._significance_test = test_significance self._effect_strength_eval = evaluate_effect_strength self._target_units = target_units self._effect_modifier_names = effect_modifiers self._confidence_intervals = confidence_intervals self._bootstrap_estimates = None # for confidence intervals and std error self._bootstrap_null_estimates = None # for significance test self._effect_modifiers = None self.method_params = kwargs # Setting the default interpret method self.interpret_method = CausalEstimator.DEFAULT_INTERPRET_METHOD self.logger = logging.getLogger(__name__) # Setting treatment and outcome values if self._data is not None: self._treatment = self._data[self._treatment_name] self._outcome = self._data[self._outcome_name] # Now saving the effect modifiers if self._effect_modifier_names: # only add the observed nodes self._effect_modifier_names = [ cname for cname in self._effect_modifier_names if cname in self._data.columns ] if len(self._effect_modifier_names) > 0: self._effect_modifiers = self._data[self._effect_modifier_names] self._effect_modifiers = pd.get_dummies(self._effect_modifiers, drop_first=True) self.logger.debug("Effect modifiers: " + ",".join(self._effect_modifier_names)) else: self._effect_modifier_names = None # Check if some parameters were set, otherwise set to default values self.num_null_simulations = num_null_simulations self.num_simulations = num_simulations self.sample_size_fraction = sample_size_fraction self.confidence_level = confidence_level self.num_quantiles_to_discretize_cont_cols = num_quantiles_to_discretize_cont_cols # Estimate conditional estimates by default self.need_conditional_estimates = ( need_conditional_estimates if need_conditional_estimates != "auto" else bool(self._effect_modifier_names) ) @staticmethod def get_estimator_object(new_data, identified_estimand, estimate): """Create a new estimator of the same type as the one passed in the estimate argument. Creates a new object with new_data and the identified_estimand :param new_data: np.ndarray, pd.Series, pd.DataFrame The newly assigned data on which the estimator should run :param identified_estimand: IdentifiedEstimand An instance of the identified estimand class that provides the information with respect to which causal pathways are employed when the treatment effects the outcome :param estimate: CausalEstimate It is an already existing estimate whose properties we wish to replicate :returns: An instance of the same estimator class that had generated the given estimate. """ estimator_class = estimate.params["estimator_class"] new_estimator = estimator_class( new_data, identified_estimand, identified_estimand.treatment_variable, identified_estimand.outcome_variable, # names of treatment and outcome control_value=estimate.control_value, treatment_value=estimate.treatment_value, test_significance=False, evaluate_effect_strength=False, confidence_intervals=estimate.params["confidence_intervals"], target_units=estimate.params["target_units"], effect_modifiers=estimate.params["effect_modifiers"], **estimate.params["method_params"], ) return new_estimator def _estimate_effect(self): """This method is to be overriden by the child classes, so that they can run the estimation technique of their choice""" raise NotImplementedError( ("Main estimation method is " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG).format(self.__class__) ) def estimate_effect(self): """Base estimation method that calls the estimate_effect method of its calling subclass. Can optionally also test significance and estimate effect strength for any returned estimate. :param self: object instance of class Estimator :returns: A CausalEstimate instance that contains point estimates of average and conditional effects. Based on the parameters provided, it optionally includes confidence intervals, standard errors,statistical significance and other statistical parameters. """ est = self._estimate_effect() est.add_estimator(self) if self._significance_test: self.test_significance(est.value, method=self._significance_test) if self._confidence_intervals: self.estimate_confidence_intervals( est.value, confidence_level=self.confidence_level, method=self._confidence_intervals ) if self._effect_strength_eval: effect_strength_dict = self.evaluate_effect_strength(est) est.add_effect_strength(effect_strength_dict) return est def estimate_effect_naive(self): # TODO Only works for binary treatment df_withtreatment = self._data.loc[self._data[self._treatment_name] == 1] df_notreatment = self._data.loc[self._data[self._treatment_name] == 0] est = np.mean(df_withtreatment[self._outcome_name]) - np.mean(df_notreatment[self._outcome_name]) return CausalEstimate(est, None, None, control_value=0, treatment_value=1) def _estimate_effect_fn(self, data_df): """Function used in conditional effect estimation. This function is to be overridden by each child estimator. The overridden function should take in a dataframe as input and return the estimate for that data. """ raise NotImplementedError( ("Conditional treatment effects are " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG).format( self.__class__ ) ) def _estimate_conditional_effects(self, estimate_effect_fn, effect_modifier_names=None, num_quantiles=None): """Estimate conditional treatment effects. Common method for all estimators that utilizes a specific estimate_effect_fn implemented by each child estimator. If a numeric effect modifier is provided, it is discretized into quantile bins. If you would like a custom discretization, you can do so yourself: create a new column containing the discretized effect modifier and then include that column's name in the effect_modifier_names argument. :param estimate_effect_fn: Function that has a single parameter (a data frame) and returns the treatment effect estimate on that data. :param effect_modifier_names: Names of effect modifier variables over which the conditional effects will be estimated. If not provided, defaults to the effect modifiers specified during creation of the CausalEstimator object. :param num_quantiles: The number of quantiles into which a numeric effect modifier variable is discretized. Does not affect any categorical effect modifiers. :returns: A (multi-index) dataframe that provides separate effects for each value of the (discretized) effect modifiers. """ # Defaulting to class default values if parameters are not provided if effect_modifier_names is None: effect_modifier_names = self._effect_modifier_names if num_quantiles is None: num_quantiles = self.num_quantiles_to_discretize_cont_cols # Checking that there is at least one effect modifier if not effect_modifier_names: raise ValueError("At least one effect modifier should be specified to compute conditional effects.") # Making sure that effect_modifier_names is a list effect_modifier_names = parse_state(effect_modifier_names) if not all(em in self._effect_modifier_names for em in effect_modifier_names): self.logger.warn( "At least one of the provided effect modifiers was not included while fitting the estimator. You may get incorrect results. To resolve, fit the estimator again by providing the updated effect modifiers in estimate_effect()." ) # Making a copy since we are going to be changing effect modifier names effect_modifier_names = effect_modifier_names.copy() prefix = CausalEstimator.TEMP_CAT_COLUMN_PREFIX # For every numeric effect modifier, adding a temp categorical column for i in range(len(effect_modifier_names)): em = effect_modifier_names[i] if pd.api.types.is_numeric_dtype(self._data[em].dtypes): self._data[prefix + str(em)] = pd.qcut(self._data[em], num_quantiles, duplicates="drop") effect_modifier_names[i] = prefix + str(em) # Grouping by effect modifiers and computing effect separately by_effect_mods = self._data.groupby(effect_modifier_names) cond_est_fn = lambda x: self._do(self._treatment_value, x) - self._do(self._control_value, x) conditional_estimates = by_effect_mods.apply(estimate_effect_fn) # Deleting the temporary categorical columns for em in effect_modifier_names: if em.startswith(prefix): self._data.pop(em) return conditional_estimates def _do(self, x, data_df=None): raise NotImplementedError( ("Do-operator is " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG).format(self.__class__) ) def do(self, x, data_df=None): """Method that implements the do-operator. Given a value x for the treatment, returns the expected value of the outcome when the treatment is intervened to a value x. :param x: Value of the treatment :param data_df: Data on which the do-operator is to be applied. :returns: Value of the outcome when treatment is intervened/set to x. """ est = self._do(x, data_df) return est def construct_symbolic_estimator(self, estimand): raise NotImplementedError(("Symbolic estimator string is ").format(self.__class__)) def _generate_bootstrap_estimates(self, num_bootstrap_simulations, sample_size_fraction): """Helper function to generate causal estimates over bootstrapped samples. :param num_bootstrap_simulations: Number of simulations for the bootstrap method. :param sample_size_fraction: Fraction of the dataset to be resampled. :returns: A collections.namedtuple containing a list of bootstrapped estimates and a dictionary containing parameters used for the bootstrap. """ # The array that stores the results of all estimations simulation_results = np.zeros(num_bootstrap_simulations) # Find the sample size the proportion with the population size sample_size = int(sample_size_fraction * len(self._data)) if sample_size > len(self._data): self.logger.warning("WARN: The sample size is greater than the data being sampled") self.logger.info("INFO: The sample size: {}".format(sample_size)) self.logger.info("INFO: The number of simulations: {}".format(num_bootstrap_simulations)) # Perform the set number of simulations for index in range(num_bootstrap_simulations): new_data = resample(self._data, n_samples=sample_size) new_estimator = type(self)( new_data, self._target_estimand, self._target_estimand.treatment_variable, self._target_estimand.outcome_variable, # names of treatment and outcome treatment_value=self._treatment_value, control_value=self._control_value, test_significance=False, evaluate_effect_strength=False, confidence_intervals=False, target_units=self._target_units, effect_modifiers=self._effect_modifier_names, **self.method_params, ) new_effect = new_estimator.estimate_effect() simulation_results[index] = new_effect.value estimates = CausalEstimator.BootstrapEstimates( simulation_results, {"num_simulations": num_bootstrap_simulations, "sample_size_fraction": sample_size_fraction}, ) return estimates def _estimate_confidence_intervals_with_bootstrap( self, estimate_value, confidence_level=None, num_simulations=None, sample_size_fraction=None ): """ Method to compute confidence interval using bootstrapped sampling. :param estimate_value: obtained estimate's value :param confidence_level: The level for which to compute CI (e.g., 95% confidence level translates to confidence_level=0.95) :param num_simulations: The number of simulations to be performed to get the bootstrap confidence intervals. :param sample_size_fraction: The fraction of the dataset to be resampled. :returns: confidence interval at the specified level. For more details on bootstrap or resampling statistics, refer to the following links: https://ocw.mit.edu/courses/mathematics/18-05-introduction-to-probability-and-statistics-spring-2014/readings/MIT18_05S14_Reading24.pdf https://projecteuclid.org/download/pdf_1/euclid.ss/1032280214 """ # Using class default parameters if not specified if num_simulations is None: num_simulations = self.num_simulations if sample_size_fraction is None: sample_size_fraction = self.sample_size_fraction # Checking if bootstrap_estimates are already computed if self._bootstrap_estimates is None: self._bootstrap_estimates = self._generate_bootstrap_estimates(num_simulations, sample_size_fraction) elif CausalEstimator.is_bootstrap_parameter_changed(self._bootstrap_estimates.params, locals()): # Checked if any parameter is changed from the previous std error estimate self._bootstrap_estimates = self._generate_bootstrap_estimates(num_simulations, sample_size_fraction) # Now use the data obtained from the simulations to get the value of the confidence estimates bootstrap_estimates = self._bootstrap_estimates.estimates # Get the variations of each bootstrap estimate and sort bootstrap_variations = [bootstrap_estimate - estimate_value for bootstrap_estimate in bootstrap_estimates] sorted_bootstrap_variations = np.sort(bootstrap_variations) # Now we take the (1- p)th and the (p)th variations, where p is the chosen confidence level upper_bound_index = int((1 - confidence_level) * len(sorted_bootstrap_variations)) lower_bound_index = int(confidence_level * len(sorted_bootstrap_variations)) # Get the lower and upper bounds by subtracting the variations from the estimate lower_bound = estimate_value - sorted_bootstrap_variations[lower_bound_index] upper_bound = estimate_value - sorted_bootstrap_variations[upper_bound_index] return lower_bound, upper_bound def _estimate_confidence_intervals(self, confidence_level=None, method=None, **kwargs): """ This method is to be overriden by the child classes, so that they can run a confidence interval estimation method suited to the specific causal estimator. """ raise NotImplementedError( ( "This method for estimating confidence intervals is " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG + " Meanwhile, you can try the bootstrap method (method='bootstrap') to estimate confidence intervals." ).format(self.__class__) ) def estimate_confidence_intervals(self, estimate_value, confidence_level=None, method=None, **kwargs): """Find the confidence intervals corresponding to any estimator By default, this is done with the help of bootstrapped confidence intervals but can be overridden if the specific estimator implements other methods of estimating confidence intervals. If the method provided is not bootstrap, this function calls the implementation of the specific estimator. :param estimate_value: obtained estimate's value :param method: Method for estimating confidence intervals. :param confidence_level: The confidence level of the confidence intervals of the estimate. :param kwargs: Other optional args to be passed to the CI method. :returns: The obtained confidence interval. """ if method is None: if self._confidence_intervals: method = self._confidence_intervals # this is either True or methodname else: method = "default" confidence_intervals = None if confidence_level is None: confidence_level = self.confidence_level if method == "default" or method is True: # user has not provided any method try: confidence_intervals = self._estimate_confidence_intervals(confidence_level, method=method, **kwargs) except NotImplementedError: confidence_intervals = self._estimate_confidence_intervals_with_bootstrap( estimate_value, confidence_level, **kwargs ) else: if method == "bootstrap": confidence_intervals = self._estimate_confidence_intervals_with_bootstrap( estimate_value, confidence_level, **kwargs ) else: confidence_intervals = self._estimate_confidence_intervals(confidence_level, method=method, **kwargs) return confidence_intervals def _estimate_std_error_with_bootstrap(self, num_simulations=None, sample_size_fraction=None): """Compute standard error using the bootstrap method. Standard error and confidence intervals use the same parameter num_simulations for the number of bootstrap simulations. :param num_simulations: Number of bootstrapped samples. :param sample_size_fraction: Fraction of data to be resampled. :returns: Standard error of the obtained estimate. """ # Use existing params, if new user defined params are not present if num_simulations is None: num_simulations = self.num_simulations if sample_size_fraction is None: sample_size_fraction = self.sample_size_fraction # Checking if bootstrap_estimates are already computed if self._bootstrap_estimates is None: self._bootstrap_estimates = self._generate_bootstrap_estimates(num_simulations, sample_size_fraction) elif CausalEstimator.is_bootstrap_parameter_changed(self._bootstrap_estimates.params, locals()): # Check if any parameter is changed from the previous std error estimate self._bootstrap_estimates = self._generate_bootstrap_estimates(num_simulations, sample_size_fraction) std_error = np.std(self._bootstrap_estimates.estimates) return std_error def _estimate_std_error(self, method=None, **kwargs): """ This method is to be overriden by the child classes, so that they can run a standard error estimation method suited to the specific causal estimator. """ raise NotImplementedError( ( "This method for estimating standard errors is " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG + " Meanwhile, you can try the bootstrap method (method='bootstrap') to estimate standard errors." ).format(self.__class__) ) def estimate_std_error(self, method=None, **kwargs): """Compute standard error of an obtained causal estimate. :param method: Method for computing the standard error. :param kwargs: Other optional parameters to be passed to the estimating method. :returns: Standard error of the causal estimate. """ if method is None: if self._confidence_intervals: method = self._confidence_intervals else: method = "default" std_error = None if method == "default" or method is True: # user has not provided any method try: std_error = self._estimate_std_error(method, **kwargs) except NotImplementedError: std_error = self._estimate_std_error_with_bootstrap(**kwargs) else: if method == "bootstrap": std_error = self._estimate_std_error_with_bootstrap(**kwargs) else: std_error = self._estimate_std_error(method, **kwargs) return std_error def _test_significance_with_bootstrap(self, estimate_value, num_null_simulations=None): """Test statistical significance of an estimate using the bootstrap method. :param estimate_value: Obtained estimate's value :param num_null_simulations: Number of simulations for the null hypothesis :returns: p-value of the statistical significance test. """ # Use existing params, if new user defined params are not present if num_null_simulations is None: num_null_simulations = self.num_null_simulations do_retest = self._bootstrap_null_estimates is None or CausalEstimator.is_bootstrap_parameter_changed( self._bootstrap_null_estimates.params, locals() ) if do_retest: null_estimates = np.zeros(num_null_simulations) for i in range(num_null_simulations): new_outcome = np.random.permutation(self._outcome) new_data = self._data.assign(dummy_outcome=new_outcome) # self._outcome = self._data["dummy_outcome"] new_estimator = type(self)( new_data, self._target_estimand, self._target_estimand.treatment_variable, ("dummy_outcome",), test_significance=False, evaluate_effect_strength=False, confidence_intervals=False, target_units=self._target_units, effect_modifiers=self._effect_modifier_names, **self.method_params, ) new_effect = new_estimator.estimate_effect() null_estimates[i] = new_effect.value self._bootstrap_null_estimates = CausalEstimator.BootstrapEstimates( null_estimates, {"num_null_simulations": num_null_simulations, "sample_size_fraction": 1} ) # Processing the null hypothesis estimates sorted_null_estimates = np.sort(self._bootstrap_null_estimates.estimates) self.logger.debug("Null estimates: {0}".format(sorted_null_estimates)) median_estimate = sorted_null_estimates[int(num_null_simulations / 2)] # Doing a two-sided test if estimate_value > median_estimate: # Being conservative with the p-value reported estimate_index = np.searchsorted(sorted_null_estimates, estimate_value, side="left") p_value = 1 - (estimate_index / num_null_simulations) if estimate_value <= median_estimate: # Being conservative with the p-value reported estimate_index = np.searchsorted(sorted_null_estimates, estimate_value, side="right") p_value = estimate_index / num_null_simulations # If the estimate_index is 0, it depends on the number of simulations if p_value == 0: p_value = (0, 1 / len(sorted_null_estimates)) # a tuple determining the range. elif p_value == 1: p_value = (1 - 1 / len(sorted_null_estimates), 1) signif_dict = {"p_value": p_value} return signif_dict def _test_significance(self, estimate_value, method=None, **kwargs): """ This method is to be overriden by the child classes, so that they can run a significance test suited to the specific causal estimator. """ raise NotImplementedError( ( "This method for testing statistical significance is " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG + " Meanwhile, you can try the bootstrap method (method='bootstrap') to test statistical significance." ).format(self.__class__) ) def test_significance(self, estimate_value, method=None, **kwargs): """Test statistical significance of obtained estimate. By default, uses resampling to create a non-parametric significance test. A general procedure. Individual child estimators can implement different methods. If the method name is different from "bootstrap", this function calls the implementation of the child estimator. :param self: object instance of class Estimator :param estimate_value: obtained estimate's value :param method: Method for checking statistical significance :returns: p-value from the significance test """ if method is None: if self._significance_test: method = self._significance_test # this is either True or methodname else: method = "default" signif_dict = None if method == "default" or method is True: # user has not provided any method try: signif_dict = self._test_significance(estimate_value, method, **kwargs) except NotImplementedError: signif_dict = self._test_significance_with_bootstrap(estimate_value, **kwargs) else: if method == "bootstrap": signif_dict = self._test_significance_with_bootstrap(estimate_value, **kwargs) else: signif_dict = self._test_significance(estimate_value, method, **kwargs) return signif_dict def evaluate_effect_strength(self, estimate): fraction_effect_explained = self._evaluate_effect_strength(estimate, method="fraction-effect") # Need to test r-squared before supporting # effect_r_squared = self._evaluate_effect_strength(estimate, method="r-squared") strength_dict = { "fraction-effect": fraction_effect_explained # 'r-squared': effect_r_squared } return strength_dict def _evaluate_effect_strength(self, estimate, method="fraction-effect"): supported_methods = ["fraction-effect"] if method not in supported_methods: raise NotImplementedError("This method is not supported for evaluating effect strength") if method == "fraction-effect": naive_obs_estimate = self.estimate_effect_naive() self.logger.debug(estimate.value, naive_obs_estimate.value) fraction_effect_explained = estimate.value / naive_obs_estimate.value return fraction_effect_explained # elif method == "r-squared": # outcome_mean = np.mean(self._outcome) # total_variance = np.sum(np.square(self._outcome - outcome_mean)) # Assuming a linear model with one variable: the treatment # Currently only works for continuous y # causal_model = outcome_mean + estimate.value*self._treatment # squared_residual = np.sum(np.square(self._outcome - causal_model)) # r_squared = 1 - (squared_residual/total_variance) # return r_squared else: return None def update_input(self, treatment_value, control_value, target_units): self._control_value = control_value self._treatment_value = treatment_value self._target_units = target_units @staticmethod def is_bootstrap_parameter_changed(bootstrap_estimates_params, given_params): """Check whether parameters of the bootstrap have changed. This is an efficiency method that checks if fresh resampling of the bootstrap samples is required. Returns True if parameters have changed and resampling should be done again. :param bootstrap_estimates_params: A dictionary of parameters for the current bootstrap samples :param given_params: A dictionary of parameters passed by the user :returns: A binary flag denoting whether the parameters are different. """ is_any_parameter_changed = False for prm, val in bootstrap_estimates_params.items(): given_val = given_params.get(prm, None) if given_val is not None and given_val != val: is_any_parameter_changed = True break return is_any_parameter_changed def target_units_tostr(self): s = "" if type(self._target_units) is str: s += self._target_units elif callable(self._target_units): s += "Data subset defined by a function" elif isinstance(self._target_units, pd.DataFrame): s += "Data subset provided as a data frame" return s def signif_results_tostr(self, signif_results): s = "" pval = signif_results["p_value"] if type(pval) is tuple: s += "[{0}, {1}]".format(pval[0], pval[1]) else: s += "{0}".format(pval) return s class CausalEstimate: """Class for the estimate object that every causal estimator returns""" def __init__( self, estimate, target_estimand, realized_estimand_expr, control_value, treatment_value, conditional_estimates=None, **kwargs, ): self.value = estimate self.target_estimand = target_estimand self.realized_estimand_expr = realized_estimand_expr self.control_value = control_value self.treatment_value = treatment_value self.conditional_estimates = conditional_estimates self.params = kwargs if self.params is not None: for key, value in self.params.items(): setattr(self, key, value) self.effect_strength = None def add_estimator(self, estimator_instance): self.estimator = estimator_instance def add_effect_strength(self, strength_dict): self.effect_strength = strength_dict def add_params(self, **kwargs): self.params.update(kwargs) def get_confidence_intervals(self, confidence_level=None, method=None, **kwargs): """Get confidence intervals of the obtained estimate. By default, this is done with the help of bootstrapped confidence intervals but can be overridden if the specific estimator implements other methods of estimating confidence intervals. If the method provided is not bootstrap, this function calls the implementation of the specific estimator. :param method: Method for estimating confidence intervals. :param confidence_level: The confidence level of the confidence intervals of the estimate. :param kwargs: Other optional args to be passed to the CI method. :returns: The obtained confidence interval. """ confidence_intervals = self.estimator.estimate_confidence_intervals( estimate_value=self.value, confidence_level=confidence_level, method=method, **kwargs ) return confidence_intervals def get_standard_error(self, method=None, **kwargs): """Get standard error of the obtained estimate. By default, this is done with the help of bootstrapped standard errors but can be overridden if the specific estimator implements other methods of estimating standard error. If the method provided is not bootstrap, this function calls the implementation of the specific estimator. :param method: Method for computing the standard error. :param kwargs: Other optional parameters to be passed to the estimating method. :returns: Standard error of the causal estimate. """ std_error = self.estimator.estimate_std_error(method=method, **kwargs) return std_error def test_stat_significance(self, method=None, **kwargs): """Test statistical significance of the estimate obtained. By default, uses resampling to create a non-parametric significance test. Individual child estimators can implement different methods. If the method name is different from "bootstrap", this function calls the implementation of the child estimator. :param method: Method for checking statistical significance :param kwargs: Other optional parameters to be passed to the estimating method. :returns: p-value from the significance test """ signif_results = self.estimator.test_significance(self.value, method=method, **kwargs) return {"p_value": signif_results["p_value"]} def estimate_conditional_effects( self, effect_modifiers=None, num_quantiles=CausalEstimator.NUM_QUANTILES_TO_DISCRETIZE_CONT_COLS ): """Estimate treatment effect conditioned on given variables. If a numeric effect modifier is provided, it is discretized into quantile bins. If you would like a custom discretization, you can do so yourself: create a new column containing the discretized effect modifier and then include that column's name in the effect_modifier_names argument. :param effect_modifiers: Names of effect modifier variables over which the conditional effects will be estimated. If not provided, defaults to the effect modifiers specified during creation of the CausalEstimator object. :param num_quantiles: The number of quantiles into which a numeric effect modifier variable is discretized. Does not affect any categorical effect modifiers. :returns: A (multi-index) dataframe that provides separate effects for each value of the (discretized) effect modifiers. """ return self.estimator._estimate_conditional_effects( self.estimator._estimate_effect_fn, effect_modifiers, num_quantiles ) def interpret(self, method_name=None, **kwargs): """Interpret the causal estimate. :param method_name: Method used (string) or a list of methods. If None, then the default for the specific estimator is used. :param kwargs:: Optional parameters that are directly passed to the interpreter method. :returns: None """ if method_name is None: method_name = self.estimator.interpret_method method_name_arr = parse_state(method_name) for method in method_name_arr: interpreter = interpreters.get_class_object(method) interpreter(self, **kwargs).interpret() def __str__(self): s = "*** Causal Estimate ***\n" # No estimand was identified (identification failed) if self.target_estimand is None: return "Estimation failed! No relevant identified estimand available for this estimation method." s += "\n## Identified estimand\n{0}".format(self.target_estimand.__str__(only_target_estimand=True)) s += "\n## Realized estimand\n{0}".format(self.realized_estimand_expr) if hasattr(self, "estimator"): s += "\nTarget units: {0}\n".format(self.estimator.target_units_tostr()) s += "\n## Estimate\n" s += "Mean value: {0}\n".format(self.value) s += "" if hasattr(self, "cate_estimates"): s += "Effect estimates: {0}\n".format(self.cate_estimates) if hasattr(self, "estimator"): if self.estimator._significance_test: s += "p-value: {0}\n".format(self.estimator.signif_results_tostr(self.test_stat_significance())) if self.estimator._confidence_intervals: s += "{0}% confidence interval: {1}\n".format( 100 * self.estimator.confidence_level, self.get_confidence_intervals() ) if self.conditional_estimates is not None: s += "### Conditional Estimates\n" s += str(self.conditional_estimates) if self.effect_strength is not None: s += "\n## Effect Strength\n" s += "Change in outcome attributable to treatment: {}\n".format(self.effect_strength["fraction-effect"]) # s += "Variance in outcome explained by treatment: {}\n".format(self.effect_strength["r-squared"]) return s class RealizedEstimand(object): def __init__(self, identified_estimand, estimator_name): self.treatment_variable = identified_estimand.treatment_variable self.outcome_variable = identified_estimand.outcome_variable self.backdoor_variables = identified_estimand.get_backdoor_variables() self.instrumental_variables = identified_estimand.instrumental_variables self.estimand_type = identified_estimand.estimand_type self.estimand_expression = None self.assumptions = None self.estimator_name = estimator_name def update_assumptions(self, estimator_assumptions): self.assumptions = estimator_assumptions def update_estimand_expression(self, estimand_expression): self.estimand_expression = estimand_expression def __str__(self): s = "Realized estimand: {0}\n".format(self.estimator_name) s += "Realized estimand type: {0}\n".format(self.estimand_type) s += "Estimand expression:\n{0}\n".format(sp.pretty(self.estimand_expression)) j = 1 for ass_name, ass_str in self.assumptions.items(): s += "Estimand assumption {0}, {1}: {2}\n".format(j, ass_name, ass_str) j += 1 return s

import logging from collections import namedtuple from typing import Dict, List, Optional, Union import numpy as np import pandas as pd import sympy as sp from sklearn.utils import resample import dowhy.interpreters as interpreters from dowhy import causal_estimators from dowhy.causal_graph import CausalGraph from dowhy.causal_identifier.identified_estimand import IdentifiedEstimand from dowhy.utils.api import parse_state logger = logging.getLogger(__name__) class CausalEstimator: """Base class for an estimator of causal effect. Subclasses implement different estimation methods. All estimation methods are in the package "dowhy.causal_estimators" """ # The default number of simulations for statistical testing DEFAULT_NUMBER_OF_SIMULATIONS_STAT_TEST = 1000 # The default number of simulations to obtain confidence intervals DEFAULT_NUMBER_OF_SIMULATIONS_CI = 100 # The portion of the total size that should be taken each time to find the confidence intervals # 1 is the recommended value # https://ocw.mit.edu/courses/mathematics/18-05-introduction-to-probability-and-statistics-spring-2014/readings/MIT18_05S14_Reading24.pdf # https://projecteuclid.org/download/pdf_1/euclid.ss/1032280214 DEFAULT_SAMPLE_SIZE_FRACTION = 1 # The default Confidence Level DEFAULT_CONFIDENCE_LEVEL = 0.95 # Number of quantiles to discretize continuous columns, for applying groupby NUM_QUANTILES_TO_DISCRETIZE_CONT_COLS = 5 # Prefix to add to temporary categorical variables created after discretization TEMP_CAT_COLUMN_PREFIX = "__categorical__" DEFAULT_NOTIMPLEMENTEDERROR_MSG = "not yet implemented for {0}. If you would this to be implemented in the next version, please raise an issue at https://github.com/microsoft/dowhy/issues" BootstrapEstimates = namedtuple("BootstrapEstimates", ["estimates", "params"]) DEFAULT_INTERPRET_METHOD = ["textual_effect_interpreter"] # std args to be removed from locals() before being passed to args_dict _STD_INIT_ARGS = ("self", "__class__", "args", "kwargs") def __init__( self, data, identified_estimand, treatment, outcome, control_value=0, treatment_value=1, test_significance=False, evaluate_effect_strength=False, confidence_intervals=False, target_units=None, effect_modifiers=None, num_null_simulations=DEFAULT_NUMBER_OF_SIMULATIONS_STAT_TEST, num_simulations=DEFAULT_NUMBER_OF_SIMULATIONS_CI, sample_size_fraction=DEFAULT_SAMPLE_SIZE_FRACTION, confidence_level=DEFAULT_CONFIDENCE_LEVEL, need_conditional_estimates="auto", num_quantiles_to_discretize_cont_cols=NUM_QUANTILES_TO_DISCRETIZE_CONT_COLS, **kwargs, ): """Initializes an estimator with data and names of relevant variables. This method is called from the constructors of its child classes. :param data: data frame containing the data :param identified_estimand: probability expression representing the target identified estimand to estimate. :param treatment: name of the treatment variable :param outcome: name of the outcome variable :param control_value: Value of the treatment in the control group, for effect estimation. If treatment is multi-variate, this can be a list. :param treatment_value: Value of the treatment in the treated group, for effect estimation. If treatment is multi-variate, this can be a list. :param test_significance: Binary flag or a string indicating whether to test significance and by which method. All estimators support test_significance="bootstrap" that estimates a p-value for the obtained estimate using the bootstrap method. Individual estimators can override this to support custom testing methods. The bootstrap method supports an optional parameter, num_null_simulations. If False, no testing is done. If True, significance of the estimate is tested using the custom method if available, otherwise by bootstrap. :param evaluate_effect_strength: (Experimental) whether to evaluate the strength of effect :param confidence_intervals: Binary flag or a string indicating whether the confidence intervals should be computed and which method should be used. All methods support estimation of confidence intervals using the bootstrap method by using the parameter confidence_intervals="bootstrap". The bootstrap method takes in two arguments (num_simulations and sample_size_fraction) that can be optionally specified in the params dictionary. Estimators may also override this to implement their own confidence interval method. If this parameter is False, no confidence intervals are computed. If True, confidence intervals are computed by the estimator's specific method if available, otherwise through bootstrap. :param target_units: The units for which the treatment effect should be estimated. This can be a string for common specifications of target units (namely, "ate", "att" and "atc"). It can also be a lambda function that can be used as an index for the data (pandas DataFrame). Alternatively, it can be a new DataFrame that contains values of the effect_modifiers and effect will be estimated only for this new data. :param effect_modifiers: Variables on which to compute separate effects, or return a heterogeneous effect function. Not all methods support this currently. :param num_null_simulations: The number of simulations for testing the statistical significance of the estimator :param num_simulations: The number of simulations for finding the confidence interval (and/or standard error) for a estimate :param sample_size_fraction: The size of the sample for the bootstrap estimator :param confidence_level: The confidence level of the confidence interval estimate :param need_conditional_estimates: Boolean flag indicating whether conditional estimates should be computed. Defaults to True if there are effect modifiers in the graph :param num_quantiles_to_discretize_cont_cols: The number of quantiles into which a numeric effect modifier is split, to enable estimation of conditional treatment effect over it. :param kwargs: (optional) Additional estimator-specific parameters :returns: an instance of the estimator class. """ self._data = data self._target_estimand = identified_estimand # Currently estimation methods only support univariate treatment and outcome self._treatment_name = treatment self._outcome_name = outcome[0] # assuming one-dimensional outcome self._control_value = control_value self._treatment_value = treatment_value self._significance_test = test_significance self._effect_strength_eval = evaluate_effect_strength self._target_units = target_units self._effect_modifier_names = effect_modifiers self._confidence_intervals = confidence_intervals self._bootstrap_estimates = None # for confidence intervals and std error self._bootstrap_null_estimates = None # for significance test self._effect_modifiers = None self.method_params = kwargs # Setting the default interpret method self.interpret_method = CausalEstimator.DEFAULT_INTERPRET_METHOD self.logger = logging.getLogger(__name__) # Setting treatment and outcome values if self._data is not None: self._treatment = self._data[self._treatment_name] self._outcome = self._data[self._outcome_name] if self._effect_modifier_names: # only add the observed nodes self._effect_modifier_names = [ cname for cname in self._effect_modifier_names if cname in self._data.columns ] if len(self._effect_modifier_names) > 0: self._effect_modifiers = self._data[self._effect_modifier_names] self._effect_modifiers = pd.get_dummies(self._effect_modifiers, drop_first=True) self.logger.debug("Effect modifiers: " + ",".join(self._effect_modifier_names)) else: self._effect_modifier_names = None # Check if some parameters were set, otherwise set to default values self.num_null_simulations = num_null_simulations self.num_simulations = num_simulations self.sample_size_fraction = sample_size_fraction self.confidence_level = confidence_level self.num_quantiles_to_discretize_cont_cols = num_quantiles_to_discretize_cont_cols # Estimate conditional estimates by default self.need_conditional_estimates = ( need_conditional_estimates if need_conditional_estimates != "auto" else bool(self._effect_modifier_names) ) @staticmethod def get_estimator_object(new_data, identified_estimand, estimate): """Create a new estimator of the same type as the one passed in the estimate argument. Creates a new object with new_data and the identified_estimand :param new_data: np.ndarray, pd.Series, pd.DataFrame The newly assigned data on which the estimator should run :param identified_estimand: IdentifiedEstimand An instance of the identified estimand class that provides the information with respect to which causal pathways are employed when the treatment effects the outcome :param estimate: CausalEstimate It is an already existing estimate whose properties we wish to replicate :returns: An instance of the same estimator class that had generated the given estimate. """ estimator_class = estimate.params["estimator_class"] new_estimator = estimator_class( new_data, identified_estimand, identified_estimand.treatment_variable, identified_estimand.outcome_variable, # names of treatment and outcome control_value=estimate.control_value, treatment_value=estimate.treatment_value, test_significance=False, evaluate_effect_strength=False, confidence_intervals=estimate.params["confidence_intervals"], target_units=estimate.params["target_units"], effect_modifiers=estimate.params["effect_modifiers"], **estimate.params["method_params"] if estimate.params["method_params"] is not None else {}, ) return new_estimator def _estimate_effect(self): """This method is to be overriden by the child classes, so that they can run the estimation technique of their choice""" raise NotImplementedError( ("Main estimation method is " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG).format(self.__class__) ) def estimate_effect(self): """Base estimation method that calls the estimate_effect method of its calling subclass. Can optionally also test significance and estimate effect strength for any returned estimate. :param self: object instance of class Estimator :returns: A CausalEstimate instance that contains point estimates of average and conditional effects. Based on the parameters provided, it optionally includes confidence intervals, standard errors,statistical significance and other statistical parameters. """ est = self._estimate_effect() est.add_estimator(self) if self._significance_test: self.test_significance(est.value, method=self._significance_test) if self._confidence_intervals: self.estimate_confidence_intervals( est.value, confidence_level=self.confidence_level, method=self._confidence_intervals ) if self._effect_strength_eval: effect_strength_dict = self.evaluate_effect_strength(est) est.add_effect_strength(effect_strength_dict) return est def estimate_effect_naive(self): # TODO Only works for binary treatment df_withtreatment = self._data.loc[self._data[self._treatment_name] == 1] df_notreatment = self._data.loc[self._data[self._treatment_name] == 0] est = np.mean(df_withtreatment[self._outcome_name]) - np.mean(df_notreatment[self._outcome_name]) return CausalEstimate(est, None, None, control_value=0, treatment_value=1) def _estimate_effect_fn(self, data_df): """Function used in conditional effect estimation. This function is to be overridden by each child estimator. The overridden function should take in a dataframe as input and return the estimate for that data. """ raise NotImplementedError( ("Conditional treatment effects are " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG).format( self.__class__ ) ) def _estimate_conditional_effects(self, estimate_effect_fn, effect_modifier_names=None, num_quantiles=None): """Estimate conditional treatment effects. Common method for all estimators that utilizes a specific estimate_effect_fn implemented by each child estimator. If a numeric effect modifier is provided, it is discretized into quantile bins. If you would like a custom discretization, you can do so yourself: create a new column containing the discretized effect modifier and then include that column's name in the effect_modifier_names argument. :param estimate_effect_fn: Function that has a single parameter (a data frame) and returns the treatment effect estimate on that data. :param effect_modifier_names: Names of effect modifier variables over which the conditional effects will be estimated. If not provided, defaults to the effect modifiers specified during creation of the CausalEstimator object. :param num_quantiles: The number of quantiles into which a numeric effect modifier variable is discretized. Does not affect any categorical effect modifiers. :returns: A (multi-index) dataframe that provides separate effects for each value of the (discretized) effect modifiers. """ # Defaulting to class default values if parameters are not provided if effect_modifier_names is None: effect_modifier_names = self._effect_modifier_names if num_quantiles is None: num_quantiles = self.num_quantiles_to_discretize_cont_cols # Checking that there is at least one effect modifier if not effect_modifier_names: raise ValueError("At least one effect modifier should be specified to compute conditional effects.") # Making sure that effect_modifier_names is a list effect_modifier_names = parse_state(effect_modifier_names) if not all(em in self._effect_modifier_names for em in effect_modifier_names): self.logger.warn( "At least one of the provided effect modifiers was not included while fitting the estimator. You may get incorrect results. To resolve, fit the estimator again by providing the updated effect modifiers in estimate_effect()." ) # Making a copy since we are going to be changing effect modifier names effect_modifier_names = effect_modifier_names.copy() prefix = CausalEstimator.TEMP_CAT_COLUMN_PREFIX # For every numeric effect modifier, adding a temp categorical column for i in range(len(effect_modifier_names)): em = effect_modifier_names[i] if pd.api.types.is_numeric_dtype(self._data[em].dtypes): self._data[prefix + str(em)] = pd.qcut(self._data[em], num_quantiles, duplicates="drop") effect_modifier_names[i] = prefix + str(em) # Grouping by effect modifiers and computing effect separately by_effect_mods = self._data.groupby(effect_modifier_names) cond_est_fn = lambda x: self._do(self._treatment_value, x) - self._do(self._control_value, x) conditional_estimates = by_effect_mods.apply(estimate_effect_fn) # Deleting the temporary categorical columns for em in effect_modifier_names: if em.startswith(prefix): self._data.pop(em) return conditional_estimates def _do(self, x, data_df=None): raise NotImplementedError( ("Do-operator is " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG).format(self.__class__) ) def do(self, x, data_df=None): """Method that implements the do-operator. Given a value x for the treatment, returns the expected value of the outcome when the treatment is intervened to a value x. :param x: Value of the treatment :param data_df: Data on which the do-operator is to be applied. :returns: Value of the outcome when treatment is intervened/set to x. """ est = self._do(x, data_df) return est def construct_symbolic_estimator(self, estimand): raise NotImplementedError(("Symbolic estimator string is ").format(self.__class__)) def _generate_bootstrap_estimates(self, num_bootstrap_simulations, sample_size_fraction): """Helper function to generate causal estimates over bootstrapped samples. :param num_bootstrap_simulations: Number of simulations for the bootstrap method. :param sample_size_fraction: Fraction of the dataset to be resampled. :returns: A collections.namedtuple containing a list of bootstrapped estimates and a dictionary containing parameters used for the bootstrap. """ # The array that stores the results of all estimations simulation_results = np.zeros(num_bootstrap_simulations) # Find the sample size the proportion with the population size sample_size = int(sample_size_fraction * len(self._data)) if sample_size > len(self._data): self.logger.warning("WARN: The sample size is greater than the data being sampled") self.logger.info("INFO: The sample size: {}".format(sample_size)) self.logger.info("INFO: The number of simulations: {}".format(num_bootstrap_simulations)) # Perform the set number of simulations for index in range(num_bootstrap_simulations): new_data = resample(self._data, n_samples=sample_size) new_estimator = type(self)( new_data, self._target_estimand, self._target_estimand.treatment_variable, self._target_estimand.outcome_variable, # names of treatment and outcome treatment_value=self._treatment_value, control_value=self._control_value, test_significance=False, evaluate_effect_strength=False, confidence_intervals=False, target_units=self._target_units, effect_modifiers=self._effect_modifier_names, **self.method_params, ) new_effect = new_estimator.estimate_effect() simulation_results[index] = new_effect.value estimates = CausalEstimator.BootstrapEstimates( simulation_results, {"num_simulations": num_bootstrap_simulations, "sample_size_fraction": sample_size_fraction}, ) return estimates def _estimate_confidence_intervals_with_bootstrap( self, estimate_value, confidence_level=None, num_simulations=None, sample_size_fraction=None ): """ Method to compute confidence interval using bootstrapped sampling. :param estimate_value: obtained estimate's value :param confidence_level: The level for which to compute CI (e.g., 95% confidence level translates to confidence_level=0.95) :param num_simulations: The number of simulations to be performed to get the bootstrap confidence intervals. :param sample_size_fraction: The fraction of the dataset to be resampled. :returns: confidence interval at the specified level. For more details on bootstrap or resampling statistics, refer to the following links: https://ocw.mit.edu/courses/mathematics/18-05-introduction-to-probability-and-statistics-spring-2014/readings/MIT18_05S14_Reading24.pdf https://projecteuclid.org/download/pdf_1/euclid.ss/1032280214 """ # Using class default parameters if not specified if num_simulations is None: num_simulations = self.num_simulations if sample_size_fraction is None: sample_size_fraction = self.sample_size_fraction # Checking if bootstrap_estimates are already computed if self._bootstrap_estimates is None: self._bootstrap_estimates = self._generate_bootstrap_estimates(num_simulations, sample_size_fraction) elif CausalEstimator.is_bootstrap_parameter_changed(self._bootstrap_estimates.params, locals()): # Checked if any parameter is changed from the previous std error estimate self._bootstrap_estimates = self._generate_bootstrap_estimates(num_simulations, sample_size_fraction) # Now use the data obtained from the simulations to get the value of the confidence estimates bootstrap_estimates = self._bootstrap_estimates.estimates # Get the variations of each bootstrap estimate and sort bootstrap_variations = [bootstrap_estimate - estimate_value for bootstrap_estimate in bootstrap_estimates] sorted_bootstrap_variations = np.sort(bootstrap_variations) # Now we take the (1- p)th and the (p)th variations, where p is the chosen confidence level upper_bound_index = int((1 - confidence_level) * len(sorted_bootstrap_variations)) lower_bound_index = int(confidence_level * len(sorted_bootstrap_variations)) # Get the lower and upper bounds by subtracting the variations from the estimate lower_bound = estimate_value - sorted_bootstrap_variations[lower_bound_index] upper_bound = estimate_value - sorted_bootstrap_variations[upper_bound_index] return lower_bound, upper_bound def _estimate_confidence_intervals(self, confidence_level=None, method=None, **kwargs): """ This method is to be overriden by the child classes, so that they can run a confidence interval estimation method suited to the specific causal estimator. """ raise NotImplementedError( ( "This method for estimating confidence intervals is " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG + " Meanwhile, you can try the bootstrap method (method='bootstrap') to estimate confidence intervals." ).format(self.__class__) ) def estimate_confidence_intervals(self, estimate_value, confidence_level=None, method=None, **kwargs): """Find the confidence intervals corresponding to any estimator By default, this is done with the help of bootstrapped confidence intervals but can be overridden if the specific estimator implements other methods of estimating confidence intervals. If the method provided is not bootstrap, this function calls the implementation of the specific estimator. :param estimate_value: obtained estimate's value :param method: Method for estimating confidence intervals. :param confidence_level: The confidence level of the confidence intervals of the estimate. :param kwargs: Other optional args to be passed to the CI method. :returns: The obtained confidence interval. """ if method is None: if self._confidence_intervals: method = self._confidence_intervals # this is either True or methodname else: method = "default" confidence_intervals = None if confidence_level is None: confidence_level = self.confidence_level if method == "default" or method is True: # user has not provided any method try: confidence_intervals = self._estimate_confidence_intervals(confidence_level, method=method, **kwargs) except NotImplementedError: confidence_intervals = self._estimate_confidence_intervals_with_bootstrap( estimate_value, confidence_level, **kwargs ) else: if method == "bootstrap": confidence_intervals = self._estimate_confidence_intervals_with_bootstrap( estimate_value, confidence_level, **kwargs ) else: confidence_intervals = self._estimate_confidence_intervals(confidence_level, method=method, **kwargs) return confidence_intervals def _estimate_std_error_with_bootstrap(self, num_simulations=None, sample_size_fraction=None): """Compute standard error using the bootstrap method. Standard error and confidence intervals use the same parameter num_simulations for the number of bootstrap simulations. :param num_simulations: Number of bootstrapped samples. :param sample_size_fraction: Fraction of data to be resampled. :returns: Standard error of the obtained estimate. """ # Use existing params, if new user defined params are not present if num_simulations is None: num_simulations = self.num_simulations if sample_size_fraction is None: sample_size_fraction = self.sample_size_fraction # Checking if bootstrap_estimates are already computed if self._bootstrap_estimates is None: self._bootstrap_estimates = self._generate_bootstrap_estimates(num_simulations, sample_size_fraction) elif CausalEstimator.is_bootstrap_parameter_changed(self._bootstrap_estimates.params, locals()): # Check if any parameter is changed from the previous std error estimate self._bootstrap_estimates = self._generate_bootstrap_estimates(num_simulations, sample_size_fraction) std_error = np.std(self._bootstrap_estimates.estimates) return std_error def _estimate_std_error(self, method=None, **kwargs): """ This method is to be overriden by the child classes, so that they can run a standard error estimation method suited to the specific causal estimator. """ raise NotImplementedError( ( "This method for estimating standard errors is " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG + " Meanwhile, you can try the bootstrap method (method='bootstrap') to estimate standard errors." ).format(self.__class__) ) def estimate_std_error(self, method=None, **kwargs): """Compute standard error of an obtained causal estimate. :param method: Method for computing the standard error. :param kwargs: Other optional parameters to be passed to the estimating method. :returns: Standard error of the causal estimate. """ if method is None: if self._confidence_intervals: method = self._confidence_intervals else: method = "default" std_error = None if method == "default" or method is True: # user has not provided any method try: std_error = self._estimate_std_error(method, **kwargs) except NotImplementedError: std_error = self._estimate_std_error_with_bootstrap(**kwargs) else: if method == "bootstrap": std_error = self._estimate_std_error_with_bootstrap(**kwargs) else: std_error = self._estimate_std_error(method, **kwargs) return std_error def _test_significance_with_bootstrap(self, estimate_value, num_null_simulations=None): """Test statistical significance of an estimate using the bootstrap method. :param estimate_value: Obtained estimate's value :param num_null_simulations: Number of simulations for the null hypothesis :returns: p-value of the statistical significance test. """ # Use existing params, if new user defined params are not present if num_null_simulations is None: num_null_simulations = self.num_null_simulations do_retest = self._bootstrap_null_estimates is None or CausalEstimator.is_bootstrap_parameter_changed( self._bootstrap_null_estimates.params, locals() ) if do_retest: null_estimates = np.zeros(num_null_simulations) for i in range(num_null_simulations): new_outcome = np.random.permutation(self._outcome) new_data = self._data.assign(dummy_outcome=new_outcome) # self._outcome = self._data["dummy_outcome"] new_estimator = type(self)( new_data, self._target_estimand, self._target_estimand.treatment_variable, ("dummy_outcome",), test_significance=False, evaluate_effect_strength=False, confidence_intervals=False, target_units=self._target_units, effect_modifiers=self._effect_modifier_names, **self.method_params, ) new_effect = new_estimator.estimate_effect() null_estimates[i] = new_effect.value self._bootstrap_null_estimates = CausalEstimator.BootstrapEstimates( null_estimates, {"num_null_simulations": num_null_simulations, "sample_size_fraction": 1} ) # Processing the null hypothesis estimates sorted_null_estimates = np.sort(self._bootstrap_null_estimates.estimates) self.logger.debug("Null estimates: {0}".format(sorted_null_estimates)) median_estimate = sorted_null_estimates[int(num_null_simulations / 2)] # Doing a two-sided test if estimate_value > median_estimate: # Being conservative with the p-value reported estimate_index = np.searchsorted(sorted_null_estimates, estimate_value, side="left") p_value = 1 - (estimate_index / num_null_simulations) if estimate_value <= median_estimate: # Being conservative with the p-value reported estimate_index = np.searchsorted(sorted_null_estimates, estimate_value, side="right") p_value = estimate_index / num_null_simulations # If the estimate_index is 0, it depends on the number of simulations if p_value == 0: p_value = (0, 1 / len(sorted_null_estimates)) # a tuple determining the range. elif p_value == 1: p_value = (1 - 1 / len(sorted_null_estimates), 1) signif_dict = {"p_value": p_value} return signif_dict def _test_significance(self, estimate_value, method=None, **kwargs): """ This method is to be overriden by the child classes, so that they can run a significance test suited to the specific causal estimator. """ raise NotImplementedError( ( "This method for testing statistical significance is " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG + " Meanwhile, you can try the bootstrap method (method='bootstrap') to test statistical significance." ).format(self.__class__) ) def test_significance(self, estimate_value, method=None, **kwargs): """Test statistical significance of obtained estimate. By default, uses resampling to create a non-parametric significance test. A general procedure. Individual child estimators can implement different methods. If the method name is different from "bootstrap", this function calls the implementation of the child estimator. :param self: object instance of class Estimator :param estimate_value: obtained estimate's value :param method: Method for checking statistical significance :returns: p-value from the significance test """ if method is None: if self._significance_test: method = self._significance_test # this is either True or methodname else: method = "default" signif_dict = None if method == "default" or method is True: # user has not provided any method try: signif_dict = self._test_significance(estimate_value, method, **kwargs) except NotImplementedError: signif_dict = self._test_significance_with_bootstrap(estimate_value, **kwargs) else: if method == "bootstrap": signif_dict = self._test_significance_with_bootstrap(estimate_value, **kwargs) else: signif_dict = self._test_significance(estimate_value, method, **kwargs) return signif_dict def evaluate_effect_strength(self, estimate): fraction_effect_explained = self._evaluate_effect_strength(estimate, method="fraction-effect") # Need to test r-squared before supporting # effect_r_squared = self._evaluate_effect_strength(estimate, method="r-squared") strength_dict = { "fraction-effect": fraction_effect_explained # 'r-squared': effect_r_squared } return strength_dict def _evaluate_effect_strength(self, estimate, method="fraction-effect"): supported_methods = ["fraction-effect"] if method not in supported_methods: raise NotImplementedError("This method is not supported for evaluating effect strength") if method == "fraction-effect": naive_obs_estimate = self.estimate_effect_naive() self.logger.debug(estimate.value, naive_obs_estimate.value) fraction_effect_explained = estimate.value / naive_obs_estimate.value return fraction_effect_explained # elif method == "r-squared": # outcome_mean = np.mean(self._outcome) # total_variance = np.sum(np.square(self._outcome - outcome_mean)) # Assuming a linear model with one variable: the treatment # Currently only works for continuous y # causal_model = outcome_mean + estimate.value*self._treatment # squared_residual = np.sum(np.square(self._outcome - causal_model)) # r_squared = 1 - (squared_residual/total_variance) # return r_squared else: return None def update_input(self, treatment_value, control_value, target_units): self._control_value = control_value self._treatment_value = treatment_value self._target_units = target_units @staticmethod def is_bootstrap_parameter_changed(bootstrap_estimates_params, given_params): """Check whether parameters of the bootstrap have changed. This is an efficiency method that checks if fresh resampling of the bootstrap samples is required. Returns True if parameters have changed and resampling should be done again. :param bootstrap_estimates_params: A dictionary of parameters for the current bootstrap samples :param given_params: A dictionary of parameters passed by the user :returns: A binary flag denoting whether the parameters are different. """ is_any_parameter_changed = False for prm, val in bootstrap_estimates_params.items(): given_val = given_params.get(prm, None) if given_val is not None and given_val != val: is_any_parameter_changed = True break return is_any_parameter_changed def target_units_tostr(self): s = "" if type(self._target_units) is str: s += self._target_units elif callable(self._target_units): s += "Data subset defined by a function" elif isinstance(self._target_units, pd.DataFrame): s += "Data subset provided as a data frame" return s def signif_results_tostr(self, signif_results): s = "" pval = signif_results["p_value"] if type(pval) is tuple: s += "[{0}, {1}]".format(pval[0], pval[1]) else: s += "{0}".format(pval) return s def estimate_effect( treatment: Union[str, List[str]], outcome: Union[str, List[str]], identified_estimand: IdentifiedEstimand, identifier_name: str, method: CausalEstimator, control_value: int = 0, treatment_value: int = 1, test_significance: Optional[bool] = None, evaluate_effect_strength: bool = False, confidence_intervals: bool = False, target_units: str = "ate", effect_modifiers: List[str] = [], fit_estimator: bool = True, method_params: Optional[Dict] = None, ): """Estimate the identified causal effect. Currently requires an explicit method name to be specified. Method names follow the convention of identification method followed by the specific estimation method: "[backdoor/iv].estimation_method_name". Following methods are supported. * Propensity Score Matching: "backdoor.propensity_score_matching" * Propensity Score Stratification: "backdoor.propensity_score_stratification" * Propensity Score-based Inverse Weighting: "backdoor.propensity_score_weighting" * Linear Regression: "backdoor.linear_regression" * Generalized Linear Models (e.g., logistic regression): "backdoor.generalized_linear_model" * Instrumental Variables: "iv.instrumental_variable" * Regression Discontinuity: "iv.regression_discontinuity" In addition, you can directly call any of the EconML estimation methods. The convention is "backdoor.econml.path-to-estimator-class". For example, for the double machine learning estimator ("DML" class) that is located inside "dml" module of EconML, you can use the method name, "backdoor.econml.dml.DML". CausalML estimators can also be called. See `this demo notebook <https://py-why.github.io/dowhy/example_notebooks/dowhy-conditional-treatment-effects.html>`_. :param treatment: Name of the treatment :param outcome: Name of the outcome :param identified_estimand: a probability expression that represents the effect to be estimated. Output of CausalModel.identify_effect method :param method_name: name of the estimation method to be used. :param control_value: Value of the treatment in the control group, for effect estimation. If treatment is multi-variate, this can be a list. :param treatment_value: Value of the treatment in the treated group, for effect estimation. If treatment is multi-variate, this can be a list. :param test_significance: Binary flag on whether to additionally do a statistical signficance test for the estimate. :param evaluate_effect_strength: (Experimental) Binary flag on whether to estimate the relative strength of the treatment's effect. This measure can be used to compare different treatments for the same outcome (by running this method with different treatments sequentially). :param confidence_intervals: (Experimental) Binary flag indicating whether confidence intervals should be computed. :param target_units: (Experimental) The units for which the treatment effect should be estimated. This can be of three types. (1) a string for common specifications of target units (namely, "ate", "att" and "atc"), (2) a lambda function that can be used as an index for the data (pandas DataFrame), or (3) a new DataFrame that contains values of the effect_modifiers and effect will be estimated only for this new data. :param effect_modifiers: Names of effect modifier variables can be (optionally) specified here too, since they do not affect identification. If None, the effect_modifiers from the CausalModel are used. :param fit_estimator: Boolean flag on whether to fit the estimator. Setting it to False is useful to estimate the effect on new data using a previously fitted estimator. :param method_params: Dictionary containing any method-specific parameters. These are passed directly to the estimating method. See the docs for each estimation method for allowed method-specific params. :returns: An instance of the CausalEstimate class, containing the causal effect estimate and other method-dependent information """ treatment = parse_state(treatment) outcome = parse_state(outcome) causal_estimator_class = method.__class__ identified_estimand.set_identifier_method(identifier_name) if identified_estimand.no_directed_path: logger.warning("No directed path from {0} to {1}.".format(treatment, outcome)) return CausalEstimate( 0, identified_estimand, None, control_value=control_value, treatment_value=treatment_value ) # Check if estimator's target estimand is identified elif identified_estimand.estimands[identifier_name] is None: logger.error("No valid identified estimand available.") return CausalEstimate(None, None, None, control_value=control_value, treatment_value=treatment_value) method.update_input(treatment_value, control_value, target_units) estimate = method.estimate_effect() # Store parameters inside estimate object for refutation methods # TODO: This add_params needs to move to the estimator class # inside estimate_effect and estimate_conditional_effect estimate.add_params( estimand_type=identified_estimand.estimand_type, estimator_class=causal_estimator_class, test_significance=test_significance, evaluate_effect_strength=evaluate_effect_strength, confidence_intervals=confidence_intervals, target_units=target_units, effect_modifiers=effect_modifiers, method_params=method_params, ) return estimate class CausalEstimate: """Class for the estimate object that every causal estimator returns""" def __init__( self, estimate, target_estimand, realized_estimand_expr, control_value, treatment_value, conditional_estimates=None, **kwargs, ): self.value = estimate self.target_estimand = target_estimand self.realized_estimand_expr = realized_estimand_expr self.control_value = control_value self.treatment_value = treatment_value self.conditional_estimates = conditional_estimates self.params = kwargs if self.params is not None: for key, value in self.params.items(): setattr(self, key, value) self.effect_strength = None def add_estimator(self, estimator_instance): self.estimator = estimator_instance def add_effect_strength(self, strength_dict): self.effect_strength = strength_dict def add_params(self, **kwargs): self.params.update(kwargs) def get_confidence_intervals(self, confidence_level=None, method=None, **kwargs): """Get confidence intervals of the obtained estimate. By default, this is done with the help of bootstrapped confidence intervals but can be overridden if the specific estimator implements other methods of estimating confidence intervals. If the method provided is not bootstrap, this function calls the implementation of the specific estimator. :param method: Method for estimating confidence intervals. :param confidence_level: The confidence level of the confidence intervals of the estimate. :param kwargs: Other optional args to be passed to the CI method. :returns: The obtained confidence interval. """ confidence_intervals = self.estimator.estimate_confidence_intervals( estimate_value=self.value, confidence_level=confidence_level, method=method, **kwargs ) return confidence_intervals def get_standard_error(self, method=None, **kwargs): """Get standard error of the obtained estimate. By default, this is done with the help of bootstrapped standard errors but can be overridden if the specific estimator implements other methods of estimating standard error. If the method provided is not bootstrap, this function calls the implementation of the specific estimator. :param method: Method for computing the standard error. :param kwargs: Other optional parameters to be passed to the estimating method. :returns: Standard error of the causal estimate. """ std_error = self.estimator.estimate_std_error(method=method, **kwargs) return std_error def test_stat_significance(self, method=None, **kwargs): """Test statistical significance of the estimate obtained. By default, uses resampling to create a non-parametric significance test. Individual child estimators can implement different methods. If the method name is different from "bootstrap", this function calls the implementation of the child estimator. :param method: Method for checking statistical significance :param kwargs: Other optional parameters to be passed to the estimating method. :returns: p-value from the significance test """ signif_results = self.estimator.test_significance(self.value, method=method, **kwargs) return {"p_value": signif_results["p_value"]} def estimate_conditional_effects( self, effect_modifiers=None, num_quantiles=CausalEstimator.NUM_QUANTILES_TO_DISCRETIZE_CONT_COLS ): """Estimate treatment effect conditioned on given variables. If a numeric effect modifier is provided, it is discretized into quantile bins. If you would like a custom discretization, you can do so yourself: create a new column containing the discretized effect modifier and then include that column's name in the effect_modifier_names argument. :param effect_modifiers: Names of effect modifier variables over which the conditional effects will be estimated. If not provided, defaults to the effect modifiers specified during creation of the CausalEstimator object. :param num_quantiles: The number of quantiles into which a numeric effect modifier variable is discretized. Does not affect any categorical effect modifiers. :returns: A (multi-index) dataframe that provides separate effects for each value of the (discretized) effect modifiers. """ return self.estimator._estimate_conditional_effects( self.estimator._estimate_effect_fn, effect_modifiers, num_quantiles ) def interpret(self, method_name=None, **kwargs): """Interpret the causal estimate. :param method_name: Method used (string) or a list of methods. If None, then the default for the specific estimator is used. :param kwargs:: Optional parameters that are directly passed to the interpreter method. :returns: None """ if method_name is None: method_name = self.estimator.interpret_method method_name_arr = parse_state(method_name) for method in method_name_arr: interpreter = interpreters.get_class_object(method) interpreter(self, **kwargs).interpret() def __str__(self): s = "*** Causal Estimate ***\n" # No estimand was identified (identification failed) if self.target_estimand is None: return "Estimation failed! No relevant identified estimand available for this estimation method." s += "\n## Identified estimand\n{0}".format(self.target_estimand.__str__(only_target_estimand=True)) s += "\n## Realized estimand\n{0}".format(self.realized_estimand_expr) if hasattr(self, "estimator"): s += "\nTarget units: {0}\n".format(self.estimator.target_units_tostr()) s += "\n## Estimate\n" s += "Mean value: {0}\n".format(self.value) s += "" if hasattr(self, "cate_estimates"): s += "Effect estimates: {0}\n".format(self.cate_estimates) if hasattr(self, "estimator"): if self.estimator._significance_test: s += "p-value: {0}\n".format(self.estimator.signif_results_tostr(self.test_stat_significance())) if self.estimator._confidence_intervals: s += "{0}% confidence interval: {1}\n".format( 100 * self.estimator.confidence_level, self.get_confidence_intervals() ) if self.conditional_estimates is not None: s += "### Conditional Estimates\n" s += str(self.conditional_estimates) if self.effect_strength is not None: s += "\n## Effect Strength\n" s += "Change in outcome attributable to treatment: {}\n".format(self.effect_strength["fraction-effect"]) # s += "Variance in outcome explained by treatment: {}\n".format(self.effect_strength["r-squared"]) return s class RealizedEstimand(object): def __init__(self, identified_estimand, estimator_name): self.treatment_variable = identified_estimand.treatment_variable self.outcome_variable = identified_estimand.outcome_variable self.backdoor_variables = identified_estimand.get_backdoor_variables() self.instrumental_variables = identified_estimand.instrumental_variables self.estimand_type = identified_estimand.estimand_type self.estimand_expression = None self.assumptions = None self.estimator_name = estimator_name def update_assumptions(self, estimator_assumptions): self.assumptions = estimator_assumptions def update_estimand_expression(self, estimand_expression): self.estimand_expression = estimand_expression def __str__(self): s = "Realized estimand: {0}\n".format(self.estimator_name) s += "Realized estimand type: {0}\n".format(self.estimand_type) s += "Estimand expression:\n{0}\n".format(sp.pretty(self.estimand_expression)) j = 1 for ass_name, ass_str in self.assumptions.items(): s += "Estimand assumption {0}, {1}: {2}\n".format(j, ass_name, ass_str) j += 1 return s

andresmor-ms

2044d216c322a4b32c6eadce5da7d83463f19c2f

05bfa49dacf0061988c96c6f3e3756219df5422a

removing all the kwargs will be done in future PRs, however i did add the object as parameter which makes things a little bit better while keeping backwards compatibility on causal_model class

andresmor-ms

py-why/dowhy

Functional api/estimate effect function

#### Estimate Effect function * Refactors the estimate effect into a separate function to keep backwards compatibility #### TODO (future PRs): * Add `fit(...)` method to estimators - Move data related parameters from the constructor to the `fit(...)` method * Refactor code to avoid `**kwargs` in `__init__(...)` constructors

2022-10-18 15:49:21+00:00

2022-10-25 17:02:02+00:00

dowhy/causal_estimator.py

import logging from collections import namedtuple import numpy as np import pandas as pd import sympy as sp from sklearn.utils import resample import dowhy.interpreters as interpreters from dowhy.utils.api import parse_state class CausalEstimator: """Base class for an estimator of causal effect. Subclasses implement different estimation methods. All estimation methods are in the package "dowhy.causal_estimators" """ # The default number of simulations for statistical testing DEFAULT_NUMBER_OF_SIMULATIONS_STAT_TEST = 1000 # The default number of simulations to obtain confidence intervals DEFAULT_NUMBER_OF_SIMULATIONS_CI = 100 # The portion of the total size that should be taken each time to find the confidence intervals # 1 is the recommended value # https://ocw.mit.edu/courses/mathematics/18-05-introduction-to-probability-and-statistics-spring-2014/readings/MIT18_05S14_Reading24.pdf # https://projecteuclid.org/download/pdf_1/euclid.ss/1032280214 DEFAULT_SAMPLE_SIZE_FRACTION = 1 # The default Confidence Level DEFAULT_CONFIDENCE_LEVEL = 0.95 # Number of quantiles to discretize continuous columns, for applying groupby NUM_QUANTILES_TO_DISCRETIZE_CONT_COLS = 5 # Prefix to add to temporary categorical variables created after discretization TEMP_CAT_COLUMN_PREFIX = "__categorical__" DEFAULT_NOTIMPLEMENTEDERROR_MSG = "not yet implemented for {0}. If you would this to be implemented in the next version, please raise an issue at https://github.com/microsoft/dowhy/issues" BootstrapEstimates = namedtuple("BootstrapEstimates", ["estimates", "params"]) DEFAULT_INTERPRET_METHOD = ["textual_effect_interpreter"] # std args to be removed from locals() before being passed to args_dict _STD_INIT_ARGS = ("self", "__class__", "args", "kwargs") def __init__( self, data, identified_estimand, treatment, outcome, control_value=0, treatment_value=1, test_significance=False, evaluate_effect_strength=False, confidence_intervals=False, target_units=None, effect_modifiers=None, num_null_simulations=DEFAULT_NUMBER_OF_SIMULATIONS_STAT_TEST, num_simulations=DEFAULT_NUMBER_OF_SIMULATIONS_CI, sample_size_fraction=DEFAULT_SAMPLE_SIZE_FRACTION, confidence_level=DEFAULT_CONFIDENCE_LEVEL, need_conditional_estimates="auto", num_quantiles_to_discretize_cont_cols=NUM_QUANTILES_TO_DISCRETIZE_CONT_COLS, **kwargs, ): """Initializes an estimator with data and names of relevant variables. This method is called from the constructors of its child classes. :param data: data frame containing the data :param identified_estimand: probability expression representing the target identified estimand to estimate. :param treatment: name of the treatment variable :param outcome: name of the outcome variable :param control_value: Value of the treatment in the control group, for effect estimation. If treatment is multi-variate, this can be a list. :param treatment_value: Value of the treatment in the treated group, for effect estimation. If treatment is multi-variate, this can be a list. :param test_significance: Binary flag or a string indicating whether to test significance and by which method. All estimators support test_significance="bootstrap" that estimates a p-value for the obtained estimate using the bootstrap method. Individual estimators can override this to support custom testing methods. The bootstrap method supports an optional parameter, num_null_simulations. If False, no testing is done. If True, significance of the estimate is tested using the custom method if available, otherwise by bootstrap. :param evaluate_effect_strength: (Experimental) whether to evaluate the strength of effect :param confidence_intervals: Binary flag or a string indicating whether the confidence intervals should be computed and which method should be used. All methods support estimation of confidence intervals using the bootstrap method by using the parameter confidence_intervals="bootstrap". The bootstrap method takes in two arguments (num_simulations and sample_size_fraction) that can be optionally specified in the params dictionary. Estimators may also override this to implement their own confidence interval method. If this parameter is False, no confidence intervals are computed. If True, confidence intervals are computed by the estimator's specific method if available, otherwise through bootstrap. :param target_units: The units for which the treatment effect should be estimated. This can be a string for common specifications of target units (namely, "ate", "att" and "atc"). It can also be a lambda function that can be used as an index for the data (pandas DataFrame). Alternatively, it can be a new DataFrame that contains values of the effect_modifiers and effect will be estimated only for this new data. :param effect_modifiers: Variables on which to compute separate effects, or return a heterogeneous effect function. Not all methods support this currently. :param num_null_simulations: The number of simulations for testing the statistical significance of the estimator :param num_simulations: The number of simulations for finding the confidence interval (and/or standard error) for a estimate :param sample_size_fraction: The size of the sample for the bootstrap estimator :param confidence_level: The confidence level of the confidence interval estimate :param need_conditional_estimates: Boolean flag indicating whether conditional estimates should be computed. Defaults to True if there are effect modifiers in the graph :param num_quantiles_to_discretize_cont_cols: The number of quantiles into which a numeric effect modifier is split, to enable estimation of conditional treatment effect over it. :param kwargs: (optional) Additional estimator-specific parameters :returns: an instance of the estimator class. """ self._data = data self._target_estimand = identified_estimand # Currently estimation methods only support univariate treatment and outcome self._treatment_name = treatment self._outcome_name = outcome[0] # assuming one-dimensional outcome self._control_value = control_value self._treatment_value = treatment_value self._significance_test = test_significance self._effect_strength_eval = evaluate_effect_strength self._target_units = target_units self._effect_modifier_names = effect_modifiers self._confidence_intervals = confidence_intervals self._bootstrap_estimates = None # for confidence intervals and std error self._bootstrap_null_estimates = None # for significance test self._effect_modifiers = None self.method_params = kwargs # Setting the default interpret method self.interpret_method = CausalEstimator.DEFAULT_INTERPRET_METHOD self.logger = logging.getLogger(__name__) # Setting treatment and outcome values if self._data is not None: self._treatment = self._data[self._treatment_name] self._outcome = self._data[self._outcome_name] # Now saving the effect modifiers if self._effect_modifier_names: # only add the observed nodes self._effect_modifier_names = [ cname for cname in self._effect_modifier_names if cname in self._data.columns ] if len(self._effect_modifier_names) > 0: self._effect_modifiers = self._data[self._effect_modifier_names] self._effect_modifiers = pd.get_dummies(self._effect_modifiers, drop_first=True) self.logger.debug("Effect modifiers: " + ",".join(self._effect_modifier_names)) else: self._effect_modifier_names = None # Check if some parameters were set, otherwise set to default values self.num_null_simulations = num_null_simulations self.num_simulations = num_simulations self.sample_size_fraction = sample_size_fraction self.confidence_level = confidence_level self.num_quantiles_to_discretize_cont_cols = num_quantiles_to_discretize_cont_cols # Estimate conditional estimates by default self.need_conditional_estimates = ( need_conditional_estimates if need_conditional_estimates != "auto" else bool(self._effect_modifier_names) ) @staticmethod def get_estimator_object(new_data, identified_estimand, estimate): """Create a new estimator of the same type as the one passed in the estimate argument. Creates a new object with new_data and the identified_estimand :param new_data: np.ndarray, pd.Series, pd.DataFrame The newly assigned data on which the estimator should run :param identified_estimand: IdentifiedEstimand An instance of the identified estimand class that provides the information with respect to which causal pathways are employed when the treatment effects the outcome :param estimate: CausalEstimate It is an already existing estimate whose properties we wish to replicate :returns: An instance of the same estimator class that had generated the given estimate. """ estimator_class = estimate.params["estimator_class"] new_estimator = estimator_class( new_data, identified_estimand, identified_estimand.treatment_variable, identified_estimand.outcome_variable, # names of treatment and outcome control_value=estimate.control_value, treatment_value=estimate.treatment_value, test_significance=False, evaluate_effect_strength=False, confidence_intervals=estimate.params["confidence_intervals"], target_units=estimate.params["target_units"], effect_modifiers=estimate.params["effect_modifiers"], **estimate.params["method_params"], ) return new_estimator def _estimate_effect(self): """This method is to be overriden by the child classes, so that they can run the estimation technique of their choice""" raise NotImplementedError( ("Main estimation method is " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG).format(self.__class__) ) def estimate_effect(self): """Base estimation method that calls the estimate_effect method of its calling subclass. Can optionally also test significance and estimate effect strength for any returned estimate. :param self: object instance of class Estimator :returns: A CausalEstimate instance that contains point estimates of average and conditional effects. Based on the parameters provided, it optionally includes confidence intervals, standard errors,statistical significance and other statistical parameters. """ est = self._estimate_effect() est.add_estimator(self) if self._significance_test: self.test_significance(est.value, method=self._significance_test) if self._confidence_intervals: self.estimate_confidence_intervals( est.value, confidence_level=self.confidence_level, method=self._confidence_intervals ) if self._effect_strength_eval: effect_strength_dict = self.evaluate_effect_strength(est) est.add_effect_strength(effect_strength_dict) return est def estimate_effect_naive(self): # TODO Only works for binary treatment df_withtreatment = self._data.loc[self._data[self._treatment_name] == 1] df_notreatment = self._data.loc[self._data[self._treatment_name] == 0] est = np.mean(df_withtreatment[self._outcome_name]) - np.mean(df_notreatment[self._outcome_name]) return CausalEstimate(est, None, None, control_value=0, treatment_value=1) def _estimate_effect_fn(self, data_df): """Function used in conditional effect estimation. This function is to be overridden by each child estimator. The overridden function should take in a dataframe as input and return the estimate for that data. """ raise NotImplementedError( ("Conditional treatment effects are " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG).format( self.__class__ ) ) def _estimate_conditional_effects(self, estimate_effect_fn, effect_modifier_names=None, num_quantiles=None): """Estimate conditional treatment effects. Common method for all estimators that utilizes a specific estimate_effect_fn implemented by each child estimator. If a numeric effect modifier is provided, it is discretized into quantile bins. If you would like a custom discretization, you can do so yourself: create a new column containing the discretized effect modifier and then include that column's name in the effect_modifier_names argument. :param estimate_effect_fn: Function that has a single parameter (a data frame) and returns the treatment effect estimate on that data. :param effect_modifier_names: Names of effect modifier variables over which the conditional effects will be estimated. If not provided, defaults to the effect modifiers specified during creation of the CausalEstimator object. :param num_quantiles: The number of quantiles into which a numeric effect modifier variable is discretized. Does not affect any categorical effect modifiers. :returns: A (multi-index) dataframe that provides separate effects for each value of the (discretized) effect modifiers. """ # Defaulting to class default values if parameters are not provided if effect_modifier_names is None: effect_modifier_names = self._effect_modifier_names if num_quantiles is None: num_quantiles = self.num_quantiles_to_discretize_cont_cols # Checking that there is at least one effect modifier if not effect_modifier_names: raise ValueError("At least one effect modifier should be specified to compute conditional effects.") # Making sure that effect_modifier_names is a list effect_modifier_names = parse_state(effect_modifier_names) if not all(em in self._effect_modifier_names for em in effect_modifier_names): self.logger.warn( "At least one of the provided effect modifiers was not included while fitting the estimator. You may get incorrect results. To resolve, fit the estimator again by providing the updated effect modifiers in estimate_effect()." ) # Making a copy since we are going to be changing effect modifier names effect_modifier_names = effect_modifier_names.copy() prefix = CausalEstimator.TEMP_CAT_COLUMN_PREFIX # For every numeric effect modifier, adding a temp categorical column for i in range(len(effect_modifier_names)): em = effect_modifier_names[i] if pd.api.types.is_numeric_dtype(self._data[em].dtypes): self._data[prefix + str(em)] = pd.qcut(self._data[em], num_quantiles, duplicates="drop") effect_modifier_names[i] = prefix + str(em) # Grouping by effect modifiers and computing effect separately by_effect_mods = self._data.groupby(effect_modifier_names) cond_est_fn = lambda x: self._do(self._treatment_value, x) - self._do(self._control_value, x) conditional_estimates = by_effect_mods.apply(estimate_effect_fn) # Deleting the temporary categorical columns for em in effect_modifier_names: if em.startswith(prefix): self._data.pop(em) return conditional_estimates def _do(self, x, data_df=None): raise NotImplementedError( ("Do-operator is " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG).format(self.__class__) ) def do(self, x, data_df=None): """Method that implements the do-operator. Given a value x for the treatment, returns the expected value of the outcome when the treatment is intervened to a value x. :param x: Value of the treatment :param data_df: Data on which the do-operator is to be applied. :returns: Value of the outcome when treatment is intervened/set to x. """ est = self._do(x, data_df) return est def construct_symbolic_estimator(self, estimand): raise NotImplementedError(("Symbolic estimator string is ").format(self.__class__)) def _generate_bootstrap_estimates(self, num_bootstrap_simulations, sample_size_fraction): """Helper function to generate causal estimates over bootstrapped samples. :param num_bootstrap_simulations: Number of simulations for the bootstrap method. :param sample_size_fraction: Fraction of the dataset to be resampled. :returns: A collections.namedtuple containing a list of bootstrapped estimates and a dictionary containing parameters used for the bootstrap. """ # The array that stores the results of all estimations simulation_results = np.zeros(num_bootstrap_simulations) # Find the sample size the proportion with the population size sample_size = int(sample_size_fraction * len(self._data)) if sample_size > len(self._data): self.logger.warning("WARN: The sample size is greater than the data being sampled") self.logger.info("INFO: The sample size: {}".format(sample_size)) self.logger.info("INFO: The number of simulations: {}".format(num_bootstrap_simulations)) # Perform the set number of simulations for index in range(num_bootstrap_simulations): new_data = resample(self._data, n_samples=sample_size) new_estimator = type(self)( new_data, self._target_estimand, self._target_estimand.treatment_variable, self._target_estimand.outcome_variable, # names of treatment and outcome treatment_value=self._treatment_value, control_value=self._control_value, test_significance=False, evaluate_effect_strength=False, confidence_intervals=False, target_units=self._target_units, effect_modifiers=self._effect_modifier_names, **self.method_params, ) new_effect = new_estimator.estimate_effect() simulation_results[index] = new_effect.value estimates = CausalEstimator.BootstrapEstimates( simulation_results, {"num_simulations": num_bootstrap_simulations, "sample_size_fraction": sample_size_fraction}, ) return estimates def _estimate_confidence_intervals_with_bootstrap( self, estimate_value, confidence_level=None, num_simulations=None, sample_size_fraction=None ): """ Method to compute confidence interval using bootstrapped sampling. :param estimate_value: obtained estimate's value :param confidence_level: The level for which to compute CI (e.g., 95% confidence level translates to confidence_level=0.95) :param num_simulations: The number of simulations to be performed to get the bootstrap confidence intervals. :param sample_size_fraction: The fraction of the dataset to be resampled. :returns: confidence interval at the specified level. For more details on bootstrap or resampling statistics, refer to the following links: https://ocw.mit.edu/courses/mathematics/18-05-introduction-to-probability-and-statistics-spring-2014/readings/MIT18_05S14_Reading24.pdf https://projecteuclid.org/download/pdf_1/euclid.ss/1032280214 """ # Using class default parameters if not specified if num_simulations is None: num_simulations = self.num_simulations if sample_size_fraction is None: sample_size_fraction = self.sample_size_fraction # Checking if bootstrap_estimates are already computed if self._bootstrap_estimates is None: self._bootstrap_estimates = self._generate_bootstrap_estimates(num_simulations, sample_size_fraction) elif CausalEstimator.is_bootstrap_parameter_changed(self._bootstrap_estimates.params, locals()): # Checked if any parameter is changed from the previous std error estimate self._bootstrap_estimates = self._generate_bootstrap_estimates(num_simulations, sample_size_fraction) # Now use the data obtained from the simulations to get the value of the confidence estimates bootstrap_estimates = self._bootstrap_estimates.estimates # Get the variations of each bootstrap estimate and sort bootstrap_variations = [bootstrap_estimate - estimate_value for bootstrap_estimate in bootstrap_estimates] sorted_bootstrap_variations = np.sort(bootstrap_variations) # Now we take the (1- p)th and the (p)th variations, where p is the chosen confidence level upper_bound_index = int((1 - confidence_level) * len(sorted_bootstrap_variations)) lower_bound_index = int(confidence_level * len(sorted_bootstrap_variations)) # Get the lower and upper bounds by subtracting the variations from the estimate lower_bound = estimate_value - sorted_bootstrap_variations[lower_bound_index] upper_bound = estimate_value - sorted_bootstrap_variations[upper_bound_index] return lower_bound, upper_bound def _estimate_confidence_intervals(self, confidence_level=None, method=None, **kwargs): """ This method is to be overriden by the child classes, so that they can run a confidence interval estimation method suited to the specific causal estimator. """ raise NotImplementedError( ( "This method for estimating confidence intervals is " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG + " Meanwhile, you can try the bootstrap method (method='bootstrap') to estimate confidence intervals." ).format(self.__class__) ) def estimate_confidence_intervals(self, estimate_value, confidence_level=None, method=None, **kwargs): """Find the confidence intervals corresponding to any estimator By default, this is done with the help of bootstrapped confidence intervals but can be overridden if the specific estimator implements other methods of estimating confidence intervals. If the method provided is not bootstrap, this function calls the implementation of the specific estimator. :param estimate_value: obtained estimate's value :param method: Method for estimating confidence intervals. :param confidence_level: The confidence level of the confidence intervals of the estimate. :param kwargs: Other optional args to be passed to the CI method. :returns: The obtained confidence interval. """ if method is None: if self._confidence_intervals: method = self._confidence_intervals # this is either True or methodname else: method = "default" confidence_intervals = None if confidence_level is None: confidence_level = self.confidence_level if method == "default" or method is True: # user has not provided any method try: confidence_intervals = self._estimate_confidence_intervals(confidence_level, method=method, **kwargs) except NotImplementedError: confidence_intervals = self._estimate_confidence_intervals_with_bootstrap( estimate_value, confidence_level, **kwargs ) else: if method == "bootstrap": confidence_intervals = self._estimate_confidence_intervals_with_bootstrap( estimate_value, confidence_level, **kwargs ) else: confidence_intervals = self._estimate_confidence_intervals(confidence_level, method=method, **kwargs) return confidence_intervals def _estimate_std_error_with_bootstrap(self, num_simulations=None, sample_size_fraction=None): """Compute standard error using the bootstrap method. Standard error and confidence intervals use the same parameter num_simulations for the number of bootstrap simulations. :param num_simulations: Number of bootstrapped samples. :param sample_size_fraction: Fraction of data to be resampled. :returns: Standard error of the obtained estimate. """ # Use existing params, if new user defined params are not present if num_simulations is None: num_simulations = self.num_simulations if sample_size_fraction is None: sample_size_fraction = self.sample_size_fraction # Checking if bootstrap_estimates are already computed if self._bootstrap_estimates is None: self._bootstrap_estimates = self._generate_bootstrap_estimates(num_simulations, sample_size_fraction) elif CausalEstimator.is_bootstrap_parameter_changed(self._bootstrap_estimates.params, locals()): # Check if any parameter is changed from the previous std error estimate self._bootstrap_estimates = self._generate_bootstrap_estimates(num_simulations, sample_size_fraction) std_error = np.std(self._bootstrap_estimates.estimates) return std_error def _estimate_std_error(self, method=None, **kwargs): """ This method is to be overriden by the child classes, so that they can run a standard error estimation method suited to the specific causal estimator. """ raise NotImplementedError( ( "This method for estimating standard errors is " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG + " Meanwhile, you can try the bootstrap method (method='bootstrap') to estimate standard errors." ).format(self.__class__) ) def estimate_std_error(self, method=None, **kwargs): """Compute standard error of an obtained causal estimate. :param method: Method for computing the standard error. :param kwargs: Other optional parameters to be passed to the estimating method. :returns: Standard error of the causal estimate. """ if method is None: if self._confidence_intervals: method = self._confidence_intervals else: method = "default" std_error = None if method == "default" or method is True: # user has not provided any method try: std_error = self._estimate_std_error(method, **kwargs) except NotImplementedError: std_error = self._estimate_std_error_with_bootstrap(**kwargs) else: if method == "bootstrap": std_error = self._estimate_std_error_with_bootstrap(**kwargs) else: std_error = self._estimate_std_error(method, **kwargs) return std_error def _test_significance_with_bootstrap(self, estimate_value, num_null_simulations=None): """Test statistical significance of an estimate using the bootstrap method. :param estimate_value: Obtained estimate's value :param num_null_simulations: Number of simulations for the null hypothesis :returns: p-value of the statistical significance test. """ # Use existing params, if new user defined params are not present if num_null_simulations is None: num_null_simulations = self.num_null_simulations do_retest = self._bootstrap_null_estimates is None or CausalEstimator.is_bootstrap_parameter_changed( self._bootstrap_null_estimates.params, locals() ) if do_retest: null_estimates = np.zeros(num_null_simulations) for i in range(num_null_simulations): new_outcome = np.random.permutation(self._outcome) new_data = self._data.assign(dummy_outcome=new_outcome) # self._outcome = self._data["dummy_outcome"] new_estimator = type(self)( new_data, self._target_estimand, self._target_estimand.treatment_variable, ("dummy_outcome",), test_significance=False, evaluate_effect_strength=False, confidence_intervals=False, target_units=self._target_units, effect_modifiers=self._effect_modifier_names, **self.method_params, ) new_effect = new_estimator.estimate_effect() null_estimates[i] = new_effect.value self._bootstrap_null_estimates = CausalEstimator.BootstrapEstimates( null_estimates, {"num_null_simulations": num_null_simulations, "sample_size_fraction": 1} ) # Processing the null hypothesis estimates sorted_null_estimates = np.sort(self._bootstrap_null_estimates.estimates) self.logger.debug("Null estimates: {0}".format(sorted_null_estimates)) median_estimate = sorted_null_estimates[int(num_null_simulations / 2)] # Doing a two-sided test if estimate_value > median_estimate: # Being conservative with the p-value reported estimate_index = np.searchsorted(sorted_null_estimates, estimate_value, side="left") p_value = 1 - (estimate_index / num_null_simulations) if estimate_value <= median_estimate: # Being conservative with the p-value reported estimate_index = np.searchsorted(sorted_null_estimates, estimate_value, side="right") p_value = estimate_index / num_null_simulations # If the estimate_index is 0, it depends on the number of simulations if p_value == 0: p_value = (0, 1 / len(sorted_null_estimates)) # a tuple determining the range. elif p_value == 1: p_value = (1 - 1 / len(sorted_null_estimates), 1) signif_dict = {"p_value": p_value} return signif_dict def _test_significance(self, estimate_value, method=None, **kwargs): """ This method is to be overriden by the child classes, so that they can run a significance test suited to the specific causal estimator. """ raise NotImplementedError( ( "This method for testing statistical significance is " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG + " Meanwhile, you can try the bootstrap method (method='bootstrap') to test statistical significance." ).format(self.__class__) ) def test_significance(self, estimate_value, method=None, **kwargs): """Test statistical significance of obtained estimate. By default, uses resampling to create a non-parametric significance test. A general procedure. Individual child estimators can implement different methods. If the method name is different from "bootstrap", this function calls the implementation of the child estimator. :param self: object instance of class Estimator :param estimate_value: obtained estimate's value :param method: Method for checking statistical significance :returns: p-value from the significance test """ if method is None: if self._significance_test: method = self._significance_test # this is either True or methodname else: method = "default" signif_dict = None if method == "default" or method is True: # user has not provided any method try: signif_dict = self._test_significance(estimate_value, method, **kwargs) except NotImplementedError: signif_dict = self._test_significance_with_bootstrap(estimate_value, **kwargs) else: if method == "bootstrap": signif_dict = self._test_significance_with_bootstrap(estimate_value, **kwargs) else: signif_dict = self._test_significance(estimate_value, method, **kwargs) return signif_dict def evaluate_effect_strength(self, estimate): fraction_effect_explained = self._evaluate_effect_strength(estimate, method="fraction-effect") # Need to test r-squared before supporting # effect_r_squared = self._evaluate_effect_strength(estimate, method="r-squared") strength_dict = { "fraction-effect": fraction_effect_explained # 'r-squared': effect_r_squared } return strength_dict def _evaluate_effect_strength(self, estimate, method="fraction-effect"): supported_methods = ["fraction-effect"] if method not in supported_methods: raise NotImplementedError("This method is not supported for evaluating effect strength") if method == "fraction-effect": naive_obs_estimate = self.estimate_effect_naive() self.logger.debug(estimate.value, naive_obs_estimate.value) fraction_effect_explained = estimate.value / naive_obs_estimate.value return fraction_effect_explained # elif method == "r-squared": # outcome_mean = np.mean(self._outcome) # total_variance = np.sum(np.square(self._outcome - outcome_mean)) # Assuming a linear model with one variable: the treatment # Currently only works for continuous y # causal_model = outcome_mean + estimate.value*self._treatment # squared_residual = np.sum(np.square(self._outcome - causal_model)) # r_squared = 1 - (squared_residual/total_variance) # return r_squared else: return None def update_input(self, treatment_value, control_value, target_units): self._control_value = control_value self._treatment_value = treatment_value self._target_units = target_units @staticmethod def is_bootstrap_parameter_changed(bootstrap_estimates_params, given_params): """Check whether parameters of the bootstrap have changed. This is an efficiency method that checks if fresh resampling of the bootstrap samples is required. Returns True if parameters have changed and resampling should be done again. :param bootstrap_estimates_params: A dictionary of parameters for the current bootstrap samples :param given_params: A dictionary of parameters passed by the user :returns: A binary flag denoting whether the parameters are different. """ is_any_parameter_changed = False for prm, val in bootstrap_estimates_params.items(): given_val = given_params.get(prm, None) if given_val is not None and given_val != val: is_any_parameter_changed = True break return is_any_parameter_changed def target_units_tostr(self): s = "" if type(self._target_units) is str: s += self._target_units elif callable(self._target_units): s += "Data subset defined by a function" elif isinstance(self._target_units, pd.DataFrame): s += "Data subset provided as a data frame" return s def signif_results_tostr(self, signif_results): s = "" pval = signif_results["p_value"] if type(pval) is tuple: s += "[{0}, {1}]".format(pval[0], pval[1]) else: s += "{0}".format(pval) return s class CausalEstimate: """Class for the estimate object that every causal estimator returns""" def __init__( self, estimate, target_estimand, realized_estimand_expr, control_value, treatment_value, conditional_estimates=None, **kwargs, ): self.value = estimate self.target_estimand = target_estimand self.realized_estimand_expr = realized_estimand_expr self.control_value = control_value self.treatment_value = treatment_value self.conditional_estimates = conditional_estimates self.params = kwargs if self.params is not None: for key, value in self.params.items(): setattr(self, key, value) self.effect_strength = None def add_estimator(self, estimator_instance): self.estimator = estimator_instance def add_effect_strength(self, strength_dict): self.effect_strength = strength_dict def add_params(self, **kwargs): self.params.update(kwargs) def get_confidence_intervals(self, confidence_level=None, method=None, **kwargs): """Get confidence intervals of the obtained estimate. By default, this is done with the help of bootstrapped confidence intervals but can be overridden if the specific estimator implements other methods of estimating confidence intervals. If the method provided is not bootstrap, this function calls the implementation of the specific estimator. :param method: Method for estimating confidence intervals. :param confidence_level: The confidence level of the confidence intervals of the estimate. :param kwargs: Other optional args to be passed to the CI method. :returns: The obtained confidence interval. """ confidence_intervals = self.estimator.estimate_confidence_intervals( estimate_value=self.value, confidence_level=confidence_level, method=method, **kwargs ) return confidence_intervals def get_standard_error(self, method=None, **kwargs): """Get standard error of the obtained estimate. By default, this is done with the help of bootstrapped standard errors but can be overridden if the specific estimator implements other methods of estimating standard error. If the method provided is not bootstrap, this function calls the implementation of the specific estimator. :param method: Method for computing the standard error. :param kwargs: Other optional parameters to be passed to the estimating method. :returns: Standard error of the causal estimate. """ std_error = self.estimator.estimate_std_error(method=method, **kwargs) return std_error def test_stat_significance(self, method=None, **kwargs): """Test statistical significance of the estimate obtained. By default, uses resampling to create a non-parametric significance test. Individual child estimators can implement different methods. If the method name is different from "bootstrap", this function calls the implementation of the child estimator. :param method: Method for checking statistical significance :param kwargs: Other optional parameters to be passed to the estimating method. :returns: p-value from the significance test """ signif_results = self.estimator.test_significance(self.value, method=method, **kwargs) return {"p_value": signif_results["p_value"]} def estimate_conditional_effects( self, effect_modifiers=None, num_quantiles=CausalEstimator.NUM_QUANTILES_TO_DISCRETIZE_CONT_COLS ): """Estimate treatment effect conditioned on given variables. If a numeric effect modifier is provided, it is discretized into quantile bins. If you would like a custom discretization, you can do so yourself: create a new column containing the discretized effect modifier and then include that column's name in the effect_modifier_names argument. :param effect_modifiers: Names of effect modifier variables over which the conditional effects will be estimated. If not provided, defaults to the effect modifiers specified during creation of the CausalEstimator object. :param num_quantiles: The number of quantiles into which a numeric effect modifier variable is discretized. Does not affect any categorical effect modifiers. :returns: A (multi-index) dataframe that provides separate effects for each value of the (discretized) effect modifiers. """ return self.estimator._estimate_conditional_effects( self.estimator._estimate_effect_fn, effect_modifiers, num_quantiles ) def interpret(self, method_name=None, **kwargs): """Interpret the causal estimate. :param method_name: Method used (string) or a list of methods. If None, then the default for the specific estimator is used. :param kwargs:: Optional parameters that are directly passed to the interpreter method. :returns: None """ if method_name is None: method_name = self.estimator.interpret_method method_name_arr = parse_state(method_name) for method in method_name_arr: interpreter = interpreters.get_class_object(method) interpreter(self, **kwargs).interpret() def __str__(self): s = "*** Causal Estimate ***\n" # No estimand was identified (identification failed) if self.target_estimand is None: return "Estimation failed! No relevant identified estimand available for this estimation method." s += "\n## Identified estimand\n{0}".format(self.target_estimand.__str__(only_target_estimand=True)) s += "\n## Realized estimand\n{0}".format(self.realized_estimand_expr) if hasattr(self, "estimator"): s += "\nTarget units: {0}\n".format(self.estimator.target_units_tostr()) s += "\n## Estimate\n" s += "Mean value: {0}\n".format(self.value) s += "" if hasattr(self, "cate_estimates"): s += "Effect estimates: {0}\n".format(self.cate_estimates) if hasattr(self, "estimator"): if self.estimator._significance_test: s += "p-value: {0}\n".format(self.estimator.signif_results_tostr(self.test_stat_significance())) if self.estimator._confidence_intervals: s += "{0}% confidence interval: {1}\n".format( 100 * self.estimator.confidence_level, self.get_confidence_intervals() ) if self.conditional_estimates is not None: s += "### Conditional Estimates\n" s += str(self.conditional_estimates) if self.effect_strength is not None: s += "\n## Effect Strength\n" s += "Change in outcome attributable to treatment: {}\n".format(self.effect_strength["fraction-effect"]) # s += "Variance in outcome explained by treatment: {}\n".format(self.effect_strength["r-squared"]) return s class RealizedEstimand(object): def __init__(self, identified_estimand, estimator_name): self.treatment_variable = identified_estimand.treatment_variable self.outcome_variable = identified_estimand.outcome_variable self.backdoor_variables = identified_estimand.get_backdoor_variables() self.instrumental_variables = identified_estimand.instrumental_variables self.estimand_type = identified_estimand.estimand_type self.estimand_expression = None self.assumptions = None self.estimator_name = estimator_name def update_assumptions(self, estimator_assumptions): self.assumptions = estimator_assumptions def update_estimand_expression(self, estimand_expression): self.estimand_expression = estimand_expression def __str__(self): s = "Realized estimand: {0}\n".format(self.estimator_name) s += "Realized estimand type: {0}\n".format(self.estimand_type) s += "Estimand expression:\n{0}\n".format(sp.pretty(self.estimand_expression)) j = 1 for ass_name, ass_str in self.assumptions.items(): s += "Estimand assumption {0}, {1}: {2}\n".format(j, ass_name, ass_str) j += 1 return s

import logging from collections import namedtuple from typing import Dict, List, Optional, Union import numpy as np import pandas as pd import sympy as sp from sklearn.utils import resample import dowhy.interpreters as interpreters from dowhy import causal_estimators from dowhy.causal_graph import CausalGraph from dowhy.causal_identifier.identified_estimand import IdentifiedEstimand from dowhy.utils.api import parse_state logger = logging.getLogger(__name__) class CausalEstimator: """Base class for an estimator of causal effect. Subclasses implement different estimation methods. All estimation methods are in the package "dowhy.causal_estimators" """ # The default number of simulations for statistical testing DEFAULT_NUMBER_OF_SIMULATIONS_STAT_TEST = 1000 # The default number of simulations to obtain confidence intervals DEFAULT_NUMBER_OF_SIMULATIONS_CI = 100 # The portion of the total size that should be taken each time to find the confidence intervals # 1 is the recommended value # https://ocw.mit.edu/courses/mathematics/18-05-introduction-to-probability-and-statistics-spring-2014/readings/MIT18_05S14_Reading24.pdf # https://projecteuclid.org/download/pdf_1/euclid.ss/1032280214 DEFAULT_SAMPLE_SIZE_FRACTION = 1 # The default Confidence Level DEFAULT_CONFIDENCE_LEVEL = 0.95 # Number of quantiles to discretize continuous columns, for applying groupby NUM_QUANTILES_TO_DISCRETIZE_CONT_COLS = 5 # Prefix to add to temporary categorical variables created after discretization TEMP_CAT_COLUMN_PREFIX = "__categorical__" DEFAULT_NOTIMPLEMENTEDERROR_MSG = "not yet implemented for {0}. If you would this to be implemented in the next version, please raise an issue at https://github.com/microsoft/dowhy/issues" BootstrapEstimates = namedtuple("BootstrapEstimates", ["estimates", "params"]) DEFAULT_INTERPRET_METHOD = ["textual_effect_interpreter"] # std args to be removed from locals() before being passed to args_dict _STD_INIT_ARGS = ("self", "__class__", "args", "kwargs") def __init__( self, data, identified_estimand, treatment, outcome, control_value=0, treatment_value=1, test_significance=False, evaluate_effect_strength=False, confidence_intervals=False, target_units=None, effect_modifiers=None, num_null_simulations=DEFAULT_NUMBER_OF_SIMULATIONS_STAT_TEST, num_simulations=DEFAULT_NUMBER_OF_SIMULATIONS_CI, sample_size_fraction=DEFAULT_SAMPLE_SIZE_FRACTION, confidence_level=DEFAULT_CONFIDENCE_LEVEL, need_conditional_estimates="auto", num_quantiles_to_discretize_cont_cols=NUM_QUANTILES_TO_DISCRETIZE_CONT_COLS, **kwargs, ): """Initializes an estimator with data and names of relevant variables. This method is called from the constructors of its child classes. :param data: data frame containing the data :param identified_estimand: probability expression representing the target identified estimand to estimate. :param treatment: name of the treatment variable :param outcome: name of the outcome variable :param control_value: Value of the treatment in the control group, for effect estimation. If treatment is multi-variate, this can be a list. :param treatment_value: Value of the treatment in the treated group, for effect estimation. If treatment is multi-variate, this can be a list. :param test_significance: Binary flag or a string indicating whether to test significance and by which method. All estimators support test_significance="bootstrap" that estimates a p-value for the obtained estimate using the bootstrap method. Individual estimators can override this to support custom testing methods. The bootstrap method supports an optional parameter, num_null_simulations. If False, no testing is done. If True, significance of the estimate is tested using the custom method if available, otherwise by bootstrap. :param evaluate_effect_strength: (Experimental) whether to evaluate the strength of effect :param confidence_intervals: Binary flag or a string indicating whether the confidence intervals should be computed and which method should be used. All methods support estimation of confidence intervals using the bootstrap method by using the parameter confidence_intervals="bootstrap". The bootstrap method takes in two arguments (num_simulations and sample_size_fraction) that can be optionally specified in the params dictionary. Estimators may also override this to implement their own confidence interval method. If this parameter is False, no confidence intervals are computed. If True, confidence intervals are computed by the estimator's specific method if available, otherwise through bootstrap. :param target_units: The units for which the treatment effect should be estimated. This can be a string for common specifications of target units (namely, "ate", "att" and "atc"). It can also be a lambda function that can be used as an index for the data (pandas DataFrame). Alternatively, it can be a new DataFrame that contains values of the effect_modifiers and effect will be estimated only for this new data. :param effect_modifiers: Variables on which to compute separate effects, or return a heterogeneous effect function. Not all methods support this currently. :param num_null_simulations: The number of simulations for testing the statistical significance of the estimator :param num_simulations: The number of simulations for finding the confidence interval (and/or standard error) for a estimate :param sample_size_fraction: The size of the sample for the bootstrap estimator :param confidence_level: The confidence level of the confidence interval estimate :param need_conditional_estimates: Boolean flag indicating whether conditional estimates should be computed. Defaults to True if there are effect modifiers in the graph :param num_quantiles_to_discretize_cont_cols: The number of quantiles into which a numeric effect modifier is split, to enable estimation of conditional treatment effect over it. :param kwargs: (optional) Additional estimator-specific parameters :returns: an instance of the estimator class. """ self._data = data self._target_estimand = identified_estimand # Currently estimation methods only support univariate treatment and outcome self._treatment_name = treatment self._outcome_name = outcome[0] # assuming one-dimensional outcome self._control_value = control_value self._treatment_value = treatment_value self._significance_test = test_significance self._effect_strength_eval = evaluate_effect_strength self._target_units = target_units self._effect_modifier_names = effect_modifiers self._confidence_intervals = confidence_intervals self._bootstrap_estimates = None # for confidence intervals and std error self._bootstrap_null_estimates = None # for significance test self._effect_modifiers = None self.method_params = kwargs # Setting the default interpret method self.interpret_method = CausalEstimator.DEFAULT_INTERPRET_METHOD self.logger = logging.getLogger(__name__) # Setting treatment and outcome values if self._data is not None: self._treatment = self._data[self._treatment_name] self._outcome = self._data[self._outcome_name] if self._effect_modifier_names: # only add the observed nodes self._effect_modifier_names = [ cname for cname in self._effect_modifier_names if cname in self._data.columns ] if len(self._effect_modifier_names) > 0: self._effect_modifiers = self._data[self._effect_modifier_names] self._effect_modifiers = pd.get_dummies(self._effect_modifiers, drop_first=True) self.logger.debug("Effect modifiers: " + ",".join(self._effect_modifier_names)) else: self._effect_modifier_names = None # Check if some parameters were set, otherwise set to default values self.num_null_simulations = num_null_simulations self.num_simulations = num_simulations self.sample_size_fraction = sample_size_fraction self.confidence_level = confidence_level self.num_quantiles_to_discretize_cont_cols = num_quantiles_to_discretize_cont_cols # Estimate conditional estimates by default self.need_conditional_estimates = ( need_conditional_estimates if need_conditional_estimates != "auto" else bool(self._effect_modifier_names) ) @staticmethod def get_estimator_object(new_data, identified_estimand, estimate): """Create a new estimator of the same type as the one passed in the estimate argument. Creates a new object with new_data and the identified_estimand :param new_data: np.ndarray, pd.Series, pd.DataFrame The newly assigned data on which the estimator should run :param identified_estimand: IdentifiedEstimand An instance of the identified estimand class that provides the information with respect to which causal pathways are employed when the treatment effects the outcome :param estimate: CausalEstimate It is an already existing estimate whose properties we wish to replicate :returns: An instance of the same estimator class that had generated the given estimate. """ estimator_class = estimate.params["estimator_class"] new_estimator = estimator_class( new_data, identified_estimand, identified_estimand.treatment_variable, identified_estimand.outcome_variable, # names of treatment and outcome control_value=estimate.control_value, treatment_value=estimate.treatment_value, test_significance=False, evaluate_effect_strength=False, confidence_intervals=estimate.params["confidence_intervals"], target_units=estimate.params["target_units"], effect_modifiers=estimate.params["effect_modifiers"], **estimate.params["method_params"] if estimate.params["method_params"] is not None else {}, ) return new_estimator def _estimate_effect(self): """This method is to be overriden by the child classes, so that they can run the estimation technique of their choice""" raise NotImplementedError( ("Main estimation method is " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG).format(self.__class__) ) def estimate_effect(self): """Base estimation method that calls the estimate_effect method of its calling subclass. Can optionally also test significance and estimate effect strength for any returned estimate. :param self: object instance of class Estimator :returns: A CausalEstimate instance that contains point estimates of average and conditional effects. Based on the parameters provided, it optionally includes confidence intervals, standard errors,statistical significance and other statistical parameters. """ est = self._estimate_effect() est.add_estimator(self) if self._significance_test: self.test_significance(est.value, method=self._significance_test) if self._confidence_intervals: self.estimate_confidence_intervals( est.value, confidence_level=self.confidence_level, method=self._confidence_intervals ) if self._effect_strength_eval: effect_strength_dict = self.evaluate_effect_strength(est) est.add_effect_strength(effect_strength_dict) return est def estimate_effect_naive(self): # TODO Only works for binary treatment df_withtreatment = self._data.loc[self._data[self._treatment_name] == 1] df_notreatment = self._data.loc[self._data[self._treatment_name] == 0] est = np.mean(df_withtreatment[self._outcome_name]) - np.mean(df_notreatment[self._outcome_name]) return CausalEstimate(est, None, None, control_value=0, treatment_value=1) def _estimate_effect_fn(self, data_df): """Function used in conditional effect estimation. This function is to be overridden by each child estimator. The overridden function should take in a dataframe as input and return the estimate for that data. """ raise NotImplementedError( ("Conditional treatment effects are " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG).format( self.__class__ ) ) def _estimate_conditional_effects(self, estimate_effect_fn, effect_modifier_names=None, num_quantiles=None): """Estimate conditional treatment effects. Common method for all estimators that utilizes a specific estimate_effect_fn implemented by each child estimator. If a numeric effect modifier is provided, it is discretized into quantile bins. If you would like a custom discretization, you can do so yourself: create a new column containing the discretized effect modifier and then include that column's name in the effect_modifier_names argument. :param estimate_effect_fn: Function that has a single parameter (a data frame) and returns the treatment effect estimate on that data. :param effect_modifier_names: Names of effect modifier variables over which the conditional effects will be estimated. If not provided, defaults to the effect modifiers specified during creation of the CausalEstimator object. :param num_quantiles: The number of quantiles into which a numeric effect modifier variable is discretized. Does not affect any categorical effect modifiers. :returns: A (multi-index) dataframe that provides separate effects for each value of the (discretized) effect modifiers. """ # Defaulting to class default values if parameters are not provided if effect_modifier_names is None: effect_modifier_names = self._effect_modifier_names if num_quantiles is None: num_quantiles = self.num_quantiles_to_discretize_cont_cols # Checking that there is at least one effect modifier if not effect_modifier_names: raise ValueError("At least one effect modifier should be specified to compute conditional effects.") # Making sure that effect_modifier_names is a list effect_modifier_names = parse_state(effect_modifier_names) if not all(em in self._effect_modifier_names for em in effect_modifier_names): self.logger.warn( "At least one of the provided effect modifiers was not included while fitting the estimator. You may get incorrect results. To resolve, fit the estimator again by providing the updated effect modifiers in estimate_effect()." ) # Making a copy since we are going to be changing effect modifier names effect_modifier_names = effect_modifier_names.copy() prefix = CausalEstimator.TEMP_CAT_COLUMN_PREFIX # For every numeric effect modifier, adding a temp categorical column for i in range(len(effect_modifier_names)): em = effect_modifier_names[i] if pd.api.types.is_numeric_dtype(self._data[em].dtypes): self._data[prefix + str(em)] = pd.qcut(self._data[em], num_quantiles, duplicates="drop") effect_modifier_names[i] = prefix + str(em) # Grouping by effect modifiers and computing effect separately by_effect_mods = self._data.groupby(effect_modifier_names) cond_est_fn = lambda x: self._do(self._treatment_value, x) - self._do(self._control_value, x) conditional_estimates = by_effect_mods.apply(estimate_effect_fn) # Deleting the temporary categorical columns for em in effect_modifier_names: if em.startswith(prefix): self._data.pop(em) return conditional_estimates def _do(self, x, data_df=None): raise NotImplementedError( ("Do-operator is " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG).format(self.__class__) ) def do(self, x, data_df=None): """Method that implements the do-operator. Given a value x for the treatment, returns the expected value of the outcome when the treatment is intervened to a value x. :param x: Value of the treatment :param data_df: Data on which the do-operator is to be applied. :returns: Value of the outcome when treatment is intervened/set to x. """ est = self._do(x, data_df) return est def construct_symbolic_estimator(self, estimand): raise NotImplementedError(("Symbolic estimator string is ").format(self.__class__)) def _generate_bootstrap_estimates(self, num_bootstrap_simulations, sample_size_fraction): """Helper function to generate causal estimates over bootstrapped samples. :param num_bootstrap_simulations: Number of simulations for the bootstrap method. :param sample_size_fraction: Fraction of the dataset to be resampled. :returns: A collections.namedtuple containing a list of bootstrapped estimates and a dictionary containing parameters used for the bootstrap. """ # The array that stores the results of all estimations simulation_results = np.zeros(num_bootstrap_simulations) # Find the sample size the proportion with the population size sample_size = int(sample_size_fraction * len(self._data)) if sample_size > len(self._data): self.logger.warning("WARN: The sample size is greater than the data being sampled") self.logger.info("INFO: The sample size: {}".format(sample_size)) self.logger.info("INFO: The number of simulations: {}".format(num_bootstrap_simulations)) # Perform the set number of simulations for index in range(num_bootstrap_simulations): new_data = resample(self._data, n_samples=sample_size) new_estimator = type(self)( new_data, self._target_estimand, self._target_estimand.treatment_variable, self._target_estimand.outcome_variable, # names of treatment and outcome treatment_value=self._treatment_value, control_value=self._control_value, test_significance=False, evaluate_effect_strength=False, confidence_intervals=False, target_units=self._target_units, effect_modifiers=self._effect_modifier_names, **self.method_params, ) new_effect = new_estimator.estimate_effect() simulation_results[index] = new_effect.value estimates = CausalEstimator.BootstrapEstimates( simulation_results, {"num_simulations": num_bootstrap_simulations, "sample_size_fraction": sample_size_fraction}, ) return estimates def _estimate_confidence_intervals_with_bootstrap( self, estimate_value, confidence_level=None, num_simulations=None, sample_size_fraction=None ): """ Method to compute confidence interval using bootstrapped sampling. :param estimate_value: obtained estimate's value :param confidence_level: The level for which to compute CI (e.g., 95% confidence level translates to confidence_level=0.95) :param num_simulations: The number of simulations to be performed to get the bootstrap confidence intervals. :param sample_size_fraction: The fraction of the dataset to be resampled. :returns: confidence interval at the specified level. For more details on bootstrap or resampling statistics, refer to the following links: https://ocw.mit.edu/courses/mathematics/18-05-introduction-to-probability-and-statistics-spring-2014/readings/MIT18_05S14_Reading24.pdf https://projecteuclid.org/download/pdf_1/euclid.ss/1032280214 """ # Using class default parameters if not specified if num_simulations is None: num_simulations = self.num_simulations if sample_size_fraction is None: sample_size_fraction = self.sample_size_fraction # Checking if bootstrap_estimates are already computed if self._bootstrap_estimates is None: self._bootstrap_estimates = self._generate_bootstrap_estimates(num_simulations, sample_size_fraction) elif CausalEstimator.is_bootstrap_parameter_changed(self._bootstrap_estimates.params, locals()): # Checked if any parameter is changed from the previous std error estimate self._bootstrap_estimates = self._generate_bootstrap_estimates(num_simulations, sample_size_fraction) # Now use the data obtained from the simulations to get the value of the confidence estimates bootstrap_estimates = self._bootstrap_estimates.estimates # Get the variations of each bootstrap estimate and sort bootstrap_variations = [bootstrap_estimate - estimate_value for bootstrap_estimate in bootstrap_estimates] sorted_bootstrap_variations = np.sort(bootstrap_variations) # Now we take the (1- p)th and the (p)th variations, where p is the chosen confidence level upper_bound_index = int((1 - confidence_level) * len(sorted_bootstrap_variations)) lower_bound_index = int(confidence_level * len(sorted_bootstrap_variations)) # Get the lower and upper bounds by subtracting the variations from the estimate lower_bound = estimate_value - sorted_bootstrap_variations[lower_bound_index] upper_bound = estimate_value - sorted_bootstrap_variations[upper_bound_index] return lower_bound, upper_bound def _estimate_confidence_intervals(self, confidence_level=None, method=None, **kwargs): """ This method is to be overriden by the child classes, so that they can run a confidence interval estimation method suited to the specific causal estimator. """ raise NotImplementedError( ( "This method for estimating confidence intervals is " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG + " Meanwhile, you can try the bootstrap method (method='bootstrap') to estimate confidence intervals." ).format(self.__class__) ) def estimate_confidence_intervals(self, estimate_value, confidence_level=None, method=None, **kwargs): """Find the confidence intervals corresponding to any estimator By default, this is done with the help of bootstrapped confidence intervals but can be overridden if the specific estimator implements other methods of estimating confidence intervals. If the method provided is not bootstrap, this function calls the implementation of the specific estimator. :param estimate_value: obtained estimate's value :param method: Method for estimating confidence intervals. :param confidence_level: The confidence level of the confidence intervals of the estimate. :param kwargs: Other optional args to be passed to the CI method. :returns: The obtained confidence interval. """ if method is None: if self._confidence_intervals: method = self._confidence_intervals # this is either True or methodname else: method = "default" confidence_intervals = None if confidence_level is None: confidence_level = self.confidence_level if method == "default" or method is True: # user has not provided any method try: confidence_intervals = self._estimate_confidence_intervals(confidence_level, method=method, **kwargs) except NotImplementedError: confidence_intervals = self._estimate_confidence_intervals_with_bootstrap( estimate_value, confidence_level, **kwargs ) else: if method == "bootstrap": confidence_intervals = self._estimate_confidence_intervals_with_bootstrap( estimate_value, confidence_level, **kwargs ) else: confidence_intervals = self._estimate_confidence_intervals(confidence_level, method=method, **kwargs) return confidence_intervals def _estimate_std_error_with_bootstrap(self, num_simulations=None, sample_size_fraction=None): """Compute standard error using the bootstrap method. Standard error and confidence intervals use the same parameter num_simulations for the number of bootstrap simulations. :param num_simulations: Number of bootstrapped samples. :param sample_size_fraction: Fraction of data to be resampled. :returns: Standard error of the obtained estimate. """ # Use existing params, if new user defined params are not present if num_simulations is None: num_simulations = self.num_simulations if sample_size_fraction is None: sample_size_fraction = self.sample_size_fraction # Checking if bootstrap_estimates are already computed if self._bootstrap_estimates is None: self._bootstrap_estimates = self._generate_bootstrap_estimates(num_simulations, sample_size_fraction) elif CausalEstimator.is_bootstrap_parameter_changed(self._bootstrap_estimates.params, locals()): # Check if any parameter is changed from the previous std error estimate self._bootstrap_estimates = self._generate_bootstrap_estimates(num_simulations, sample_size_fraction) std_error = np.std(self._bootstrap_estimates.estimates) return std_error def _estimate_std_error(self, method=None, **kwargs): """ This method is to be overriden by the child classes, so that they can run a standard error estimation method suited to the specific causal estimator. """ raise NotImplementedError( ( "This method for estimating standard errors is " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG + " Meanwhile, you can try the bootstrap method (method='bootstrap') to estimate standard errors." ).format(self.__class__) ) def estimate_std_error(self, method=None, **kwargs): """Compute standard error of an obtained causal estimate. :param method: Method for computing the standard error. :param kwargs: Other optional parameters to be passed to the estimating method. :returns: Standard error of the causal estimate. """ if method is None: if self._confidence_intervals: method = self._confidence_intervals else: method = "default" std_error = None if method == "default" or method is True: # user has not provided any method try: std_error = self._estimate_std_error(method, **kwargs) except NotImplementedError: std_error = self._estimate_std_error_with_bootstrap(**kwargs) else: if method == "bootstrap": std_error = self._estimate_std_error_with_bootstrap(**kwargs) else: std_error = self._estimate_std_error(method, **kwargs) return std_error def _test_significance_with_bootstrap(self, estimate_value, num_null_simulations=None): """Test statistical significance of an estimate using the bootstrap method. :param estimate_value: Obtained estimate's value :param num_null_simulations: Number of simulations for the null hypothesis :returns: p-value of the statistical significance test. """ # Use existing params, if new user defined params are not present if num_null_simulations is None: num_null_simulations = self.num_null_simulations do_retest = self._bootstrap_null_estimates is None or CausalEstimator.is_bootstrap_parameter_changed( self._bootstrap_null_estimates.params, locals() ) if do_retest: null_estimates = np.zeros(num_null_simulations) for i in range(num_null_simulations): new_outcome = np.random.permutation(self._outcome) new_data = self._data.assign(dummy_outcome=new_outcome) # self._outcome = self._data["dummy_outcome"] new_estimator = type(self)( new_data, self._target_estimand, self._target_estimand.treatment_variable, ("dummy_outcome",), test_significance=False, evaluate_effect_strength=False, confidence_intervals=False, target_units=self._target_units, effect_modifiers=self._effect_modifier_names, **self.method_params, ) new_effect = new_estimator.estimate_effect() null_estimates[i] = new_effect.value self._bootstrap_null_estimates = CausalEstimator.BootstrapEstimates( null_estimates, {"num_null_simulations": num_null_simulations, "sample_size_fraction": 1} ) # Processing the null hypothesis estimates sorted_null_estimates = np.sort(self._bootstrap_null_estimates.estimates) self.logger.debug("Null estimates: {0}".format(sorted_null_estimates)) median_estimate = sorted_null_estimates[int(num_null_simulations / 2)] # Doing a two-sided test if estimate_value > median_estimate: # Being conservative with the p-value reported estimate_index = np.searchsorted(sorted_null_estimates, estimate_value, side="left") p_value = 1 - (estimate_index / num_null_simulations) if estimate_value <= median_estimate: # Being conservative with the p-value reported estimate_index = np.searchsorted(sorted_null_estimates, estimate_value, side="right") p_value = estimate_index / num_null_simulations # If the estimate_index is 0, it depends on the number of simulations if p_value == 0: p_value = (0, 1 / len(sorted_null_estimates)) # a tuple determining the range. elif p_value == 1: p_value = (1 - 1 / len(sorted_null_estimates), 1) signif_dict = {"p_value": p_value} return signif_dict def _test_significance(self, estimate_value, method=None, **kwargs): """ This method is to be overriden by the child classes, so that they can run a significance test suited to the specific causal estimator. """ raise NotImplementedError( ( "This method for testing statistical significance is " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG + " Meanwhile, you can try the bootstrap method (method='bootstrap') to test statistical significance." ).format(self.__class__) ) def test_significance(self, estimate_value, method=None, **kwargs): """Test statistical significance of obtained estimate. By default, uses resampling to create a non-parametric significance test. A general procedure. Individual child estimators can implement different methods. If the method name is different from "bootstrap", this function calls the implementation of the child estimator. :param self: object instance of class Estimator :param estimate_value: obtained estimate's value :param method: Method for checking statistical significance :returns: p-value from the significance test """ if method is None: if self._significance_test: method = self._significance_test # this is either True or methodname else: method = "default" signif_dict = None if method == "default" or method is True: # user has not provided any method try: signif_dict = self._test_significance(estimate_value, method, **kwargs) except NotImplementedError: signif_dict = self._test_significance_with_bootstrap(estimate_value, **kwargs) else: if method == "bootstrap": signif_dict = self._test_significance_with_bootstrap(estimate_value, **kwargs) else: signif_dict = self._test_significance(estimate_value, method, **kwargs) return signif_dict def evaluate_effect_strength(self, estimate): fraction_effect_explained = self._evaluate_effect_strength(estimate, method="fraction-effect") # Need to test r-squared before supporting # effect_r_squared = self._evaluate_effect_strength(estimate, method="r-squared") strength_dict = { "fraction-effect": fraction_effect_explained # 'r-squared': effect_r_squared } return strength_dict def _evaluate_effect_strength(self, estimate, method="fraction-effect"): supported_methods = ["fraction-effect"] if method not in supported_methods: raise NotImplementedError("This method is not supported for evaluating effect strength") if method == "fraction-effect": naive_obs_estimate = self.estimate_effect_naive() self.logger.debug(estimate.value, naive_obs_estimate.value) fraction_effect_explained = estimate.value / naive_obs_estimate.value return fraction_effect_explained # elif method == "r-squared": # outcome_mean = np.mean(self._outcome) # total_variance = np.sum(np.square(self._outcome - outcome_mean)) # Assuming a linear model with one variable: the treatment # Currently only works for continuous y # causal_model = outcome_mean + estimate.value*self._treatment # squared_residual = np.sum(np.square(self._outcome - causal_model)) # r_squared = 1 - (squared_residual/total_variance) # return r_squared else: return None def update_input(self, treatment_value, control_value, target_units): self._control_value = control_value self._treatment_value = treatment_value self._target_units = target_units @staticmethod def is_bootstrap_parameter_changed(bootstrap_estimates_params, given_params): """Check whether parameters of the bootstrap have changed. This is an efficiency method that checks if fresh resampling of the bootstrap samples is required. Returns True if parameters have changed and resampling should be done again. :param bootstrap_estimates_params: A dictionary of parameters for the current bootstrap samples :param given_params: A dictionary of parameters passed by the user :returns: A binary flag denoting whether the parameters are different. """ is_any_parameter_changed = False for prm, val in bootstrap_estimates_params.items(): given_val = given_params.get(prm, None) if given_val is not None and given_val != val: is_any_parameter_changed = True break return is_any_parameter_changed def target_units_tostr(self): s = "" if type(self._target_units) is str: s += self._target_units elif callable(self._target_units): s += "Data subset defined by a function" elif isinstance(self._target_units, pd.DataFrame): s += "Data subset provided as a data frame" return s def signif_results_tostr(self, signif_results): s = "" pval = signif_results["p_value"] if type(pval) is tuple: s += "[{0}, {1}]".format(pval[0], pval[1]) else: s += "{0}".format(pval) return s def estimate_effect( treatment: Union[str, List[str]], outcome: Union[str, List[str]], identified_estimand: IdentifiedEstimand, identifier_name: str, method: CausalEstimator, control_value: int = 0, treatment_value: int = 1, test_significance: Optional[bool] = None, evaluate_effect_strength: bool = False, confidence_intervals: bool = False, target_units: str = "ate", effect_modifiers: List[str] = [], fit_estimator: bool = True, method_params: Optional[Dict] = None, ): """Estimate the identified causal effect. Currently requires an explicit method name to be specified. Method names follow the convention of identification method followed by the specific estimation method: "[backdoor/iv].estimation_method_name". Following methods are supported. * Propensity Score Matching: "backdoor.propensity_score_matching" * Propensity Score Stratification: "backdoor.propensity_score_stratification" * Propensity Score-based Inverse Weighting: "backdoor.propensity_score_weighting" * Linear Regression: "backdoor.linear_regression" * Generalized Linear Models (e.g., logistic regression): "backdoor.generalized_linear_model" * Instrumental Variables: "iv.instrumental_variable" * Regression Discontinuity: "iv.regression_discontinuity" In addition, you can directly call any of the EconML estimation methods. The convention is "backdoor.econml.path-to-estimator-class". For example, for the double machine learning estimator ("DML" class) that is located inside "dml" module of EconML, you can use the method name, "backdoor.econml.dml.DML". CausalML estimators can also be called. See `this demo notebook <https://py-why.github.io/dowhy/example_notebooks/dowhy-conditional-treatment-effects.html>`_. :param treatment: Name of the treatment :param outcome: Name of the outcome :param identified_estimand: a probability expression that represents the effect to be estimated. Output of CausalModel.identify_effect method :param method_name: name of the estimation method to be used. :param control_value: Value of the treatment in the control group, for effect estimation. If treatment is multi-variate, this can be a list. :param treatment_value: Value of the treatment in the treated group, for effect estimation. If treatment is multi-variate, this can be a list. :param test_significance: Binary flag on whether to additionally do a statistical signficance test for the estimate. :param evaluate_effect_strength: (Experimental) Binary flag on whether to estimate the relative strength of the treatment's effect. This measure can be used to compare different treatments for the same outcome (by running this method with different treatments sequentially). :param confidence_intervals: (Experimental) Binary flag indicating whether confidence intervals should be computed. :param target_units: (Experimental) The units for which the treatment effect should be estimated. This can be of three types. (1) a string for common specifications of target units (namely, "ate", "att" and "atc"), (2) a lambda function that can be used as an index for the data (pandas DataFrame), or (3) a new DataFrame that contains values of the effect_modifiers and effect will be estimated only for this new data. :param effect_modifiers: Names of effect modifier variables can be (optionally) specified here too, since they do not affect identification. If None, the effect_modifiers from the CausalModel are used. :param fit_estimator: Boolean flag on whether to fit the estimator. Setting it to False is useful to estimate the effect on new data using a previously fitted estimator. :param method_params: Dictionary containing any method-specific parameters. These are passed directly to the estimating method. See the docs for each estimation method for allowed method-specific params. :returns: An instance of the CausalEstimate class, containing the causal effect estimate and other method-dependent information """ treatment = parse_state(treatment) outcome = parse_state(outcome) causal_estimator_class = method.__class__ identified_estimand.set_identifier_method(identifier_name) if identified_estimand.no_directed_path: logger.warning("No directed path from {0} to {1}.".format(treatment, outcome)) return CausalEstimate( 0, identified_estimand, None, control_value=control_value, treatment_value=treatment_value ) # Check if estimator's target estimand is identified elif identified_estimand.estimands[identifier_name] is None: logger.error("No valid identified estimand available.") return CausalEstimate(None, None, None, control_value=control_value, treatment_value=treatment_value) method.update_input(treatment_value, control_value, target_units) estimate = method.estimate_effect() # Store parameters inside estimate object for refutation methods # TODO: This add_params needs to move to the estimator class # inside estimate_effect and estimate_conditional_effect estimate.add_params( estimand_type=identified_estimand.estimand_type, estimator_class=causal_estimator_class, test_significance=test_significance, evaluate_effect_strength=evaluate_effect_strength, confidence_intervals=confidence_intervals, target_units=target_units, effect_modifiers=effect_modifiers, method_params=method_params, ) return estimate class CausalEstimate: """Class for the estimate object that every causal estimator returns""" def __init__( self, estimate, target_estimand, realized_estimand_expr, control_value, treatment_value, conditional_estimates=None, **kwargs, ): self.value = estimate self.target_estimand = target_estimand self.realized_estimand_expr = realized_estimand_expr self.control_value = control_value self.treatment_value = treatment_value self.conditional_estimates = conditional_estimates self.params = kwargs if self.params is not None: for key, value in self.params.items(): setattr(self, key, value) self.effect_strength = None def add_estimator(self, estimator_instance): self.estimator = estimator_instance def add_effect_strength(self, strength_dict): self.effect_strength = strength_dict def add_params(self, **kwargs): self.params.update(kwargs) def get_confidence_intervals(self, confidence_level=None, method=None, **kwargs): """Get confidence intervals of the obtained estimate. By default, this is done with the help of bootstrapped confidence intervals but can be overridden if the specific estimator implements other methods of estimating confidence intervals. If the method provided is not bootstrap, this function calls the implementation of the specific estimator. :param method: Method for estimating confidence intervals. :param confidence_level: The confidence level of the confidence intervals of the estimate. :param kwargs: Other optional args to be passed to the CI method. :returns: The obtained confidence interval. """ confidence_intervals = self.estimator.estimate_confidence_intervals( estimate_value=self.value, confidence_level=confidence_level, method=method, **kwargs ) return confidence_intervals def get_standard_error(self, method=None, **kwargs): """Get standard error of the obtained estimate. By default, this is done with the help of bootstrapped standard errors but can be overridden if the specific estimator implements other methods of estimating standard error. If the method provided is not bootstrap, this function calls the implementation of the specific estimator. :param method: Method for computing the standard error. :param kwargs: Other optional parameters to be passed to the estimating method. :returns: Standard error of the causal estimate. """ std_error = self.estimator.estimate_std_error(method=method, **kwargs) return std_error def test_stat_significance(self, method=None, **kwargs): """Test statistical significance of the estimate obtained. By default, uses resampling to create a non-parametric significance test. Individual child estimators can implement different methods. If the method name is different from "bootstrap", this function calls the implementation of the child estimator. :param method: Method for checking statistical significance :param kwargs: Other optional parameters to be passed to the estimating method. :returns: p-value from the significance test """ signif_results = self.estimator.test_significance(self.value, method=method, **kwargs) return {"p_value": signif_results["p_value"]} def estimate_conditional_effects( self, effect_modifiers=None, num_quantiles=CausalEstimator.NUM_QUANTILES_TO_DISCRETIZE_CONT_COLS ): """Estimate treatment effect conditioned on given variables. If a numeric effect modifier is provided, it is discretized into quantile bins. If you would like a custom discretization, you can do so yourself: create a new column containing the discretized effect modifier and then include that column's name in the effect_modifier_names argument. :param effect_modifiers: Names of effect modifier variables over which the conditional effects will be estimated. If not provided, defaults to the effect modifiers specified during creation of the CausalEstimator object. :param num_quantiles: The number of quantiles into which a numeric effect modifier variable is discretized. Does not affect any categorical effect modifiers. :returns: A (multi-index) dataframe that provides separate effects for each value of the (discretized) effect modifiers. """ return self.estimator._estimate_conditional_effects( self.estimator._estimate_effect_fn, effect_modifiers, num_quantiles ) def interpret(self, method_name=None, **kwargs): """Interpret the causal estimate. :param method_name: Method used (string) or a list of methods. If None, then the default for the specific estimator is used. :param kwargs:: Optional parameters that are directly passed to the interpreter method. :returns: None """ if method_name is None: method_name = self.estimator.interpret_method method_name_arr = parse_state(method_name) for method in method_name_arr: interpreter = interpreters.get_class_object(method) interpreter(self, **kwargs).interpret() def __str__(self): s = "*** Causal Estimate ***\n" # No estimand was identified (identification failed) if self.target_estimand is None: return "Estimation failed! No relevant identified estimand available for this estimation method." s += "\n## Identified estimand\n{0}".format(self.target_estimand.__str__(only_target_estimand=True)) s += "\n## Realized estimand\n{0}".format(self.realized_estimand_expr) if hasattr(self, "estimator"): s += "\nTarget units: {0}\n".format(self.estimator.target_units_tostr()) s += "\n## Estimate\n" s += "Mean value: {0}\n".format(self.value) s += "" if hasattr(self, "cate_estimates"): s += "Effect estimates: {0}\n".format(self.cate_estimates) if hasattr(self, "estimator"): if self.estimator._significance_test: s += "p-value: {0}\n".format(self.estimator.signif_results_tostr(self.test_stat_significance())) if self.estimator._confidence_intervals: s += "{0}% confidence interval: {1}\n".format( 100 * self.estimator.confidence_level, self.get_confidence_intervals() ) if self.conditional_estimates is not None: s += "### Conditional Estimates\n" s += str(self.conditional_estimates) if self.effect_strength is not None: s += "\n## Effect Strength\n" s += "Change in outcome attributable to treatment: {}\n".format(self.effect_strength["fraction-effect"]) # s += "Variance in outcome explained by treatment: {}\n".format(self.effect_strength["r-squared"]) return s class RealizedEstimand(object): def __init__(self, identified_estimand, estimator_name): self.treatment_variable = identified_estimand.treatment_variable self.outcome_variable = identified_estimand.outcome_variable self.backdoor_variables = identified_estimand.get_backdoor_variables() self.instrumental_variables = identified_estimand.instrumental_variables self.estimand_type = identified_estimand.estimand_type self.estimand_expression = None self.assumptions = None self.estimator_name = estimator_name def update_assumptions(self, estimator_assumptions): self.assumptions = estimator_assumptions def update_estimand_expression(self, estimand_expression): self.estimand_expression = estimand_expression def __str__(self): s = "Realized estimand: {0}\n".format(self.estimator_name) s += "Realized estimand type: {0}\n".format(self.estimand_type) s += "Estimand expression:\n{0}\n".format(sp.pretty(self.estimand_expression)) j = 1 for ass_name, ass_str in self.assumptions.items(): s += "Estimand assumption {0}, {1}: {2}\n".format(j, ass_name, ass_str) j += 1 return s

andresmor-ms

2044d216c322a4b32c6eadce5da7d83463f19c2f

05bfa49dacf0061988c96c6f3e3756219df5422a

treatment, outcome need to be added to docstring. identifier_name to be added to docstring.

amit-sharma

py-why/dowhy

Functional api/estimate effect function

#### Estimate Effect function * Refactors the estimate effect into a separate function to keep backwards compatibility #### TODO (future PRs): * Add `fit(...)` method to estimators - Move data related parameters from the constructor to the `fit(...)` method * Refactor code to avoid `**kwargs` in `__init__(...)` constructors

2022-10-18 15:49:21+00:00

2022-10-25 17:02:02+00:00

dowhy/causal_estimator.py

import logging from collections import namedtuple import numpy as np import pandas as pd import sympy as sp from sklearn.utils import resample import dowhy.interpreters as interpreters from dowhy.utils.api import parse_state class CausalEstimator: """Base class for an estimator of causal effect. Subclasses implement different estimation methods. All estimation methods are in the package "dowhy.causal_estimators" """ # The default number of simulations for statistical testing DEFAULT_NUMBER_OF_SIMULATIONS_STAT_TEST = 1000 # The default number of simulations to obtain confidence intervals DEFAULT_NUMBER_OF_SIMULATIONS_CI = 100 # The portion of the total size that should be taken each time to find the confidence intervals # 1 is the recommended value # https://ocw.mit.edu/courses/mathematics/18-05-introduction-to-probability-and-statistics-spring-2014/readings/MIT18_05S14_Reading24.pdf # https://projecteuclid.org/download/pdf_1/euclid.ss/1032280214 DEFAULT_SAMPLE_SIZE_FRACTION = 1 # The default Confidence Level DEFAULT_CONFIDENCE_LEVEL = 0.95 # Number of quantiles to discretize continuous columns, for applying groupby NUM_QUANTILES_TO_DISCRETIZE_CONT_COLS = 5 # Prefix to add to temporary categorical variables created after discretization TEMP_CAT_COLUMN_PREFIX = "__categorical__" DEFAULT_NOTIMPLEMENTEDERROR_MSG = "not yet implemented for {0}. If you would this to be implemented in the next version, please raise an issue at https://github.com/microsoft/dowhy/issues" BootstrapEstimates = namedtuple("BootstrapEstimates", ["estimates", "params"]) DEFAULT_INTERPRET_METHOD = ["textual_effect_interpreter"] # std args to be removed from locals() before being passed to args_dict _STD_INIT_ARGS = ("self", "__class__", "args", "kwargs") def __init__( self, data, identified_estimand, treatment, outcome, control_value=0, treatment_value=1, test_significance=False, evaluate_effect_strength=False, confidence_intervals=False, target_units=None, effect_modifiers=None, num_null_simulations=DEFAULT_NUMBER_OF_SIMULATIONS_STAT_TEST, num_simulations=DEFAULT_NUMBER_OF_SIMULATIONS_CI, sample_size_fraction=DEFAULT_SAMPLE_SIZE_FRACTION, confidence_level=DEFAULT_CONFIDENCE_LEVEL, need_conditional_estimates="auto", num_quantiles_to_discretize_cont_cols=NUM_QUANTILES_TO_DISCRETIZE_CONT_COLS, **kwargs, ): """Initializes an estimator with data and names of relevant variables. This method is called from the constructors of its child classes. :param data: data frame containing the data :param identified_estimand: probability expression representing the target identified estimand to estimate. :param treatment: name of the treatment variable :param outcome: name of the outcome variable :param control_value: Value of the treatment in the control group, for effect estimation. If treatment is multi-variate, this can be a list. :param treatment_value: Value of the treatment in the treated group, for effect estimation. If treatment is multi-variate, this can be a list. :param test_significance: Binary flag or a string indicating whether to test significance and by which method. All estimators support test_significance="bootstrap" that estimates a p-value for the obtained estimate using the bootstrap method. Individual estimators can override this to support custom testing methods. The bootstrap method supports an optional parameter, num_null_simulations. If False, no testing is done. If True, significance of the estimate is tested using the custom method if available, otherwise by bootstrap. :param evaluate_effect_strength: (Experimental) whether to evaluate the strength of effect :param confidence_intervals: Binary flag or a string indicating whether the confidence intervals should be computed and which method should be used. All methods support estimation of confidence intervals using the bootstrap method by using the parameter confidence_intervals="bootstrap". The bootstrap method takes in two arguments (num_simulations and sample_size_fraction) that can be optionally specified in the params dictionary. Estimators may also override this to implement their own confidence interval method. If this parameter is False, no confidence intervals are computed. If True, confidence intervals are computed by the estimator's specific method if available, otherwise through bootstrap. :param target_units: The units for which the treatment effect should be estimated. This can be a string for common specifications of target units (namely, "ate", "att" and "atc"). It can also be a lambda function that can be used as an index for the data (pandas DataFrame). Alternatively, it can be a new DataFrame that contains values of the effect_modifiers and effect will be estimated only for this new data. :param effect_modifiers: Variables on which to compute separate effects, or return a heterogeneous effect function. Not all methods support this currently. :param num_null_simulations: The number of simulations for testing the statistical significance of the estimator :param num_simulations: The number of simulations for finding the confidence interval (and/or standard error) for a estimate :param sample_size_fraction: The size of the sample for the bootstrap estimator :param confidence_level: The confidence level of the confidence interval estimate :param need_conditional_estimates: Boolean flag indicating whether conditional estimates should be computed. Defaults to True if there are effect modifiers in the graph :param num_quantiles_to_discretize_cont_cols: The number of quantiles into which a numeric effect modifier is split, to enable estimation of conditional treatment effect over it. :param kwargs: (optional) Additional estimator-specific parameters :returns: an instance of the estimator class. """ self._data = data self._target_estimand = identified_estimand # Currently estimation methods only support univariate treatment and outcome self._treatment_name = treatment self._outcome_name = outcome[0] # assuming one-dimensional outcome self._control_value = control_value self._treatment_value = treatment_value self._significance_test = test_significance self._effect_strength_eval = evaluate_effect_strength self._target_units = target_units self._effect_modifier_names = effect_modifiers self._confidence_intervals = confidence_intervals self._bootstrap_estimates = None # for confidence intervals and std error self._bootstrap_null_estimates = None # for significance test self._effect_modifiers = None self.method_params = kwargs # Setting the default interpret method self.interpret_method = CausalEstimator.DEFAULT_INTERPRET_METHOD self.logger = logging.getLogger(__name__) # Setting treatment and outcome values if self._data is not None: self._treatment = self._data[self._treatment_name] self._outcome = self._data[self._outcome_name] # Now saving the effect modifiers if self._effect_modifier_names: # only add the observed nodes self._effect_modifier_names = [ cname for cname in self._effect_modifier_names if cname in self._data.columns ] if len(self._effect_modifier_names) > 0: self._effect_modifiers = self._data[self._effect_modifier_names] self._effect_modifiers = pd.get_dummies(self._effect_modifiers, drop_first=True) self.logger.debug("Effect modifiers: " + ",".join(self._effect_modifier_names)) else: self._effect_modifier_names = None # Check if some parameters were set, otherwise set to default values self.num_null_simulations = num_null_simulations self.num_simulations = num_simulations self.sample_size_fraction = sample_size_fraction self.confidence_level = confidence_level self.num_quantiles_to_discretize_cont_cols = num_quantiles_to_discretize_cont_cols # Estimate conditional estimates by default self.need_conditional_estimates = ( need_conditional_estimates if need_conditional_estimates != "auto" else bool(self._effect_modifier_names) ) @staticmethod def get_estimator_object(new_data, identified_estimand, estimate): """Create a new estimator of the same type as the one passed in the estimate argument. Creates a new object with new_data and the identified_estimand :param new_data: np.ndarray, pd.Series, pd.DataFrame The newly assigned data on which the estimator should run :param identified_estimand: IdentifiedEstimand An instance of the identified estimand class that provides the information with respect to which causal pathways are employed when the treatment effects the outcome :param estimate: CausalEstimate It is an already existing estimate whose properties we wish to replicate :returns: An instance of the same estimator class that had generated the given estimate. """ estimator_class = estimate.params["estimator_class"] new_estimator = estimator_class( new_data, identified_estimand, identified_estimand.treatment_variable, identified_estimand.outcome_variable, # names of treatment and outcome control_value=estimate.control_value, treatment_value=estimate.treatment_value, test_significance=False, evaluate_effect_strength=False, confidence_intervals=estimate.params["confidence_intervals"], target_units=estimate.params["target_units"], effect_modifiers=estimate.params["effect_modifiers"], **estimate.params["method_params"], ) return new_estimator def _estimate_effect(self): """This method is to be overriden by the child classes, so that they can run the estimation technique of their choice""" raise NotImplementedError( ("Main estimation method is " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG).format(self.__class__) ) def estimate_effect(self): """Base estimation method that calls the estimate_effect method of its calling subclass. Can optionally also test significance and estimate effect strength for any returned estimate. :param self: object instance of class Estimator :returns: A CausalEstimate instance that contains point estimates of average and conditional effects. Based on the parameters provided, it optionally includes confidence intervals, standard errors,statistical significance and other statistical parameters. """ est = self._estimate_effect() est.add_estimator(self) if self._significance_test: self.test_significance(est.value, method=self._significance_test) if self._confidence_intervals: self.estimate_confidence_intervals( est.value, confidence_level=self.confidence_level, method=self._confidence_intervals ) if self._effect_strength_eval: effect_strength_dict = self.evaluate_effect_strength(est) est.add_effect_strength(effect_strength_dict) return est def estimate_effect_naive(self): # TODO Only works for binary treatment df_withtreatment = self._data.loc[self._data[self._treatment_name] == 1] df_notreatment = self._data.loc[self._data[self._treatment_name] == 0] est = np.mean(df_withtreatment[self._outcome_name]) - np.mean(df_notreatment[self._outcome_name]) return CausalEstimate(est, None, None, control_value=0, treatment_value=1) def _estimate_effect_fn(self, data_df): """Function used in conditional effect estimation. This function is to be overridden by each child estimator. The overridden function should take in a dataframe as input and return the estimate for that data. """ raise NotImplementedError( ("Conditional treatment effects are " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG).format( self.__class__ ) ) def _estimate_conditional_effects(self, estimate_effect_fn, effect_modifier_names=None, num_quantiles=None): """Estimate conditional treatment effects. Common method for all estimators that utilizes a specific estimate_effect_fn implemented by each child estimator. If a numeric effect modifier is provided, it is discretized into quantile bins. If you would like a custom discretization, you can do so yourself: create a new column containing the discretized effect modifier and then include that column's name in the effect_modifier_names argument. :param estimate_effect_fn: Function that has a single parameter (a data frame) and returns the treatment effect estimate on that data. :param effect_modifier_names: Names of effect modifier variables over which the conditional effects will be estimated. If not provided, defaults to the effect modifiers specified during creation of the CausalEstimator object. :param num_quantiles: The number of quantiles into which a numeric effect modifier variable is discretized. Does not affect any categorical effect modifiers. :returns: A (multi-index) dataframe that provides separate effects for each value of the (discretized) effect modifiers. """ # Defaulting to class default values if parameters are not provided if effect_modifier_names is None: effect_modifier_names = self._effect_modifier_names if num_quantiles is None: num_quantiles = self.num_quantiles_to_discretize_cont_cols # Checking that there is at least one effect modifier if not effect_modifier_names: raise ValueError("At least one effect modifier should be specified to compute conditional effects.") # Making sure that effect_modifier_names is a list effect_modifier_names = parse_state(effect_modifier_names) if not all(em in self._effect_modifier_names for em in effect_modifier_names): self.logger.warn( "At least one of the provided effect modifiers was not included while fitting the estimator. You may get incorrect results. To resolve, fit the estimator again by providing the updated effect modifiers in estimate_effect()." ) # Making a copy since we are going to be changing effect modifier names effect_modifier_names = effect_modifier_names.copy() prefix = CausalEstimator.TEMP_CAT_COLUMN_PREFIX # For every numeric effect modifier, adding a temp categorical column for i in range(len(effect_modifier_names)): em = effect_modifier_names[i] if pd.api.types.is_numeric_dtype(self._data[em].dtypes): self._data[prefix + str(em)] = pd.qcut(self._data[em], num_quantiles, duplicates="drop") effect_modifier_names[i] = prefix + str(em) # Grouping by effect modifiers and computing effect separately by_effect_mods = self._data.groupby(effect_modifier_names) cond_est_fn = lambda x: self._do(self._treatment_value, x) - self._do(self._control_value, x) conditional_estimates = by_effect_mods.apply(estimate_effect_fn) # Deleting the temporary categorical columns for em in effect_modifier_names: if em.startswith(prefix): self._data.pop(em) return conditional_estimates def _do(self, x, data_df=None): raise NotImplementedError( ("Do-operator is " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG).format(self.__class__) ) def do(self, x, data_df=None): """Method that implements the do-operator. Given a value x for the treatment, returns the expected value of the outcome when the treatment is intervened to a value x. :param x: Value of the treatment :param data_df: Data on which the do-operator is to be applied. :returns: Value of the outcome when treatment is intervened/set to x. """ est = self._do(x, data_df) return est def construct_symbolic_estimator(self, estimand): raise NotImplementedError(("Symbolic estimator string is ").format(self.__class__)) def _generate_bootstrap_estimates(self, num_bootstrap_simulations, sample_size_fraction): """Helper function to generate causal estimates over bootstrapped samples. :param num_bootstrap_simulations: Number of simulations for the bootstrap method. :param sample_size_fraction: Fraction of the dataset to be resampled. :returns: A collections.namedtuple containing a list of bootstrapped estimates and a dictionary containing parameters used for the bootstrap. """ # The array that stores the results of all estimations simulation_results = np.zeros(num_bootstrap_simulations) # Find the sample size the proportion with the population size sample_size = int(sample_size_fraction * len(self._data)) if sample_size > len(self._data): self.logger.warning("WARN: The sample size is greater than the data being sampled") self.logger.info("INFO: The sample size: {}".format(sample_size)) self.logger.info("INFO: The number of simulations: {}".format(num_bootstrap_simulations)) # Perform the set number of simulations for index in range(num_bootstrap_simulations): new_data = resample(self._data, n_samples=sample_size) new_estimator = type(self)( new_data, self._target_estimand, self._target_estimand.treatment_variable, self._target_estimand.outcome_variable, # names of treatment and outcome treatment_value=self._treatment_value, control_value=self._control_value, test_significance=False, evaluate_effect_strength=False, confidence_intervals=False, target_units=self._target_units, effect_modifiers=self._effect_modifier_names, **self.method_params, ) new_effect = new_estimator.estimate_effect() simulation_results[index] = new_effect.value estimates = CausalEstimator.BootstrapEstimates( simulation_results, {"num_simulations": num_bootstrap_simulations, "sample_size_fraction": sample_size_fraction}, ) return estimates def _estimate_confidence_intervals_with_bootstrap( self, estimate_value, confidence_level=None, num_simulations=None, sample_size_fraction=None ): """ Method to compute confidence interval using bootstrapped sampling. :param estimate_value: obtained estimate's value :param confidence_level: The level for which to compute CI (e.g., 95% confidence level translates to confidence_level=0.95) :param num_simulations: The number of simulations to be performed to get the bootstrap confidence intervals. :param sample_size_fraction: The fraction of the dataset to be resampled. :returns: confidence interval at the specified level. For more details on bootstrap or resampling statistics, refer to the following links: https://ocw.mit.edu/courses/mathematics/18-05-introduction-to-probability-and-statistics-spring-2014/readings/MIT18_05S14_Reading24.pdf https://projecteuclid.org/download/pdf_1/euclid.ss/1032280214 """ # Using class default parameters if not specified if num_simulations is None: num_simulations = self.num_simulations if sample_size_fraction is None: sample_size_fraction = self.sample_size_fraction # Checking if bootstrap_estimates are already computed if self._bootstrap_estimates is None: self._bootstrap_estimates = self._generate_bootstrap_estimates(num_simulations, sample_size_fraction) elif CausalEstimator.is_bootstrap_parameter_changed(self._bootstrap_estimates.params, locals()): # Checked if any parameter is changed from the previous std error estimate self._bootstrap_estimates = self._generate_bootstrap_estimates(num_simulations, sample_size_fraction) # Now use the data obtained from the simulations to get the value of the confidence estimates bootstrap_estimates = self._bootstrap_estimates.estimates # Get the variations of each bootstrap estimate and sort bootstrap_variations = [bootstrap_estimate - estimate_value for bootstrap_estimate in bootstrap_estimates] sorted_bootstrap_variations = np.sort(bootstrap_variations) # Now we take the (1- p)th and the (p)th variations, where p is the chosen confidence level upper_bound_index = int((1 - confidence_level) * len(sorted_bootstrap_variations)) lower_bound_index = int(confidence_level * len(sorted_bootstrap_variations)) # Get the lower and upper bounds by subtracting the variations from the estimate lower_bound = estimate_value - sorted_bootstrap_variations[lower_bound_index] upper_bound = estimate_value - sorted_bootstrap_variations[upper_bound_index] return lower_bound, upper_bound def _estimate_confidence_intervals(self, confidence_level=None, method=None, **kwargs): """ This method is to be overriden by the child classes, so that they can run a confidence interval estimation method suited to the specific causal estimator. """ raise NotImplementedError( ( "This method for estimating confidence intervals is " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG + " Meanwhile, you can try the bootstrap method (method='bootstrap') to estimate confidence intervals." ).format(self.__class__) ) def estimate_confidence_intervals(self, estimate_value, confidence_level=None, method=None, **kwargs): """Find the confidence intervals corresponding to any estimator By default, this is done with the help of bootstrapped confidence intervals but can be overridden if the specific estimator implements other methods of estimating confidence intervals. If the method provided is not bootstrap, this function calls the implementation of the specific estimator. :param estimate_value: obtained estimate's value :param method: Method for estimating confidence intervals. :param confidence_level: The confidence level of the confidence intervals of the estimate. :param kwargs: Other optional args to be passed to the CI method. :returns: The obtained confidence interval. """ if method is None: if self._confidence_intervals: method = self._confidence_intervals # this is either True or methodname else: method = "default" confidence_intervals = None if confidence_level is None: confidence_level = self.confidence_level if method == "default" or method is True: # user has not provided any method try: confidence_intervals = self._estimate_confidence_intervals(confidence_level, method=method, **kwargs) except NotImplementedError: confidence_intervals = self._estimate_confidence_intervals_with_bootstrap( estimate_value, confidence_level, **kwargs ) else: if method == "bootstrap": confidence_intervals = self._estimate_confidence_intervals_with_bootstrap( estimate_value, confidence_level, **kwargs ) else: confidence_intervals = self._estimate_confidence_intervals(confidence_level, method=method, **kwargs) return confidence_intervals def _estimate_std_error_with_bootstrap(self, num_simulations=None, sample_size_fraction=None): """Compute standard error using the bootstrap method. Standard error and confidence intervals use the same parameter num_simulations for the number of bootstrap simulations. :param num_simulations: Number of bootstrapped samples. :param sample_size_fraction: Fraction of data to be resampled. :returns: Standard error of the obtained estimate. """ # Use existing params, if new user defined params are not present if num_simulations is None: num_simulations = self.num_simulations if sample_size_fraction is None: sample_size_fraction = self.sample_size_fraction # Checking if bootstrap_estimates are already computed if self._bootstrap_estimates is None: self._bootstrap_estimates = self._generate_bootstrap_estimates(num_simulations, sample_size_fraction) elif CausalEstimator.is_bootstrap_parameter_changed(self._bootstrap_estimates.params, locals()): # Check if any parameter is changed from the previous std error estimate self._bootstrap_estimates = self._generate_bootstrap_estimates(num_simulations, sample_size_fraction) std_error = np.std(self._bootstrap_estimates.estimates) return std_error def _estimate_std_error(self, method=None, **kwargs): """ This method is to be overriden by the child classes, so that they can run a standard error estimation method suited to the specific causal estimator. """ raise NotImplementedError( ( "This method for estimating standard errors is " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG + " Meanwhile, you can try the bootstrap method (method='bootstrap') to estimate standard errors." ).format(self.__class__) ) def estimate_std_error(self, method=None, **kwargs): """Compute standard error of an obtained causal estimate. :param method: Method for computing the standard error. :param kwargs: Other optional parameters to be passed to the estimating method. :returns: Standard error of the causal estimate. """ if method is None: if self._confidence_intervals: method = self._confidence_intervals else: method = "default" std_error = None if method == "default" or method is True: # user has not provided any method try: std_error = self._estimate_std_error(method, **kwargs) except NotImplementedError: std_error = self._estimate_std_error_with_bootstrap(**kwargs) else: if method == "bootstrap": std_error = self._estimate_std_error_with_bootstrap(**kwargs) else: std_error = self._estimate_std_error(method, **kwargs) return std_error def _test_significance_with_bootstrap(self, estimate_value, num_null_simulations=None): """Test statistical significance of an estimate using the bootstrap method. :param estimate_value: Obtained estimate's value :param num_null_simulations: Number of simulations for the null hypothesis :returns: p-value of the statistical significance test. """ # Use existing params, if new user defined params are not present if num_null_simulations is None: num_null_simulations = self.num_null_simulations do_retest = self._bootstrap_null_estimates is None or CausalEstimator.is_bootstrap_parameter_changed( self._bootstrap_null_estimates.params, locals() ) if do_retest: null_estimates = np.zeros(num_null_simulations) for i in range(num_null_simulations): new_outcome = np.random.permutation(self._outcome) new_data = self._data.assign(dummy_outcome=new_outcome) # self._outcome = self._data["dummy_outcome"] new_estimator = type(self)( new_data, self._target_estimand, self._target_estimand.treatment_variable, ("dummy_outcome",), test_significance=False, evaluate_effect_strength=False, confidence_intervals=False, target_units=self._target_units, effect_modifiers=self._effect_modifier_names, **self.method_params, ) new_effect = new_estimator.estimate_effect() null_estimates[i] = new_effect.value self._bootstrap_null_estimates = CausalEstimator.BootstrapEstimates( null_estimates, {"num_null_simulations": num_null_simulations, "sample_size_fraction": 1} ) # Processing the null hypothesis estimates sorted_null_estimates = np.sort(self._bootstrap_null_estimates.estimates) self.logger.debug("Null estimates: {0}".format(sorted_null_estimates)) median_estimate = sorted_null_estimates[int(num_null_simulations / 2)] # Doing a two-sided test if estimate_value > median_estimate: # Being conservative with the p-value reported estimate_index = np.searchsorted(sorted_null_estimates, estimate_value, side="left") p_value = 1 - (estimate_index / num_null_simulations) if estimate_value <= median_estimate: # Being conservative with the p-value reported estimate_index = np.searchsorted(sorted_null_estimates, estimate_value, side="right") p_value = estimate_index / num_null_simulations # If the estimate_index is 0, it depends on the number of simulations if p_value == 0: p_value = (0, 1 / len(sorted_null_estimates)) # a tuple determining the range. elif p_value == 1: p_value = (1 - 1 / len(sorted_null_estimates), 1) signif_dict = {"p_value": p_value} return signif_dict def _test_significance(self, estimate_value, method=None, **kwargs): """ This method is to be overriden by the child classes, so that they can run a significance test suited to the specific causal estimator. """ raise NotImplementedError( ( "This method for testing statistical significance is " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG + " Meanwhile, you can try the bootstrap method (method='bootstrap') to test statistical significance." ).format(self.__class__) ) def test_significance(self, estimate_value, method=None, **kwargs): """Test statistical significance of obtained estimate. By default, uses resampling to create a non-parametric significance test. A general procedure. Individual child estimators can implement different methods. If the method name is different from "bootstrap", this function calls the implementation of the child estimator. :param self: object instance of class Estimator :param estimate_value: obtained estimate's value :param method: Method for checking statistical significance :returns: p-value from the significance test """ if method is None: if self._significance_test: method = self._significance_test # this is either True or methodname else: method = "default" signif_dict = None if method == "default" or method is True: # user has not provided any method try: signif_dict = self._test_significance(estimate_value, method, **kwargs) except NotImplementedError: signif_dict = self._test_significance_with_bootstrap(estimate_value, **kwargs) else: if method == "bootstrap": signif_dict = self._test_significance_with_bootstrap(estimate_value, **kwargs) else: signif_dict = self._test_significance(estimate_value, method, **kwargs) return signif_dict def evaluate_effect_strength(self, estimate): fraction_effect_explained = self._evaluate_effect_strength(estimate, method="fraction-effect") # Need to test r-squared before supporting # effect_r_squared = self._evaluate_effect_strength(estimate, method="r-squared") strength_dict = { "fraction-effect": fraction_effect_explained # 'r-squared': effect_r_squared } return strength_dict def _evaluate_effect_strength(self, estimate, method="fraction-effect"): supported_methods = ["fraction-effect"] if method not in supported_methods: raise NotImplementedError("This method is not supported for evaluating effect strength") if method == "fraction-effect": naive_obs_estimate = self.estimate_effect_naive() self.logger.debug(estimate.value, naive_obs_estimate.value) fraction_effect_explained = estimate.value / naive_obs_estimate.value return fraction_effect_explained # elif method == "r-squared": # outcome_mean = np.mean(self._outcome) # total_variance = np.sum(np.square(self._outcome - outcome_mean)) # Assuming a linear model with one variable: the treatment # Currently only works for continuous y # causal_model = outcome_mean + estimate.value*self._treatment # squared_residual = np.sum(np.square(self._outcome - causal_model)) # r_squared = 1 - (squared_residual/total_variance) # return r_squared else: return None def update_input(self, treatment_value, control_value, target_units): self._control_value = control_value self._treatment_value = treatment_value self._target_units = target_units @staticmethod def is_bootstrap_parameter_changed(bootstrap_estimates_params, given_params): """Check whether parameters of the bootstrap have changed. This is an efficiency method that checks if fresh resampling of the bootstrap samples is required. Returns True if parameters have changed and resampling should be done again. :param bootstrap_estimates_params: A dictionary of parameters for the current bootstrap samples :param given_params: A dictionary of parameters passed by the user :returns: A binary flag denoting whether the parameters are different. """ is_any_parameter_changed = False for prm, val in bootstrap_estimates_params.items(): given_val = given_params.get(prm, None) if given_val is not None and given_val != val: is_any_parameter_changed = True break return is_any_parameter_changed def target_units_tostr(self): s = "" if type(self._target_units) is str: s += self._target_units elif callable(self._target_units): s += "Data subset defined by a function" elif isinstance(self._target_units, pd.DataFrame): s += "Data subset provided as a data frame" return s def signif_results_tostr(self, signif_results): s = "" pval = signif_results["p_value"] if type(pval) is tuple: s += "[{0}, {1}]".format(pval[0], pval[1]) else: s += "{0}".format(pval) return s class CausalEstimate: """Class for the estimate object that every causal estimator returns""" def __init__( self, estimate, target_estimand, realized_estimand_expr, control_value, treatment_value, conditional_estimates=None, **kwargs, ): self.value = estimate self.target_estimand = target_estimand self.realized_estimand_expr = realized_estimand_expr self.control_value = control_value self.treatment_value = treatment_value self.conditional_estimates = conditional_estimates self.params = kwargs if self.params is not None: for key, value in self.params.items(): setattr(self, key, value) self.effect_strength = None def add_estimator(self, estimator_instance): self.estimator = estimator_instance def add_effect_strength(self, strength_dict): self.effect_strength = strength_dict def add_params(self, **kwargs): self.params.update(kwargs) def get_confidence_intervals(self, confidence_level=None, method=None, **kwargs): """Get confidence intervals of the obtained estimate. By default, this is done with the help of bootstrapped confidence intervals but can be overridden if the specific estimator implements other methods of estimating confidence intervals. If the method provided is not bootstrap, this function calls the implementation of the specific estimator. :param method: Method for estimating confidence intervals. :param confidence_level: The confidence level of the confidence intervals of the estimate. :param kwargs: Other optional args to be passed to the CI method. :returns: The obtained confidence interval. """ confidence_intervals = self.estimator.estimate_confidence_intervals( estimate_value=self.value, confidence_level=confidence_level, method=method, **kwargs ) return confidence_intervals def get_standard_error(self, method=None, **kwargs): """Get standard error of the obtained estimate. By default, this is done with the help of bootstrapped standard errors but can be overridden if the specific estimator implements other methods of estimating standard error. If the method provided is not bootstrap, this function calls the implementation of the specific estimator. :param method: Method for computing the standard error. :param kwargs: Other optional parameters to be passed to the estimating method. :returns: Standard error of the causal estimate. """ std_error = self.estimator.estimate_std_error(method=method, **kwargs) return std_error def test_stat_significance(self, method=None, **kwargs): """Test statistical significance of the estimate obtained. By default, uses resampling to create a non-parametric significance test. Individual child estimators can implement different methods. If the method name is different from "bootstrap", this function calls the implementation of the child estimator. :param method: Method for checking statistical significance :param kwargs: Other optional parameters to be passed to the estimating method. :returns: p-value from the significance test """ signif_results = self.estimator.test_significance(self.value, method=method, **kwargs) return {"p_value": signif_results["p_value"]} def estimate_conditional_effects( self, effect_modifiers=None, num_quantiles=CausalEstimator.NUM_QUANTILES_TO_DISCRETIZE_CONT_COLS ): """Estimate treatment effect conditioned on given variables. If a numeric effect modifier is provided, it is discretized into quantile bins. If you would like a custom discretization, you can do so yourself: create a new column containing the discretized effect modifier and then include that column's name in the effect_modifier_names argument. :param effect_modifiers: Names of effect modifier variables over which the conditional effects will be estimated. If not provided, defaults to the effect modifiers specified during creation of the CausalEstimator object. :param num_quantiles: The number of quantiles into which a numeric effect modifier variable is discretized. Does not affect any categorical effect modifiers. :returns: A (multi-index) dataframe that provides separate effects for each value of the (discretized) effect modifiers. """ return self.estimator._estimate_conditional_effects( self.estimator._estimate_effect_fn, effect_modifiers, num_quantiles ) def interpret(self, method_name=None, **kwargs): """Interpret the causal estimate. :param method_name: Method used (string) or a list of methods. If None, then the default for the specific estimator is used. :param kwargs:: Optional parameters that are directly passed to the interpreter method. :returns: None """ if method_name is None: method_name = self.estimator.interpret_method method_name_arr = parse_state(method_name) for method in method_name_arr: interpreter = interpreters.get_class_object(method) interpreter(self, **kwargs).interpret() def __str__(self): s = "*** Causal Estimate ***\n" # No estimand was identified (identification failed) if self.target_estimand is None: return "Estimation failed! No relevant identified estimand available for this estimation method." s += "\n## Identified estimand\n{0}".format(self.target_estimand.__str__(only_target_estimand=True)) s += "\n## Realized estimand\n{0}".format(self.realized_estimand_expr) if hasattr(self, "estimator"): s += "\nTarget units: {0}\n".format(self.estimator.target_units_tostr()) s += "\n## Estimate\n" s += "Mean value: {0}\n".format(self.value) s += "" if hasattr(self, "cate_estimates"): s += "Effect estimates: {0}\n".format(self.cate_estimates) if hasattr(self, "estimator"): if self.estimator._significance_test: s += "p-value: {0}\n".format(self.estimator.signif_results_tostr(self.test_stat_significance())) if self.estimator._confidence_intervals: s += "{0}% confidence interval: {1}\n".format( 100 * self.estimator.confidence_level, self.get_confidence_intervals() ) if self.conditional_estimates is not None: s += "### Conditional Estimates\n" s += str(self.conditional_estimates) if self.effect_strength is not None: s += "\n## Effect Strength\n" s += "Change in outcome attributable to treatment: {}\n".format(self.effect_strength["fraction-effect"]) # s += "Variance in outcome explained by treatment: {}\n".format(self.effect_strength["r-squared"]) return s class RealizedEstimand(object): def __init__(self, identified_estimand, estimator_name): self.treatment_variable = identified_estimand.treatment_variable self.outcome_variable = identified_estimand.outcome_variable self.backdoor_variables = identified_estimand.get_backdoor_variables() self.instrumental_variables = identified_estimand.instrumental_variables self.estimand_type = identified_estimand.estimand_type self.estimand_expression = None self.assumptions = None self.estimator_name = estimator_name def update_assumptions(self, estimator_assumptions): self.assumptions = estimator_assumptions def update_estimand_expression(self, estimand_expression): self.estimand_expression = estimand_expression def __str__(self): s = "Realized estimand: {0}\n".format(self.estimator_name) s += "Realized estimand type: {0}\n".format(self.estimand_type) s += "Estimand expression:\n{0}\n".format(sp.pretty(self.estimand_expression)) j = 1 for ass_name, ass_str in self.assumptions.items(): s += "Estimand assumption {0}, {1}: {2}\n".format(j, ass_name, ass_str) j += 1 return s

import logging from collections import namedtuple from typing import Dict, List, Optional, Union import numpy as np import pandas as pd import sympy as sp from sklearn.utils import resample import dowhy.interpreters as interpreters from dowhy import causal_estimators from dowhy.causal_graph import CausalGraph from dowhy.causal_identifier.identified_estimand import IdentifiedEstimand from dowhy.utils.api import parse_state logger = logging.getLogger(__name__) class CausalEstimator: """Base class for an estimator of causal effect. Subclasses implement different estimation methods. All estimation methods are in the package "dowhy.causal_estimators" """ # The default number of simulations for statistical testing DEFAULT_NUMBER_OF_SIMULATIONS_STAT_TEST = 1000 # The default number of simulations to obtain confidence intervals DEFAULT_NUMBER_OF_SIMULATIONS_CI = 100 # The portion of the total size that should be taken each time to find the confidence intervals # 1 is the recommended value # https://ocw.mit.edu/courses/mathematics/18-05-introduction-to-probability-and-statistics-spring-2014/readings/MIT18_05S14_Reading24.pdf # https://projecteuclid.org/download/pdf_1/euclid.ss/1032280214 DEFAULT_SAMPLE_SIZE_FRACTION = 1 # The default Confidence Level DEFAULT_CONFIDENCE_LEVEL = 0.95 # Number of quantiles to discretize continuous columns, for applying groupby NUM_QUANTILES_TO_DISCRETIZE_CONT_COLS = 5 # Prefix to add to temporary categorical variables created after discretization TEMP_CAT_COLUMN_PREFIX = "__categorical__" DEFAULT_NOTIMPLEMENTEDERROR_MSG = "not yet implemented for {0}. If you would this to be implemented in the next version, please raise an issue at https://github.com/microsoft/dowhy/issues" BootstrapEstimates = namedtuple("BootstrapEstimates", ["estimates", "params"]) DEFAULT_INTERPRET_METHOD = ["textual_effect_interpreter"] # std args to be removed from locals() before being passed to args_dict _STD_INIT_ARGS = ("self", "__class__", "args", "kwargs") def __init__( self, data, identified_estimand, treatment, outcome, control_value=0, treatment_value=1, test_significance=False, evaluate_effect_strength=False, confidence_intervals=False, target_units=None, effect_modifiers=None, num_null_simulations=DEFAULT_NUMBER_OF_SIMULATIONS_STAT_TEST, num_simulations=DEFAULT_NUMBER_OF_SIMULATIONS_CI, sample_size_fraction=DEFAULT_SAMPLE_SIZE_FRACTION, confidence_level=DEFAULT_CONFIDENCE_LEVEL, need_conditional_estimates="auto", num_quantiles_to_discretize_cont_cols=NUM_QUANTILES_TO_DISCRETIZE_CONT_COLS, **kwargs, ): """Initializes an estimator with data and names of relevant variables. This method is called from the constructors of its child classes. :param data: data frame containing the data :param identified_estimand: probability expression representing the target identified estimand to estimate. :param treatment: name of the treatment variable :param outcome: name of the outcome variable :param control_value: Value of the treatment in the control group, for effect estimation. If treatment is multi-variate, this can be a list. :param treatment_value: Value of the treatment in the treated group, for effect estimation. If treatment is multi-variate, this can be a list. :param test_significance: Binary flag or a string indicating whether to test significance and by which method. All estimators support test_significance="bootstrap" that estimates a p-value for the obtained estimate using the bootstrap method. Individual estimators can override this to support custom testing methods. The bootstrap method supports an optional parameter, num_null_simulations. If False, no testing is done. If True, significance of the estimate is tested using the custom method if available, otherwise by bootstrap. :param evaluate_effect_strength: (Experimental) whether to evaluate the strength of effect :param confidence_intervals: Binary flag or a string indicating whether the confidence intervals should be computed and which method should be used. All methods support estimation of confidence intervals using the bootstrap method by using the parameter confidence_intervals="bootstrap". The bootstrap method takes in two arguments (num_simulations and sample_size_fraction) that can be optionally specified in the params dictionary. Estimators may also override this to implement their own confidence interval method. If this parameter is False, no confidence intervals are computed. If True, confidence intervals are computed by the estimator's specific method if available, otherwise through bootstrap. :param target_units: The units for which the treatment effect should be estimated. This can be a string for common specifications of target units (namely, "ate", "att" and "atc"). It can also be a lambda function that can be used as an index for the data (pandas DataFrame). Alternatively, it can be a new DataFrame that contains values of the effect_modifiers and effect will be estimated only for this new data. :param effect_modifiers: Variables on which to compute separate effects, or return a heterogeneous effect function. Not all methods support this currently. :param num_null_simulations: The number of simulations for testing the statistical significance of the estimator :param num_simulations: The number of simulations for finding the confidence interval (and/or standard error) for a estimate :param sample_size_fraction: The size of the sample for the bootstrap estimator :param confidence_level: The confidence level of the confidence interval estimate :param need_conditional_estimates: Boolean flag indicating whether conditional estimates should be computed. Defaults to True if there are effect modifiers in the graph :param num_quantiles_to_discretize_cont_cols: The number of quantiles into which a numeric effect modifier is split, to enable estimation of conditional treatment effect over it. :param kwargs: (optional) Additional estimator-specific parameters :returns: an instance of the estimator class. """ self._data = data self._target_estimand = identified_estimand # Currently estimation methods only support univariate treatment and outcome self._treatment_name = treatment self._outcome_name = outcome[0] # assuming one-dimensional outcome self._control_value = control_value self._treatment_value = treatment_value self._significance_test = test_significance self._effect_strength_eval = evaluate_effect_strength self._target_units = target_units self._effect_modifier_names = effect_modifiers self._confidence_intervals = confidence_intervals self._bootstrap_estimates = None # for confidence intervals and std error self._bootstrap_null_estimates = None # for significance test self._effect_modifiers = None self.method_params = kwargs # Setting the default interpret method self.interpret_method = CausalEstimator.DEFAULT_INTERPRET_METHOD self.logger = logging.getLogger(__name__) # Setting treatment and outcome values if self._data is not None: self._treatment = self._data[self._treatment_name] self._outcome = self._data[self._outcome_name] if self._effect_modifier_names: # only add the observed nodes self._effect_modifier_names = [ cname for cname in self._effect_modifier_names if cname in self._data.columns ] if len(self._effect_modifier_names) > 0: self._effect_modifiers = self._data[self._effect_modifier_names] self._effect_modifiers = pd.get_dummies(self._effect_modifiers, drop_first=True) self.logger.debug("Effect modifiers: " + ",".join(self._effect_modifier_names)) else: self._effect_modifier_names = None # Check if some parameters were set, otherwise set to default values self.num_null_simulations = num_null_simulations self.num_simulations = num_simulations self.sample_size_fraction = sample_size_fraction self.confidence_level = confidence_level self.num_quantiles_to_discretize_cont_cols = num_quantiles_to_discretize_cont_cols # Estimate conditional estimates by default self.need_conditional_estimates = ( need_conditional_estimates if need_conditional_estimates != "auto" else bool(self._effect_modifier_names) ) @staticmethod def get_estimator_object(new_data, identified_estimand, estimate): """Create a new estimator of the same type as the one passed in the estimate argument. Creates a new object with new_data and the identified_estimand :param new_data: np.ndarray, pd.Series, pd.DataFrame The newly assigned data on which the estimator should run :param identified_estimand: IdentifiedEstimand An instance of the identified estimand class that provides the information with respect to which causal pathways are employed when the treatment effects the outcome :param estimate: CausalEstimate It is an already existing estimate whose properties we wish to replicate :returns: An instance of the same estimator class that had generated the given estimate. """ estimator_class = estimate.params["estimator_class"] new_estimator = estimator_class( new_data, identified_estimand, identified_estimand.treatment_variable, identified_estimand.outcome_variable, # names of treatment and outcome control_value=estimate.control_value, treatment_value=estimate.treatment_value, test_significance=False, evaluate_effect_strength=False, confidence_intervals=estimate.params["confidence_intervals"], target_units=estimate.params["target_units"], effect_modifiers=estimate.params["effect_modifiers"], **estimate.params["method_params"] if estimate.params["method_params"] is not None else {}, ) return new_estimator def _estimate_effect(self): """This method is to be overriden by the child classes, so that they can run the estimation technique of their choice""" raise NotImplementedError( ("Main estimation method is " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG).format(self.__class__) ) def estimate_effect(self): """Base estimation method that calls the estimate_effect method of its calling subclass. Can optionally also test significance and estimate effect strength for any returned estimate. :param self: object instance of class Estimator :returns: A CausalEstimate instance that contains point estimates of average and conditional effects. Based on the parameters provided, it optionally includes confidence intervals, standard errors,statistical significance and other statistical parameters. """ est = self._estimate_effect() est.add_estimator(self) if self._significance_test: self.test_significance(est.value, method=self._significance_test) if self._confidence_intervals: self.estimate_confidence_intervals( est.value, confidence_level=self.confidence_level, method=self._confidence_intervals ) if self._effect_strength_eval: effect_strength_dict = self.evaluate_effect_strength(est) est.add_effect_strength(effect_strength_dict) return est def estimate_effect_naive(self): # TODO Only works for binary treatment df_withtreatment = self._data.loc[self._data[self._treatment_name] == 1] df_notreatment = self._data.loc[self._data[self._treatment_name] == 0] est = np.mean(df_withtreatment[self._outcome_name]) - np.mean(df_notreatment[self._outcome_name]) return CausalEstimate(est, None, None, control_value=0, treatment_value=1) def _estimate_effect_fn(self, data_df): """Function used in conditional effect estimation. This function is to be overridden by each child estimator. The overridden function should take in a dataframe as input and return the estimate for that data. """ raise NotImplementedError( ("Conditional treatment effects are " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG).format( self.__class__ ) ) def _estimate_conditional_effects(self, estimate_effect_fn, effect_modifier_names=None, num_quantiles=None): """Estimate conditional treatment effects. Common method for all estimators that utilizes a specific estimate_effect_fn implemented by each child estimator. If a numeric effect modifier is provided, it is discretized into quantile bins. If you would like a custom discretization, you can do so yourself: create a new column containing the discretized effect modifier and then include that column's name in the effect_modifier_names argument. :param estimate_effect_fn: Function that has a single parameter (a data frame) and returns the treatment effect estimate on that data. :param effect_modifier_names: Names of effect modifier variables over which the conditional effects will be estimated. If not provided, defaults to the effect modifiers specified during creation of the CausalEstimator object. :param num_quantiles: The number of quantiles into which a numeric effect modifier variable is discretized. Does not affect any categorical effect modifiers. :returns: A (multi-index) dataframe that provides separate effects for each value of the (discretized) effect modifiers. """ # Defaulting to class default values if parameters are not provided if effect_modifier_names is None: effect_modifier_names = self._effect_modifier_names if num_quantiles is None: num_quantiles = self.num_quantiles_to_discretize_cont_cols # Checking that there is at least one effect modifier if not effect_modifier_names: raise ValueError("At least one effect modifier should be specified to compute conditional effects.") # Making sure that effect_modifier_names is a list effect_modifier_names = parse_state(effect_modifier_names) if not all(em in self._effect_modifier_names for em in effect_modifier_names): self.logger.warn( "At least one of the provided effect modifiers was not included while fitting the estimator. You may get incorrect results. To resolve, fit the estimator again by providing the updated effect modifiers in estimate_effect()." ) # Making a copy since we are going to be changing effect modifier names effect_modifier_names = effect_modifier_names.copy() prefix = CausalEstimator.TEMP_CAT_COLUMN_PREFIX # For every numeric effect modifier, adding a temp categorical column for i in range(len(effect_modifier_names)): em = effect_modifier_names[i] if pd.api.types.is_numeric_dtype(self._data[em].dtypes): self._data[prefix + str(em)] = pd.qcut(self._data[em], num_quantiles, duplicates="drop") effect_modifier_names[i] = prefix + str(em) # Grouping by effect modifiers and computing effect separately by_effect_mods = self._data.groupby(effect_modifier_names) cond_est_fn = lambda x: self._do(self._treatment_value, x) - self._do(self._control_value, x) conditional_estimates = by_effect_mods.apply(estimate_effect_fn) # Deleting the temporary categorical columns for em in effect_modifier_names: if em.startswith(prefix): self._data.pop(em) return conditional_estimates def _do(self, x, data_df=None): raise NotImplementedError( ("Do-operator is " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG).format(self.__class__) ) def do(self, x, data_df=None): """Method that implements the do-operator. Given a value x for the treatment, returns the expected value of the outcome when the treatment is intervened to a value x. :param x: Value of the treatment :param data_df: Data on which the do-operator is to be applied. :returns: Value of the outcome when treatment is intervened/set to x. """ est = self._do(x, data_df) return est def construct_symbolic_estimator(self, estimand): raise NotImplementedError(("Symbolic estimator string is ").format(self.__class__)) def _generate_bootstrap_estimates(self, num_bootstrap_simulations, sample_size_fraction): """Helper function to generate causal estimates over bootstrapped samples. :param num_bootstrap_simulations: Number of simulations for the bootstrap method. :param sample_size_fraction: Fraction of the dataset to be resampled. :returns: A collections.namedtuple containing a list of bootstrapped estimates and a dictionary containing parameters used for the bootstrap. """ # The array that stores the results of all estimations simulation_results = np.zeros(num_bootstrap_simulations) # Find the sample size the proportion with the population size sample_size = int(sample_size_fraction * len(self._data)) if sample_size > len(self._data): self.logger.warning("WARN: The sample size is greater than the data being sampled") self.logger.info("INFO: The sample size: {}".format(sample_size)) self.logger.info("INFO: The number of simulations: {}".format(num_bootstrap_simulations)) # Perform the set number of simulations for index in range(num_bootstrap_simulations): new_data = resample(self._data, n_samples=sample_size) new_estimator = type(self)( new_data, self._target_estimand, self._target_estimand.treatment_variable, self._target_estimand.outcome_variable, # names of treatment and outcome treatment_value=self._treatment_value, control_value=self._control_value, test_significance=False, evaluate_effect_strength=False, confidence_intervals=False, target_units=self._target_units, effect_modifiers=self._effect_modifier_names, **self.method_params, ) new_effect = new_estimator.estimate_effect() simulation_results[index] = new_effect.value estimates = CausalEstimator.BootstrapEstimates( simulation_results, {"num_simulations": num_bootstrap_simulations, "sample_size_fraction": sample_size_fraction}, ) return estimates def _estimate_confidence_intervals_with_bootstrap( self, estimate_value, confidence_level=None, num_simulations=None, sample_size_fraction=None ): """ Method to compute confidence interval using bootstrapped sampling. :param estimate_value: obtained estimate's value :param confidence_level: The level for which to compute CI (e.g., 95% confidence level translates to confidence_level=0.95) :param num_simulations: The number of simulations to be performed to get the bootstrap confidence intervals. :param sample_size_fraction: The fraction of the dataset to be resampled. :returns: confidence interval at the specified level. For more details on bootstrap or resampling statistics, refer to the following links: https://ocw.mit.edu/courses/mathematics/18-05-introduction-to-probability-and-statistics-spring-2014/readings/MIT18_05S14_Reading24.pdf https://projecteuclid.org/download/pdf_1/euclid.ss/1032280214 """ # Using class default parameters if not specified if num_simulations is None: num_simulations = self.num_simulations if sample_size_fraction is None: sample_size_fraction = self.sample_size_fraction # Checking if bootstrap_estimates are already computed if self._bootstrap_estimates is None: self._bootstrap_estimates = self._generate_bootstrap_estimates(num_simulations, sample_size_fraction) elif CausalEstimator.is_bootstrap_parameter_changed(self._bootstrap_estimates.params, locals()): # Checked if any parameter is changed from the previous std error estimate self._bootstrap_estimates = self._generate_bootstrap_estimates(num_simulations, sample_size_fraction) # Now use the data obtained from the simulations to get the value of the confidence estimates bootstrap_estimates = self._bootstrap_estimates.estimates # Get the variations of each bootstrap estimate and sort bootstrap_variations = [bootstrap_estimate - estimate_value for bootstrap_estimate in bootstrap_estimates] sorted_bootstrap_variations = np.sort(bootstrap_variations) # Now we take the (1- p)th and the (p)th variations, where p is the chosen confidence level upper_bound_index = int((1 - confidence_level) * len(sorted_bootstrap_variations)) lower_bound_index = int(confidence_level * len(sorted_bootstrap_variations)) # Get the lower and upper bounds by subtracting the variations from the estimate lower_bound = estimate_value - sorted_bootstrap_variations[lower_bound_index] upper_bound = estimate_value - sorted_bootstrap_variations[upper_bound_index] return lower_bound, upper_bound def _estimate_confidence_intervals(self, confidence_level=None, method=None, **kwargs): """ This method is to be overriden by the child classes, so that they can run a confidence interval estimation method suited to the specific causal estimator. """ raise NotImplementedError( ( "This method for estimating confidence intervals is " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG + " Meanwhile, you can try the bootstrap method (method='bootstrap') to estimate confidence intervals." ).format(self.__class__) ) def estimate_confidence_intervals(self, estimate_value, confidence_level=None, method=None, **kwargs): """Find the confidence intervals corresponding to any estimator By default, this is done with the help of bootstrapped confidence intervals but can be overridden if the specific estimator implements other methods of estimating confidence intervals. If the method provided is not bootstrap, this function calls the implementation of the specific estimator. :param estimate_value: obtained estimate's value :param method: Method for estimating confidence intervals. :param confidence_level: The confidence level of the confidence intervals of the estimate. :param kwargs: Other optional args to be passed to the CI method. :returns: The obtained confidence interval. """ if method is None: if self._confidence_intervals: method = self._confidence_intervals # this is either True or methodname else: method = "default" confidence_intervals = None if confidence_level is None: confidence_level = self.confidence_level if method == "default" or method is True: # user has not provided any method try: confidence_intervals = self._estimate_confidence_intervals(confidence_level, method=method, **kwargs) except NotImplementedError: confidence_intervals = self._estimate_confidence_intervals_with_bootstrap( estimate_value, confidence_level, **kwargs ) else: if method == "bootstrap": confidence_intervals = self._estimate_confidence_intervals_with_bootstrap( estimate_value, confidence_level, **kwargs ) else: confidence_intervals = self._estimate_confidence_intervals(confidence_level, method=method, **kwargs) return confidence_intervals def _estimate_std_error_with_bootstrap(self, num_simulations=None, sample_size_fraction=None): """Compute standard error using the bootstrap method. Standard error and confidence intervals use the same parameter num_simulations for the number of bootstrap simulations. :param num_simulations: Number of bootstrapped samples. :param sample_size_fraction: Fraction of data to be resampled. :returns: Standard error of the obtained estimate. """ # Use existing params, if new user defined params are not present if num_simulations is None: num_simulations = self.num_simulations if sample_size_fraction is None: sample_size_fraction = self.sample_size_fraction # Checking if bootstrap_estimates are already computed if self._bootstrap_estimates is None: self._bootstrap_estimates = self._generate_bootstrap_estimates(num_simulations, sample_size_fraction) elif CausalEstimator.is_bootstrap_parameter_changed(self._bootstrap_estimates.params, locals()): # Check if any parameter is changed from the previous std error estimate self._bootstrap_estimates = self._generate_bootstrap_estimates(num_simulations, sample_size_fraction) std_error = np.std(self._bootstrap_estimates.estimates) return std_error def _estimate_std_error(self, method=None, **kwargs): """ This method is to be overriden by the child classes, so that they can run a standard error estimation method suited to the specific causal estimator. """ raise NotImplementedError( ( "This method for estimating standard errors is " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG + " Meanwhile, you can try the bootstrap method (method='bootstrap') to estimate standard errors." ).format(self.__class__) ) def estimate_std_error(self, method=None, **kwargs): """Compute standard error of an obtained causal estimate. :param method: Method for computing the standard error. :param kwargs: Other optional parameters to be passed to the estimating method. :returns: Standard error of the causal estimate. """ if method is None: if self._confidence_intervals: method = self._confidence_intervals else: method = "default" std_error = None if method == "default" or method is True: # user has not provided any method try: std_error = self._estimate_std_error(method, **kwargs) except NotImplementedError: std_error = self._estimate_std_error_with_bootstrap(**kwargs) else: if method == "bootstrap": std_error = self._estimate_std_error_with_bootstrap(**kwargs) else: std_error = self._estimate_std_error(method, **kwargs) return std_error def _test_significance_with_bootstrap(self, estimate_value, num_null_simulations=None): """Test statistical significance of an estimate using the bootstrap method. :param estimate_value: Obtained estimate's value :param num_null_simulations: Number of simulations for the null hypothesis :returns: p-value of the statistical significance test. """ # Use existing params, if new user defined params are not present if num_null_simulations is None: num_null_simulations = self.num_null_simulations do_retest = self._bootstrap_null_estimates is None or CausalEstimator.is_bootstrap_parameter_changed( self._bootstrap_null_estimates.params, locals() ) if do_retest: null_estimates = np.zeros(num_null_simulations) for i in range(num_null_simulations): new_outcome = np.random.permutation(self._outcome) new_data = self._data.assign(dummy_outcome=new_outcome) # self._outcome = self._data["dummy_outcome"] new_estimator = type(self)( new_data, self._target_estimand, self._target_estimand.treatment_variable, ("dummy_outcome",), test_significance=False, evaluate_effect_strength=False, confidence_intervals=False, target_units=self._target_units, effect_modifiers=self._effect_modifier_names, **self.method_params, ) new_effect = new_estimator.estimate_effect() null_estimates[i] = new_effect.value self._bootstrap_null_estimates = CausalEstimator.BootstrapEstimates( null_estimates, {"num_null_simulations": num_null_simulations, "sample_size_fraction": 1} ) # Processing the null hypothesis estimates sorted_null_estimates = np.sort(self._bootstrap_null_estimates.estimates) self.logger.debug("Null estimates: {0}".format(sorted_null_estimates)) median_estimate = sorted_null_estimates[int(num_null_simulations / 2)] # Doing a two-sided test if estimate_value > median_estimate: # Being conservative with the p-value reported estimate_index = np.searchsorted(sorted_null_estimates, estimate_value, side="left") p_value = 1 - (estimate_index / num_null_simulations) if estimate_value <= median_estimate: # Being conservative with the p-value reported estimate_index = np.searchsorted(sorted_null_estimates, estimate_value, side="right") p_value = estimate_index / num_null_simulations # If the estimate_index is 0, it depends on the number of simulations if p_value == 0: p_value = (0, 1 / len(sorted_null_estimates)) # a tuple determining the range. elif p_value == 1: p_value = (1 - 1 / len(sorted_null_estimates), 1) signif_dict = {"p_value": p_value} return signif_dict def _test_significance(self, estimate_value, method=None, **kwargs): """ This method is to be overriden by the child classes, so that they can run a significance test suited to the specific causal estimator. """ raise NotImplementedError( ( "This method for testing statistical significance is " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG + " Meanwhile, you can try the bootstrap method (method='bootstrap') to test statistical significance." ).format(self.__class__) ) def test_significance(self, estimate_value, method=None, **kwargs): """Test statistical significance of obtained estimate. By default, uses resampling to create a non-parametric significance test. A general procedure. Individual child estimators can implement different methods. If the method name is different from "bootstrap", this function calls the implementation of the child estimator. :param self: object instance of class Estimator :param estimate_value: obtained estimate's value :param method: Method for checking statistical significance :returns: p-value from the significance test """ if method is None: if self._significance_test: method = self._significance_test # this is either True or methodname else: method = "default" signif_dict = None if method == "default" or method is True: # user has not provided any method try: signif_dict = self._test_significance(estimate_value, method, **kwargs) except NotImplementedError: signif_dict = self._test_significance_with_bootstrap(estimate_value, **kwargs) else: if method == "bootstrap": signif_dict = self._test_significance_with_bootstrap(estimate_value, **kwargs) else: signif_dict = self._test_significance(estimate_value, method, **kwargs) return signif_dict def evaluate_effect_strength(self, estimate): fraction_effect_explained = self._evaluate_effect_strength(estimate, method="fraction-effect") # Need to test r-squared before supporting # effect_r_squared = self._evaluate_effect_strength(estimate, method="r-squared") strength_dict = { "fraction-effect": fraction_effect_explained # 'r-squared': effect_r_squared } return strength_dict def _evaluate_effect_strength(self, estimate, method="fraction-effect"): supported_methods = ["fraction-effect"] if method not in supported_methods: raise NotImplementedError("This method is not supported for evaluating effect strength") if method == "fraction-effect": naive_obs_estimate = self.estimate_effect_naive() self.logger.debug(estimate.value, naive_obs_estimate.value) fraction_effect_explained = estimate.value / naive_obs_estimate.value return fraction_effect_explained # elif method == "r-squared": # outcome_mean = np.mean(self._outcome) # total_variance = np.sum(np.square(self._outcome - outcome_mean)) # Assuming a linear model with one variable: the treatment # Currently only works for continuous y # causal_model = outcome_mean + estimate.value*self._treatment # squared_residual = np.sum(np.square(self._outcome - causal_model)) # r_squared = 1 - (squared_residual/total_variance) # return r_squared else: return None def update_input(self, treatment_value, control_value, target_units): self._control_value = control_value self._treatment_value = treatment_value self._target_units = target_units @staticmethod def is_bootstrap_parameter_changed(bootstrap_estimates_params, given_params): """Check whether parameters of the bootstrap have changed. This is an efficiency method that checks if fresh resampling of the bootstrap samples is required. Returns True if parameters have changed and resampling should be done again. :param bootstrap_estimates_params: A dictionary of parameters for the current bootstrap samples :param given_params: A dictionary of parameters passed by the user :returns: A binary flag denoting whether the parameters are different. """ is_any_parameter_changed = False for prm, val in bootstrap_estimates_params.items(): given_val = given_params.get(prm, None) if given_val is not None and given_val != val: is_any_parameter_changed = True break return is_any_parameter_changed def target_units_tostr(self): s = "" if type(self._target_units) is str: s += self._target_units elif callable(self._target_units): s += "Data subset defined by a function" elif isinstance(self._target_units, pd.DataFrame): s += "Data subset provided as a data frame" return s def signif_results_tostr(self, signif_results): s = "" pval = signif_results["p_value"] if type(pval) is tuple: s += "[{0}, {1}]".format(pval[0], pval[1]) else: s += "{0}".format(pval) return s def estimate_effect( treatment: Union[str, List[str]], outcome: Union[str, List[str]], identified_estimand: IdentifiedEstimand, identifier_name: str, method: CausalEstimator, control_value: int = 0, treatment_value: int = 1, test_significance: Optional[bool] = None, evaluate_effect_strength: bool = False, confidence_intervals: bool = False, target_units: str = "ate", effect_modifiers: List[str] = [], fit_estimator: bool = True, method_params: Optional[Dict] = None, ): """Estimate the identified causal effect. Currently requires an explicit method name to be specified. Method names follow the convention of identification method followed by the specific estimation method: "[backdoor/iv].estimation_method_name". Following methods are supported. * Propensity Score Matching: "backdoor.propensity_score_matching" * Propensity Score Stratification: "backdoor.propensity_score_stratification" * Propensity Score-based Inverse Weighting: "backdoor.propensity_score_weighting" * Linear Regression: "backdoor.linear_regression" * Generalized Linear Models (e.g., logistic regression): "backdoor.generalized_linear_model" * Instrumental Variables: "iv.instrumental_variable" * Regression Discontinuity: "iv.regression_discontinuity" In addition, you can directly call any of the EconML estimation methods. The convention is "backdoor.econml.path-to-estimator-class". For example, for the double machine learning estimator ("DML" class) that is located inside "dml" module of EconML, you can use the method name, "backdoor.econml.dml.DML". CausalML estimators can also be called. See `this demo notebook <https://py-why.github.io/dowhy/example_notebooks/dowhy-conditional-treatment-effects.html>`_. :param treatment: Name of the treatment :param outcome: Name of the outcome :param identified_estimand: a probability expression that represents the effect to be estimated. Output of CausalModel.identify_effect method :param method_name: name of the estimation method to be used. :param control_value: Value of the treatment in the control group, for effect estimation. If treatment is multi-variate, this can be a list. :param treatment_value: Value of the treatment in the treated group, for effect estimation. If treatment is multi-variate, this can be a list. :param test_significance: Binary flag on whether to additionally do a statistical signficance test for the estimate. :param evaluate_effect_strength: (Experimental) Binary flag on whether to estimate the relative strength of the treatment's effect. This measure can be used to compare different treatments for the same outcome (by running this method with different treatments sequentially). :param confidence_intervals: (Experimental) Binary flag indicating whether confidence intervals should be computed. :param target_units: (Experimental) The units for which the treatment effect should be estimated. This can be of three types. (1) a string for common specifications of target units (namely, "ate", "att" and "atc"), (2) a lambda function that can be used as an index for the data (pandas DataFrame), or (3) a new DataFrame that contains values of the effect_modifiers and effect will be estimated only for this new data. :param effect_modifiers: Names of effect modifier variables can be (optionally) specified here too, since they do not affect identification. If None, the effect_modifiers from the CausalModel are used. :param fit_estimator: Boolean flag on whether to fit the estimator. Setting it to False is useful to estimate the effect on new data using a previously fitted estimator. :param method_params: Dictionary containing any method-specific parameters. These are passed directly to the estimating method. See the docs for each estimation method for allowed method-specific params. :returns: An instance of the CausalEstimate class, containing the causal effect estimate and other method-dependent information """ treatment = parse_state(treatment) outcome = parse_state(outcome) causal_estimator_class = method.__class__ identified_estimand.set_identifier_method(identifier_name) if identified_estimand.no_directed_path: logger.warning("No directed path from {0} to {1}.".format(treatment, outcome)) return CausalEstimate( 0, identified_estimand, None, control_value=control_value, treatment_value=treatment_value ) # Check if estimator's target estimand is identified elif identified_estimand.estimands[identifier_name] is None: logger.error("No valid identified estimand available.") return CausalEstimate(None, None, None, control_value=control_value, treatment_value=treatment_value) method.update_input(treatment_value, control_value, target_units) estimate = method.estimate_effect() # Store parameters inside estimate object for refutation methods # TODO: This add_params needs to move to the estimator class # inside estimate_effect and estimate_conditional_effect estimate.add_params( estimand_type=identified_estimand.estimand_type, estimator_class=causal_estimator_class, test_significance=test_significance, evaluate_effect_strength=evaluate_effect_strength, confidence_intervals=confidence_intervals, target_units=target_units, effect_modifiers=effect_modifiers, method_params=method_params, ) return estimate class CausalEstimate: """Class for the estimate object that every causal estimator returns""" def __init__( self, estimate, target_estimand, realized_estimand_expr, control_value, treatment_value, conditional_estimates=None, **kwargs, ): self.value = estimate self.target_estimand = target_estimand self.realized_estimand_expr = realized_estimand_expr self.control_value = control_value self.treatment_value = treatment_value self.conditional_estimates = conditional_estimates self.params = kwargs if self.params is not None: for key, value in self.params.items(): setattr(self, key, value) self.effect_strength = None def add_estimator(self, estimator_instance): self.estimator = estimator_instance def add_effect_strength(self, strength_dict): self.effect_strength = strength_dict def add_params(self, **kwargs): self.params.update(kwargs) def get_confidence_intervals(self, confidence_level=None, method=None, **kwargs): """Get confidence intervals of the obtained estimate. By default, this is done with the help of bootstrapped confidence intervals but can be overridden if the specific estimator implements other methods of estimating confidence intervals. If the method provided is not bootstrap, this function calls the implementation of the specific estimator. :param method: Method for estimating confidence intervals. :param confidence_level: The confidence level of the confidence intervals of the estimate. :param kwargs: Other optional args to be passed to the CI method. :returns: The obtained confidence interval. """ confidence_intervals = self.estimator.estimate_confidence_intervals( estimate_value=self.value, confidence_level=confidence_level, method=method, **kwargs ) return confidence_intervals def get_standard_error(self, method=None, **kwargs): """Get standard error of the obtained estimate. By default, this is done with the help of bootstrapped standard errors but can be overridden if the specific estimator implements other methods of estimating standard error. If the method provided is not bootstrap, this function calls the implementation of the specific estimator. :param method: Method for computing the standard error. :param kwargs: Other optional parameters to be passed to the estimating method. :returns: Standard error of the causal estimate. """ std_error = self.estimator.estimate_std_error(method=method, **kwargs) return std_error def test_stat_significance(self, method=None, **kwargs): """Test statistical significance of the estimate obtained. By default, uses resampling to create a non-parametric significance test. Individual child estimators can implement different methods. If the method name is different from "bootstrap", this function calls the implementation of the child estimator. :param method: Method for checking statistical significance :param kwargs: Other optional parameters to be passed to the estimating method. :returns: p-value from the significance test """ signif_results = self.estimator.test_significance(self.value, method=method, **kwargs) return {"p_value": signif_results["p_value"]} def estimate_conditional_effects( self, effect_modifiers=None, num_quantiles=CausalEstimator.NUM_QUANTILES_TO_DISCRETIZE_CONT_COLS ): """Estimate treatment effect conditioned on given variables. If a numeric effect modifier is provided, it is discretized into quantile bins. If you would like a custom discretization, you can do so yourself: create a new column containing the discretized effect modifier and then include that column's name in the effect_modifier_names argument. :param effect_modifiers: Names of effect modifier variables over which the conditional effects will be estimated. If not provided, defaults to the effect modifiers specified during creation of the CausalEstimator object. :param num_quantiles: The number of quantiles into which a numeric effect modifier variable is discretized. Does not affect any categorical effect modifiers. :returns: A (multi-index) dataframe that provides separate effects for each value of the (discretized) effect modifiers. """ return self.estimator._estimate_conditional_effects( self.estimator._estimate_effect_fn, effect_modifiers, num_quantiles ) def interpret(self, method_name=None, **kwargs): """Interpret the causal estimate. :param method_name: Method used (string) or a list of methods. If None, then the default for the specific estimator is used. :param kwargs:: Optional parameters that are directly passed to the interpreter method. :returns: None """ if method_name is None: method_name = self.estimator.interpret_method method_name_arr = parse_state(method_name) for method in method_name_arr: interpreter = interpreters.get_class_object(method) interpreter(self, **kwargs).interpret() def __str__(self): s = "*** Causal Estimate ***\n" # No estimand was identified (identification failed) if self.target_estimand is None: return "Estimation failed! No relevant identified estimand available for this estimation method." s += "\n## Identified estimand\n{0}".format(self.target_estimand.__str__(only_target_estimand=True)) s += "\n## Realized estimand\n{0}".format(self.realized_estimand_expr) if hasattr(self, "estimator"): s += "\nTarget units: {0}\n".format(self.estimator.target_units_tostr()) s += "\n## Estimate\n" s += "Mean value: {0}\n".format(self.value) s += "" if hasattr(self, "cate_estimates"): s += "Effect estimates: {0}\n".format(self.cate_estimates) if hasattr(self, "estimator"): if self.estimator._significance_test: s += "p-value: {0}\n".format(self.estimator.signif_results_tostr(self.test_stat_significance())) if self.estimator._confidence_intervals: s += "{0}% confidence interval: {1}\n".format( 100 * self.estimator.confidence_level, self.get_confidence_intervals() ) if self.conditional_estimates is not None: s += "### Conditional Estimates\n" s += str(self.conditional_estimates) if self.effect_strength is not None: s += "\n## Effect Strength\n" s += "Change in outcome attributable to treatment: {}\n".format(self.effect_strength["fraction-effect"]) # s += "Variance in outcome explained by treatment: {}\n".format(self.effect_strength["r-squared"]) return s class RealizedEstimand(object): def __init__(self, identified_estimand, estimator_name): self.treatment_variable = identified_estimand.treatment_variable self.outcome_variable = identified_estimand.outcome_variable self.backdoor_variables = identified_estimand.get_backdoor_variables() self.instrumental_variables = identified_estimand.instrumental_variables self.estimand_type = identified_estimand.estimand_type self.estimand_expression = None self.assumptions = None self.estimator_name = estimator_name def update_assumptions(self, estimator_assumptions): self.assumptions = estimator_assumptions def update_estimand_expression(self, estimand_expression): self.estimand_expression = estimand_expression def __str__(self): s = "Realized estimand: {0}\n".format(self.estimator_name) s += "Realized estimand type: {0}\n".format(self.estimand_type) s += "Estimand expression:\n{0}\n".format(sp.pretty(self.estimand_expression)) j = 1 for ass_name, ass_str in self.assumptions.items(): s += "Estimand assumption {0}, {1}: {2}\n".format(j, ass_name, ass_str) j += 1 return s

andresmor-ms

2044d216c322a4b32c6eadce5da7d83463f19c2f

05bfa49dacf0061988c96c6f3e3756219df5422a

since we are now passing the method object, fit_estimator makes more sense for the next line, the estimate_effect method of the Estimator. Here we can simply do the two if-else checks and then sequentially do "method.update_input". Just the "if fit_estimator" line can be removed.

amit-sharma

py-why/dowhy

Functional api/estimate effect function

#### Estimate Effect function * Refactors the estimate effect into a separate function to keep backwards compatibility #### TODO (future PRs): * Add `fit(...)` method to estimators - Move data related parameters from the constructor to the `fit(...)` method * Refactor code to avoid `**kwargs` in `__init__(...)` constructors

2022-10-18 15:49:21+00:00

2022-10-25 17:02:02+00:00

dowhy/causal_estimator.py

import logging from collections import namedtuple import numpy as np import pandas as pd import sympy as sp from sklearn.utils import resample import dowhy.interpreters as interpreters from dowhy.utils.api import parse_state class CausalEstimator: """Base class for an estimator of causal effect. Subclasses implement different estimation methods. All estimation methods are in the package "dowhy.causal_estimators" """ # The default number of simulations for statistical testing DEFAULT_NUMBER_OF_SIMULATIONS_STAT_TEST = 1000 # The default number of simulations to obtain confidence intervals DEFAULT_NUMBER_OF_SIMULATIONS_CI = 100 # The portion of the total size that should be taken each time to find the confidence intervals # 1 is the recommended value # https://ocw.mit.edu/courses/mathematics/18-05-introduction-to-probability-and-statistics-spring-2014/readings/MIT18_05S14_Reading24.pdf # https://projecteuclid.org/download/pdf_1/euclid.ss/1032280214 DEFAULT_SAMPLE_SIZE_FRACTION = 1 # The default Confidence Level DEFAULT_CONFIDENCE_LEVEL = 0.95 # Number of quantiles to discretize continuous columns, for applying groupby NUM_QUANTILES_TO_DISCRETIZE_CONT_COLS = 5 # Prefix to add to temporary categorical variables created after discretization TEMP_CAT_COLUMN_PREFIX = "__categorical__" DEFAULT_NOTIMPLEMENTEDERROR_MSG = "not yet implemented for {0}. If you would this to be implemented in the next version, please raise an issue at https://github.com/microsoft/dowhy/issues" BootstrapEstimates = namedtuple("BootstrapEstimates", ["estimates", "params"]) DEFAULT_INTERPRET_METHOD = ["textual_effect_interpreter"] # std args to be removed from locals() before being passed to args_dict _STD_INIT_ARGS = ("self", "__class__", "args", "kwargs") def __init__( self, data, identified_estimand, treatment, outcome, control_value=0, treatment_value=1, test_significance=False, evaluate_effect_strength=False, confidence_intervals=False, target_units=None, effect_modifiers=None, num_null_simulations=DEFAULT_NUMBER_OF_SIMULATIONS_STAT_TEST, num_simulations=DEFAULT_NUMBER_OF_SIMULATIONS_CI, sample_size_fraction=DEFAULT_SAMPLE_SIZE_FRACTION, confidence_level=DEFAULT_CONFIDENCE_LEVEL, need_conditional_estimates="auto", num_quantiles_to_discretize_cont_cols=NUM_QUANTILES_TO_DISCRETIZE_CONT_COLS, **kwargs, ): """Initializes an estimator with data and names of relevant variables. This method is called from the constructors of its child classes. :param data: data frame containing the data :param identified_estimand: probability expression representing the target identified estimand to estimate. :param treatment: name of the treatment variable :param outcome: name of the outcome variable :param control_value: Value of the treatment in the control group, for effect estimation. If treatment is multi-variate, this can be a list. :param treatment_value: Value of the treatment in the treated group, for effect estimation. If treatment is multi-variate, this can be a list. :param test_significance: Binary flag or a string indicating whether to test significance and by which method. All estimators support test_significance="bootstrap" that estimates a p-value for the obtained estimate using the bootstrap method. Individual estimators can override this to support custom testing methods. The bootstrap method supports an optional parameter, num_null_simulations. If False, no testing is done. If True, significance of the estimate is tested using the custom method if available, otherwise by bootstrap. :param evaluate_effect_strength: (Experimental) whether to evaluate the strength of effect :param confidence_intervals: Binary flag or a string indicating whether the confidence intervals should be computed and which method should be used. All methods support estimation of confidence intervals using the bootstrap method by using the parameter confidence_intervals="bootstrap". The bootstrap method takes in two arguments (num_simulations and sample_size_fraction) that can be optionally specified in the params dictionary. Estimators may also override this to implement their own confidence interval method. If this parameter is False, no confidence intervals are computed. If True, confidence intervals are computed by the estimator's specific method if available, otherwise through bootstrap. :param target_units: The units for which the treatment effect should be estimated. This can be a string for common specifications of target units (namely, "ate", "att" and "atc"). It can also be a lambda function that can be used as an index for the data (pandas DataFrame). Alternatively, it can be a new DataFrame that contains values of the effect_modifiers and effect will be estimated only for this new data. :param effect_modifiers: Variables on which to compute separate effects, or return a heterogeneous effect function. Not all methods support this currently. :param num_null_simulations: The number of simulations for testing the statistical significance of the estimator :param num_simulations: The number of simulations for finding the confidence interval (and/or standard error) for a estimate :param sample_size_fraction: The size of the sample for the bootstrap estimator :param confidence_level: The confidence level of the confidence interval estimate :param need_conditional_estimates: Boolean flag indicating whether conditional estimates should be computed. Defaults to True if there are effect modifiers in the graph :param num_quantiles_to_discretize_cont_cols: The number of quantiles into which a numeric effect modifier is split, to enable estimation of conditional treatment effect over it. :param kwargs: (optional) Additional estimator-specific parameters :returns: an instance of the estimator class. """ self._data = data self._target_estimand = identified_estimand # Currently estimation methods only support univariate treatment and outcome self._treatment_name = treatment self._outcome_name = outcome[0] # assuming one-dimensional outcome self._control_value = control_value self._treatment_value = treatment_value self._significance_test = test_significance self._effect_strength_eval = evaluate_effect_strength self._target_units = target_units self._effect_modifier_names = effect_modifiers self._confidence_intervals = confidence_intervals self._bootstrap_estimates = None # for confidence intervals and std error self._bootstrap_null_estimates = None # for significance test self._effect_modifiers = None self.method_params = kwargs # Setting the default interpret method self.interpret_method = CausalEstimator.DEFAULT_INTERPRET_METHOD self.logger = logging.getLogger(__name__) # Setting treatment and outcome values if self._data is not None: self._treatment = self._data[self._treatment_name] self._outcome = self._data[self._outcome_name] # Now saving the effect modifiers if self._effect_modifier_names: # only add the observed nodes self._effect_modifier_names = [ cname for cname in self._effect_modifier_names if cname in self._data.columns ] if len(self._effect_modifier_names) > 0: self._effect_modifiers = self._data[self._effect_modifier_names] self._effect_modifiers = pd.get_dummies(self._effect_modifiers, drop_first=True) self.logger.debug("Effect modifiers: " + ",".join(self._effect_modifier_names)) else: self._effect_modifier_names = None # Check if some parameters were set, otherwise set to default values self.num_null_simulations = num_null_simulations self.num_simulations = num_simulations self.sample_size_fraction = sample_size_fraction self.confidence_level = confidence_level self.num_quantiles_to_discretize_cont_cols = num_quantiles_to_discretize_cont_cols # Estimate conditional estimates by default self.need_conditional_estimates = ( need_conditional_estimates if need_conditional_estimates != "auto" else bool(self._effect_modifier_names) ) @staticmethod def get_estimator_object(new_data, identified_estimand, estimate): """Create a new estimator of the same type as the one passed in the estimate argument. Creates a new object with new_data and the identified_estimand :param new_data: np.ndarray, pd.Series, pd.DataFrame The newly assigned data on which the estimator should run :param identified_estimand: IdentifiedEstimand An instance of the identified estimand class that provides the information with respect to which causal pathways are employed when the treatment effects the outcome :param estimate: CausalEstimate It is an already existing estimate whose properties we wish to replicate :returns: An instance of the same estimator class that had generated the given estimate. """ estimator_class = estimate.params["estimator_class"] new_estimator = estimator_class( new_data, identified_estimand, identified_estimand.treatment_variable, identified_estimand.outcome_variable, # names of treatment and outcome control_value=estimate.control_value, treatment_value=estimate.treatment_value, test_significance=False, evaluate_effect_strength=False, confidence_intervals=estimate.params["confidence_intervals"], target_units=estimate.params["target_units"], effect_modifiers=estimate.params["effect_modifiers"], **estimate.params["method_params"], ) return new_estimator def _estimate_effect(self): """This method is to be overriden by the child classes, so that they can run the estimation technique of their choice""" raise NotImplementedError( ("Main estimation method is " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG).format(self.__class__) ) def estimate_effect(self): """Base estimation method that calls the estimate_effect method of its calling subclass. Can optionally also test significance and estimate effect strength for any returned estimate. :param self: object instance of class Estimator :returns: A CausalEstimate instance that contains point estimates of average and conditional effects. Based on the parameters provided, it optionally includes confidence intervals, standard errors,statistical significance and other statistical parameters. """ est = self._estimate_effect() est.add_estimator(self) if self._significance_test: self.test_significance(est.value, method=self._significance_test) if self._confidence_intervals: self.estimate_confidence_intervals( est.value, confidence_level=self.confidence_level, method=self._confidence_intervals ) if self._effect_strength_eval: effect_strength_dict = self.evaluate_effect_strength(est) est.add_effect_strength(effect_strength_dict) return est def estimate_effect_naive(self): # TODO Only works for binary treatment df_withtreatment = self._data.loc[self._data[self._treatment_name] == 1] df_notreatment = self._data.loc[self._data[self._treatment_name] == 0] est = np.mean(df_withtreatment[self._outcome_name]) - np.mean(df_notreatment[self._outcome_name]) return CausalEstimate(est, None, None, control_value=0, treatment_value=1) def _estimate_effect_fn(self, data_df): """Function used in conditional effect estimation. This function is to be overridden by each child estimator. The overridden function should take in a dataframe as input and return the estimate for that data. """ raise NotImplementedError( ("Conditional treatment effects are " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG).format( self.__class__ ) ) def _estimate_conditional_effects(self, estimate_effect_fn, effect_modifier_names=None, num_quantiles=None): """Estimate conditional treatment effects. Common method for all estimators that utilizes a specific estimate_effect_fn implemented by each child estimator. If a numeric effect modifier is provided, it is discretized into quantile bins. If you would like a custom discretization, you can do so yourself: create a new column containing the discretized effect modifier and then include that column's name in the effect_modifier_names argument. :param estimate_effect_fn: Function that has a single parameter (a data frame) and returns the treatment effect estimate on that data. :param effect_modifier_names: Names of effect modifier variables over which the conditional effects will be estimated. If not provided, defaults to the effect modifiers specified during creation of the CausalEstimator object. :param num_quantiles: The number of quantiles into which a numeric effect modifier variable is discretized. Does not affect any categorical effect modifiers. :returns: A (multi-index) dataframe that provides separate effects for each value of the (discretized) effect modifiers. """ # Defaulting to class default values if parameters are not provided if effect_modifier_names is None: effect_modifier_names = self._effect_modifier_names if num_quantiles is None: num_quantiles = self.num_quantiles_to_discretize_cont_cols # Checking that there is at least one effect modifier if not effect_modifier_names: raise ValueError("At least one effect modifier should be specified to compute conditional effects.") # Making sure that effect_modifier_names is a list effect_modifier_names = parse_state(effect_modifier_names) if not all(em in self._effect_modifier_names for em in effect_modifier_names): self.logger.warn( "At least one of the provided effect modifiers was not included while fitting the estimator. You may get incorrect results. To resolve, fit the estimator again by providing the updated effect modifiers in estimate_effect()." ) # Making a copy since we are going to be changing effect modifier names effect_modifier_names = effect_modifier_names.copy() prefix = CausalEstimator.TEMP_CAT_COLUMN_PREFIX # For every numeric effect modifier, adding a temp categorical column for i in range(len(effect_modifier_names)): em = effect_modifier_names[i] if pd.api.types.is_numeric_dtype(self._data[em].dtypes): self._data[prefix + str(em)] = pd.qcut(self._data[em], num_quantiles, duplicates="drop") effect_modifier_names[i] = prefix + str(em) # Grouping by effect modifiers and computing effect separately by_effect_mods = self._data.groupby(effect_modifier_names) cond_est_fn = lambda x: self._do(self._treatment_value, x) - self._do(self._control_value, x) conditional_estimates = by_effect_mods.apply(estimate_effect_fn) # Deleting the temporary categorical columns for em in effect_modifier_names: if em.startswith(prefix): self._data.pop(em) return conditional_estimates def _do(self, x, data_df=None): raise NotImplementedError( ("Do-operator is " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG).format(self.__class__) ) def do(self, x, data_df=None): """Method that implements the do-operator. Given a value x for the treatment, returns the expected value of the outcome when the treatment is intervened to a value x. :param x: Value of the treatment :param data_df: Data on which the do-operator is to be applied. :returns: Value of the outcome when treatment is intervened/set to x. """ est = self._do(x, data_df) return est def construct_symbolic_estimator(self, estimand): raise NotImplementedError(("Symbolic estimator string is ").format(self.__class__)) def _generate_bootstrap_estimates(self, num_bootstrap_simulations, sample_size_fraction): """Helper function to generate causal estimates over bootstrapped samples. :param num_bootstrap_simulations: Number of simulations for the bootstrap method. :param sample_size_fraction: Fraction of the dataset to be resampled. :returns: A collections.namedtuple containing a list of bootstrapped estimates and a dictionary containing parameters used for the bootstrap. """ # The array that stores the results of all estimations simulation_results = np.zeros(num_bootstrap_simulations) # Find the sample size the proportion with the population size sample_size = int(sample_size_fraction * len(self._data)) if sample_size > len(self._data): self.logger.warning("WARN: The sample size is greater than the data being sampled") self.logger.info("INFO: The sample size: {}".format(sample_size)) self.logger.info("INFO: The number of simulations: {}".format(num_bootstrap_simulations)) # Perform the set number of simulations for index in range(num_bootstrap_simulations): new_data = resample(self._data, n_samples=sample_size) new_estimator = type(self)( new_data, self._target_estimand, self._target_estimand.treatment_variable, self._target_estimand.outcome_variable, # names of treatment and outcome treatment_value=self._treatment_value, control_value=self._control_value, test_significance=False, evaluate_effect_strength=False, confidence_intervals=False, target_units=self._target_units, effect_modifiers=self._effect_modifier_names, **self.method_params, ) new_effect = new_estimator.estimate_effect() simulation_results[index] = new_effect.value estimates = CausalEstimator.BootstrapEstimates( simulation_results, {"num_simulations": num_bootstrap_simulations, "sample_size_fraction": sample_size_fraction}, ) return estimates def _estimate_confidence_intervals_with_bootstrap( self, estimate_value, confidence_level=None, num_simulations=None, sample_size_fraction=None ): """ Method to compute confidence interval using bootstrapped sampling. :param estimate_value: obtained estimate's value :param confidence_level: The level for which to compute CI (e.g., 95% confidence level translates to confidence_level=0.95) :param num_simulations: The number of simulations to be performed to get the bootstrap confidence intervals. :param sample_size_fraction: The fraction of the dataset to be resampled. :returns: confidence interval at the specified level. For more details on bootstrap or resampling statistics, refer to the following links: https://ocw.mit.edu/courses/mathematics/18-05-introduction-to-probability-and-statistics-spring-2014/readings/MIT18_05S14_Reading24.pdf https://projecteuclid.org/download/pdf_1/euclid.ss/1032280214 """ # Using class default parameters if not specified if num_simulations is None: num_simulations = self.num_simulations if sample_size_fraction is None: sample_size_fraction = self.sample_size_fraction # Checking if bootstrap_estimates are already computed if self._bootstrap_estimates is None: self._bootstrap_estimates = self._generate_bootstrap_estimates(num_simulations, sample_size_fraction) elif CausalEstimator.is_bootstrap_parameter_changed(self._bootstrap_estimates.params, locals()): # Checked if any parameter is changed from the previous std error estimate self._bootstrap_estimates = self._generate_bootstrap_estimates(num_simulations, sample_size_fraction) # Now use the data obtained from the simulations to get the value of the confidence estimates bootstrap_estimates = self._bootstrap_estimates.estimates # Get the variations of each bootstrap estimate and sort bootstrap_variations = [bootstrap_estimate - estimate_value for bootstrap_estimate in bootstrap_estimates] sorted_bootstrap_variations = np.sort(bootstrap_variations) # Now we take the (1- p)th and the (p)th variations, where p is the chosen confidence level upper_bound_index = int((1 - confidence_level) * len(sorted_bootstrap_variations)) lower_bound_index = int(confidence_level * len(sorted_bootstrap_variations)) # Get the lower and upper bounds by subtracting the variations from the estimate lower_bound = estimate_value - sorted_bootstrap_variations[lower_bound_index] upper_bound = estimate_value - sorted_bootstrap_variations[upper_bound_index] return lower_bound, upper_bound def _estimate_confidence_intervals(self, confidence_level=None, method=None, **kwargs): """ This method is to be overriden by the child classes, so that they can run a confidence interval estimation method suited to the specific causal estimator. """ raise NotImplementedError( ( "This method for estimating confidence intervals is " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG + " Meanwhile, you can try the bootstrap method (method='bootstrap') to estimate confidence intervals." ).format(self.__class__) ) def estimate_confidence_intervals(self, estimate_value, confidence_level=None, method=None, **kwargs): """Find the confidence intervals corresponding to any estimator By default, this is done with the help of bootstrapped confidence intervals but can be overridden if the specific estimator implements other methods of estimating confidence intervals. If the method provided is not bootstrap, this function calls the implementation of the specific estimator. :param estimate_value: obtained estimate's value :param method: Method for estimating confidence intervals. :param confidence_level: The confidence level of the confidence intervals of the estimate. :param kwargs: Other optional args to be passed to the CI method. :returns: The obtained confidence interval. """ if method is None: if self._confidence_intervals: method = self._confidence_intervals # this is either True or methodname else: method = "default" confidence_intervals = None if confidence_level is None: confidence_level = self.confidence_level if method == "default" or method is True: # user has not provided any method try: confidence_intervals = self._estimate_confidence_intervals(confidence_level, method=method, **kwargs) except NotImplementedError: confidence_intervals = self._estimate_confidence_intervals_with_bootstrap( estimate_value, confidence_level, **kwargs ) else: if method == "bootstrap": confidence_intervals = self._estimate_confidence_intervals_with_bootstrap( estimate_value, confidence_level, **kwargs ) else: confidence_intervals = self._estimate_confidence_intervals(confidence_level, method=method, **kwargs) return confidence_intervals def _estimate_std_error_with_bootstrap(self, num_simulations=None, sample_size_fraction=None): """Compute standard error using the bootstrap method. Standard error and confidence intervals use the same parameter num_simulations for the number of bootstrap simulations. :param num_simulations: Number of bootstrapped samples. :param sample_size_fraction: Fraction of data to be resampled. :returns: Standard error of the obtained estimate. """ # Use existing params, if new user defined params are not present if num_simulations is None: num_simulations = self.num_simulations if sample_size_fraction is None: sample_size_fraction = self.sample_size_fraction # Checking if bootstrap_estimates are already computed if self._bootstrap_estimates is None: self._bootstrap_estimates = self._generate_bootstrap_estimates(num_simulations, sample_size_fraction) elif CausalEstimator.is_bootstrap_parameter_changed(self._bootstrap_estimates.params, locals()): # Check if any parameter is changed from the previous std error estimate self._bootstrap_estimates = self._generate_bootstrap_estimates(num_simulations, sample_size_fraction) std_error = np.std(self._bootstrap_estimates.estimates) return std_error def _estimate_std_error(self, method=None, **kwargs): """ This method is to be overriden by the child classes, so that they can run a standard error estimation method suited to the specific causal estimator. """ raise NotImplementedError( ( "This method for estimating standard errors is " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG + " Meanwhile, you can try the bootstrap method (method='bootstrap') to estimate standard errors." ).format(self.__class__) ) def estimate_std_error(self, method=None, **kwargs): """Compute standard error of an obtained causal estimate. :param method: Method for computing the standard error. :param kwargs: Other optional parameters to be passed to the estimating method. :returns: Standard error of the causal estimate. """ if method is None: if self._confidence_intervals: method = self._confidence_intervals else: method = "default" std_error = None if method == "default" or method is True: # user has not provided any method try: std_error = self._estimate_std_error(method, **kwargs) except NotImplementedError: std_error = self._estimate_std_error_with_bootstrap(**kwargs) else: if method == "bootstrap": std_error = self._estimate_std_error_with_bootstrap(**kwargs) else: std_error = self._estimate_std_error(method, **kwargs) return std_error def _test_significance_with_bootstrap(self, estimate_value, num_null_simulations=None): """Test statistical significance of an estimate using the bootstrap method. :param estimate_value: Obtained estimate's value :param num_null_simulations: Number of simulations for the null hypothesis :returns: p-value of the statistical significance test. """ # Use existing params, if new user defined params are not present if num_null_simulations is None: num_null_simulations = self.num_null_simulations do_retest = self._bootstrap_null_estimates is None or CausalEstimator.is_bootstrap_parameter_changed( self._bootstrap_null_estimates.params, locals() ) if do_retest: null_estimates = np.zeros(num_null_simulations) for i in range(num_null_simulations): new_outcome = np.random.permutation(self._outcome) new_data = self._data.assign(dummy_outcome=new_outcome) # self._outcome = self._data["dummy_outcome"] new_estimator = type(self)( new_data, self._target_estimand, self._target_estimand.treatment_variable, ("dummy_outcome",), test_significance=False, evaluate_effect_strength=False, confidence_intervals=False, target_units=self._target_units, effect_modifiers=self._effect_modifier_names, **self.method_params, ) new_effect = new_estimator.estimate_effect() null_estimates[i] = new_effect.value self._bootstrap_null_estimates = CausalEstimator.BootstrapEstimates( null_estimates, {"num_null_simulations": num_null_simulations, "sample_size_fraction": 1} ) # Processing the null hypothesis estimates sorted_null_estimates = np.sort(self._bootstrap_null_estimates.estimates) self.logger.debug("Null estimates: {0}".format(sorted_null_estimates)) median_estimate = sorted_null_estimates[int(num_null_simulations / 2)] # Doing a two-sided test if estimate_value > median_estimate: # Being conservative with the p-value reported estimate_index = np.searchsorted(sorted_null_estimates, estimate_value, side="left") p_value = 1 - (estimate_index / num_null_simulations) if estimate_value <= median_estimate: # Being conservative with the p-value reported estimate_index = np.searchsorted(sorted_null_estimates, estimate_value, side="right") p_value = estimate_index / num_null_simulations # If the estimate_index is 0, it depends on the number of simulations if p_value == 0: p_value = (0, 1 / len(sorted_null_estimates)) # a tuple determining the range. elif p_value == 1: p_value = (1 - 1 / len(sorted_null_estimates), 1) signif_dict = {"p_value": p_value} return signif_dict def _test_significance(self, estimate_value, method=None, **kwargs): """ This method is to be overriden by the child classes, so that they can run a significance test suited to the specific causal estimator. """ raise NotImplementedError( ( "This method for testing statistical significance is " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG + " Meanwhile, you can try the bootstrap method (method='bootstrap') to test statistical significance." ).format(self.__class__) ) def test_significance(self, estimate_value, method=None, **kwargs): """Test statistical significance of obtained estimate. By default, uses resampling to create a non-parametric significance test. A general procedure. Individual child estimators can implement different methods. If the method name is different from "bootstrap", this function calls the implementation of the child estimator. :param self: object instance of class Estimator :param estimate_value: obtained estimate's value :param method: Method for checking statistical significance :returns: p-value from the significance test """ if method is None: if self._significance_test: method = self._significance_test # this is either True or methodname else: method = "default" signif_dict = None if method == "default" or method is True: # user has not provided any method try: signif_dict = self._test_significance(estimate_value, method, **kwargs) except NotImplementedError: signif_dict = self._test_significance_with_bootstrap(estimate_value, **kwargs) else: if method == "bootstrap": signif_dict = self._test_significance_with_bootstrap(estimate_value, **kwargs) else: signif_dict = self._test_significance(estimate_value, method, **kwargs) return signif_dict def evaluate_effect_strength(self, estimate): fraction_effect_explained = self._evaluate_effect_strength(estimate, method="fraction-effect") # Need to test r-squared before supporting # effect_r_squared = self._evaluate_effect_strength(estimate, method="r-squared") strength_dict = { "fraction-effect": fraction_effect_explained # 'r-squared': effect_r_squared } return strength_dict def _evaluate_effect_strength(self, estimate, method="fraction-effect"): supported_methods = ["fraction-effect"] if method not in supported_methods: raise NotImplementedError("This method is not supported for evaluating effect strength") if method == "fraction-effect": naive_obs_estimate = self.estimate_effect_naive() self.logger.debug(estimate.value, naive_obs_estimate.value) fraction_effect_explained = estimate.value / naive_obs_estimate.value return fraction_effect_explained # elif method == "r-squared": # outcome_mean = np.mean(self._outcome) # total_variance = np.sum(np.square(self._outcome - outcome_mean)) # Assuming a linear model with one variable: the treatment # Currently only works for continuous y # causal_model = outcome_mean + estimate.value*self._treatment # squared_residual = np.sum(np.square(self._outcome - causal_model)) # r_squared = 1 - (squared_residual/total_variance) # return r_squared else: return None def update_input(self, treatment_value, control_value, target_units): self._control_value = control_value self._treatment_value = treatment_value self._target_units = target_units @staticmethod def is_bootstrap_parameter_changed(bootstrap_estimates_params, given_params): """Check whether parameters of the bootstrap have changed. This is an efficiency method that checks if fresh resampling of the bootstrap samples is required. Returns True if parameters have changed and resampling should be done again. :param bootstrap_estimates_params: A dictionary of parameters for the current bootstrap samples :param given_params: A dictionary of parameters passed by the user :returns: A binary flag denoting whether the parameters are different. """ is_any_parameter_changed = False for prm, val in bootstrap_estimates_params.items(): given_val = given_params.get(prm, None) if given_val is not None and given_val != val: is_any_parameter_changed = True break return is_any_parameter_changed def target_units_tostr(self): s = "" if type(self._target_units) is str: s += self._target_units elif callable(self._target_units): s += "Data subset defined by a function" elif isinstance(self._target_units, pd.DataFrame): s += "Data subset provided as a data frame" return s def signif_results_tostr(self, signif_results): s = "" pval = signif_results["p_value"] if type(pval) is tuple: s += "[{0}, {1}]".format(pval[0], pval[1]) else: s += "{0}".format(pval) return s class CausalEstimate: """Class for the estimate object that every causal estimator returns""" def __init__( self, estimate, target_estimand, realized_estimand_expr, control_value, treatment_value, conditional_estimates=None, **kwargs, ): self.value = estimate self.target_estimand = target_estimand self.realized_estimand_expr = realized_estimand_expr self.control_value = control_value self.treatment_value = treatment_value self.conditional_estimates = conditional_estimates self.params = kwargs if self.params is not None: for key, value in self.params.items(): setattr(self, key, value) self.effect_strength = None def add_estimator(self, estimator_instance): self.estimator = estimator_instance def add_effect_strength(self, strength_dict): self.effect_strength = strength_dict def add_params(self, **kwargs): self.params.update(kwargs) def get_confidence_intervals(self, confidence_level=None, method=None, **kwargs): """Get confidence intervals of the obtained estimate. By default, this is done with the help of bootstrapped confidence intervals but can be overridden if the specific estimator implements other methods of estimating confidence intervals. If the method provided is not bootstrap, this function calls the implementation of the specific estimator. :param method: Method for estimating confidence intervals. :param confidence_level: The confidence level of the confidence intervals of the estimate. :param kwargs: Other optional args to be passed to the CI method. :returns: The obtained confidence interval. """ confidence_intervals = self.estimator.estimate_confidence_intervals( estimate_value=self.value, confidence_level=confidence_level, method=method, **kwargs ) return confidence_intervals def get_standard_error(self, method=None, **kwargs): """Get standard error of the obtained estimate. By default, this is done with the help of bootstrapped standard errors but can be overridden if the specific estimator implements other methods of estimating standard error. If the method provided is not bootstrap, this function calls the implementation of the specific estimator. :param method: Method for computing the standard error. :param kwargs: Other optional parameters to be passed to the estimating method. :returns: Standard error of the causal estimate. """ std_error = self.estimator.estimate_std_error(method=method, **kwargs) return std_error def test_stat_significance(self, method=None, **kwargs): """Test statistical significance of the estimate obtained. By default, uses resampling to create a non-parametric significance test. Individual child estimators can implement different methods. If the method name is different from "bootstrap", this function calls the implementation of the child estimator. :param method: Method for checking statistical significance :param kwargs: Other optional parameters to be passed to the estimating method. :returns: p-value from the significance test """ signif_results = self.estimator.test_significance(self.value, method=method, **kwargs) return {"p_value": signif_results["p_value"]} def estimate_conditional_effects( self, effect_modifiers=None, num_quantiles=CausalEstimator.NUM_QUANTILES_TO_DISCRETIZE_CONT_COLS ): """Estimate treatment effect conditioned on given variables. If a numeric effect modifier is provided, it is discretized into quantile bins. If you would like a custom discretization, you can do so yourself: create a new column containing the discretized effect modifier and then include that column's name in the effect_modifier_names argument. :param effect_modifiers: Names of effect modifier variables over which the conditional effects will be estimated. If not provided, defaults to the effect modifiers specified during creation of the CausalEstimator object. :param num_quantiles: The number of quantiles into which a numeric effect modifier variable is discretized. Does not affect any categorical effect modifiers. :returns: A (multi-index) dataframe that provides separate effects for each value of the (discretized) effect modifiers. """ return self.estimator._estimate_conditional_effects( self.estimator._estimate_effect_fn, effect_modifiers, num_quantiles ) def interpret(self, method_name=None, **kwargs): """Interpret the causal estimate. :param method_name: Method used (string) or a list of methods. If None, then the default for the specific estimator is used. :param kwargs:: Optional parameters that are directly passed to the interpreter method. :returns: None """ if method_name is None: method_name = self.estimator.interpret_method method_name_arr = parse_state(method_name) for method in method_name_arr: interpreter = interpreters.get_class_object(method) interpreter(self, **kwargs).interpret() def __str__(self): s = "*** Causal Estimate ***\n" # No estimand was identified (identification failed) if self.target_estimand is None: return "Estimation failed! No relevant identified estimand available for this estimation method." s += "\n## Identified estimand\n{0}".format(self.target_estimand.__str__(only_target_estimand=True)) s += "\n## Realized estimand\n{0}".format(self.realized_estimand_expr) if hasattr(self, "estimator"): s += "\nTarget units: {0}\n".format(self.estimator.target_units_tostr()) s += "\n## Estimate\n" s += "Mean value: {0}\n".format(self.value) s += "" if hasattr(self, "cate_estimates"): s += "Effect estimates: {0}\n".format(self.cate_estimates) if hasattr(self, "estimator"): if self.estimator._significance_test: s += "p-value: {0}\n".format(self.estimator.signif_results_tostr(self.test_stat_significance())) if self.estimator._confidence_intervals: s += "{0}% confidence interval: {1}\n".format( 100 * self.estimator.confidence_level, self.get_confidence_intervals() ) if self.conditional_estimates is not None: s += "### Conditional Estimates\n" s += str(self.conditional_estimates) if self.effect_strength is not None: s += "\n## Effect Strength\n" s += "Change in outcome attributable to treatment: {}\n".format(self.effect_strength["fraction-effect"]) # s += "Variance in outcome explained by treatment: {}\n".format(self.effect_strength["r-squared"]) return s class RealizedEstimand(object): def __init__(self, identified_estimand, estimator_name): self.treatment_variable = identified_estimand.treatment_variable self.outcome_variable = identified_estimand.outcome_variable self.backdoor_variables = identified_estimand.get_backdoor_variables() self.instrumental_variables = identified_estimand.instrumental_variables self.estimand_type = identified_estimand.estimand_type self.estimand_expression = None self.assumptions = None self.estimator_name = estimator_name def update_assumptions(self, estimator_assumptions): self.assumptions = estimator_assumptions def update_estimand_expression(self, estimand_expression): self.estimand_expression = estimand_expression def __str__(self): s = "Realized estimand: {0}\n".format(self.estimator_name) s += "Realized estimand type: {0}\n".format(self.estimand_type) s += "Estimand expression:\n{0}\n".format(sp.pretty(self.estimand_expression)) j = 1 for ass_name, ass_str in self.assumptions.items(): s += "Estimand assumption {0}, {1}: {2}\n".format(j, ass_name, ass_str) j += 1 return s

import logging from collections import namedtuple from typing import Dict, List, Optional, Union import numpy as np import pandas as pd import sympy as sp from sklearn.utils import resample import dowhy.interpreters as interpreters from dowhy import causal_estimators from dowhy.causal_graph import CausalGraph from dowhy.causal_identifier.identified_estimand import IdentifiedEstimand from dowhy.utils.api import parse_state logger = logging.getLogger(__name__) class CausalEstimator: """Base class for an estimator of causal effect. Subclasses implement different estimation methods. All estimation methods are in the package "dowhy.causal_estimators" """ # The default number of simulations for statistical testing DEFAULT_NUMBER_OF_SIMULATIONS_STAT_TEST = 1000 # The default number of simulations to obtain confidence intervals DEFAULT_NUMBER_OF_SIMULATIONS_CI = 100 # The portion of the total size that should be taken each time to find the confidence intervals # 1 is the recommended value # https://ocw.mit.edu/courses/mathematics/18-05-introduction-to-probability-and-statistics-spring-2014/readings/MIT18_05S14_Reading24.pdf # https://projecteuclid.org/download/pdf_1/euclid.ss/1032280214 DEFAULT_SAMPLE_SIZE_FRACTION = 1 # The default Confidence Level DEFAULT_CONFIDENCE_LEVEL = 0.95 # Number of quantiles to discretize continuous columns, for applying groupby NUM_QUANTILES_TO_DISCRETIZE_CONT_COLS = 5 # Prefix to add to temporary categorical variables created after discretization TEMP_CAT_COLUMN_PREFIX = "__categorical__" DEFAULT_NOTIMPLEMENTEDERROR_MSG = "not yet implemented for {0}. If you would this to be implemented in the next version, please raise an issue at https://github.com/microsoft/dowhy/issues" BootstrapEstimates = namedtuple("BootstrapEstimates", ["estimates", "params"]) DEFAULT_INTERPRET_METHOD = ["textual_effect_interpreter"] # std args to be removed from locals() before being passed to args_dict _STD_INIT_ARGS = ("self", "__class__", "args", "kwargs") def __init__( self, data, identified_estimand, treatment, outcome, control_value=0, treatment_value=1, test_significance=False, evaluate_effect_strength=False, confidence_intervals=False, target_units=None, effect_modifiers=None, num_null_simulations=DEFAULT_NUMBER_OF_SIMULATIONS_STAT_TEST, num_simulations=DEFAULT_NUMBER_OF_SIMULATIONS_CI, sample_size_fraction=DEFAULT_SAMPLE_SIZE_FRACTION, confidence_level=DEFAULT_CONFIDENCE_LEVEL, need_conditional_estimates="auto", num_quantiles_to_discretize_cont_cols=NUM_QUANTILES_TO_DISCRETIZE_CONT_COLS, **kwargs, ): """Initializes an estimator with data and names of relevant variables. This method is called from the constructors of its child classes. :param data: data frame containing the data :param identified_estimand: probability expression representing the target identified estimand to estimate. :param treatment: name of the treatment variable :param outcome: name of the outcome variable :param control_value: Value of the treatment in the control group, for effect estimation. If treatment is multi-variate, this can be a list. :param treatment_value: Value of the treatment in the treated group, for effect estimation. If treatment is multi-variate, this can be a list. :param test_significance: Binary flag or a string indicating whether to test significance and by which method. All estimators support test_significance="bootstrap" that estimates a p-value for the obtained estimate using the bootstrap method. Individual estimators can override this to support custom testing methods. The bootstrap method supports an optional parameter, num_null_simulations. If False, no testing is done. If True, significance of the estimate is tested using the custom method if available, otherwise by bootstrap. :param evaluate_effect_strength: (Experimental) whether to evaluate the strength of effect :param confidence_intervals: Binary flag or a string indicating whether the confidence intervals should be computed and which method should be used. All methods support estimation of confidence intervals using the bootstrap method by using the parameter confidence_intervals="bootstrap". The bootstrap method takes in two arguments (num_simulations and sample_size_fraction) that can be optionally specified in the params dictionary. Estimators may also override this to implement their own confidence interval method. If this parameter is False, no confidence intervals are computed. If True, confidence intervals are computed by the estimator's specific method if available, otherwise through bootstrap. :param target_units: The units for which the treatment effect should be estimated. This can be a string for common specifications of target units (namely, "ate", "att" and "atc"). It can also be a lambda function that can be used as an index for the data (pandas DataFrame). Alternatively, it can be a new DataFrame that contains values of the effect_modifiers and effect will be estimated only for this new data. :param effect_modifiers: Variables on which to compute separate effects, or return a heterogeneous effect function. Not all methods support this currently. :param num_null_simulations: The number of simulations for testing the statistical significance of the estimator :param num_simulations: The number of simulations for finding the confidence interval (and/or standard error) for a estimate :param sample_size_fraction: The size of the sample for the bootstrap estimator :param confidence_level: The confidence level of the confidence interval estimate :param need_conditional_estimates: Boolean flag indicating whether conditional estimates should be computed. Defaults to True if there are effect modifiers in the graph :param num_quantiles_to_discretize_cont_cols: The number of quantiles into which a numeric effect modifier is split, to enable estimation of conditional treatment effect over it. :param kwargs: (optional) Additional estimator-specific parameters :returns: an instance of the estimator class. """ self._data = data self._target_estimand = identified_estimand # Currently estimation methods only support univariate treatment and outcome self._treatment_name = treatment self._outcome_name = outcome[0] # assuming one-dimensional outcome self._control_value = control_value self._treatment_value = treatment_value self._significance_test = test_significance self._effect_strength_eval = evaluate_effect_strength self._target_units = target_units self._effect_modifier_names = effect_modifiers self._confidence_intervals = confidence_intervals self._bootstrap_estimates = None # for confidence intervals and std error self._bootstrap_null_estimates = None # for significance test self._effect_modifiers = None self.method_params = kwargs # Setting the default interpret method self.interpret_method = CausalEstimator.DEFAULT_INTERPRET_METHOD self.logger = logging.getLogger(__name__) # Setting treatment and outcome values if self._data is not None: self._treatment = self._data[self._treatment_name] self._outcome = self._data[self._outcome_name] if self._effect_modifier_names: # only add the observed nodes self._effect_modifier_names = [ cname for cname in self._effect_modifier_names if cname in self._data.columns ] if len(self._effect_modifier_names) > 0: self._effect_modifiers = self._data[self._effect_modifier_names] self._effect_modifiers = pd.get_dummies(self._effect_modifiers, drop_first=True) self.logger.debug("Effect modifiers: " + ",".join(self._effect_modifier_names)) else: self._effect_modifier_names = None # Check if some parameters were set, otherwise set to default values self.num_null_simulations = num_null_simulations self.num_simulations = num_simulations self.sample_size_fraction = sample_size_fraction self.confidence_level = confidence_level self.num_quantiles_to_discretize_cont_cols = num_quantiles_to_discretize_cont_cols # Estimate conditional estimates by default self.need_conditional_estimates = ( need_conditional_estimates if need_conditional_estimates != "auto" else bool(self._effect_modifier_names) ) @staticmethod def get_estimator_object(new_data, identified_estimand, estimate): """Create a new estimator of the same type as the one passed in the estimate argument. Creates a new object with new_data and the identified_estimand :param new_data: np.ndarray, pd.Series, pd.DataFrame The newly assigned data on which the estimator should run :param identified_estimand: IdentifiedEstimand An instance of the identified estimand class that provides the information with respect to which causal pathways are employed when the treatment effects the outcome :param estimate: CausalEstimate It is an already existing estimate whose properties we wish to replicate :returns: An instance of the same estimator class that had generated the given estimate. """ estimator_class = estimate.params["estimator_class"] new_estimator = estimator_class( new_data, identified_estimand, identified_estimand.treatment_variable, identified_estimand.outcome_variable, # names of treatment and outcome control_value=estimate.control_value, treatment_value=estimate.treatment_value, test_significance=False, evaluate_effect_strength=False, confidence_intervals=estimate.params["confidence_intervals"], target_units=estimate.params["target_units"], effect_modifiers=estimate.params["effect_modifiers"], **estimate.params["method_params"] if estimate.params["method_params"] is not None else {}, ) return new_estimator def _estimate_effect(self): """This method is to be overriden by the child classes, so that they can run the estimation technique of their choice""" raise NotImplementedError( ("Main estimation method is " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG).format(self.__class__) ) def estimate_effect(self): """Base estimation method that calls the estimate_effect method of its calling subclass. Can optionally also test significance and estimate effect strength for any returned estimate. :param self: object instance of class Estimator :returns: A CausalEstimate instance that contains point estimates of average and conditional effects. Based on the parameters provided, it optionally includes confidence intervals, standard errors,statistical significance and other statistical parameters. """ est = self._estimate_effect() est.add_estimator(self) if self._significance_test: self.test_significance(est.value, method=self._significance_test) if self._confidence_intervals: self.estimate_confidence_intervals( est.value, confidence_level=self.confidence_level, method=self._confidence_intervals ) if self._effect_strength_eval: effect_strength_dict = self.evaluate_effect_strength(est) est.add_effect_strength(effect_strength_dict) return est def estimate_effect_naive(self): # TODO Only works for binary treatment df_withtreatment = self._data.loc[self._data[self._treatment_name] == 1] df_notreatment = self._data.loc[self._data[self._treatment_name] == 0] est = np.mean(df_withtreatment[self._outcome_name]) - np.mean(df_notreatment[self._outcome_name]) return CausalEstimate(est, None, None, control_value=0, treatment_value=1) def _estimate_effect_fn(self, data_df): """Function used in conditional effect estimation. This function is to be overridden by each child estimator. The overridden function should take in a dataframe as input and return the estimate for that data. """ raise NotImplementedError( ("Conditional treatment effects are " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG).format( self.__class__ ) ) def _estimate_conditional_effects(self, estimate_effect_fn, effect_modifier_names=None, num_quantiles=None): """Estimate conditional treatment effects. Common method for all estimators that utilizes a specific estimate_effect_fn implemented by each child estimator. If a numeric effect modifier is provided, it is discretized into quantile bins. If you would like a custom discretization, you can do so yourself: create a new column containing the discretized effect modifier and then include that column's name in the effect_modifier_names argument. :param estimate_effect_fn: Function that has a single parameter (a data frame) and returns the treatment effect estimate on that data. :param effect_modifier_names: Names of effect modifier variables over which the conditional effects will be estimated. If not provided, defaults to the effect modifiers specified during creation of the CausalEstimator object. :param num_quantiles: The number of quantiles into which a numeric effect modifier variable is discretized. Does not affect any categorical effect modifiers. :returns: A (multi-index) dataframe that provides separate effects for each value of the (discretized) effect modifiers. """ # Defaulting to class default values if parameters are not provided if effect_modifier_names is None: effect_modifier_names = self._effect_modifier_names if num_quantiles is None: num_quantiles = self.num_quantiles_to_discretize_cont_cols # Checking that there is at least one effect modifier if not effect_modifier_names: raise ValueError("At least one effect modifier should be specified to compute conditional effects.") # Making sure that effect_modifier_names is a list effect_modifier_names = parse_state(effect_modifier_names) if not all(em in self._effect_modifier_names for em in effect_modifier_names): self.logger.warn( "At least one of the provided effect modifiers was not included while fitting the estimator. You may get incorrect results. To resolve, fit the estimator again by providing the updated effect modifiers in estimate_effect()." ) # Making a copy since we are going to be changing effect modifier names effect_modifier_names = effect_modifier_names.copy() prefix = CausalEstimator.TEMP_CAT_COLUMN_PREFIX # For every numeric effect modifier, adding a temp categorical column for i in range(len(effect_modifier_names)): em = effect_modifier_names[i] if pd.api.types.is_numeric_dtype(self._data[em].dtypes): self._data[prefix + str(em)] = pd.qcut(self._data[em], num_quantiles, duplicates="drop") effect_modifier_names[i] = prefix + str(em) # Grouping by effect modifiers and computing effect separately by_effect_mods = self._data.groupby(effect_modifier_names) cond_est_fn = lambda x: self._do(self._treatment_value, x) - self._do(self._control_value, x) conditional_estimates = by_effect_mods.apply(estimate_effect_fn) # Deleting the temporary categorical columns for em in effect_modifier_names: if em.startswith(prefix): self._data.pop(em) return conditional_estimates def _do(self, x, data_df=None): raise NotImplementedError( ("Do-operator is " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG).format(self.__class__) ) def do(self, x, data_df=None): """Method that implements the do-operator. Given a value x for the treatment, returns the expected value of the outcome when the treatment is intervened to a value x. :param x: Value of the treatment :param data_df: Data on which the do-operator is to be applied. :returns: Value of the outcome when treatment is intervened/set to x. """ est = self._do(x, data_df) return est def construct_symbolic_estimator(self, estimand): raise NotImplementedError(("Symbolic estimator string is ").format(self.__class__)) def _generate_bootstrap_estimates(self, num_bootstrap_simulations, sample_size_fraction): """Helper function to generate causal estimates over bootstrapped samples. :param num_bootstrap_simulations: Number of simulations for the bootstrap method. :param sample_size_fraction: Fraction of the dataset to be resampled. :returns: A collections.namedtuple containing a list of bootstrapped estimates and a dictionary containing parameters used for the bootstrap. """ # The array that stores the results of all estimations simulation_results = np.zeros(num_bootstrap_simulations) # Find the sample size the proportion with the population size sample_size = int(sample_size_fraction * len(self._data)) if sample_size > len(self._data): self.logger.warning("WARN: The sample size is greater than the data being sampled") self.logger.info("INFO: The sample size: {}".format(sample_size)) self.logger.info("INFO: The number of simulations: {}".format(num_bootstrap_simulations)) # Perform the set number of simulations for index in range(num_bootstrap_simulations): new_data = resample(self._data, n_samples=sample_size) new_estimator = type(self)( new_data, self._target_estimand, self._target_estimand.treatment_variable, self._target_estimand.outcome_variable, # names of treatment and outcome treatment_value=self._treatment_value, control_value=self._control_value, test_significance=False, evaluate_effect_strength=False, confidence_intervals=False, target_units=self._target_units, effect_modifiers=self._effect_modifier_names, **self.method_params, ) new_effect = new_estimator.estimate_effect() simulation_results[index] = new_effect.value estimates = CausalEstimator.BootstrapEstimates( simulation_results, {"num_simulations": num_bootstrap_simulations, "sample_size_fraction": sample_size_fraction}, ) return estimates def _estimate_confidence_intervals_with_bootstrap( self, estimate_value, confidence_level=None, num_simulations=None, sample_size_fraction=None ): """ Method to compute confidence interval using bootstrapped sampling. :param estimate_value: obtained estimate's value :param confidence_level: The level for which to compute CI (e.g., 95% confidence level translates to confidence_level=0.95) :param num_simulations: The number of simulations to be performed to get the bootstrap confidence intervals. :param sample_size_fraction: The fraction of the dataset to be resampled. :returns: confidence interval at the specified level. For more details on bootstrap or resampling statistics, refer to the following links: https://ocw.mit.edu/courses/mathematics/18-05-introduction-to-probability-and-statistics-spring-2014/readings/MIT18_05S14_Reading24.pdf https://projecteuclid.org/download/pdf_1/euclid.ss/1032280214 """ # Using class default parameters if not specified if num_simulations is None: num_simulations = self.num_simulations if sample_size_fraction is None: sample_size_fraction = self.sample_size_fraction # Checking if bootstrap_estimates are already computed if self._bootstrap_estimates is None: self._bootstrap_estimates = self._generate_bootstrap_estimates(num_simulations, sample_size_fraction) elif CausalEstimator.is_bootstrap_parameter_changed(self._bootstrap_estimates.params, locals()): # Checked if any parameter is changed from the previous std error estimate self._bootstrap_estimates = self._generate_bootstrap_estimates(num_simulations, sample_size_fraction) # Now use the data obtained from the simulations to get the value of the confidence estimates bootstrap_estimates = self._bootstrap_estimates.estimates # Get the variations of each bootstrap estimate and sort bootstrap_variations = [bootstrap_estimate - estimate_value for bootstrap_estimate in bootstrap_estimates] sorted_bootstrap_variations = np.sort(bootstrap_variations) # Now we take the (1- p)th and the (p)th variations, where p is the chosen confidence level upper_bound_index = int((1 - confidence_level) * len(sorted_bootstrap_variations)) lower_bound_index = int(confidence_level * len(sorted_bootstrap_variations)) # Get the lower and upper bounds by subtracting the variations from the estimate lower_bound = estimate_value - sorted_bootstrap_variations[lower_bound_index] upper_bound = estimate_value - sorted_bootstrap_variations[upper_bound_index] return lower_bound, upper_bound def _estimate_confidence_intervals(self, confidence_level=None, method=None, **kwargs): """ This method is to be overriden by the child classes, so that they can run a confidence interval estimation method suited to the specific causal estimator. """ raise NotImplementedError( ( "This method for estimating confidence intervals is " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG + " Meanwhile, you can try the bootstrap method (method='bootstrap') to estimate confidence intervals." ).format(self.__class__) ) def estimate_confidence_intervals(self, estimate_value, confidence_level=None, method=None, **kwargs): """Find the confidence intervals corresponding to any estimator By default, this is done with the help of bootstrapped confidence intervals but can be overridden if the specific estimator implements other methods of estimating confidence intervals. If the method provided is not bootstrap, this function calls the implementation of the specific estimator. :param estimate_value: obtained estimate's value :param method: Method for estimating confidence intervals. :param confidence_level: The confidence level of the confidence intervals of the estimate. :param kwargs: Other optional args to be passed to the CI method. :returns: The obtained confidence interval. """ if method is None: if self._confidence_intervals: method = self._confidence_intervals # this is either True or methodname else: method = "default" confidence_intervals = None if confidence_level is None: confidence_level = self.confidence_level if method == "default" or method is True: # user has not provided any method try: confidence_intervals = self._estimate_confidence_intervals(confidence_level, method=method, **kwargs) except NotImplementedError: confidence_intervals = self._estimate_confidence_intervals_with_bootstrap( estimate_value, confidence_level, **kwargs ) else: if method == "bootstrap": confidence_intervals = self._estimate_confidence_intervals_with_bootstrap( estimate_value, confidence_level, **kwargs ) else: confidence_intervals = self._estimate_confidence_intervals(confidence_level, method=method, **kwargs) return confidence_intervals def _estimate_std_error_with_bootstrap(self, num_simulations=None, sample_size_fraction=None): """Compute standard error using the bootstrap method. Standard error and confidence intervals use the same parameter num_simulations for the number of bootstrap simulations. :param num_simulations: Number of bootstrapped samples. :param sample_size_fraction: Fraction of data to be resampled. :returns: Standard error of the obtained estimate. """ # Use existing params, if new user defined params are not present if num_simulations is None: num_simulations = self.num_simulations if sample_size_fraction is None: sample_size_fraction = self.sample_size_fraction # Checking if bootstrap_estimates are already computed if self._bootstrap_estimates is None: self._bootstrap_estimates = self._generate_bootstrap_estimates(num_simulations, sample_size_fraction) elif CausalEstimator.is_bootstrap_parameter_changed(self._bootstrap_estimates.params, locals()): # Check if any parameter is changed from the previous std error estimate self._bootstrap_estimates = self._generate_bootstrap_estimates(num_simulations, sample_size_fraction) std_error = np.std(self._bootstrap_estimates.estimates) return std_error def _estimate_std_error(self, method=None, **kwargs): """ This method is to be overriden by the child classes, so that they can run a standard error estimation method suited to the specific causal estimator. """ raise NotImplementedError( ( "This method for estimating standard errors is " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG + " Meanwhile, you can try the bootstrap method (method='bootstrap') to estimate standard errors." ).format(self.__class__) ) def estimate_std_error(self, method=None, **kwargs): """Compute standard error of an obtained causal estimate. :param method: Method for computing the standard error. :param kwargs: Other optional parameters to be passed to the estimating method. :returns: Standard error of the causal estimate. """ if method is None: if self._confidence_intervals: method = self._confidence_intervals else: method = "default" std_error = None if method == "default" or method is True: # user has not provided any method try: std_error = self._estimate_std_error(method, **kwargs) except NotImplementedError: std_error = self._estimate_std_error_with_bootstrap(**kwargs) else: if method == "bootstrap": std_error = self._estimate_std_error_with_bootstrap(**kwargs) else: std_error = self._estimate_std_error(method, **kwargs) return std_error def _test_significance_with_bootstrap(self, estimate_value, num_null_simulations=None): """Test statistical significance of an estimate using the bootstrap method. :param estimate_value: Obtained estimate's value :param num_null_simulations: Number of simulations for the null hypothesis :returns: p-value of the statistical significance test. """ # Use existing params, if new user defined params are not present if num_null_simulations is None: num_null_simulations = self.num_null_simulations do_retest = self._bootstrap_null_estimates is None or CausalEstimator.is_bootstrap_parameter_changed( self._bootstrap_null_estimates.params, locals() ) if do_retest: null_estimates = np.zeros(num_null_simulations) for i in range(num_null_simulations): new_outcome = np.random.permutation(self._outcome) new_data = self._data.assign(dummy_outcome=new_outcome) # self._outcome = self._data["dummy_outcome"] new_estimator = type(self)( new_data, self._target_estimand, self._target_estimand.treatment_variable, ("dummy_outcome",), test_significance=False, evaluate_effect_strength=False, confidence_intervals=False, target_units=self._target_units, effect_modifiers=self._effect_modifier_names, **self.method_params, ) new_effect = new_estimator.estimate_effect() null_estimates[i] = new_effect.value self._bootstrap_null_estimates = CausalEstimator.BootstrapEstimates( null_estimates, {"num_null_simulations": num_null_simulations, "sample_size_fraction": 1} ) # Processing the null hypothesis estimates sorted_null_estimates = np.sort(self._bootstrap_null_estimates.estimates) self.logger.debug("Null estimates: {0}".format(sorted_null_estimates)) median_estimate = sorted_null_estimates[int(num_null_simulations / 2)] # Doing a two-sided test if estimate_value > median_estimate: # Being conservative with the p-value reported estimate_index = np.searchsorted(sorted_null_estimates, estimate_value, side="left") p_value = 1 - (estimate_index / num_null_simulations) if estimate_value <= median_estimate: # Being conservative with the p-value reported estimate_index = np.searchsorted(sorted_null_estimates, estimate_value, side="right") p_value = estimate_index / num_null_simulations # If the estimate_index is 0, it depends on the number of simulations if p_value == 0: p_value = (0, 1 / len(sorted_null_estimates)) # a tuple determining the range. elif p_value == 1: p_value = (1 - 1 / len(sorted_null_estimates), 1) signif_dict = {"p_value": p_value} return signif_dict def _test_significance(self, estimate_value, method=None, **kwargs): """ This method is to be overriden by the child classes, so that they can run a significance test suited to the specific causal estimator. """ raise NotImplementedError( ( "This method for testing statistical significance is " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG + " Meanwhile, you can try the bootstrap method (method='bootstrap') to test statistical significance." ).format(self.__class__) ) def test_significance(self, estimate_value, method=None, **kwargs): """Test statistical significance of obtained estimate. By default, uses resampling to create a non-parametric significance test. A general procedure. Individual child estimators can implement different methods. If the method name is different from "bootstrap", this function calls the implementation of the child estimator. :param self: object instance of class Estimator :param estimate_value: obtained estimate's value :param method: Method for checking statistical significance :returns: p-value from the significance test """ if method is None: if self._significance_test: method = self._significance_test # this is either True or methodname else: method = "default" signif_dict = None if method == "default" or method is True: # user has not provided any method try: signif_dict = self._test_significance(estimate_value, method, **kwargs) except NotImplementedError: signif_dict = self._test_significance_with_bootstrap(estimate_value, **kwargs) else: if method == "bootstrap": signif_dict = self._test_significance_with_bootstrap(estimate_value, **kwargs) else: signif_dict = self._test_significance(estimate_value, method, **kwargs) return signif_dict def evaluate_effect_strength(self, estimate): fraction_effect_explained = self._evaluate_effect_strength(estimate, method="fraction-effect") # Need to test r-squared before supporting # effect_r_squared = self._evaluate_effect_strength(estimate, method="r-squared") strength_dict = { "fraction-effect": fraction_effect_explained # 'r-squared': effect_r_squared } return strength_dict def _evaluate_effect_strength(self, estimate, method="fraction-effect"): supported_methods = ["fraction-effect"] if method not in supported_methods: raise NotImplementedError("This method is not supported for evaluating effect strength") if method == "fraction-effect": naive_obs_estimate = self.estimate_effect_naive() self.logger.debug(estimate.value, naive_obs_estimate.value) fraction_effect_explained = estimate.value / naive_obs_estimate.value return fraction_effect_explained # elif method == "r-squared": # outcome_mean = np.mean(self._outcome) # total_variance = np.sum(np.square(self._outcome - outcome_mean)) # Assuming a linear model with one variable: the treatment # Currently only works for continuous y # causal_model = outcome_mean + estimate.value*self._treatment # squared_residual = np.sum(np.square(self._outcome - causal_model)) # r_squared = 1 - (squared_residual/total_variance) # return r_squared else: return None def update_input(self, treatment_value, control_value, target_units): self._control_value = control_value self._treatment_value = treatment_value self._target_units = target_units @staticmethod def is_bootstrap_parameter_changed(bootstrap_estimates_params, given_params): """Check whether parameters of the bootstrap have changed. This is an efficiency method that checks if fresh resampling of the bootstrap samples is required. Returns True if parameters have changed and resampling should be done again. :param bootstrap_estimates_params: A dictionary of parameters for the current bootstrap samples :param given_params: A dictionary of parameters passed by the user :returns: A binary flag denoting whether the parameters are different. """ is_any_parameter_changed = False for prm, val in bootstrap_estimates_params.items(): given_val = given_params.get(prm, None) if given_val is not None and given_val != val: is_any_parameter_changed = True break return is_any_parameter_changed def target_units_tostr(self): s = "" if type(self._target_units) is str: s += self._target_units elif callable(self._target_units): s += "Data subset defined by a function" elif isinstance(self._target_units, pd.DataFrame): s += "Data subset provided as a data frame" return s def signif_results_tostr(self, signif_results): s = "" pval = signif_results["p_value"] if type(pval) is tuple: s += "[{0}, {1}]".format(pval[0], pval[1]) else: s += "{0}".format(pval) return s def estimate_effect( treatment: Union[str, List[str]], outcome: Union[str, List[str]], identified_estimand: IdentifiedEstimand, identifier_name: str, method: CausalEstimator, control_value: int = 0, treatment_value: int = 1, test_significance: Optional[bool] = None, evaluate_effect_strength: bool = False, confidence_intervals: bool = False, target_units: str = "ate", effect_modifiers: List[str] = [], fit_estimator: bool = True, method_params: Optional[Dict] = None, ): """Estimate the identified causal effect. Currently requires an explicit method name to be specified. Method names follow the convention of identification method followed by the specific estimation method: "[backdoor/iv].estimation_method_name". Following methods are supported. * Propensity Score Matching: "backdoor.propensity_score_matching" * Propensity Score Stratification: "backdoor.propensity_score_stratification" * Propensity Score-based Inverse Weighting: "backdoor.propensity_score_weighting" * Linear Regression: "backdoor.linear_regression" * Generalized Linear Models (e.g., logistic regression): "backdoor.generalized_linear_model" * Instrumental Variables: "iv.instrumental_variable" * Regression Discontinuity: "iv.regression_discontinuity" In addition, you can directly call any of the EconML estimation methods. The convention is "backdoor.econml.path-to-estimator-class". For example, for the double machine learning estimator ("DML" class) that is located inside "dml" module of EconML, you can use the method name, "backdoor.econml.dml.DML". CausalML estimators can also be called. See `this demo notebook <https://py-why.github.io/dowhy/example_notebooks/dowhy-conditional-treatment-effects.html>`_. :param treatment: Name of the treatment :param outcome: Name of the outcome :param identified_estimand: a probability expression that represents the effect to be estimated. Output of CausalModel.identify_effect method :param method_name: name of the estimation method to be used. :param control_value: Value of the treatment in the control group, for effect estimation. If treatment is multi-variate, this can be a list. :param treatment_value: Value of the treatment in the treated group, for effect estimation. If treatment is multi-variate, this can be a list. :param test_significance: Binary flag on whether to additionally do a statistical signficance test for the estimate. :param evaluate_effect_strength: (Experimental) Binary flag on whether to estimate the relative strength of the treatment's effect. This measure can be used to compare different treatments for the same outcome (by running this method with different treatments sequentially). :param confidence_intervals: (Experimental) Binary flag indicating whether confidence intervals should be computed. :param target_units: (Experimental) The units for which the treatment effect should be estimated. This can be of three types. (1) a string for common specifications of target units (namely, "ate", "att" and "atc"), (2) a lambda function that can be used as an index for the data (pandas DataFrame), or (3) a new DataFrame that contains values of the effect_modifiers and effect will be estimated only for this new data. :param effect_modifiers: Names of effect modifier variables can be (optionally) specified here too, since they do not affect identification. If None, the effect_modifiers from the CausalModel are used. :param fit_estimator: Boolean flag on whether to fit the estimator. Setting it to False is useful to estimate the effect on new data using a previously fitted estimator. :param method_params: Dictionary containing any method-specific parameters. These are passed directly to the estimating method. See the docs for each estimation method for allowed method-specific params. :returns: An instance of the CausalEstimate class, containing the causal effect estimate and other method-dependent information """ treatment = parse_state(treatment) outcome = parse_state(outcome) causal_estimator_class = method.__class__ identified_estimand.set_identifier_method(identifier_name) if identified_estimand.no_directed_path: logger.warning("No directed path from {0} to {1}.".format(treatment, outcome)) return CausalEstimate( 0, identified_estimand, None, control_value=control_value, treatment_value=treatment_value ) # Check if estimator's target estimand is identified elif identified_estimand.estimands[identifier_name] is None: logger.error("No valid identified estimand available.") return CausalEstimate(None, None, None, control_value=control_value, treatment_value=treatment_value) method.update_input(treatment_value, control_value, target_units) estimate = method.estimate_effect() # Store parameters inside estimate object for refutation methods # TODO: This add_params needs to move to the estimator class # inside estimate_effect and estimate_conditional_effect estimate.add_params( estimand_type=identified_estimand.estimand_type, estimator_class=causal_estimator_class, test_significance=test_significance, evaluate_effect_strength=evaluate_effect_strength, confidence_intervals=confidence_intervals, target_units=target_units, effect_modifiers=effect_modifiers, method_params=method_params, ) return estimate class CausalEstimate: """Class for the estimate object that every causal estimator returns""" def __init__( self, estimate, target_estimand, realized_estimand_expr, control_value, treatment_value, conditional_estimates=None, **kwargs, ): self.value = estimate self.target_estimand = target_estimand self.realized_estimand_expr = realized_estimand_expr self.control_value = control_value self.treatment_value = treatment_value self.conditional_estimates = conditional_estimates self.params = kwargs if self.params is not None: for key, value in self.params.items(): setattr(self, key, value) self.effect_strength = None def add_estimator(self, estimator_instance): self.estimator = estimator_instance def add_effect_strength(self, strength_dict): self.effect_strength = strength_dict def add_params(self, **kwargs): self.params.update(kwargs) def get_confidence_intervals(self, confidence_level=None, method=None, **kwargs): """Get confidence intervals of the obtained estimate. By default, this is done with the help of bootstrapped confidence intervals but can be overridden if the specific estimator implements other methods of estimating confidence intervals. If the method provided is not bootstrap, this function calls the implementation of the specific estimator. :param method: Method for estimating confidence intervals. :param confidence_level: The confidence level of the confidence intervals of the estimate. :param kwargs: Other optional args to be passed to the CI method. :returns: The obtained confidence interval. """ confidence_intervals = self.estimator.estimate_confidence_intervals( estimate_value=self.value, confidence_level=confidence_level, method=method, **kwargs ) return confidence_intervals def get_standard_error(self, method=None, **kwargs): """Get standard error of the obtained estimate. By default, this is done with the help of bootstrapped standard errors but can be overridden if the specific estimator implements other methods of estimating standard error. If the method provided is not bootstrap, this function calls the implementation of the specific estimator. :param method: Method for computing the standard error. :param kwargs: Other optional parameters to be passed to the estimating method. :returns: Standard error of the causal estimate. """ std_error = self.estimator.estimate_std_error(method=method, **kwargs) return std_error def test_stat_significance(self, method=None, **kwargs): """Test statistical significance of the estimate obtained. By default, uses resampling to create a non-parametric significance test. Individual child estimators can implement different methods. If the method name is different from "bootstrap", this function calls the implementation of the child estimator. :param method: Method for checking statistical significance :param kwargs: Other optional parameters to be passed to the estimating method. :returns: p-value from the significance test """ signif_results = self.estimator.test_significance(self.value, method=method, **kwargs) return {"p_value": signif_results["p_value"]} def estimate_conditional_effects( self, effect_modifiers=None, num_quantiles=CausalEstimator.NUM_QUANTILES_TO_DISCRETIZE_CONT_COLS ): """Estimate treatment effect conditioned on given variables. If a numeric effect modifier is provided, it is discretized into quantile bins. If you would like a custom discretization, you can do so yourself: create a new column containing the discretized effect modifier and then include that column's name in the effect_modifier_names argument. :param effect_modifiers: Names of effect modifier variables over which the conditional effects will be estimated. If not provided, defaults to the effect modifiers specified during creation of the CausalEstimator object. :param num_quantiles: The number of quantiles into which a numeric effect modifier variable is discretized. Does not affect any categorical effect modifiers. :returns: A (multi-index) dataframe that provides separate effects for each value of the (discretized) effect modifiers. """ return self.estimator._estimate_conditional_effects( self.estimator._estimate_effect_fn, effect_modifiers, num_quantiles ) def interpret(self, method_name=None, **kwargs): """Interpret the causal estimate. :param method_name: Method used (string) or a list of methods. If None, then the default for the specific estimator is used. :param kwargs:: Optional parameters that are directly passed to the interpreter method. :returns: None """ if method_name is None: method_name = self.estimator.interpret_method method_name_arr = parse_state(method_name) for method in method_name_arr: interpreter = interpreters.get_class_object(method) interpreter(self, **kwargs).interpret() def __str__(self): s = "*** Causal Estimate ***\n" # No estimand was identified (identification failed) if self.target_estimand is None: return "Estimation failed! No relevant identified estimand available for this estimation method." s += "\n## Identified estimand\n{0}".format(self.target_estimand.__str__(only_target_estimand=True)) s += "\n## Realized estimand\n{0}".format(self.realized_estimand_expr) if hasattr(self, "estimator"): s += "\nTarget units: {0}\n".format(self.estimator.target_units_tostr()) s += "\n## Estimate\n" s += "Mean value: {0}\n".format(self.value) s += "" if hasattr(self, "cate_estimates"): s += "Effect estimates: {0}\n".format(self.cate_estimates) if hasattr(self, "estimator"): if self.estimator._significance_test: s += "p-value: {0}\n".format(self.estimator.signif_results_tostr(self.test_stat_significance())) if self.estimator._confidence_intervals: s += "{0}% confidence interval: {1}\n".format( 100 * self.estimator.confidence_level, self.get_confidence_intervals() ) if self.conditional_estimates is not None: s += "### Conditional Estimates\n" s += str(self.conditional_estimates) if self.effect_strength is not None: s += "\n## Effect Strength\n" s += "Change in outcome attributable to treatment: {}\n".format(self.effect_strength["fraction-effect"]) # s += "Variance in outcome explained by treatment: {}\n".format(self.effect_strength["r-squared"]) return s class RealizedEstimand(object): def __init__(self, identified_estimand, estimator_name): self.treatment_variable = identified_estimand.treatment_variable self.outcome_variable = identified_estimand.outcome_variable self.backdoor_variables = identified_estimand.get_backdoor_variables() self.instrumental_variables = identified_estimand.instrumental_variables self.estimand_type = identified_estimand.estimand_type self.estimand_expression = None self.assumptions = None self.estimator_name = estimator_name def update_assumptions(self, estimator_assumptions): self.assumptions = estimator_assumptions def update_estimand_expression(self, estimand_expression): self.estimand_expression = estimand_expression def __str__(self): s = "Realized estimand: {0}\n".format(self.estimator_name) s += "Realized estimand type: {0}\n".format(self.estimand_type) s += "Estimand expression:\n{0}\n".format(sp.pretty(self.estimand_expression)) j = 1 for ass_name, ass_str in self.assumptions.items(): s += "Estimand assumption {0}, {1}: {2}\n".format(j, ass_name, ass_str) j += 1 return s

andresmor-ms

2044d216c322a4b32c6eadce5da7d83463f19c2f

05bfa49dacf0061988c96c6f3e3756219df5422a

data should be one of the arguments for estimate_effect. Actually it should be the first argument. Just like sklearn, the `estimate_effect` method of an Estimator object (or later, the fit method) should be passed the data.

amit-sharma

py-why/dowhy

Functional api/estimate effect function

#### Estimate Effect function * Refactors the estimate effect into a separate function to keep backwards compatibility #### TODO (future PRs): * Add `fit(...)` method to estimators - Move data related parameters from the constructor to the `fit(...)` method * Refactor code to avoid `**kwargs` in `__init__(...)` constructors

2022-10-18 15:49:21+00:00

2022-10-25 17:02:02+00:00

dowhy/causal_estimator.py

import logging from collections import namedtuple import numpy as np import pandas as pd import sympy as sp from sklearn.utils import resample import dowhy.interpreters as interpreters from dowhy.utils.api import parse_state class CausalEstimator: """Base class for an estimator of causal effect. Subclasses implement different estimation methods. All estimation methods are in the package "dowhy.causal_estimators" """ # The default number of simulations for statistical testing DEFAULT_NUMBER_OF_SIMULATIONS_STAT_TEST = 1000 # The default number of simulations to obtain confidence intervals DEFAULT_NUMBER_OF_SIMULATIONS_CI = 100 # The portion of the total size that should be taken each time to find the confidence intervals # 1 is the recommended value # https://ocw.mit.edu/courses/mathematics/18-05-introduction-to-probability-and-statistics-spring-2014/readings/MIT18_05S14_Reading24.pdf # https://projecteuclid.org/download/pdf_1/euclid.ss/1032280214 DEFAULT_SAMPLE_SIZE_FRACTION = 1 # The default Confidence Level DEFAULT_CONFIDENCE_LEVEL = 0.95 # Number of quantiles to discretize continuous columns, for applying groupby NUM_QUANTILES_TO_DISCRETIZE_CONT_COLS = 5 # Prefix to add to temporary categorical variables created after discretization TEMP_CAT_COLUMN_PREFIX = "__categorical__" DEFAULT_NOTIMPLEMENTEDERROR_MSG = "not yet implemented for {0}. If you would this to be implemented in the next version, please raise an issue at https://github.com/microsoft/dowhy/issues" BootstrapEstimates = namedtuple("BootstrapEstimates", ["estimates", "params"]) DEFAULT_INTERPRET_METHOD = ["textual_effect_interpreter"] # std args to be removed from locals() before being passed to args_dict _STD_INIT_ARGS = ("self", "__class__", "args", "kwargs") def __init__( self, data, identified_estimand, treatment, outcome, control_value=0, treatment_value=1, test_significance=False, evaluate_effect_strength=False, confidence_intervals=False, target_units=None, effect_modifiers=None, num_null_simulations=DEFAULT_NUMBER_OF_SIMULATIONS_STAT_TEST, num_simulations=DEFAULT_NUMBER_OF_SIMULATIONS_CI, sample_size_fraction=DEFAULT_SAMPLE_SIZE_FRACTION, confidence_level=DEFAULT_CONFIDENCE_LEVEL, need_conditional_estimates="auto", num_quantiles_to_discretize_cont_cols=NUM_QUANTILES_TO_DISCRETIZE_CONT_COLS, **kwargs, ): """Initializes an estimator with data and names of relevant variables. This method is called from the constructors of its child classes. :param data: data frame containing the data :param identified_estimand: probability expression representing the target identified estimand to estimate. :param treatment: name of the treatment variable :param outcome: name of the outcome variable :param control_value: Value of the treatment in the control group, for effect estimation. If treatment is multi-variate, this can be a list. :param treatment_value: Value of the treatment in the treated group, for effect estimation. If treatment is multi-variate, this can be a list. :param test_significance: Binary flag or a string indicating whether to test significance and by which method. All estimators support test_significance="bootstrap" that estimates a p-value for the obtained estimate using the bootstrap method. Individual estimators can override this to support custom testing methods. The bootstrap method supports an optional parameter, num_null_simulations. If False, no testing is done. If True, significance of the estimate is tested using the custom method if available, otherwise by bootstrap. :param evaluate_effect_strength: (Experimental) whether to evaluate the strength of effect :param confidence_intervals: Binary flag or a string indicating whether the confidence intervals should be computed and which method should be used. All methods support estimation of confidence intervals using the bootstrap method by using the parameter confidence_intervals="bootstrap". The bootstrap method takes in two arguments (num_simulations and sample_size_fraction) that can be optionally specified in the params dictionary. Estimators may also override this to implement their own confidence interval method. If this parameter is False, no confidence intervals are computed. If True, confidence intervals are computed by the estimator's specific method if available, otherwise through bootstrap. :param target_units: The units for which the treatment effect should be estimated. This can be a string for common specifications of target units (namely, "ate", "att" and "atc"). It can also be a lambda function that can be used as an index for the data (pandas DataFrame). Alternatively, it can be a new DataFrame that contains values of the effect_modifiers and effect will be estimated only for this new data. :param effect_modifiers: Variables on which to compute separate effects, or return a heterogeneous effect function. Not all methods support this currently. :param num_null_simulations: The number of simulations for testing the statistical significance of the estimator :param num_simulations: The number of simulations for finding the confidence interval (and/or standard error) for a estimate :param sample_size_fraction: The size of the sample for the bootstrap estimator :param confidence_level: The confidence level of the confidence interval estimate :param need_conditional_estimates: Boolean flag indicating whether conditional estimates should be computed. Defaults to True if there are effect modifiers in the graph :param num_quantiles_to_discretize_cont_cols: The number of quantiles into which a numeric effect modifier is split, to enable estimation of conditional treatment effect over it. :param kwargs: (optional) Additional estimator-specific parameters :returns: an instance of the estimator class. """ self._data = data self._target_estimand = identified_estimand # Currently estimation methods only support univariate treatment and outcome self._treatment_name = treatment self._outcome_name = outcome[0] # assuming one-dimensional outcome self._control_value = control_value self._treatment_value = treatment_value self._significance_test = test_significance self._effect_strength_eval = evaluate_effect_strength self._target_units = target_units self._effect_modifier_names = effect_modifiers self._confidence_intervals = confidence_intervals self._bootstrap_estimates = None # for confidence intervals and std error self._bootstrap_null_estimates = None # for significance test self._effect_modifiers = None self.method_params = kwargs # Setting the default interpret method self.interpret_method = CausalEstimator.DEFAULT_INTERPRET_METHOD self.logger = logging.getLogger(__name__) # Setting treatment and outcome values if self._data is not None: self._treatment = self._data[self._treatment_name] self._outcome = self._data[self._outcome_name] # Now saving the effect modifiers if self._effect_modifier_names: # only add the observed nodes self._effect_modifier_names = [ cname for cname in self._effect_modifier_names if cname in self._data.columns ] if len(self._effect_modifier_names) > 0: self._effect_modifiers = self._data[self._effect_modifier_names] self._effect_modifiers = pd.get_dummies(self._effect_modifiers, drop_first=True) self.logger.debug("Effect modifiers: " + ",".join(self._effect_modifier_names)) else: self._effect_modifier_names = None # Check if some parameters were set, otherwise set to default values self.num_null_simulations = num_null_simulations self.num_simulations = num_simulations self.sample_size_fraction = sample_size_fraction self.confidence_level = confidence_level self.num_quantiles_to_discretize_cont_cols = num_quantiles_to_discretize_cont_cols # Estimate conditional estimates by default self.need_conditional_estimates = ( need_conditional_estimates if need_conditional_estimates != "auto" else bool(self._effect_modifier_names) ) @staticmethod def get_estimator_object(new_data, identified_estimand, estimate): """Create a new estimator of the same type as the one passed in the estimate argument. Creates a new object with new_data and the identified_estimand :param new_data: np.ndarray, pd.Series, pd.DataFrame The newly assigned data on which the estimator should run :param identified_estimand: IdentifiedEstimand An instance of the identified estimand class that provides the information with respect to which causal pathways are employed when the treatment effects the outcome :param estimate: CausalEstimate It is an already existing estimate whose properties we wish to replicate :returns: An instance of the same estimator class that had generated the given estimate. """ estimator_class = estimate.params["estimator_class"] new_estimator = estimator_class( new_data, identified_estimand, identified_estimand.treatment_variable, identified_estimand.outcome_variable, # names of treatment and outcome control_value=estimate.control_value, treatment_value=estimate.treatment_value, test_significance=False, evaluate_effect_strength=False, confidence_intervals=estimate.params["confidence_intervals"], target_units=estimate.params["target_units"], effect_modifiers=estimate.params["effect_modifiers"], **estimate.params["method_params"], ) return new_estimator def _estimate_effect(self): """This method is to be overriden by the child classes, so that they can run the estimation technique of their choice""" raise NotImplementedError( ("Main estimation method is " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG).format(self.__class__) ) def estimate_effect(self): """Base estimation method that calls the estimate_effect method of its calling subclass. Can optionally also test significance and estimate effect strength for any returned estimate. :param self: object instance of class Estimator :returns: A CausalEstimate instance that contains point estimates of average and conditional effects. Based on the parameters provided, it optionally includes confidence intervals, standard errors,statistical significance and other statistical parameters. """ est = self._estimate_effect() est.add_estimator(self) if self._significance_test: self.test_significance(est.value, method=self._significance_test) if self._confidence_intervals: self.estimate_confidence_intervals( est.value, confidence_level=self.confidence_level, method=self._confidence_intervals ) if self._effect_strength_eval: effect_strength_dict = self.evaluate_effect_strength(est) est.add_effect_strength(effect_strength_dict) return est def estimate_effect_naive(self): # TODO Only works for binary treatment df_withtreatment = self._data.loc[self._data[self._treatment_name] == 1] df_notreatment = self._data.loc[self._data[self._treatment_name] == 0] est = np.mean(df_withtreatment[self._outcome_name]) - np.mean(df_notreatment[self._outcome_name]) return CausalEstimate(est, None, None, control_value=0, treatment_value=1) def _estimate_effect_fn(self, data_df): """Function used in conditional effect estimation. This function is to be overridden by each child estimator. The overridden function should take in a dataframe as input and return the estimate for that data. """ raise NotImplementedError( ("Conditional treatment effects are " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG).format( self.__class__ ) ) def _estimate_conditional_effects(self, estimate_effect_fn, effect_modifier_names=None, num_quantiles=None): """Estimate conditional treatment effects. Common method for all estimators that utilizes a specific estimate_effect_fn implemented by each child estimator. If a numeric effect modifier is provided, it is discretized into quantile bins. If you would like a custom discretization, you can do so yourself: create a new column containing the discretized effect modifier and then include that column's name in the effect_modifier_names argument. :param estimate_effect_fn: Function that has a single parameter (a data frame) and returns the treatment effect estimate on that data. :param effect_modifier_names: Names of effect modifier variables over which the conditional effects will be estimated. If not provided, defaults to the effect modifiers specified during creation of the CausalEstimator object. :param num_quantiles: The number of quantiles into which a numeric effect modifier variable is discretized. Does not affect any categorical effect modifiers. :returns: A (multi-index) dataframe that provides separate effects for each value of the (discretized) effect modifiers. """ # Defaulting to class default values if parameters are not provided if effect_modifier_names is None: effect_modifier_names = self._effect_modifier_names if num_quantiles is None: num_quantiles = self.num_quantiles_to_discretize_cont_cols # Checking that there is at least one effect modifier if not effect_modifier_names: raise ValueError("At least one effect modifier should be specified to compute conditional effects.") # Making sure that effect_modifier_names is a list effect_modifier_names = parse_state(effect_modifier_names) if not all(em in self._effect_modifier_names for em in effect_modifier_names): self.logger.warn( "At least one of the provided effect modifiers was not included while fitting the estimator. You may get incorrect results. To resolve, fit the estimator again by providing the updated effect modifiers in estimate_effect()." ) # Making a copy since we are going to be changing effect modifier names effect_modifier_names = effect_modifier_names.copy() prefix = CausalEstimator.TEMP_CAT_COLUMN_PREFIX # For every numeric effect modifier, adding a temp categorical column for i in range(len(effect_modifier_names)): em = effect_modifier_names[i] if pd.api.types.is_numeric_dtype(self._data[em].dtypes): self._data[prefix + str(em)] = pd.qcut(self._data[em], num_quantiles, duplicates="drop") effect_modifier_names[i] = prefix + str(em) # Grouping by effect modifiers and computing effect separately by_effect_mods = self._data.groupby(effect_modifier_names) cond_est_fn = lambda x: self._do(self._treatment_value, x) - self._do(self._control_value, x) conditional_estimates = by_effect_mods.apply(estimate_effect_fn) # Deleting the temporary categorical columns for em in effect_modifier_names: if em.startswith(prefix): self._data.pop(em) return conditional_estimates def _do(self, x, data_df=None): raise NotImplementedError( ("Do-operator is " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG).format(self.__class__) ) def do(self, x, data_df=None): """Method that implements the do-operator. Given a value x for the treatment, returns the expected value of the outcome when the treatment is intervened to a value x. :param x: Value of the treatment :param data_df: Data on which the do-operator is to be applied. :returns: Value of the outcome when treatment is intervened/set to x. """ est = self._do(x, data_df) return est def construct_symbolic_estimator(self, estimand): raise NotImplementedError(("Symbolic estimator string is ").format(self.__class__)) def _generate_bootstrap_estimates(self, num_bootstrap_simulations, sample_size_fraction): """Helper function to generate causal estimates over bootstrapped samples. :param num_bootstrap_simulations: Number of simulations for the bootstrap method. :param sample_size_fraction: Fraction of the dataset to be resampled. :returns: A collections.namedtuple containing a list of bootstrapped estimates and a dictionary containing parameters used for the bootstrap. """ # The array that stores the results of all estimations simulation_results = np.zeros(num_bootstrap_simulations) # Find the sample size the proportion with the population size sample_size = int(sample_size_fraction * len(self._data)) if sample_size > len(self._data): self.logger.warning("WARN: The sample size is greater than the data being sampled") self.logger.info("INFO: The sample size: {}".format(sample_size)) self.logger.info("INFO: The number of simulations: {}".format(num_bootstrap_simulations)) # Perform the set number of simulations for index in range(num_bootstrap_simulations): new_data = resample(self._data, n_samples=sample_size) new_estimator = type(self)( new_data, self._target_estimand, self._target_estimand.treatment_variable, self._target_estimand.outcome_variable, # names of treatment and outcome treatment_value=self._treatment_value, control_value=self._control_value, test_significance=False, evaluate_effect_strength=False, confidence_intervals=False, target_units=self._target_units, effect_modifiers=self._effect_modifier_names, **self.method_params, ) new_effect = new_estimator.estimate_effect() simulation_results[index] = new_effect.value estimates = CausalEstimator.BootstrapEstimates( simulation_results, {"num_simulations": num_bootstrap_simulations, "sample_size_fraction": sample_size_fraction}, ) return estimates def _estimate_confidence_intervals_with_bootstrap( self, estimate_value, confidence_level=None, num_simulations=None, sample_size_fraction=None ): """ Method to compute confidence interval using bootstrapped sampling. :param estimate_value: obtained estimate's value :param confidence_level: The level for which to compute CI (e.g., 95% confidence level translates to confidence_level=0.95) :param num_simulations: The number of simulations to be performed to get the bootstrap confidence intervals. :param sample_size_fraction: The fraction of the dataset to be resampled. :returns: confidence interval at the specified level. For more details on bootstrap or resampling statistics, refer to the following links: https://ocw.mit.edu/courses/mathematics/18-05-introduction-to-probability-and-statistics-spring-2014/readings/MIT18_05S14_Reading24.pdf https://projecteuclid.org/download/pdf_1/euclid.ss/1032280214 """ # Using class default parameters if not specified if num_simulations is None: num_simulations = self.num_simulations if sample_size_fraction is None: sample_size_fraction = self.sample_size_fraction # Checking if bootstrap_estimates are already computed if self._bootstrap_estimates is None: self._bootstrap_estimates = self._generate_bootstrap_estimates(num_simulations, sample_size_fraction) elif CausalEstimator.is_bootstrap_parameter_changed(self._bootstrap_estimates.params, locals()): # Checked if any parameter is changed from the previous std error estimate self._bootstrap_estimates = self._generate_bootstrap_estimates(num_simulations, sample_size_fraction) # Now use the data obtained from the simulations to get the value of the confidence estimates bootstrap_estimates = self._bootstrap_estimates.estimates # Get the variations of each bootstrap estimate and sort bootstrap_variations = [bootstrap_estimate - estimate_value for bootstrap_estimate in bootstrap_estimates] sorted_bootstrap_variations = np.sort(bootstrap_variations) # Now we take the (1- p)th and the (p)th variations, where p is the chosen confidence level upper_bound_index = int((1 - confidence_level) * len(sorted_bootstrap_variations)) lower_bound_index = int(confidence_level * len(sorted_bootstrap_variations)) # Get the lower and upper bounds by subtracting the variations from the estimate lower_bound = estimate_value - sorted_bootstrap_variations[lower_bound_index] upper_bound = estimate_value - sorted_bootstrap_variations[upper_bound_index] return lower_bound, upper_bound def _estimate_confidence_intervals(self, confidence_level=None, method=None, **kwargs): """ This method is to be overriden by the child classes, so that they can run a confidence interval estimation method suited to the specific causal estimator. """ raise NotImplementedError( ( "This method for estimating confidence intervals is " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG + " Meanwhile, you can try the bootstrap method (method='bootstrap') to estimate confidence intervals." ).format(self.__class__) ) def estimate_confidence_intervals(self, estimate_value, confidence_level=None, method=None, **kwargs): """Find the confidence intervals corresponding to any estimator By default, this is done with the help of bootstrapped confidence intervals but can be overridden if the specific estimator implements other methods of estimating confidence intervals. If the method provided is not bootstrap, this function calls the implementation of the specific estimator. :param estimate_value: obtained estimate's value :param method: Method for estimating confidence intervals. :param confidence_level: The confidence level of the confidence intervals of the estimate. :param kwargs: Other optional args to be passed to the CI method. :returns: The obtained confidence interval. """ if method is None: if self._confidence_intervals: method = self._confidence_intervals # this is either True or methodname else: method = "default" confidence_intervals = None if confidence_level is None: confidence_level = self.confidence_level if method == "default" or method is True: # user has not provided any method try: confidence_intervals = self._estimate_confidence_intervals(confidence_level, method=method, **kwargs) except NotImplementedError: confidence_intervals = self._estimate_confidence_intervals_with_bootstrap( estimate_value, confidence_level, **kwargs ) else: if method == "bootstrap": confidence_intervals = self._estimate_confidence_intervals_with_bootstrap( estimate_value, confidence_level, **kwargs ) else: confidence_intervals = self._estimate_confidence_intervals(confidence_level, method=method, **kwargs) return confidence_intervals def _estimate_std_error_with_bootstrap(self, num_simulations=None, sample_size_fraction=None): """Compute standard error using the bootstrap method. Standard error and confidence intervals use the same parameter num_simulations for the number of bootstrap simulations. :param num_simulations: Number of bootstrapped samples. :param sample_size_fraction: Fraction of data to be resampled. :returns: Standard error of the obtained estimate. """ # Use existing params, if new user defined params are not present if num_simulations is None: num_simulations = self.num_simulations if sample_size_fraction is None: sample_size_fraction = self.sample_size_fraction # Checking if bootstrap_estimates are already computed if self._bootstrap_estimates is None: self._bootstrap_estimates = self._generate_bootstrap_estimates(num_simulations, sample_size_fraction) elif CausalEstimator.is_bootstrap_parameter_changed(self._bootstrap_estimates.params, locals()): # Check if any parameter is changed from the previous std error estimate self._bootstrap_estimates = self._generate_bootstrap_estimates(num_simulations, sample_size_fraction) std_error = np.std(self._bootstrap_estimates.estimates) return std_error def _estimate_std_error(self, method=None, **kwargs): """ This method is to be overriden by the child classes, so that they can run a standard error estimation method suited to the specific causal estimator. """ raise NotImplementedError( ( "This method for estimating standard errors is " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG + " Meanwhile, you can try the bootstrap method (method='bootstrap') to estimate standard errors." ).format(self.__class__) ) def estimate_std_error(self, method=None, **kwargs): """Compute standard error of an obtained causal estimate. :param method: Method for computing the standard error. :param kwargs: Other optional parameters to be passed to the estimating method. :returns: Standard error of the causal estimate. """ if method is None: if self._confidence_intervals: method = self._confidence_intervals else: method = "default" std_error = None if method == "default" or method is True: # user has not provided any method try: std_error = self._estimate_std_error(method, **kwargs) except NotImplementedError: std_error = self._estimate_std_error_with_bootstrap(**kwargs) else: if method == "bootstrap": std_error = self._estimate_std_error_with_bootstrap(**kwargs) else: std_error = self._estimate_std_error(method, **kwargs) return std_error def _test_significance_with_bootstrap(self, estimate_value, num_null_simulations=None): """Test statistical significance of an estimate using the bootstrap method. :param estimate_value: Obtained estimate's value :param num_null_simulations: Number of simulations for the null hypothesis :returns: p-value of the statistical significance test. """ # Use existing params, if new user defined params are not present if num_null_simulations is None: num_null_simulations = self.num_null_simulations do_retest = self._bootstrap_null_estimates is None or CausalEstimator.is_bootstrap_parameter_changed( self._bootstrap_null_estimates.params, locals() ) if do_retest: null_estimates = np.zeros(num_null_simulations) for i in range(num_null_simulations): new_outcome = np.random.permutation(self._outcome) new_data = self._data.assign(dummy_outcome=new_outcome) # self._outcome = self._data["dummy_outcome"] new_estimator = type(self)( new_data, self._target_estimand, self._target_estimand.treatment_variable, ("dummy_outcome",), test_significance=False, evaluate_effect_strength=False, confidence_intervals=False, target_units=self._target_units, effect_modifiers=self._effect_modifier_names, **self.method_params, ) new_effect = new_estimator.estimate_effect() null_estimates[i] = new_effect.value self._bootstrap_null_estimates = CausalEstimator.BootstrapEstimates( null_estimates, {"num_null_simulations": num_null_simulations, "sample_size_fraction": 1} ) # Processing the null hypothesis estimates sorted_null_estimates = np.sort(self._bootstrap_null_estimates.estimates) self.logger.debug("Null estimates: {0}".format(sorted_null_estimates)) median_estimate = sorted_null_estimates[int(num_null_simulations / 2)] # Doing a two-sided test if estimate_value > median_estimate: # Being conservative with the p-value reported estimate_index = np.searchsorted(sorted_null_estimates, estimate_value, side="left") p_value = 1 - (estimate_index / num_null_simulations) if estimate_value <= median_estimate: # Being conservative with the p-value reported estimate_index = np.searchsorted(sorted_null_estimates, estimate_value, side="right") p_value = estimate_index / num_null_simulations # If the estimate_index is 0, it depends on the number of simulations if p_value == 0: p_value = (0, 1 / len(sorted_null_estimates)) # a tuple determining the range. elif p_value == 1: p_value = (1 - 1 / len(sorted_null_estimates), 1) signif_dict = {"p_value": p_value} return signif_dict def _test_significance(self, estimate_value, method=None, **kwargs): """ This method is to be overriden by the child classes, so that they can run a significance test suited to the specific causal estimator. """ raise NotImplementedError( ( "This method for testing statistical significance is " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG + " Meanwhile, you can try the bootstrap method (method='bootstrap') to test statistical significance." ).format(self.__class__) ) def test_significance(self, estimate_value, method=None, **kwargs): """Test statistical significance of obtained estimate. By default, uses resampling to create a non-parametric significance test. A general procedure. Individual child estimators can implement different methods. If the method name is different from "bootstrap", this function calls the implementation of the child estimator. :param self: object instance of class Estimator :param estimate_value: obtained estimate's value :param method: Method for checking statistical significance :returns: p-value from the significance test """ if method is None: if self._significance_test: method = self._significance_test # this is either True or methodname else: method = "default" signif_dict = None if method == "default" or method is True: # user has not provided any method try: signif_dict = self._test_significance(estimate_value, method, **kwargs) except NotImplementedError: signif_dict = self._test_significance_with_bootstrap(estimate_value, **kwargs) else: if method == "bootstrap": signif_dict = self._test_significance_with_bootstrap(estimate_value, **kwargs) else: signif_dict = self._test_significance(estimate_value, method, **kwargs) return signif_dict def evaluate_effect_strength(self, estimate): fraction_effect_explained = self._evaluate_effect_strength(estimate, method="fraction-effect") # Need to test r-squared before supporting # effect_r_squared = self._evaluate_effect_strength(estimate, method="r-squared") strength_dict = { "fraction-effect": fraction_effect_explained # 'r-squared': effect_r_squared } return strength_dict def _evaluate_effect_strength(self, estimate, method="fraction-effect"): supported_methods = ["fraction-effect"] if method not in supported_methods: raise NotImplementedError("This method is not supported for evaluating effect strength") if method == "fraction-effect": naive_obs_estimate = self.estimate_effect_naive() self.logger.debug(estimate.value, naive_obs_estimate.value) fraction_effect_explained = estimate.value / naive_obs_estimate.value return fraction_effect_explained # elif method == "r-squared": # outcome_mean = np.mean(self._outcome) # total_variance = np.sum(np.square(self._outcome - outcome_mean)) # Assuming a linear model with one variable: the treatment # Currently only works for continuous y # causal_model = outcome_mean + estimate.value*self._treatment # squared_residual = np.sum(np.square(self._outcome - causal_model)) # r_squared = 1 - (squared_residual/total_variance) # return r_squared else: return None def update_input(self, treatment_value, control_value, target_units): self._control_value = control_value self._treatment_value = treatment_value self._target_units = target_units @staticmethod def is_bootstrap_parameter_changed(bootstrap_estimates_params, given_params): """Check whether parameters of the bootstrap have changed. This is an efficiency method that checks if fresh resampling of the bootstrap samples is required. Returns True if parameters have changed and resampling should be done again. :param bootstrap_estimates_params: A dictionary of parameters for the current bootstrap samples :param given_params: A dictionary of parameters passed by the user :returns: A binary flag denoting whether the parameters are different. """ is_any_parameter_changed = False for prm, val in bootstrap_estimates_params.items(): given_val = given_params.get(prm, None) if given_val is not None and given_val != val: is_any_parameter_changed = True break return is_any_parameter_changed def target_units_tostr(self): s = "" if type(self._target_units) is str: s += self._target_units elif callable(self._target_units): s += "Data subset defined by a function" elif isinstance(self._target_units, pd.DataFrame): s += "Data subset provided as a data frame" return s def signif_results_tostr(self, signif_results): s = "" pval = signif_results["p_value"] if type(pval) is tuple: s += "[{0}, {1}]".format(pval[0], pval[1]) else: s += "{0}".format(pval) return s class CausalEstimate: """Class for the estimate object that every causal estimator returns""" def __init__( self, estimate, target_estimand, realized_estimand_expr, control_value, treatment_value, conditional_estimates=None, **kwargs, ): self.value = estimate self.target_estimand = target_estimand self.realized_estimand_expr = realized_estimand_expr self.control_value = control_value self.treatment_value = treatment_value self.conditional_estimates = conditional_estimates self.params = kwargs if self.params is not None: for key, value in self.params.items(): setattr(self, key, value) self.effect_strength = None def add_estimator(self, estimator_instance): self.estimator = estimator_instance def add_effect_strength(self, strength_dict): self.effect_strength = strength_dict def add_params(self, **kwargs): self.params.update(kwargs) def get_confidence_intervals(self, confidence_level=None, method=None, **kwargs): """Get confidence intervals of the obtained estimate. By default, this is done with the help of bootstrapped confidence intervals but can be overridden if the specific estimator implements other methods of estimating confidence intervals. If the method provided is not bootstrap, this function calls the implementation of the specific estimator. :param method: Method for estimating confidence intervals. :param confidence_level: The confidence level of the confidence intervals of the estimate. :param kwargs: Other optional args to be passed to the CI method. :returns: The obtained confidence interval. """ confidence_intervals = self.estimator.estimate_confidence_intervals( estimate_value=self.value, confidence_level=confidence_level, method=method, **kwargs ) return confidence_intervals def get_standard_error(self, method=None, **kwargs): """Get standard error of the obtained estimate. By default, this is done with the help of bootstrapped standard errors but can be overridden if the specific estimator implements other methods of estimating standard error. If the method provided is not bootstrap, this function calls the implementation of the specific estimator. :param method: Method for computing the standard error. :param kwargs: Other optional parameters to be passed to the estimating method. :returns: Standard error of the causal estimate. """ std_error = self.estimator.estimate_std_error(method=method, **kwargs) return std_error def test_stat_significance(self, method=None, **kwargs): """Test statistical significance of the estimate obtained. By default, uses resampling to create a non-parametric significance test. Individual child estimators can implement different methods. If the method name is different from "bootstrap", this function calls the implementation of the child estimator. :param method: Method for checking statistical significance :param kwargs: Other optional parameters to be passed to the estimating method. :returns: p-value from the significance test """ signif_results = self.estimator.test_significance(self.value, method=method, **kwargs) return {"p_value": signif_results["p_value"]} def estimate_conditional_effects( self, effect_modifiers=None, num_quantiles=CausalEstimator.NUM_QUANTILES_TO_DISCRETIZE_CONT_COLS ): """Estimate treatment effect conditioned on given variables. If a numeric effect modifier is provided, it is discretized into quantile bins. If you would like a custom discretization, you can do so yourself: create a new column containing the discretized effect modifier and then include that column's name in the effect_modifier_names argument. :param effect_modifiers: Names of effect modifier variables over which the conditional effects will be estimated. If not provided, defaults to the effect modifiers specified during creation of the CausalEstimator object. :param num_quantiles: The number of quantiles into which a numeric effect modifier variable is discretized. Does not affect any categorical effect modifiers. :returns: A (multi-index) dataframe that provides separate effects for each value of the (discretized) effect modifiers. """ return self.estimator._estimate_conditional_effects( self.estimator._estimate_effect_fn, effect_modifiers, num_quantiles ) def interpret(self, method_name=None, **kwargs): """Interpret the causal estimate. :param method_name: Method used (string) or a list of methods. If None, then the default for the specific estimator is used. :param kwargs:: Optional parameters that are directly passed to the interpreter method. :returns: None """ if method_name is None: method_name = self.estimator.interpret_method method_name_arr = parse_state(method_name) for method in method_name_arr: interpreter = interpreters.get_class_object(method) interpreter(self, **kwargs).interpret() def __str__(self): s = "*** Causal Estimate ***\n" # No estimand was identified (identification failed) if self.target_estimand is None: return "Estimation failed! No relevant identified estimand available for this estimation method." s += "\n## Identified estimand\n{0}".format(self.target_estimand.__str__(only_target_estimand=True)) s += "\n## Realized estimand\n{0}".format(self.realized_estimand_expr) if hasattr(self, "estimator"): s += "\nTarget units: {0}\n".format(self.estimator.target_units_tostr()) s += "\n## Estimate\n" s += "Mean value: {0}\n".format(self.value) s += "" if hasattr(self, "cate_estimates"): s += "Effect estimates: {0}\n".format(self.cate_estimates) if hasattr(self, "estimator"): if self.estimator._significance_test: s += "p-value: {0}\n".format(self.estimator.signif_results_tostr(self.test_stat_significance())) if self.estimator._confidence_intervals: s += "{0}% confidence interval: {1}\n".format( 100 * self.estimator.confidence_level, self.get_confidence_intervals() ) if self.conditional_estimates is not None: s += "### Conditional Estimates\n" s += str(self.conditional_estimates) if self.effect_strength is not None: s += "\n## Effect Strength\n" s += "Change in outcome attributable to treatment: {}\n".format(self.effect_strength["fraction-effect"]) # s += "Variance in outcome explained by treatment: {}\n".format(self.effect_strength["r-squared"]) return s class RealizedEstimand(object): def __init__(self, identified_estimand, estimator_name): self.treatment_variable = identified_estimand.treatment_variable self.outcome_variable = identified_estimand.outcome_variable self.backdoor_variables = identified_estimand.get_backdoor_variables() self.instrumental_variables = identified_estimand.instrumental_variables self.estimand_type = identified_estimand.estimand_type self.estimand_expression = None self.assumptions = None self.estimator_name = estimator_name def update_assumptions(self, estimator_assumptions): self.assumptions = estimator_assumptions def update_estimand_expression(self, estimand_expression): self.estimand_expression = estimand_expression def __str__(self): s = "Realized estimand: {0}\n".format(self.estimator_name) s += "Realized estimand type: {0}\n".format(self.estimand_type) s += "Estimand expression:\n{0}\n".format(sp.pretty(self.estimand_expression)) j = 1 for ass_name, ass_str in self.assumptions.items(): s += "Estimand assumption {0}, {1}: {2}\n".format(j, ass_name, ass_str) j += 1 return s

import logging from collections import namedtuple from typing import Dict, List, Optional, Union import numpy as np import pandas as pd import sympy as sp from sklearn.utils import resample import dowhy.interpreters as interpreters from dowhy import causal_estimators from dowhy.causal_graph import CausalGraph from dowhy.causal_identifier.identified_estimand import IdentifiedEstimand from dowhy.utils.api import parse_state logger = logging.getLogger(__name__) class CausalEstimator: """Base class for an estimator of causal effect. Subclasses implement different estimation methods. All estimation methods are in the package "dowhy.causal_estimators" """ # The default number of simulations for statistical testing DEFAULT_NUMBER_OF_SIMULATIONS_STAT_TEST = 1000 # The default number of simulations to obtain confidence intervals DEFAULT_NUMBER_OF_SIMULATIONS_CI = 100 # The portion of the total size that should be taken each time to find the confidence intervals # 1 is the recommended value # https://ocw.mit.edu/courses/mathematics/18-05-introduction-to-probability-and-statistics-spring-2014/readings/MIT18_05S14_Reading24.pdf # https://projecteuclid.org/download/pdf_1/euclid.ss/1032280214 DEFAULT_SAMPLE_SIZE_FRACTION = 1 # The default Confidence Level DEFAULT_CONFIDENCE_LEVEL = 0.95 # Number of quantiles to discretize continuous columns, for applying groupby NUM_QUANTILES_TO_DISCRETIZE_CONT_COLS = 5 # Prefix to add to temporary categorical variables created after discretization TEMP_CAT_COLUMN_PREFIX = "__categorical__" DEFAULT_NOTIMPLEMENTEDERROR_MSG = "not yet implemented for {0}. If you would this to be implemented in the next version, please raise an issue at https://github.com/microsoft/dowhy/issues" BootstrapEstimates = namedtuple("BootstrapEstimates", ["estimates", "params"]) DEFAULT_INTERPRET_METHOD = ["textual_effect_interpreter"] # std args to be removed from locals() before being passed to args_dict _STD_INIT_ARGS = ("self", "__class__", "args", "kwargs") def __init__( self, data, identified_estimand, treatment, outcome, control_value=0, treatment_value=1, test_significance=False, evaluate_effect_strength=False, confidence_intervals=False, target_units=None, effect_modifiers=None, num_null_simulations=DEFAULT_NUMBER_OF_SIMULATIONS_STAT_TEST, num_simulations=DEFAULT_NUMBER_OF_SIMULATIONS_CI, sample_size_fraction=DEFAULT_SAMPLE_SIZE_FRACTION, confidence_level=DEFAULT_CONFIDENCE_LEVEL, need_conditional_estimates="auto", num_quantiles_to_discretize_cont_cols=NUM_QUANTILES_TO_DISCRETIZE_CONT_COLS, **kwargs, ): """Initializes an estimator with data and names of relevant variables. This method is called from the constructors of its child classes. :param data: data frame containing the data :param identified_estimand: probability expression representing the target identified estimand to estimate. :param treatment: name of the treatment variable :param outcome: name of the outcome variable :param control_value: Value of the treatment in the control group, for effect estimation. If treatment is multi-variate, this can be a list. :param treatment_value: Value of the treatment in the treated group, for effect estimation. If treatment is multi-variate, this can be a list. :param test_significance: Binary flag or a string indicating whether to test significance and by which method. All estimators support test_significance="bootstrap" that estimates a p-value for the obtained estimate using the bootstrap method. Individual estimators can override this to support custom testing methods. The bootstrap method supports an optional parameter, num_null_simulations. If False, no testing is done. If True, significance of the estimate is tested using the custom method if available, otherwise by bootstrap. :param evaluate_effect_strength: (Experimental) whether to evaluate the strength of effect :param confidence_intervals: Binary flag or a string indicating whether the confidence intervals should be computed and which method should be used. All methods support estimation of confidence intervals using the bootstrap method by using the parameter confidence_intervals="bootstrap". The bootstrap method takes in two arguments (num_simulations and sample_size_fraction) that can be optionally specified in the params dictionary. Estimators may also override this to implement their own confidence interval method. If this parameter is False, no confidence intervals are computed. If True, confidence intervals are computed by the estimator's specific method if available, otherwise through bootstrap. :param target_units: The units for which the treatment effect should be estimated. This can be a string for common specifications of target units (namely, "ate", "att" and "atc"). It can also be a lambda function that can be used as an index for the data (pandas DataFrame). Alternatively, it can be a new DataFrame that contains values of the effect_modifiers and effect will be estimated only for this new data. :param effect_modifiers: Variables on which to compute separate effects, or return a heterogeneous effect function. Not all methods support this currently. :param num_null_simulations: The number of simulations for testing the statistical significance of the estimator :param num_simulations: The number of simulations for finding the confidence interval (and/or standard error) for a estimate :param sample_size_fraction: The size of the sample for the bootstrap estimator :param confidence_level: The confidence level of the confidence interval estimate :param need_conditional_estimates: Boolean flag indicating whether conditional estimates should be computed. Defaults to True if there are effect modifiers in the graph :param num_quantiles_to_discretize_cont_cols: The number of quantiles into which a numeric effect modifier is split, to enable estimation of conditional treatment effect over it. :param kwargs: (optional) Additional estimator-specific parameters :returns: an instance of the estimator class. """ self._data = data self._target_estimand = identified_estimand # Currently estimation methods only support univariate treatment and outcome self._treatment_name = treatment self._outcome_name = outcome[0] # assuming one-dimensional outcome self._control_value = control_value self._treatment_value = treatment_value self._significance_test = test_significance self._effect_strength_eval = evaluate_effect_strength self._target_units = target_units self._effect_modifier_names = effect_modifiers self._confidence_intervals = confidence_intervals self._bootstrap_estimates = None # for confidence intervals and std error self._bootstrap_null_estimates = None # for significance test self._effect_modifiers = None self.method_params = kwargs # Setting the default interpret method self.interpret_method = CausalEstimator.DEFAULT_INTERPRET_METHOD self.logger = logging.getLogger(__name__) # Setting treatment and outcome values if self._data is not None: self._treatment = self._data[self._treatment_name] self._outcome = self._data[self._outcome_name] if self._effect_modifier_names: # only add the observed nodes self._effect_modifier_names = [ cname for cname in self._effect_modifier_names if cname in self._data.columns ] if len(self._effect_modifier_names) > 0: self._effect_modifiers = self._data[self._effect_modifier_names] self._effect_modifiers = pd.get_dummies(self._effect_modifiers, drop_first=True) self.logger.debug("Effect modifiers: " + ",".join(self._effect_modifier_names)) else: self._effect_modifier_names = None # Check if some parameters were set, otherwise set to default values self.num_null_simulations = num_null_simulations self.num_simulations = num_simulations self.sample_size_fraction = sample_size_fraction self.confidence_level = confidence_level self.num_quantiles_to_discretize_cont_cols = num_quantiles_to_discretize_cont_cols # Estimate conditional estimates by default self.need_conditional_estimates = ( need_conditional_estimates if need_conditional_estimates != "auto" else bool(self._effect_modifier_names) ) @staticmethod def get_estimator_object(new_data, identified_estimand, estimate): """Create a new estimator of the same type as the one passed in the estimate argument. Creates a new object with new_data and the identified_estimand :param new_data: np.ndarray, pd.Series, pd.DataFrame The newly assigned data on which the estimator should run :param identified_estimand: IdentifiedEstimand An instance of the identified estimand class that provides the information with respect to which causal pathways are employed when the treatment effects the outcome :param estimate: CausalEstimate It is an already existing estimate whose properties we wish to replicate :returns: An instance of the same estimator class that had generated the given estimate. """ estimator_class = estimate.params["estimator_class"] new_estimator = estimator_class( new_data, identified_estimand, identified_estimand.treatment_variable, identified_estimand.outcome_variable, # names of treatment and outcome control_value=estimate.control_value, treatment_value=estimate.treatment_value, test_significance=False, evaluate_effect_strength=False, confidence_intervals=estimate.params["confidence_intervals"], target_units=estimate.params["target_units"], effect_modifiers=estimate.params["effect_modifiers"], **estimate.params["method_params"] if estimate.params["method_params"] is not None else {}, ) return new_estimator def _estimate_effect(self): """This method is to be overriden by the child classes, so that they can run the estimation technique of their choice""" raise NotImplementedError( ("Main estimation method is " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG).format(self.__class__) ) def estimate_effect(self): """Base estimation method that calls the estimate_effect method of its calling subclass. Can optionally also test significance and estimate effect strength for any returned estimate. :param self: object instance of class Estimator :returns: A CausalEstimate instance that contains point estimates of average and conditional effects. Based on the parameters provided, it optionally includes confidence intervals, standard errors,statistical significance and other statistical parameters. """ est = self._estimate_effect() est.add_estimator(self) if self._significance_test: self.test_significance(est.value, method=self._significance_test) if self._confidence_intervals: self.estimate_confidence_intervals( est.value, confidence_level=self.confidence_level, method=self._confidence_intervals ) if self._effect_strength_eval: effect_strength_dict = self.evaluate_effect_strength(est) est.add_effect_strength(effect_strength_dict) return est def estimate_effect_naive(self): # TODO Only works for binary treatment df_withtreatment = self._data.loc[self._data[self._treatment_name] == 1] df_notreatment = self._data.loc[self._data[self._treatment_name] == 0] est = np.mean(df_withtreatment[self._outcome_name]) - np.mean(df_notreatment[self._outcome_name]) return CausalEstimate(est, None, None, control_value=0, treatment_value=1) def _estimate_effect_fn(self, data_df): """Function used in conditional effect estimation. This function is to be overridden by each child estimator. The overridden function should take in a dataframe as input and return the estimate for that data. """ raise NotImplementedError( ("Conditional treatment effects are " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG).format( self.__class__ ) ) def _estimate_conditional_effects(self, estimate_effect_fn, effect_modifier_names=None, num_quantiles=None): """Estimate conditional treatment effects. Common method for all estimators that utilizes a specific estimate_effect_fn implemented by each child estimator. If a numeric effect modifier is provided, it is discretized into quantile bins. If you would like a custom discretization, you can do so yourself: create a new column containing the discretized effect modifier and then include that column's name in the effect_modifier_names argument. :param estimate_effect_fn: Function that has a single parameter (a data frame) and returns the treatment effect estimate on that data. :param effect_modifier_names: Names of effect modifier variables over which the conditional effects will be estimated. If not provided, defaults to the effect modifiers specified during creation of the CausalEstimator object. :param num_quantiles: The number of quantiles into which a numeric effect modifier variable is discretized. Does not affect any categorical effect modifiers. :returns: A (multi-index) dataframe that provides separate effects for each value of the (discretized) effect modifiers. """ # Defaulting to class default values if parameters are not provided if effect_modifier_names is None: effect_modifier_names = self._effect_modifier_names if num_quantiles is None: num_quantiles = self.num_quantiles_to_discretize_cont_cols # Checking that there is at least one effect modifier if not effect_modifier_names: raise ValueError("At least one effect modifier should be specified to compute conditional effects.") # Making sure that effect_modifier_names is a list effect_modifier_names = parse_state(effect_modifier_names) if not all(em in self._effect_modifier_names for em in effect_modifier_names): self.logger.warn( "At least one of the provided effect modifiers was not included while fitting the estimator. You may get incorrect results. To resolve, fit the estimator again by providing the updated effect modifiers in estimate_effect()." ) # Making a copy since we are going to be changing effect modifier names effect_modifier_names = effect_modifier_names.copy() prefix = CausalEstimator.TEMP_CAT_COLUMN_PREFIX # For every numeric effect modifier, adding a temp categorical column for i in range(len(effect_modifier_names)): em = effect_modifier_names[i] if pd.api.types.is_numeric_dtype(self._data[em].dtypes): self._data[prefix + str(em)] = pd.qcut(self._data[em], num_quantiles, duplicates="drop") effect_modifier_names[i] = prefix + str(em) # Grouping by effect modifiers and computing effect separately by_effect_mods = self._data.groupby(effect_modifier_names) cond_est_fn = lambda x: self._do(self._treatment_value, x) - self._do(self._control_value, x) conditional_estimates = by_effect_mods.apply(estimate_effect_fn) # Deleting the temporary categorical columns for em in effect_modifier_names: if em.startswith(prefix): self._data.pop(em) return conditional_estimates def _do(self, x, data_df=None): raise NotImplementedError( ("Do-operator is " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG).format(self.__class__) ) def do(self, x, data_df=None): """Method that implements the do-operator. Given a value x for the treatment, returns the expected value of the outcome when the treatment is intervened to a value x. :param x: Value of the treatment :param data_df: Data on which the do-operator is to be applied. :returns: Value of the outcome when treatment is intervened/set to x. """ est = self._do(x, data_df) return est def construct_symbolic_estimator(self, estimand): raise NotImplementedError(("Symbolic estimator string is ").format(self.__class__)) def _generate_bootstrap_estimates(self, num_bootstrap_simulations, sample_size_fraction): """Helper function to generate causal estimates over bootstrapped samples. :param num_bootstrap_simulations: Number of simulations for the bootstrap method. :param sample_size_fraction: Fraction of the dataset to be resampled. :returns: A collections.namedtuple containing a list of bootstrapped estimates and a dictionary containing parameters used for the bootstrap. """ # The array that stores the results of all estimations simulation_results = np.zeros(num_bootstrap_simulations) # Find the sample size the proportion with the population size sample_size = int(sample_size_fraction * len(self._data)) if sample_size > len(self._data): self.logger.warning("WARN: The sample size is greater than the data being sampled") self.logger.info("INFO: The sample size: {}".format(sample_size)) self.logger.info("INFO: The number of simulations: {}".format(num_bootstrap_simulations)) # Perform the set number of simulations for index in range(num_bootstrap_simulations): new_data = resample(self._data, n_samples=sample_size) new_estimator = type(self)( new_data, self._target_estimand, self._target_estimand.treatment_variable, self._target_estimand.outcome_variable, # names of treatment and outcome treatment_value=self._treatment_value, control_value=self._control_value, test_significance=False, evaluate_effect_strength=False, confidence_intervals=False, target_units=self._target_units, effect_modifiers=self._effect_modifier_names, **self.method_params, ) new_effect = new_estimator.estimate_effect() simulation_results[index] = new_effect.value estimates = CausalEstimator.BootstrapEstimates( simulation_results, {"num_simulations": num_bootstrap_simulations, "sample_size_fraction": sample_size_fraction}, ) return estimates def _estimate_confidence_intervals_with_bootstrap( self, estimate_value, confidence_level=None, num_simulations=None, sample_size_fraction=None ): """ Method to compute confidence interval using bootstrapped sampling. :param estimate_value: obtained estimate's value :param confidence_level: The level for which to compute CI (e.g., 95% confidence level translates to confidence_level=0.95) :param num_simulations: The number of simulations to be performed to get the bootstrap confidence intervals. :param sample_size_fraction: The fraction of the dataset to be resampled. :returns: confidence interval at the specified level. For more details on bootstrap or resampling statistics, refer to the following links: https://ocw.mit.edu/courses/mathematics/18-05-introduction-to-probability-and-statistics-spring-2014/readings/MIT18_05S14_Reading24.pdf https://projecteuclid.org/download/pdf_1/euclid.ss/1032280214 """ # Using class default parameters if not specified if num_simulations is None: num_simulations = self.num_simulations if sample_size_fraction is None: sample_size_fraction = self.sample_size_fraction # Checking if bootstrap_estimates are already computed if self._bootstrap_estimates is None: self._bootstrap_estimates = self._generate_bootstrap_estimates(num_simulations, sample_size_fraction) elif CausalEstimator.is_bootstrap_parameter_changed(self._bootstrap_estimates.params, locals()): # Checked if any parameter is changed from the previous std error estimate self._bootstrap_estimates = self._generate_bootstrap_estimates(num_simulations, sample_size_fraction) # Now use the data obtained from the simulations to get the value of the confidence estimates bootstrap_estimates = self._bootstrap_estimates.estimates # Get the variations of each bootstrap estimate and sort bootstrap_variations = [bootstrap_estimate - estimate_value for bootstrap_estimate in bootstrap_estimates] sorted_bootstrap_variations = np.sort(bootstrap_variations) # Now we take the (1- p)th and the (p)th variations, where p is the chosen confidence level upper_bound_index = int((1 - confidence_level) * len(sorted_bootstrap_variations)) lower_bound_index = int(confidence_level * len(sorted_bootstrap_variations)) # Get the lower and upper bounds by subtracting the variations from the estimate lower_bound = estimate_value - sorted_bootstrap_variations[lower_bound_index] upper_bound = estimate_value - sorted_bootstrap_variations[upper_bound_index] return lower_bound, upper_bound def _estimate_confidence_intervals(self, confidence_level=None, method=None, **kwargs): """ This method is to be overriden by the child classes, so that they can run a confidence interval estimation method suited to the specific causal estimator. """ raise NotImplementedError( ( "This method for estimating confidence intervals is " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG + " Meanwhile, you can try the bootstrap method (method='bootstrap') to estimate confidence intervals." ).format(self.__class__) ) def estimate_confidence_intervals(self, estimate_value, confidence_level=None, method=None, **kwargs): """Find the confidence intervals corresponding to any estimator By default, this is done with the help of bootstrapped confidence intervals but can be overridden if the specific estimator implements other methods of estimating confidence intervals. If the method provided is not bootstrap, this function calls the implementation of the specific estimator. :param estimate_value: obtained estimate's value :param method: Method for estimating confidence intervals. :param confidence_level: The confidence level of the confidence intervals of the estimate. :param kwargs: Other optional args to be passed to the CI method. :returns: The obtained confidence interval. """ if method is None: if self._confidence_intervals: method = self._confidence_intervals # this is either True or methodname else: method = "default" confidence_intervals = None if confidence_level is None: confidence_level = self.confidence_level if method == "default" or method is True: # user has not provided any method try: confidence_intervals = self._estimate_confidence_intervals(confidence_level, method=method, **kwargs) except NotImplementedError: confidence_intervals = self._estimate_confidence_intervals_with_bootstrap( estimate_value, confidence_level, **kwargs ) else: if method == "bootstrap": confidence_intervals = self._estimate_confidence_intervals_with_bootstrap( estimate_value, confidence_level, **kwargs ) else: confidence_intervals = self._estimate_confidence_intervals(confidence_level, method=method, **kwargs) return confidence_intervals def _estimate_std_error_with_bootstrap(self, num_simulations=None, sample_size_fraction=None): """Compute standard error using the bootstrap method. Standard error and confidence intervals use the same parameter num_simulations for the number of bootstrap simulations. :param num_simulations: Number of bootstrapped samples. :param sample_size_fraction: Fraction of data to be resampled. :returns: Standard error of the obtained estimate. """ # Use existing params, if new user defined params are not present if num_simulations is None: num_simulations = self.num_simulations if sample_size_fraction is None: sample_size_fraction = self.sample_size_fraction # Checking if bootstrap_estimates are already computed if self._bootstrap_estimates is None: self._bootstrap_estimates = self._generate_bootstrap_estimates(num_simulations, sample_size_fraction) elif CausalEstimator.is_bootstrap_parameter_changed(self._bootstrap_estimates.params, locals()): # Check if any parameter is changed from the previous std error estimate self._bootstrap_estimates = self._generate_bootstrap_estimates(num_simulations, sample_size_fraction) std_error = np.std(self._bootstrap_estimates.estimates) return std_error def _estimate_std_error(self, method=None, **kwargs): """ This method is to be overriden by the child classes, so that they can run a standard error estimation method suited to the specific causal estimator. """ raise NotImplementedError( ( "This method for estimating standard errors is " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG + " Meanwhile, you can try the bootstrap method (method='bootstrap') to estimate standard errors." ).format(self.__class__) ) def estimate_std_error(self, method=None, **kwargs): """Compute standard error of an obtained causal estimate. :param method: Method for computing the standard error. :param kwargs: Other optional parameters to be passed to the estimating method. :returns: Standard error of the causal estimate. """ if method is None: if self._confidence_intervals: method = self._confidence_intervals else: method = "default" std_error = None if method == "default" or method is True: # user has not provided any method try: std_error = self._estimate_std_error(method, **kwargs) except NotImplementedError: std_error = self._estimate_std_error_with_bootstrap(**kwargs) else: if method == "bootstrap": std_error = self._estimate_std_error_with_bootstrap(**kwargs) else: std_error = self._estimate_std_error(method, **kwargs) return std_error def _test_significance_with_bootstrap(self, estimate_value, num_null_simulations=None): """Test statistical significance of an estimate using the bootstrap method. :param estimate_value: Obtained estimate's value :param num_null_simulations: Number of simulations for the null hypothesis :returns: p-value of the statistical significance test. """ # Use existing params, if new user defined params are not present if num_null_simulations is None: num_null_simulations = self.num_null_simulations do_retest = self._bootstrap_null_estimates is None or CausalEstimator.is_bootstrap_parameter_changed( self._bootstrap_null_estimates.params, locals() ) if do_retest: null_estimates = np.zeros(num_null_simulations) for i in range(num_null_simulations): new_outcome = np.random.permutation(self._outcome) new_data = self._data.assign(dummy_outcome=new_outcome) # self._outcome = self._data["dummy_outcome"] new_estimator = type(self)( new_data, self._target_estimand, self._target_estimand.treatment_variable, ("dummy_outcome",), test_significance=False, evaluate_effect_strength=False, confidence_intervals=False, target_units=self._target_units, effect_modifiers=self._effect_modifier_names, **self.method_params, ) new_effect = new_estimator.estimate_effect() null_estimates[i] = new_effect.value self._bootstrap_null_estimates = CausalEstimator.BootstrapEstimates( null_estimates, {"num_null_simulations": num_null_simulations, "sample_size_fraction": 1} ) # Processing the null hypothesis estimates sorted_null_estimates = np.sort(self._bootstrap_null_estimates.estimates) self.logger.debug("Null estimates: {0}".format(sorted_null_estimates)) median_estimate = sorted_null_estimates[int(num_null_simulations / 2)] # Doing a two-sided test if estimate_value > median_estimate: # Being conservative with the p-value reported estimate_index = np.searchsorted(sorted_null_estimates, estimate_value, side="left") p_value = 1 - (estimate_index / num_null_simulations) if estimate_value <= median_estimate: # Being conservative with the p-value reported estimate_index = np.searchsorted(sorted_null_estimates, estimate_value, side="right") p_value = estimate_index / num_null_simulations # If the estimate_index is 0, it depends on the number of simulations if p_value == 0: p_value = (0, 1 / len(sorted_null_estimates)) # a tuple determining the range. elif p_value == 1: p_value = (1 - 1 / len(sorted_null_estimates), 1) signif_dict = {"p_value": p_value} return signif_dict def _test_significance(self, estimate_value, method=None, **kwargs): """ This method is to be overriden by the child classes, so that they can run a significance test suited to the specific causal estimator. """ raise NotImplementedError( ( "This method for testing statistical significance is " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG + " Meanwhile, you can try the bootstrap method (method='bootstrap') to test statistical significance." ).format(self.__class__) ) def test_significance(self, estimate_value, method=None, **kwargs): """Test statistical significance of obtained estimate. By default, uses resampling to create a non-parametric significance test. A general procedure. Individual child estimators can implement different methods. If the method name is different from "bootstrap", this function calls the implementation of the child estimator. :param self: object instance of class Estimator :param estimate_value: obtained estimate's value :param method: Method for checking statistical significance :returns: p-value from the significance test """ if method is None: if self._significance_test: method = self._significance_test # this is either True or methodname else: method = "default" signif_dict = None if method == "default" or method is True: # user has not provided any method try: signif_dict = self._test_significance(estimate_value, method, **kwargs) except NotImplementedError: signif_dict = self._test_significance_with_bootstrap(estimate_value, **kwargs) else: if method == "bootstrap": signif_dict = self._test_significance_with_bootstrap(estimate_value, **kwargs) else: signif_dict = self._test_significance(estimate_value, method, **kwargs) return signif_dict def evaluate_effect_strength(self, estimate): fraction_effect_explained = self._evaluate_effect_strength(estimate, method="fraction-effect") # Need to test r-squared before supporting # effect_r_squared = self._evaluate_effect_strength(estimate, method="r-squared") strength_dict = { "fraction-effect": fraction_effect_explained # 'r-squared': effect_r_squared } return strength_dict def _evaluate_effect_strength(self, estimate, method="fraction-effect"): supported_methods = ["fraction-effect"] if method not in supported_methods: raise NotImplementedError("This method is not supported for evaluating effect strength") if method == "fraction-effect": naive_obs_estimate = self.estimate_effect_naive() self.logger.debug(estimate.value, naive_obs_estimate.value) fraction_effect_explained = estimate.value / naive_obs_estimate.value return fraction_effect_explained # elif method == "r-squared": # outcome_mean = np.mean(self._outcome) # total_variance = np.sum(np.square(self._outcome - outcome_mean)) # Assuming a linear model with one variable: the treatment # Currently only works for continuous y # causal_model = outcome_mean + estimate.value*self._treatment # squared_residual = np.sum(np.square(self._outcome - causal_model)) # r_squared = 1 - (squared_residual/total_variance) # return r_squared else: return None def update_input(self, treatment_value, control_value, target_units): self._control_value = control_value self._treatment_value = treatment_value self._target_units = target_units @staticmethod def is_bootstrap_parameter_changed(bootstrap_estimates_params, given_params): """Check whether parameters of the bootstrap have changed. This is an efficiency method that checks if fresh resampling of the bootstrap samples is required. Returns True if parameters have changed and resampling should be done again. :param bootstrap_estimates_params: A dictionary of parameters for the current bootstrap samples :param given_params: A dictionary of parameters passed by the user :returns: A binary flag denoting whether the parameters are different. """ is_any_parameter_changed = False for prm, val in bootstrap_estimates_params.items(): given_val = given_params.get(prm, None) if given_val is not None and given_val != val: is_any_parameter_changed = True break return is_any_parameter_changed def target_units_tostr(self): s = "" if type(self._target_units) is str: s += self._target_units elif callable(self._target_units): s += "Data subset defined by a function" elif isinstance(self._target_units, pd.DataFrame): s += "Data subset provided as a data frame" return s def signif_results_tostr(self, signif_results): s = "" pval = signif_results["p_value"] if type(pval) is tuple: s += "[{0}, {1}]".format(pval[0], pval[1]) else: s += "{0}".format(pval) return s def estimate_effect( treatment: Union[str, List[str]], outcome: Union[str, List[str]], identified_estimand: IdentifiedEstimand, identifier_name: str, method: CausalEstimator, control_value: int = 0, treatment_value: int = 1, test_significance: Optional[bool] = None, evaluate_effect_strength: bool = False, confidence_intervals: bool = False, target_units: str = "ate", effect_modifiers: List[str] = [], fit_estimator: bool = True, method_params: Optional[Dict] = None, ): """Estimate the identified causal effect. Currently requires an explicit method name to be specified. Method names follow the convention of identification method followed by the specific estimation method: "[backdoor/iv].estimation_method_name". Following methods are supported. * Propensity Score Matching: "backdoor.propensity_score_matching" * Propensity Score Stratification: "backdoor.propensity_score_stratification" * Propensity Score-based Inverse Weighting: "backdoor.propensity_score_weighting" * Linear Regression: "backdoor.linear_regression" * Generalized Linear Models (e.g., logistic regression): "backdoor.generalized_linear_model" * Instrumental Variables: "iv.instrumental_variable" * Regression Discontinuity: "iv.regression_discontinuity" In addition, you can directly call any of the EconML estimation methods. The convention is "backdoor.econml.path-to-estimator-class". For example, for the double machine learning estimator ("DML" class) that is located inside "dml" module of EconML, you can use the method name, "backdoor.econml.dml.DML". CausalML estimators can also be called. See `this demo notebook <https://py-why.github.io/dowhy/example_notebooks/dowhy-conditional-treatment-effects.html>`_. :param treatment: Name of the treatment :param outcome: Name of the outcome :param identified_estimand: a probability expression that represents the effect to be estimated. Output of CausalModel.identify_effect method :param method_name: name of the estimation method to be used. :param control_value: Value of the treatment in the control group, for effect estimation. If treatment is multi-variate, this can be a list. :param treatment_value: Value of the treatment in the treated group, for effect estimation. If treatment is multi-variate, this can be a list. :param test_significance: Binary flag on whether to additionally do a statistical signficance test for the estimate. :param evaluate_effect_strength: (Experimental) Binary flag on whether to estimate the relative strength of the treatment's effect. This measure can be used to compare different treatments for the same outcome (by running this method with different treatments sequentially). :param confidence_intervals: (Experimental) Binary flag indicating whether confidence intervals should be computed. :param target_units: (Experimental) The units for which the treatment effect should be estimated. This can be of three types. (1) a string for common specifications of target units (namely, "ate", "att" and "atc"), (2) a lambda function that can be used as an index for the data (pandas DataFrame), or (3) a new DataFrame that contains values of the effect_modifiers and effect will be estimated only for this new data. :param effect_modifiers: Names of effect modifier variables can be (optionally) specified here too, since they do not affect identification. If None, the effect_modifiers from the CausalModel are used. :param fit_estimator: Boolean flag on whether to fit the estimator. Setting it to False is useful to estimate the effect on new data using a previously fitted estimator. :param method_params: Dictionary containing any method-specific parameters. These are passed directly to the estimating method. See the docs for each estimation method for allowed method-specific params. :returns: An instance of the CausalEstimate class, containing the causal effect estimate and other method-dependent information """ treatment = parse_state(treatment) outcome = parse_state(outcome) causal_estimator_class = method.__class__ identified_estimand.set_identifier_method(identifier_name) if identified_estimand.no_directed_path: logger.warning("No directed path from {0} to {1}.".format(treatment, outcome)) return CausalEstimate( 0, identified_estimand, None, control_value=control_value, treatment_value=treatment_value ) # Check if estimator's target estimand is identified elif identified_estimand.estimands[identifier_name] is None: logger.error("No valid identified estimand available.") return CausalEstimate(None, None, None, control_value=control_value, treatment_value=treatment_value) method.update_input(treatment_value, control_value, target_units) estimate = method.estimate_effect() # Store parameters inside estimate object for refutation methods # TODO: This add_params needs to move to the estimator class # inside estimate_effect and estimate_conditional_effect estimate.add_params( estimand_type=identified_estimand.estimand_type, estimator_class=causal_estimator_class, test_significance=test_significance, evaluate_effect_strength=evaluate_effect_strength, confidence_intervals=confidence_intervals, target_units=target_units, effect_modifiers=effect_modifiers, method_params=method_params, ) return estimate class CausalEstimate: """Class for the estimate object that every causal estimator returns""" def __init__( self, estimate, target_estimand, realized_estimand_expr, control_value, treatment_value, conditional_estimates=None, **kwargs, ): self.value = estimate self.target_estimand = target_estimand self.realized_estimand_expr = realized_estimand_expr self.control_value = control_value self.treatment_value = treatment_value self.conditional_estimates = conditional_estimates self.params = kwargs if self.params is not None: for key, value in self.params.items(): setattr(self, key, value) self.effect_strength = None def add_estimator(self, estimator_instance): self.estimator = estimator_instance def add_effect_strength(self, strength_dict): self.effect_strength = strength_dict def add_params(self, **kwargs): self.params.update(kwargs) def get_confidence_intervals(self, confidence_level=None, method=None, **kwargs): """Get confidence intervals of the obtained estimate. By default, this is done with the help of bootstrapped confidence intervals but can be overridden if the specific estimator implements other methods of estimating confidence intervals. If the method provided is not bootstrap, this function calls the implementation of the specific estimator. :param method: Method for estimating confidence intervals. :param confidence_level: The confidence level of the confidence intervals of the estimate. :param kwargs: Other optional args to be passed to the CI method. :returns: The obtained confidence interval. """ confidence_intervals = self.estimator.estimate_confidence_intervals( estimate_value=self.value, confidence_level=confidence_level, method=method, **kwargs ) return confidence_intervals def get_standard_error(self, method=None, **kwargs): """Get standard error of the obtained estimate. By default, this is done with the help of bootstrapped standard errors but can be overridden if the specific estimator implements other methods of estimating standard error. If the method provided is not bootstrap, this function calls the implementation of the specific estimator. :param method: Method for computing the standard error. :param kwargs: Other optional parameters to be passed to the estimating method. :returns: Standard error of the causal estimate. """ std_error = self.estimator.estimate_std_error(method=method, **kwargs) return std_error def test_stat_significance(self, method=None, **kwargs): """Test statistical significance of the estimate obtained. By default, uses resampling to create a non-parametric significance test. Individual child estimators can implement different methods. If the method name is different from "bootstrap", this function calls the implementation of the child estimator. :param method: Method for checking statistical significance :param kwargs: Other optional parameters to be passed to the estimating method. :returns: p-value from the significance test """ signif_results = self.estimator.test_significance(self.value, method=method, **kwargs) return {"p_value": signif_results["p_value"]} def estimate_conditional_effects( self, effect_modifiers=None, num_quantiles=CausalEstimator.NUM_QUANTILES_TO_DISCRETIZE_CONT_COLS ): """Estimate treatment effect conditioned on given variables. If a numeric effect modifier is provided, it is discretized into quantile bins. If you would like a custom discretization, you can do so yourself: create a new column containing the discretized effect modifier and then include that column's name in the effect_modifier_names argument. :param effect_modifiers: Names of effect modifier variables over which the conditional effects will be estimated. If not provided, defaults to the effect modifiers specified during creation of the CausalEstimator object. :param num_quantiles: The number of quantiles into which a numeric effect modifier variable is discretized. Does not affect any categorical effect modifiers. :returns: A (multi-index) dataframe that provides separate effects for each value of the (discretized) effect modifiers. """ return self.estimator._estimate_conditional_effects( self.estimator._estimate_effect_fn, effect_modifiers, num_quantiles ) def interpret(self, method_name=None, **kwargs): """Interpret the causal estimate. :param method_name: Method used (string) or a list of methods. If None, then the default for the specific estimator is used. :param kwargs:: Optional parameters that are directly passed to the interpreter method. :returns: None """ if method_name is None: method_name = self.estimator.interpret_method method_name_arr = parse_state(method_name) for method in method_name_arr: interpreter = interpreters.get_class_object(method) interpreter(self, **kwargs).interpret() def __str__(self): s = "*** Causal Estimate ***\n" # No estimand was identified (identification failed) if self.target_estimand is None: return "Estimation failed! No relevant identified estimand available for this estimation method." s += "\n## Identified estimand\n{0}".format(self.target_estimand.__str__(only_target_estimand=True)) s += "\n## Realized estimand\n{0}".format(self.realized_estimand_expr) if hasattr(self, "estimator"): s += "\nTarget units: {0}\n".format(self.estimator.target_units_tostr()) s += "\n## Estimate\n" s += "Mean value: {0}\n".format(self.value) s += "" if hasattr(self, "cate_estimates"): s += "Effect estimates: {0}\n".format(self.cate_estimates) if hasattr(self, "estimator"): if self.estimator._significance_test: s += "p-value: {0}\n".format(self.estimator.signif_results_tostr(self.test_stat_significance())) if self.estimator._confidence_intervals: s += "{0}% confidence interval: {1}\n".format( 100 * self.estimator.confidence_level, self.get_confidence_intervals() ) if self.conditional_estimates is not None: s += "### Conditional Estimates\n" s += str(self.conditional_estimates) if self.effect_strength is not None: s += "\n## Effect Strength\n" s += "Change in outcome attributable to treatment: {}\n".format(self.effect_strength["fraction-effect"]) # s += "Variance in outcome explained by treatment: {}\n".format(self.effect_strength["r-squared"]) return s class RealizedEstimand(object): def __init__(self, identified_estimand, estimator_name): self.treatment_variable = identified_estimand.treatment_variable self.outcome_variable = identified_estimand.outcome_variable self.backdoor_variables = identified_estimand.get_backdoor_variables() self.instrumental_variables = identified_estimand.instrumental_variables self.estimand_type = identified_estimand.estimand_type self.estimand_expression = None self.assumptions = None self.estimator_name = estimator_name def update_assumptions(self, estimator_assumptions): self.assumptions = estimator_assumptions def update_estimand_expression(self, estimand_expression): self.estimand_expression = estimand_expression def __str__(self): s = "Realized estimand: {0}\n".format(self.estimator_name) s += "Realized estimand type: {0}\n".format(self.estimand_type) s += "Estimand expression:\n{0}\n".format(sp.pretty(self.estimand_expression)) j = 1 for ass_name, ass_str in self.assumptions.items(): s += "Estimand assumption {0}, {1}: {2}\n".format(j, ass_name, ass_str) j += 1 return s

andresmor-ms

2044d216c322a4b32c6eadce5da7d83463f19c2f

05bfa49dacf0061988c96c6f3e3756219df5422a

let's follow the sklearn protocol and provide "data" to the estimate_effect method. For backwards compatibility, the data parameter can be optional. Inside the estimate_effect method, we can check that if data parameter is None, then use self.data

amit-sharma

py-why/dowhy

Functional api/estimate effect function

#### Estimate Effect function * Refactors the estimate effect into a separate function to keep backwards compatibility #### TODO (future PRs): * Add `fit(...)` method to estimators - Move data related parameters from the constructor to the `fit(...)` method * Refactor code to avoid `**kwargs` in `__init__(...)` constructors

2022-10-18 15:49:21+00:00

2022-10-25 17:02:02+00:00

dowhy/causal_estimator.py

import logging from collections import namedtuple import numpy as np import pandas as pd import sympy as sp from sklearn.utils import resample import dowhy.interpreters as interpreters from dowhy.utils.api import parse_state class CausalEstimator: """Base class for an estimator of causal effect. Subclasses implement different estimation methods. All estimation methods are in the package "dowhy.causal_estimators" """ # The default number of simulations for statistical testing DEFAULT_NUMBER_OF_SIMULATIONS_STAT_TEST = 1000 # The default number of simulations to obtain confidence intervals DEFAULT_NUMBER_OF_SIMULATIONS_CI = 100 # The portion of the total size that should be taken each time to find the confidence intervals # 1 is the recommended value # https://ocw.mit.edu/courses/mathematics/18-05-introduction-to-probability-and-statistics-spring-2014/readings/MIT18_05S14_Reading24.pdf # https://projecteuclid.org/download/pdf_1/euclid.ss/1032280214 DEFAULT_SAMPLE_SIZE_FRACTION = 1 # The default Confidence Level DEFAULT_CONFIDENCE_LEVEL = 0.95 # Number of quantiles to discretize continuous columns, for applying groupby NUM_QUANTILES_TO_DISCRETIZE_CONT_COLS = 5 # Prefix to add to temporary categorical variables created after discretization TEMP_CAT_COLUMN_PREFIX = "__categorical__" DEFAULT_NOTIMPLEMENTEDERROR_MSG = "not yet implemented for {0}. If you would this to be implemented in the next version, please raise an issue at https://github.com/microsoft/dowhy/issues" BootstrapEstimates = namedtuple("BootstrapEstimates", ["estimates", "params"]) DEFAULT_INTERPRET_METHOD = ["textual_effect_interpreter"] # std args to be removed from locals() before being passed to args_dict _STD_INIT_ARGS = ("self", "__class__", "args", "kwargs") def __init__( self, data, identified_estimand, treatment, outcome, control_value=0, treatment_value=1, test_significance=False, evaluate_effect_strength=False, confidence_intervals=False, target_units=None, effect_modifiers=None, num_null_simulations=DEFAULT_NUMBER_OF_SIMULATIONS_STAT_TEST, num_simulations=DEFAULT_NUMBER_OF_SIMULATIONS_CI, sample_size_fraction=DEFAULT_SAMPLE_SIZE_FRACTION, confidence_level=DEFAULT_CONFIDENCE_LEVEL, need_conditional_estimates="auto", num_quantiles_to_discretize_cont_cols=NUM_QUANTILES_TO_DISCRETIZE_CONT_COLS, **kwargs, ): """Initializes an estimator with data and names of relevant variables. This method is called from the constructors of its child classes. :param data: data frame containing the data :param identified_estimand: probability expression representing the target identified estimand to estimate. :param treatment: name of the treatment variable :param outcome: name of the outcome variable :param control_value: Value of the treatment in the control group, for effect estimation. If treatment is multi-variate, this can be a list. :param treatment_value: Value of the treatment in the treated group, for effect estimation. If treatment is multi-variate, this can be a list. :param test_significance: Binary flag or a string indicating whether to test significance and by which method. All estimators support test_significance="bootstrap" that estimates a p-value for the obtained estimate using the bootstrap method. Individual estimators can override this to support custom testing methods. The bootstrap method supports an optional parameter, num_null_simulations. If False, no testing is done. If True, significance of the estimate is tested using the custom method if available, otherwise by bootstrap. :param evaluate_effect_strength: (Experimental) whether to evaluate the strength of effect :param confidence_intervals: Binary flag or a string indicating whether the confidence intervals should be computed and which method should be used. All methods support estimation of confidence intervals using the bootstrap method by using the parameter confidence_intervals="bootstrap". The bootstrap method takes in two arguments (num_simulations and sample_size_fraction) that can be optionally specified in the params dictionary. Estimators may also override this to implement their own confidence interval method. If this parameter is False, no confidence intervals are computed. If True, confidence intervals are computed by the estimator's specific method if available, otherwise through bootstrap. :param target_units: The units for which the treatment effect should be estimated. This can be a string for common specifications of target units (namely, "ate", "att" and "atc"). It can also be a lambda function that can be used as an index for the data (pandas DataFrame). Alternatively, it can be a new DataFrame that contains values of the effect_modifiers and effect will be estimated only for this new data. :param effect_modifiers: Variables on which to compute separate effects, or return a heterogeneous effect function. Not all methods support this currently. :param num_null_simulations: The number of simulations for testing the statistical significance of the estimator :param num_simulations: The number of simulations for finding the confidence interval (and/or standard error) for a estimate :param sample_size_fraction: The size of the sample for the bootstrap estimator :param confidence_level: The confidence level of the confidence interval estimate :param need_conditional_estimates: Boolean flag indicating whether conditional estimates should be computed. Defaults to True if there are effect modifiers in the graph :param num_quantiles_to_discretize_cont_cols: The number of quantiles into which a numeric effect modifier is split, to enable estimation of conditional treatment effect over it. :param kwargs: (optional) Additional estimator-specific parameters :returns: an instance of the estimator class. """ self._data = data self._target_estimand = identified_estimand # Currently estimation methods only support univariate treatment and outcome self._treatment_name = treatment self._outcome_name = outcome[0] # assuming one-dimensional outcome self._control_value = control_value self._treatment_value = treatment_value self._significance_test = test_significance self._effect_strength_eval = evaluate_effect_strength self._target_units = target_units self._effect_modifier_names = effect_modifiers self._confidence_intervals = confidence_intervals self._bootstrap_estimates = None # for confidence intervals and std error self._bootstrap_null_estimates = None # for significance test self._effect_modifiers = None self.method_params = kwargs # Setting the default interpret method self.interpret_method = CausalEstimator.DEFAULT_INTERPRET_METHOD self.logger = logging.getLogger(__name__) # Setting treatment and outcome values if self._data is not None: self._treatment = self._data[self._treatment_name] self._outcome = self._data[self._outcome_name] # Now saving the effect modifiers if self._effect_modifier_names: # only add the observed nodes self._effect_modifier_names = [ cname for cname in self._effect_modifier_names if cname in self._data.columns ] if len(self._effect_modifier_names) > 0: self._effect_modifiers = self._data[self._effect_modifier_names] self._effect_modifiers = pd.get_dummies(self._effect_modifiers, drop_first=True) self.logger.debug("Effect modifiers: " + ",".join(self._effect_modifier_names)) else: self._effect_modifier_names = None # Check if some parameters were set, otherwise set to default values self.num_null_simulations = num_null_simulations self.num_simulations = num_simulations self.sample_size_fraction = sample_size_fraction self.confidence_level = confidence_level self.num_quantiles_to_discretize_cont_cols = num_quantiles_to_discretize_cont_cols # Estimate conditional estimates by default self.need_conditional_estimates = ( need_conditional_estimates if need_conditional_estimates != "auto" else bool(self._effect_modifier_names) ) @staticmethod def get_estimator_object(new_data, identified_estimand, estimate): """Create a new estimator of the same type as the one passed in the estimate argument. Creates a new object with new_data and the identified_estimand :param new_data: np.ndarray, pd.Series, pd.DataFrame The newly assigned data on which the estimator should run :param identified_estimand: IdentifiedEstimand An instance of the identified estimand class that provides the information with respect to which causal pathways are employed when the treatment effects the outcome :param estimate: CausalEstimate It is an already existing estimate whose properties we wish to replicate :returns: An instance of the same estimator class that had generated the given estimate. """ estimator_class = estimate.params["estimator_class"] new_estimator = estimator_class( new_data, identified_estimand, identified_estimand.treatment_variable, identified_estimand.outcome_variable, # names of treatment and outcome control_value=estimate.control_value, treatment_value=estimate.treatment_value, test_significance=False, evaluate_effect_strength=False, confidence_intervals=estimate.params["confidence_intervals"], target_units=estimate.params["target_units"], effect_modifiers=estimate.params["effect_modifiers"], **estimate.params["method_params"], ) return new_estimator def _estimate_effect(self): """This method is to be overriden by the child classes, so that they can run the estimation technique of their choice""" raise NotImplementedError( ("Main estimation method is " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG).format(self.__class__) ) def estimate_effect(self): """Base estimation method that calls the estimate_effect method of its calling subclass. Can optionally also test significance and estimate effect strength for any returned estimate. :param self: object instance of class Estimator :returns: A CausalEstimate instance that contains point estimates of average and conditional effects. Based on the parameters provided, it optionally includes confidence intervals, standard errors,statistical significance and other statistical parameters. """ est = self._estimate_effect() est.add_estimator(self) if self._significance_test: self.test_significance(est.value, method=self._significance_test) if self._confidence_intervals: self.estimate_confidence_intervals( est.value, confidence_level=self.confidence_level, method=self._confidence_intervals ) if self._effect_strength_eval: effect_strength_dict = self.evaluate_effect_strength(est) est.add_effect_strength(effect_strength_dict) return est def estimate_effect_naive(self): # TODO Only works for binary treatment df_withtreatment = self._data.loc[self._data[self._treatment_name] == 1] df_notreatment = self._data.loc[self._data[self._treatment_name] == 0] est = np.mean(df_withtreatment[self._outcome_name]) - np.mean(df_notreatment[self._outcome_name]) return CausalEstimate(est, None, None, control_value=0, treatment_value=1) def _estimate_effect_fn(self, data_df): """Function used in conditional effect estimation. This function is to be overridden by each child estimator. The overridden function should take in a dataframe as input and return the estimate for that data. """ raise NotImplementedError( ("Conditional treatment effects are " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG).format( self.__class__ ) ) def _estimate_conditional_effects(self, estimate_effect_fn, effect_modifier_names=None, num_quantiles=None): """Estimate conditional treatment effects. Common method for all estimators that utilizes a specific estimate_effect_fn implemented by each child estimator. If a numeric effect modifier is provided, it is discretized into quantile bins. If you would like a custom discretization, you can do so yourself: create a new column containing the discretized effect modifier and then include that column's name in the effect_modifier_names argument. :param estimate_effect_fn: Function that has a single parameter (a data frame) and returns the treatment effect estimate on that data. :param effect_modifier_names: Names of effect modifier variables over which the conditional effects will be estimated. If not provided, defaults to the effect modifiers specified during creation of the CausalEstimator object. :param num_quantiles: The number of quantiles into which a numeric effect modifier variable is discretized. Does not affect any categorical effect modifiers. :returns: A (multi-index) dataframe that provides separate effects for each value of the (discretized) effect modifiers. """ # Defaulting to class default values if parameters are not provided if effect_modifier_names is None: effect_modifier_names = self._effect_modifier_names if num_quantiles is None: num_quantiles = self.num_quantiles_to_discretize_cont_cols # Checking that there is at least one effect modifier if not effect_modifier_names: raise ValueError("At least one effect modifier should be specified to compute conditional effects.") # Making sure that effect_modifier_names is a list effect_modifier_names = parse_state(effect_modifier_names) if not all(em in self._effect_modifier_names for em in effect_modifier_names): self.logger.warn( "At least one of the provided effect modifiers was not included while fitting the estimator. You may get incorrect results. To resolve, fit the estimator again by providing the updated effect modifiers in estimate_effect()." ) # Making a copy since we are going to be changing effect modifier names effect_modifier_names = effect_modifier_names.copy() prefix = CausalEstimator.TEMP_CAT_COLUMN_PREFIX # For every numeric effect modifier, adding a temp categorical column for i in range(len(effect_modifier_names)): em = effect_modifier_names[i] if pd.api.types.is_numeric_dtype(self._data[em].dtypes): self._data[prefix + str(em)] = pd.qcut(self._data[em], num_quantiles, duplicates="drop") effect_modifier_names[i] = prefix + str(em) # Grouping by effect modifiers and computing effect separately by_effect_mods = self._data.groupby(effect_modifier_names) cond_est_fn = lambda x: self._do(self._treatment_value, x) - self._do(self._control_value, x) conditional_estimates = by_effect_mods.apply(estimate_effect_fn) # Deleting the temporary categorical columns for em in effect_modifier_names: if em.startswith(prefix): self._data.pop(em) return conditional_estimates def _do(self, x, data_df=None): raise NotImplementedError( ("Do-operator is " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG).format(self.__class__) ) def do(self, x, data_df=None): """Method that implements the do-operator. Given a value x for the treatment, returns the expected value of the outcome when the treatment is intervened to a value x. :param x: Value of the treatment :param data_df: Data on which the do-operator is to be applied. :returns: Value of the outcome when treatment is intervened/set to x. """ est = self._do(x, data_df) return est def construct_symbolic_estimator(self, estimand): raise NotImplementedError(("Symbolic estimator string is ").format(self.__class__)) def _generate_bootstrap_estimates(self, num_bootstrap_simulations, sample_size_fraction): """Helper function to generate causal estimates over bootstrapped samples. :param num_bootstrap_simulations: Number of simulations for the bootstrap method. :param sample_size_fraction: Fraction of the dataset to be resampled. :returns: A collections.namedtuple containing a list of bootstrapped estimates and a dictionary containing parameters used for the bootstrap. """ # The array that stores the results of all estimations simulation_results = np.zeros(num_bootstrap_simulations) # Find the sample size the proportion with the population size sample_size = int(sample_size_fraction * len(self._data)) if sample_size > len(self._data): self.logger.warning("WARN: The sample size is greater than the data being sampled") self.logger.info("INFO: The sample size: {}".format(sample_size)) self.logger.info("INFO: The number of simulations: {}".format(num_bootstrap_simulations)) # Perform the set number of simulations for index in range(num_bootstrap_simulations): new_data = resample(self._data, n_samples=sample_size) new_estimator = type(self)( new_data, self._target_estimand, self._target_estimand.treatment_variable, self._target_estimand.outcome_variable, # names of treatment and outcome treatment_value=self._treatment_value, control_value=self._control_value, test_significance=False, evaluate_effect_strength=False, confidence_intervals=False, target_units=self._target_units, effect_modifiers=self._effect_modifier_names, **self.method_params, ) new_effect = new_estimator.estimate_effect() simulation_results[index] = new_effect.value estimates = CausalEstimator.BootstrapEstimates( simulation_results, {"num_simulations": num_bootstrap_simulations, "sample_size_fraction": sample_size_fraction}, ) return estimates def _estimate_confidence_intervals_with_bootstrap( self, estimate_value, confidence_level=None, num_simulations=None, sample_size_fraction=None ): """ Method to compute confidence interval using bootstrapped sampling. :param estimate_value: obtained estimate's value :param confidence_level: The level for which to compute CI (e.g., 95% confidence level translates to confidence_level=0.95) :param num_simulations: The number of simulations to be performed to get the bootstrap confidence intervals. :param sample_size_fraction: The fraction of the dataset to be resampled. :returns: confidence interval at the specified level. For more details on bootstrap or resampling statistics, refer to the following links: https://ocw.mit.edu/courses/mathematics/18-05-introduction-to-probability-and-statistics-spring-2014/readings/MIT18_05S14_Reading24.pdf https://projecteuclid.org/download/pdf_1/euclid.ss/1032280214 """ # Using class default parameters if not specified if num_simulations is None: num_simulations = self.num_simulations if sample_size_fraction is None: sample_size_fraction = self.sample_size_fraction # Checking if bootstrap_estimates are already computed if self._bootstrap_estimates is None: self._bootstrap_estimates = self._generate_bootstrap_estimates(num_simulations, sample_size_fraction) elif CausalEstimator.is_bootstrap_parameter_changed(self._bootstrap_estimates.params, locals()): # Checked if any parameter is changed from the previous std error estimate self._bootstrap_estimates = self._generate_bootstrap_estimates(num_simulations, sample_size_fraction) # Now use the data obtained from the simulations to get the value of the confidence estimates bootstrap_estimates = self._bootstrap_estimates.estimates # Get the variations of each bootstrap estimate and sort bootstrap_variations = [bootstrap_estimate - estimate_value for bootstrap_estimate in bootstrap_estimates] sorted_bootstrap_variations = np.sort(bootstrap_variations) # Now we take the (1- p)th and the (p)th variations, where p is the chosen confidence level upper_bound_index = int((1 - confidence_level) * len(sorted_bootstrap_variations)) lower_bound_index = int(confidence_level * len(sorted_bootstrap_variations)) # Get the lower and upper bounds by subtracting the variations from the estimate lower_bound = estimate_value - sorted_bootstrap_variations[lower_bound_index] upper_bound = estimate_value - sorted_bootstrap_variations[upper_bound_index] return lower_bound, upper_bound def _estimate_confidence_intervals(self, confidence_level=None, method=None, **kwargs): """ This method is to be overriden by the child classes, so that they can run a confidence interval estimation method suited to the specific causal estimator. """ raise NotImplementedError( ( "This method for estimating confidence intervals is " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG + " Meanwhile, you can try the bootstrap method (method='bootstrap') to estimate confidence intervals." ).format(self.__class__) ) def estimate_confidence_intervals(self, estimate_value, confidence_level=None, method=None, **kwargs): """Find the confidence intervals corresponding to any estimator By default, this is done with the help of bootstrapped confidence intervals but can be overridden if the specific estimator implements other methods of estimating confidence intervals. If the method provided is not bootstrap, this function calls the implementation of the specific estimator. :param estimate_value: obtained estimate's value :param method: Method for estimating confidence intervals. :param confidence_level: The confidence level of the confidence intervals of the estimate. :param kwargs: Other optional args to be passed to the CI method. :returns: The obtained confidence interval. """ if method is None: if self._confidence_intervals: method = self._confidence_intervals # this is either True or methodname else: method = "default" confidence_intervals = None if confidence_level is None: confidence_level = self.confidence_level if method == "default" or method is True: # user has not provided any method try: confidence_intervals = self._estimate_confidence_intervals(confidence_level, method=method, **kwargs) except NotImplementedError: confidence_intervals = self._estimate_confidence_intervals_with_bootstrap( estimate_value, confidence_level, **kwargs ) else: if method == "bootstrap": confidence_intervals = self._estimate_confidence_intervals_with_bootstrap( estimate_value, confidence_level, **kwargs ) else: confidence_intervals = self._estimate_confidence_intervals(confidence_level, method=method, **kwargs) return confidence_intervals def _estimate_std_error_with_bootstrap(self, num_simulations=None, sample_size_fraction=None): """Compute standard error using the bootstrap method. Standard error and confidence intervals use the same parameter num_simulations for the number of bootstrap simulations. :param num_simulations: Number of bootstrapped samples. :param sample_size_fraction: Fraction of data to be resampled. :returns: Standard error of the obtained estimate. """ # Use existing params, if new user defined params are not present if num_simulations is None: num_simulations = self.num_simulations if sample_size_fraction is None: sample_size_fraction = self.sample_size_fraction # Checking if bootstrap_estimates are already computed if self._bootstrap_estimates is None: self._bootstrap_estimates = self._generate_bootstrap_estimates(num_simulations, sample_size_fraction) elif CausalEstimator.is_bootstrap_parameter_changed(self._bootstrap_estimates.params, locals()): # Check if any parameter is changed from the previous std error estimate self._bootstrap_estimates = self._generate_bootstrap_estimates(num_simulations, sample_size_fraction) std_error = np.std(self._bootstrap_estimates.estimates) return std_error def _estimate_std_error(self, method=None, **kwargs): """ This method is to be overriden by the child classes, so that they can run a standard error estimation method suited to the specific causal estimator. """ raise NotImplementedError( ( "This method for estimating standard errors is " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG + " Meanwhile, you can try the bootstrap method (method='bootstrap') to estimate standard errors." ).format(self.__class__) ) def estimate_std_error(self, method=None, **kwargs): """Compute standard error of an obtained causal estimate. :param method: Method for computing the standard error. :param kwargs: Other optional parameters to be passed to the estimating method. :returns: Standard error of the causal estimate. """ if method is None: if self._confidence_intervals: method = self._confidence_intervals else: method = "default" std_error = None if method == "default" or method is True: # user has not provided any method try: std_error = self._estimate_std_error(method, **kwargs) except NotImplementedError: std_error = self._estimate_std_error_with_bootstrap(**kwargs) else: if method == "bootstrap": std_error = self._estimate_std_error_with_bootstrap(**kwargs) else: std_error = self._estimate_std_error(method, **kwargs) return std_error def _test_significance_with_bootstrap(self, estimate_value, num_null_simulations=None): """Test statistical significance of an estimate using the bootstrap method. :param estimate_value: Obtained estimate's value :param num_null_simulations: Number of simulations for the null hypothesis :returns: p-value of the statistical significance test. """ # Use existing params, if new user defined params are not present if num_null_simulations is None: num_null_simulations = self.num_null_simulations do_retest = self._bootstrap_null_estimates is None or CausalEstimator.is_bootstrap_parameter_changed( self._bootstrap_null_estimates.params, locals() ) if do_retest: null_estimates = np.zeros(num_null_simulations) for i in range(num_null_simulations): new_outcome = np.random.permutation(self._outcome) new_data = self._data.assign(dummy_outcome=new_outcome) # self._outcome = self._data["dummy_outcome"] new_estimator = type(self)( new_data, self._target_estimand, self._target_estimand.treatment_variable, ("dummy_outcome",), test_significance=False, evaluate_effect_strength=False, confidence_intervals=False, target_units=self._target_units, effect_modifiers=self._effect_modifier_names, **self.method_params, ) new_effect = new_estimator.estimate_effect() null_estimates[i] = new_effect.value self._bootstrap_null_estimates = CausalEstimator.BootstrapEstimates( null_estimates, {"num_null_simulations": num_null_simulations, "sample_size_fraction": 1} ) # Processing the null hypothesis estimates sorted_null_estimates = np.sort(self._bootstrap_null_estimates.estimates) self.logger.debug("Null estimates: {0}".format(sorted_null_estimates)) median_estimate = sorted_null_estimates[int(num_null_simulations / 2)] # Doing a two-sided test if estimate_value > median_estimate: # Being conservative with the p-value reported estimate_index = np.searchsorted(sorted_null_estimates, estimate_value, side="left") p_value = 1 - (estimate_index / num_null_simulations) if estimate_value <= median_estimate: # Being conservative with the p-value reported estimate_index = np.searchsorted(sorted_null_estimates, estimate_value, side="right") p_value = estimate_index / num_null_simulations # If the estimate_index is 0, it depends on the number of simulations if p_value == 0: p_value = (0, 1 / len(sorted_null_estimates)) # a tuple determining the range. elif p_value == 1: p_value = (1 - 1 / len(sorted_null_estimates), 1) signif_dict = {"p_value": p_value} return signif_dict def _test_significance(self, estimate_value, method=None, **kwargs): """ This method is to be overriden by the child classes, so that they can run a significance test suited to the specific causal estimator. """ raise NotImplementedError( ( "This method for testing statistical significance is " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG + " Meanwhile, you can try the bootstrap method (method='bootstrap') to test statistical significance." ).format(self.__class__) ) def test_significance(self, estimate_value, method=None, **kwargs): """Test statistical significance of obtained estimate. By default, uses resampling to create a non-parametric significance test. A general procedure. Individual child estimators can implement different methods. If the method name is different from "bootstrap", this function calls the implementation of the child estimator. :param self: object instance of class Estimator :param estimate_value: obtained estimate's value :param method: Method for checking statistical significance :returns: p-value from the significance test """ if method is None: if self._significance_test: method = self._significance_test # this is either True or methodname else: method = "default" signif_dict = None if method == "default" or method is True: # user has not provided any method try: signif_dict = self._test_significance(estimate_value, method, **kwargs) except NotImplementedError: signif_dict = self._test_significance_with_bootstrap(estimate_value, **kwargs) else: if method == "bootstrap": signif_dict = self._test_significance_with_bootstrap(estimate_value, **kwargs) else: signif_dict = self._test_significance(estimate_value, method, **kwargs) return signif_dict def evaluate_effect_strength(self, estimate): fraction_effect_explained = self._evaluate_effect_strength(estimate, method="fraction-effect") # Need to test r-squared before supporting # effect_r_squared = self._evaluate_effect_strength(estimate, method="r-squared") strength_dict = { "fraction-effect": fraction_effect_explained # 'r-squared': effect_r_squared } return strength_dict def _evaluate_effect_strength(self, estimate, method="fraction-effect"): supported_methods = ["fraction-effect"] if method not in supported_methods: raise NotImplementedError("This method is not supported for evaluating effect strength") if method == "fraction-effect": naive_obs_estimate = self.estimate_effect_naive() self.logger.debug(estimate.value, naive_obs_estimate.value) fraction_effect_explained = estimate.value / naive_obs_estimate.value return fraction_effect_explained # elif method == "r-squared": # outcome_mean = np.mean(self._outcome) # total_variance = np.sum(np.square(self._outcome - outcome_mean)) # Assuming a linear model with one variable: the treatment # Currently only works for continuous y # causal_model = outcome_mean + estimate.value*self._treatment # squared_residual = np.sum(np.square(self._outcome - causal_model)) # r_squared = 1 - (squared_residual/total_variance) # return r_squared else: return None def update_input(self, treatment_value, control_value, target_units): self._control_value = control_value self._treatment_value = treatment_value self._target_units = target_units @staticmethod def is_bootstrap_parameter_changed(bootstrap_estimates_params, given_params): """Check whether parameters of the bootstrap have changed. This is an efficiency method that checks if fresh resampling of the bootstrap samples is required. Returns True if parameters have changed and resampling should be done again. :param bootstrap_estimates_params: A dictionary of parameters for the current bootstrap samples :param given_params: A dictionary of parameters passed by the user :returns: A binary flag denoting whether the parameters are different. """ is_any_parameter_changed = False for prm, val in bootstrap_estimates_params.items(): given_val = given_params.get(prm, None) if given_val is not None and given_val != val: is_any_parameter_changed = True break return is_any_parameter_changed def target_units_tostr(self): s = "" if type(self._target_units) is str: s += self._target_units elif callable(self._target_units): s += "Data subset defined by a function" elif isinstance(self._target_units, pd.DataFrame): s += "Data subset provided as a data frame" return s def signif_results_tostr(self, signif_results): s = "" pval = signif_results["p_value"] if type(pval) is tuple: s += "[{0}, {1}]".format(pval[0], pval[1]) else: s += "{0}".format(pval) return s class CausalEstimate: """Class for the estimate object that every causal estimator returns""" def __init__( self, estimate, target_estimand, realized_estimand_expr, control_value, treatment_value, conditional_estimates=None, **kwargs, ): self.value = estimate self.target_estimand = target_estimand self.realized_estimand_expr = realized_estimand_expr self.control_value = control_value self.treatment_value = treatment_value self.conditional_estimates = conditional_estimates self.params = kwargs if self.params is not None: for key, value in self.params.items(): setattr(self, key, value) self.effect_strength = None def add_estimator(self, estimator_instance): self.estimator = estimator_instance def add_effect_strength(self, strength_dict): self.effect_strength = strength_dict def add_params(self, **kwargs): self.params.update(kwargs) def get_confidence_intervals(self, confidence_level=None, method=None, **kwargs): """Get confidence intervals of the obtained estimate. By default, this is done with the help of bootstrapped confidence intervals but can be overridden if the specific estimator implements other methods of estimating confidence intervals. If the method provided is not bootstrap, this function calls the implementation of the specific estimator. :param method: Method for estimating confidence intervals. :param confidence_level: The confidence level of the confidence intervals of the estimate. :param kwargs: Other optional args to be passed to the CI method. :returns: The obtained confidence interval. """ confidence_intervals = self.estimator.estimate_confidence_intervals( estimate_value=self.value, confidence_level=confidence_level, method=method, **kwargs ) return confidence_intervals def get_standard_error(self, method=None, **kwargs): """Get standard error of the obtained estimate. By default, this is done with the help of bootstrapped standard errors but can be overridden if the specific estimator implements other methods of estimating standard error. If the method provided is not bootstrap, this function calls the implementation of the specific estimator. :param method: Method for computing the standard error. :param kwargs: Other optional parameters to be passed to the estimating method. :returns: Standard error of the causal estimate. """ std_error = self.estimator.estimate_std_error(method=method, **kwargs) return std_error def test_stat_significance(self, method=None, **kwargs): """Test statistical significance of the estimate obtained. By default, uses resampling to create a non-parametric significance test. Individual child estimators can implement different methods. If the method name is different from "bootstrap", this function calls the implementation of the child estimator. :param method: Method for checking statistical significance :param kwargs: Other optional parameters to be passed to the estimating method. :returns: p-value from the significance test """ signif_results = self.estimator.test_significance(self.value, method=method, **kwargs) return {"p_value": signif_results["p_value"]} def estimate_conditional_effects( self, effect_modifiers=None, num_quantiles=CausalEstimator.NUM_QUANTILES_TO_DISCRETIZE_CONT_COLS ): """Estimate treatment effect conditioned on given variables. If a numeric effect modifier is provided, it is discretized into quantile bins. If you would like a custom discretization, you can do so yourself: create a new column containing the discretized effect modifier and then include that column's name in the effect_modifier_names argument. :param effect_modifiers: Names of effect modifier variables over which the conditional effects will be estimated. If not provided, defaults to the effect modifiers specified during creation of the CausalEstimator object. :param num_quantiles: The number of quantiles into which a numeric effect modifier variable is discretized. Does not affect any categorical effect modifiers. :returns: A (multi-index) dataframe that provides separate effects for each value of the (discretized) effect modifiers. """ return self.estimator._estimate_conditional_effects( self.estimator._estimate_effect_fn, effect_modifiers, num_quantiles ) def interpret(self, method_name=None, **kwargs): """Interpret the causal estimate. :param method_name: Method used (string) or a list of methods. If None, then the default for the specific estimator is used. :param kwargs:: Optional parameters that are directly passed to the interpreter method. :returns: None """ if method_name is None: method_name = self.estimator.interpret_method method_name_arr = parse_state(method_name) for method in method_name_arr: interpreter = interpreters.get_class_object(method) interpreter(self, **kwargs).interpret() def __str__(self): s = "*** Causal Estimate ***\n" # No estimand was identified (identification failed) if self.target_estimand is None: return "Estimation failed! No relevant identified estimand available for this estimation method." s += "\n## Identified estimand\n{0}".format(self.target_estimand.__str__(only_target_estimand=True)) s += "\n## Realized estimand\n{0}".format(self.realized_estimand_expr) if hasattr(self, "estimator"): s += "\nTarget units: {0}\n".format(self.estimator.target_units_tostr()) s += "\n## Estimate\n" s += "Mean value: {0}\n".format(self.value) s += "" if hasattr(self, "cate_estimates"): s += "Effect estimates: {0}\n".format(self.cate_estimates) if hasattr(self, "estimator"): if self.estimator._significance_test: s += "p-value: {0}\n".format(self.estimator.signif_results_tostr(self.test_stat_significance())) if self.estimator._confidence_intervals: s += "{0}% confidence interval: {1}\n".format( 100 * self.estimator.confidence_level, self.get_confidence_intervals() ) if self.conditional_estimates is not None: s += "### Conditional Estimates\n" s += str(self.conditional_estimates) if self.effect_strength is not None: s += "\n## Effect Strength\n" s += "Change in outcome attributable to treatment: {}\n".format(self.effect_strength["fraction-effect"]) # s += "Variance in outcome explained by treatment: {}\n".format(self.effect_strength["r-squared"]) return s class RealizedEstimand(object): def __init__(self, identified_estimand, estimator_name): self.treatment_variable = identified_estimand.treatment_variable self.outcome_variable = identified_estimand.outcome_variable self.backdoor_variables = identified_estimand.get_backdoor_variables() self.instrumental_variables = identified_estimand.instrumental_variables self.estimand_type = identified_estimand.estimand_type self.estimand_expression = None self.assumptions = None self.estimator_name = estimator_name def update_assumptions(self, estimator_assumptions): self.assumptions = estimator_assumptions def update_estimand_expression(self, estimand_expression): self.estimand_expression = estimand_expression def __str__(self): s = "Realized estimand: {0}\n".format(self.estimator_name) s += "Realized estimand type: {0}\n".format(self.estimand_type) s += "Estimand expression:\n{0}\n".format(sp.pretty(self.estimand_expression)) j = 1 for ass_name, ass_str in self.assumptions.items(): s += "Estimand assumption {0}, {1}: {2}\n".format(j, ass_name, ass_str) j += 1 return s

import logging from collections import namedtuple from typing import Dict, List, Optional, Union import numpy as np import pandas as pd import sympy as sp from sklearn.utils import resample import dowhy.interpreters as interpreters from dowhy import causal_estimators from dowhy.causal_graph import CausalGraph from dowhy.causal_identifier.identified_estimand import IdentifiedEstimand from dowhy.utils.api import parse_state logger = logging.getLogger(__name__) class CausalEstimator: """Base class for an estimator of causal effect. Subclasses implement different estimation methods. All estimation methods are in the package "dowhy.causal_estimators" """ # The default number of simulations for statistical testing DEFAULT_NUMBER_OF_SIMULATIONS_STAT_TEST = 1000 # The default number of simulations to obtain confidence intervals DEFAULT_NUMBER_OF_SIMULATIONS_CI = 100 # The portion of the total size that should be taken each time to find the confidence intervals # 1 is the recommended value # https://ocw.mit.edu/courses/mathematics/18-05-introduction-to-probability-and-statistics-spring-2014/readings/MIT18_05S14_Reading24.pdf # https://projecteuclid.org/download/pdf_1/euclid.ss/1032280214 DEFAULT_SAMPLE_SIZE_FRACTION = 1 # The default Confidence Level DEFAULT_CONFIDENCE_LEVEL = 0.95 # Number of quantiles to discretize continuous columns, for applying groupby NUM_QUANTILES_TO_DISCRETIZE_CONT_COLS = 5 # Prefix to add to temporary categorical variables created after discretization TEMP_CAT_COLUMN_PREFIX = "__categorical__" DEFAULT_NOTIMPLEMENTEDERROR_MSG = "not yet implemented for {0}. If you would this to be implemented in the next version, please raise an issue at https://github.com/microsoft/dowhy/issues" BootstrapEstimates = namedtuple("BootstrapEstimates", ["estimates", "params"]) DEFAULT_INTERPRET_METHOD = ["textual_effect_interpreter"] # std args to be removed from locals() before being passed to args_dict _STD_INIT_ARGS = ("self", "__class__", "args", "kwargs") def __init__( self, data, identified_estimand, treatment, outcome, control_value=0, treatment_value=1, test_significance=False, evaluate_effect_strength=False, confidence_intervals=False, target_units=None, effect_modifiers=None, num_null_simulations=DEFAULT_NUMBER_OF_SIMULATIONS_STAT_TEST, num_simulations=DEFAULT_NUMBER_OF_SIMULATIONS_CI, sample_size_fraction=DEFAULT_SAMPLE_SIZE_FRACTION, confidence_level=DEFAULT_CONFIDENCE_LEVEL, need_conditional_estimates="auto", num_quantiles_to_discretize_cont_cols=NUM_QUANTILES_TO_DISCRETIZE_CONT_COLS, **kwargs, ): """Initializes an estimator with data and names of relevant variables. This method is called from the constructors of its child classes. :param data: data frame containing the data :param identified_estimand: probability expression representing the target identified estimand to estimate. :param treatment: name of the treatment variable :param outcome: name of the outcome variable :param control_value: Value of the treatment in the control group, for effect estimation. If treatment is multi-variate, this can be a list. :param treatment_value: Value of the treatment in the treated group, for effect estimation. If treatment is multi-variate, this can be a list. :param test_significance: Binary flag or a string indicating whether to test significance and by which method. All estimators support test_significance="bootstrap" that estimates a p-value for the obtained estimate using the bootstrap method. Individual estimators can override this to support custom testing methods. The bootstrap method supports an optional parameter, num_null_simulations. If False, no testing is done. If True, significance of the estimate is tested using the custom method if available, otherwise by bootstrap. :param evaluate_effect_strength: (Experimental) whether to evaluate the strength of effect :param confidence_intervals: Binary flag or a string indicating whether the confidence intervals should be computed and which method should be used. All methods support estimation of confidence intervals using the bootstrap method by using the parameter confidence_intervals="bootstrap". The bootstrap method takes in two arguments (num_simulations and sample_size_fraction) that can be optionally specified in the params dictionary. Estimators may also override this to implement their own confidence interval method. If this parameter is False, no confidence intervals are computed. If True, confidence intervals are computed by the estimator's specific method if available, otherwise through bootstrap. :param target_units: The units for which the treatment effect should be estimated. This can be a string for common specifications of target units (namely, "ate", "att" and "atc"). It can also be a lambda function that can be used as an index for the data (pandas DataFrame). Alternatively, it can be a new DataFrame that contains values of the effect_modifiers and effect will be estimated only for this new data. :param effect_modifiers: Variables on which to compute separate effects, or return a heterogeneous effect function. Not all methods support this currently. :param num_null_simulations: The number of simulations for testing the statistical significance of the estimator :param num_simulations: The number of simulations for finding the confidence interval (and/or standard error) for a estimate :param sample_size_fraction: The size of the sample for the bootstrap estimator :param confidence_level: The confidence level of the confidence interval estimate :param need_conditional_estimates: Boolean flag indicating whether conditional estimates should be computed. Defaults to True if there are effect modifiers in the graph :param num_quantiles_to_discretize_cont_cols: The number of quantiles into which a numeric effect modifier is split, to enable estimation of conditional treatment effect over it. :param kwargs: (optional) Additional estimator-specific parameters :returns: an instance of the estimator class. """ self._data = data self._target_estimand = identified_estimand # Currently estimation methods only support univariate treatment and outcome self._treatment_name = treatment self._outcome_name = outcome[0] # assuming one-dimensional outcome self._control_value = control_value self._treatment_value = treatment_value self._significance_test = test_significance self._effect_strength_eval = evaluate_effect_strength self._target_units = target_units self._effect_modifier_names = effect_modifiers self._confidence_intervals = confidence_intervals self._bootstrap_estimates = None # for confidence intervals and std error self._bootstrap_null_estimates = None # for significance test self._effect_modifiers = None self.method_params = kwargs # Setting the default interpret method self.interpret_method = CausalEstimator.DEFAULT_INTERPRET_METHOD self.logger = logging.getLogger(__name__) # Setting treatment and outcome values if self._data is not None: self._treatment = self._data[self._treatment_name] self._outcome = self._data[self._outcome_name] if self._effect_modifier_names: # only add the observed nodes self._effect_modifier_names = [ cname for cname in self._effect_modifier_names if cname in self._data.columns ] if len(self._effect_modifier_names) > 0: self._effect_modifiers = self._data[self._effect_modifier_names] self._effect_modifiers = pd.get_dummies(self._effect_modifiers, drop_first=True) self.logger.debug("Effect modifiers: " + ",".join(self._effect_modifier_names)) else: self._effect_modifier_names = None # Check if some parameters were set, otherwise set to default values self.num_null_simulations = num_null_simulations self.num_simulations = num_simulations self.sample_size_fraction = sample_size_fraction self.confidence_level = confidence_level self.num_quantiles_to_discretize_cont_cols = num_quantiles_to_discretize_cont_cols # Estimate conditional estimates by default self.need_conditional_estimates = ( need_conditional_estimates if need_conditional_estimates != "auto" else bool(self._effect_modifier_names) ) @staticmethod def get_estimator_object(new_data, identified_estimand, estimate): """Create a new estimator of the same type as the one passed in the estimate argument. Creates a new object with new_data and the identified_estimand :param new_data: np.ndarray, pd.Series, pd.DataFrame The newly assigned data on which the estimator should run :param identified_estimand: IdentifiedEstimand An instance of the identified estimand class that provides the information with respect to which causal pathways are employed when the treatment effects the outcome :param estimate: CausalEstimate It is an already existing estimate whose properties we wish to replicate :returns: An instance of the same estimator class that had generated the given estimate. """ estimator_class = estimate.params["estimator_class"] new_estimator = estimator_class( new_data, identified_estimand, identified_estimand.treatment_variable, identified_estimand.outcome_variable, # names of treatment and outcome control_value=estimate.control_value, treatment_value=estimate.treatment_value, test_significance=False, evaluate_effect_strength=False, confidence_intervals=estimate.params["confidence_intervals"], target_units=estimate.params["target_units"], effect_modifiers=estimate.params["effect_modifiers"], **estimate.params["method_params"] if estimate.params["method_params"] is not None else {}, ) return new_estimator def _estimate_effect(self): """This method is to be overriden by the child classes, so that they can run the estimation technique of their choice""" raise NotImplementedError( ("Main estimation method is " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG).format(self.__class__) ) def estimate_effect(self): """Base estimation method that calls the estimate_effect method of its calling subclass. Can optionally also test significance and estimate effect strength for any returned estimate. :param self: object instance of class Estimator :returns: A CausalEstimate instance that contains point estimates of average and conditional effects. Based on the parameters provided, it optionally includes confidence intervals, standard errors,statistical significance and other statistical parameters. """ est = self._estimate_effect() est.add_estimator(self) if self._significance_test: self.test_significance(est.value, method=self._significance_test) if self._confidence_intervals: self.estimate_confidence_intervals( est.value, confidence_level=self.confidence_level, method=self._confidence_intervals ) if self._effect_strength_eval: effect_strength_dict = self.evaluate_effect_strength(est) est.add_effect_strength(effect_strength_dict) return est def estimate_effect_naive(self): # TODO Only works for binary treatment df_withtreatment = self._data.loc[self._data[self._treatment_name] == 1] df_notreatment = self._data.loc[self._data[self._treatment_name] == 0] est = np.mean(df_withtreatment[self._outcome_name]) - np.mean(df_notreatment[self._outcome_name]) return CausalEstimate(est, None, None, control_value=0, treatment_value=1) def _estimate_effect_fn(self, data_df): """Function used in conditional effect estimation. This function is to be overridden by each child estimator. The overridden function should take in a dataframe as input and return the estimate for that data. """ raise NotImplementedError( ("Conditional treatment effects are " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG).format( self.__class__ ) ) def _estimate_conditional_effects(self, estimate_effect_fn, effect_modifier_names=None, num_quantiles=None): """Estimate conditional treatment effects. Common method for all estimators that utilizes a specific estimate_effect_fn implemented by each child estimator. If a numeric effect modifier is provided, it is discretized into quantile bins. If you would like a custom discretization, you can do so yourself: create a new column containing the discretized effect modifier and then include that column's name in the effect_modifier_names argument. :param estimate_effect_fn: Function that has a single parameter (a data frame) and returns the treatment effect estimate on that data. :param effect_modifier_names: Names of effect modifier variables over which the conditional effects will be estimated. If not provided, defaults to the effect modifiers specified during creation of the CausalEstimator object. :param num_quantiles: The number of quantiles into which a numeric effect modifier variable is discretized. Does not affect any categorical effect modifiers. :returns: A (multi-index) dataframe that provides separate effects for each value of the (discretized) effect modifiers. """ # Defaulting to class default values if parameters are not provided if effect_modifier_names is None: effect_modifier_names = self._effect_modifier_names if num_quantiles is None: num_quantiles = self.num_quantiles_to_discretize_cont_cols # Checking that there is at least one effect modifier if not effect_modifier_names: raise ValueError("At least one effect modifier should be specified to compute conditional effects.") # Making sure that effect_modifier_names is a list effect_modifier_names = parse_state(effect_modifier_names) if not all(em in self._effect_modifier_names for em in effect_modifier_names): self.logger.warn( "At least one of the provided effect modifiers was not included while fitting the estimator. You may get incorrect results. To resolve, fit the estimator again by providing the updated effect modifiers in estimate_effect()." ) # Making a copy since we are going to be changing effect modifier names effect_modifier_names = effect_modifier_names.copy() prefix = CausalEstimator.TEMP_CAT_COLUMN_PREFIX # For every numeric effect modifier, adding a temp categorical column for i in range(len(effect_modifier_names)): em = effect_modifier_names[i] if pd.api.types.is_numeric_dtype(self._data[em].dtypes): self._data[prefix + str(em)] = pd.qcut(self._data[em], num_quantiles, duplicates="drop") effect_modifier_names[i] = prefix + str(em) # Grouping by effect modifiers and computing effect separately by_effect_mods = self._data.groupby(effect_modifier_names) cond_est_fn = lambda x: self._do(self._treatment_value, x) - self._do(self._control_value, x) conditional_estimates = by_effect_mods.apply(estimate_effect_fn) # Deleting the temporary categorical columns for em in effect_modifier_names: if em.startswith(prefix): self._data.pop(em) return conditional_estimates def _do(self, x, data_df=None): raise NotImplementedError( ("Do-operator is " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG).format(self.__class__) ) def do(self, x, data_df=None): """Method that implements the do-operator. Given a value x for the treatment, returns the expected value of the outcome when the treatment is intervened to a value x. :param x: Value of the treatment :param data_df: Data on which the do-operator is to be applied. :returns: Value of the outcome when treatment is intervened/set to x. """ est = self._do(x, data_df) return est def construct_symbolic_estimator(self, estimand): raise NotImplementedError(("Symbolic estimator string is ").format(self.__class__)) def _generate_bootstrap_estimates(self, num_bootstrap_simulations, sample_size_fraction): """Helper function to generate causal estimates over bootstrapped samples. :param num_bootstrap_simulations: Number of simulations for the bootstrap method. :param sample_size_fraction: Fraction of the dataset to be resampled. :returns: A collections.namedtuple containing a list of bootstrapped estimates and a dictionary containing parameters used for the bootstrap. """ # The array that stores the results of all estimations simulation_results = np.zeros(num_bootstrap_simulations) # Find the sample size the proportion with the population size sample_size = int(sample_size_fraction * len(self._data)) if sample_size > len(self._data): self.logger.warning("WARN: The sample size is greater than the data being sampled") self.logger.info("INFO: The sample size: {}".format(sample_size)) self.logger.info("INFO: The number of simulations: {}".format(num_bootstrap_simulations)) # Perform the set number of simulations for index in range(num_bootstrap_simulations): new_data = resample(self._data, n_samples=sample_size) new_estimator = type(self)( new_data, self._target_estimand, self._target_estimand.treatment_variable, self._target_estimand.outcome_variable, # names of treatment and outcome treatment_value=self._treatment_value, control_value=self._control_value, test_significance=False, evaluate_effect_strength=False, confidence_intervals=False, target_units=self._target_units, effect_modifiers=self._effect_modifier_names, **self.method_params, ) new_effect = new_estimator.estimate_effect() simulation_results[index] = new_effect.value estimates = CausalEstimator.BootstrapEstimates( simulation_results, {"num_simulations": num_bootstrap_simulations, "sample_size_fraction": sample_size_fraction}, ) return estimates def _estimate_confidence_intervals_with_bootstrap( self, estimate_value, confidence_level=None, num_simulations=None, sample_size_fraction=None ): """ Method to compute confidence interval using bootstrapped sampling. :param estimate_value: obtained estimate's value :param confidence_level: The level for which to compute CI (e.g., 95% confidence level translates to confidence_level=0.95) :param num_simulations: The number of simulations to be performed to get the bootstrap confidence intervals. :param sample_size_fraction: The fraction of the dataset to be resampled. :returns: confidence interval at the specified level. For more details on bootstrap or resampling statistics, refer to the following links: https://ocw.mit.edu/courses/mathematics/18-05-introduction-to-probability-and-statistics-spring-2014/readings/MIT18_05S14_Reading24.pdf https://projecteuclid.org/download/pdf_1/euclid.ss/1032280214 """ # Using class default parameters if not specified if num_simulations is None: num_simulations = self.num_simulations if sample_size_fraction is None: sample_size_fraction = self.sample_size_fraction # Checking if bootstrap_estimates are already computed if self._bootstrap_estimates is None: self._bootstrap_estimates = self._generate_bootstrap_estimates(num_simulations, sample_size_fraction) elif CausalEstimator.is_bootstrap_parameter_changed(self._bootstrap_estimates.params, locals()): # Checked if any parameter is changed from the previous std error estimate self._bootstrap_estimates = self._generate_bootstrap_estimates(num_simulations, sample_size_fraction) # Now use the data obtained from the simulations to get the value of the confidence estimates bootstrap_estimates = self._bootstrap_estimates.estimates # Get the variations of each bootstrap estimate and sort bootstrap_variations = [bootstrap_estimate - estimate_value for bootstrap_estimate in bootstrap_estimates] sorted_bootstrap_variations = np.sort(bootstrap_variations) # Now we take the (1- p)th and the (p)th variations, where p is the chosen confidence level upper_bound_index = int((1 - confidence_level) * len(sorted_bootstrap_variations)) lower_bound_index = int(confidence_level * len(sorted_bootstrap_variations)) # Get the lower and upper bounds by subtracting the variations from the estimate lower_bound = estimate_value - sorted_bootstrap_variations[lower_bound_index] upper_bound = estimate_value - sorted_bootstrap_variations[upper_bound_index] return lower_bound, upper_bound def _estimate_confidence_intervals(self, confidence_level=None, method=None, **kwargs): """ This method is to be overriden by the child classes, so that they can run a confidence interval estimation method suited to the specific causal estimator. """ raise NotImplementedError( ( "This method for estimating confidence intervals is " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG + " Meanwhile, you can try the bootstrap method (method='bootstrap') to estimate confidence intervals." ).format(self.__class__) ) def estimate_confidence_intervals(self, estimate_value, confidence_level=None, method=None, **kwargs): """Find the confidence intervals corresponding to any estimator By default, this is done with the help of bootstrapped confidence intervals but can be overridden if the specific estimator implements other methods of estimating confidence intervals. If the method provided is not bootstrap, this function calls the implementation of the specific estimator. :param estimate_value: obtained estimate's value :param method: Method for estimating confidence intervals. :param confidence_level: The confidence level of the confidence intervals of the estimate. :param kwargs: Other optional args to be passed to the CI method. :returns: The obtained confidence interval. """ if method is None: if self._confidence_intervals: method = self._confidence_intervals # this is either True or methodname else: method = "default" confidence_intervals = None if confidence_level is None: confidence_level = self.confidence_level if method == "default" or method is True: # user has not provided any method try: confidence_intervals = self._estimate_confidence_intervals(confidence_level, method=method, **kwargs) except NotImplementedError: confidence_intervals = self._estimate_confidence_intervals_with_bootstrap( estimate_value, confidence_level, **kwargs ) else: if method == "bootstrap": confidence_intervals = self._estimate_confidence_intervals_with_bootstrap( estimate_value, confidence_level, **kwargs ) else: confidence_intervals = self._estimate_confidence_intervals(confidence_level, method=method, **kwargs) return confidence_intervals def _estimate_std_error_with_bootstrap(self, num_simulations=None, sample_size_fraction=None): """Compute standard error using the bootstrap method. Standard error and confidence intervals use the same parameter num_simulations for the number of bootstrap simulations. :param num_simulations: Number of bootstrapped samples. :param sample_size_fraction: Fraction of data to be resampled. :returns: Standard error of the obtained estimate. """ # Use existing params, if new user defined params are not present if num_simulations is None: num_simulations = self.num_simulations if sample_size_fraction is None: sample_size_fraction = self.sample_size_fraction # Checking if bootstrap_estimates are already computed if self._bootstrap_estimates is None: self._bootstrap_estimates = self._generate_bootstrap_estimates(num_simulations, sample_size_fraction) elif CausalEstimator.is_bootstrap_parameter_changed(self._bootstrap_estimates.params, locals()): # Check if any parameter is changed from the previous std error estimate self._bootstrap_estimates = self._generate_bootstrap_estimates(num_simulations, sample_size_fraction) std_error = np.std(self._bootstrap_estimates.estimates) return std_error def _estimate_std_error(self, method=None, **kwargs): """ This method is to be overriden by the child classes, so that they can run a standard error estimation method suited to the specific causal estimator. """ raise NotImplementedError( ( "This method for estimating standard errors is " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG + " Meanwhile, you can try the bootstrap method (method='bootstrap') to estimate standard errors." ).format(self.__class__) ) def estimate_std_error(self, method=None, **kwargs): """Compute standard error of an obtained causal estimate. :param method: Method for computing the standard error. :param kwargs: Other optional parameters to be passed to the estimating method. :returns: Standard error of the causal estimate. """ if method is None: if self._confidence_intervals: method = self._confidence_intervals else: method = "default" std_error = None if method == "default" or method is True: # user has not provided any method try: std_error = self._estimate_std_error(method, **kwargs) except NotImplementedError: std_error = self._estimate_std_error_with_bootstrap(**kwargs) else: if method == "bootstrap": std_error = self._estimate_std_error_with_bootstrap(**kwargs) else: std_error = self._estimate_std_error(method, **kwargs) return std_error def _test_significance_with_bootstrap(self, estimate_value, num_null_simulations=None): """Test statistical significance of an estimate using the bootstrap method. :param estimate_value: Obtained estimate's value :param num_null_simulations: Number of simulations for the null hypothesis :returns: p-value of the statistical significance test. """ # Use existing params, if new user defined params are not present if num_null_simulations is None: num_null_simulations = self.num_null_simulations do_retest = self._bootstrap_null_estimates is None or CausalEstimator.is_bootstrap_parameter_changed( self._bootstrap_null_estimates.params, locals() ) if do_retest: null_estimates = np.zeros(num_null_simulations) for i in range(num_null_simulations): new_outcome = np.random.permutation(self._outcome) new_data = self._data.assign(dummy_outcome=new_outcome) # self._outcome = self._data["dummy_outcome"] new_estimator = type(self)( new_data, self._target_estimand, self._target_estimand.treatment_variable, ("dummy_outcome",), test_significance=False, evaluate_effect_strength=False, confidence_intervals=False, target_units=self._target_units, effect_modifiers=self._effect_modifier_names, **self.method_params, ) new_effect = new_estimator.estimate_effect() null_estimates[i] = new_effect.value self._bootstrap_null_estimates = CausalEstimator.BootstrapEstimates( null_estimates, {"num_null_simulations": num_null_simulations, "sample_size_fraction": 1} ) # Processing the null hypothesis estimates sorted_null_estimates = np.sort(self._bootstrap_null_estimates.estimates) self.logger.debug("Null estimates: {0}".format(sorted_null_estimates)) median_estimate = sorted_null_estimates[int(num_null_simulations / 2)] # Doing a two-sided test if estimate_value > median_estimate: # Being conservative with the p-value reported estimate_index = np.searchsorted(sorted_null_estimates, estimate_value, side="left") p_value = 1 - (estimate_index / num_null_simulations) if estimate_value <= median_estimate: # Being conservative with the p-value reported estimate_index = np.searchsorted(sorted_null_estimates, estimate_value, side="right") p_value = estimate_index / num_null_simulations # If the estimate_index is 0, it depends on the number of simulations if p_value == 0: p_value = (0, 1 / len(sorted_null_estimates)) # a tuple determining the range. elif p_value == 1: p_value = (1 - 1 / len(sorted_null_estimates), 1) signif_dict = {"p_value": p_value} return signif_dict def _test_significance(self, estimate_value, method=None, **kwargs): """ This method is to be overriden by the child classes, so that they can run a significance test suited to the specific causal estimator. """ raise NotImplementedError( ( "This method for testing statistical significance is " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG + " Meanwhile, you can try the bootstrap method (method='bootstrap') to test statistical significance." ).format(self.__class__) ) def test_significance(self, estimate_value, method=None, **kwargs): """Test statistical significance of obtained estimate. By default, uses resampling to create a non-parametric significance test. A general procedure. Individual child estimators can implement different methods. If the method name is different from "bootstrap", this function calls the implementation of the child estimator. :param self: object instance of class Estimator :param estimate_value: obtained estimate's value :param method: Method for checking statistical significance :returns: p-value from the significance test """ if method is None: if self._significance_test: method = self._significance_test # this is either True or methodname else: method = "default" signif_dict = None if method == "default" or method is True: # user has not provided any method try: signif_dict = self._test_significance(estimate_value, method, **kwargs) except NotImplementedError: signif_dict = self._test_significance_with_bootstrap(estimate_value, **kwargs) else: if method == "bootstrap": signif_dict = self._test_significance_with_bootstrap(estimate_value, **kwargs) else: signif_dict = self._test_significance(estimate_value, method, **kwargs) return signif_dict def evaluate_effect_strength(self, estimate): fraction_effect_explained = self._evaluate_effect_strength(estimate, method="fraction-effect") # Need to test r-squared before supporting # effect_r_squared = self._evaluate_effect_strength(estimate, method="r-squared") strength_dict = { "fraction-effect": fraction_effect_explained # 'r-squared': effect_r_squared } return strength_dict def _evaluate_effect_strength(self, estimate, method="fraction-effect"): supported_methods = ["fraction-effect"] if method not in supported_methods: raise NotImplementedError("This method is not supported for evaluating effect strength") if method == "fraction-effect": naive_obs_estimate = self.estimate_effect_naive() self.logger.debug(estimate.value, naive_obs_estimate.value) fraction_effect_explained = estimate.value / naive_obs_estimate.value return fraction_effect_explained # elif method == "r-squared": # outcome_mean = np.mean(self._outcome) # total_variance = np.sum(np.square(self._outcome - outcome_mean)) # Assuming a linear model with one variable: the treatment # Currently only works for continuous y # causal_model = outcome_mean + estimate.value*self._treatment # squared_residual = np.sum(np.square(self._outcome - causal_model)) # r_squared = 1 - (squared_residual/total_variance) # return r_squared else: return None def update_input(self, treatment_value, control_value, target_units): self._control_value = control_value self._treatment_value = treatment_value self._target_units = target_units @staticmethod def is_bootstrap_parameter_changed(bootstrap_estimates_params, given_params): """Check whether parameters of the bootstrap have changed. This is an efficiency method that checks if fresh resampling of the bootstrap samples is required. Returns True if parameters have changed and resampling should be done again. :param bootstrap_estimates_params: A dictionary of parameters for the current bootstrap samples :param given_params: A dictionary of parameters passed by the user :returns: A binary flag denoting whether the parameters are different. """ is_any_parameter_changed = False for prm, val in bootstrap_estimates_params.items(): given_val = given_params.get(prm, None) if given_val is not None and given_val != val: is_any_parameter_changed = True break return is_any_parameter_changed def target_units_tostr(self): s = "" if type(self._target_units) is str: s += self._target_units elif callable(self._target_units): s += "Data subset defined by a function" elif isinstance(self._target_units, pd.DataFrame): s += "Data subset provided as a data frame" return s def signif_results_tostr(self, signif_results): s = "" pval = signif_results["p_value"] if type(pval) is tuple: s += "[{0}, {1}]".format(pval[0], pval[1]) else: s += "{0}".format(pval) return s def estimate_effect( treatment: Union[str, List[str]], outcome: Union[str, List[str]], identified_estimand: IdentifiedEstimand, identifier_name: str, method: CausalEstimator, control_value: int = 0, treatment_value: int = 1, test_significance: Optional[bool] = None, evaluate_effect_strength: bool = False, confidence_intervals: bool = False, target_units: str = "ate", effect_modifiers: List[str] = [], fit_estimator: bool = True, method_params: Optional[Dict] = None, ): """Estimate the identified causal effect. Currently requires an explicit method name to be specified. Method names follow the convention of identification method followed by the specific estimation method: "[backdoor/iv].estimation_method_name". Following methods are supported. * Propensity Score Matching: "backdoor.propensity_score_matching" * Propensity Score Stratification: "backdoor.propensity_score_stratification" * Propensity Score-based Inverse Weighting: "backdoor.propensity_score_weighting" * Linear Regression: "backdoor.linear_regression" * Generalized Linear Models (e.g., logistic regression): "backdoor.generalized_linear_model" * Instrumental Variables: "iv.instrumental_variable" * Regression Discontinuity: "iv.regression_discontinuity" In addition, you can directly call any of the EconML estimation methods. The convention is "backdoor.econml.path-to-estimator-class". For example, for the double machine learning estimator ("DML" class) that is located inside "dml" module of EconML, you can use the method name, "backdoor.econml.dml.DML". CausalML estimators can also be called. See `this demo notebook <https://py-why.github.io/dowhy/example_notebooks/dowhy-conditional-treatment-effects.html>`_. :param treatment: Name of the treatment :param outcome: Name of the outcome :param identified_estimand: a probability expression that represents the effect to be estimated. Output of CausalModel.identify_effect method :param method_name: name of the estimation method to be used. :param control_value: Value of the treatment in the control group, for effect estimation. If treatment is multi-variate, this can be a list. :param treatment_value: Value of the treatment in the treated group, for effect estimation. If treatment is multi-variate, this can be a list. :param test_significance: Binary flag on whether to additionally do a statistical signficance test for the estimate. :param evaluate_effect_strength: (Experimental) Binary flag on whether to estimate the relative strength of the treatment's effect. This measure can be used to compare different treatments for the same outcome (by running this method with different treatments sequentially). :param confidence_intervals: (Experimental) Binary flag indicating whether confidence intervals should be computed. :param target_units: (Experimental) The units for which the treatment effect should be estimated. This can be of three types. (1) a string for common specifications of target units (namely, "ate", "att" and "atc"), (2) a lambda function that can be used as an index for the data (pandas DataFrame), or (3) a new DataFrame that contains values of the effect_modifiers and effect will be estimated only for this new data. :param effect_modifiers: Names of effect modifier variables can be (optionally) specified here too, since they do not affect identification. If None, the effect_modifiers from the CausalModel are used. :param fit_estimator: Boolean flag on whether to fit the estimator. Setting it to False is useful to estimate the effect on new data using a previously fitted estimator. :param method_params: Dictionary containing any method-specific parameters. These are passed directly to the estimating method. See the docs for each estimation method for allowed method-specific params. :returns: An instance of the CausalEstimate class, containing the causal effect estimate and other method-dependent information """ treatment = parse_state(treatment) outcome = parse_state(outcome) causal_estimator_class = method.__class__ identified_estimand.set_identifier_method(identifier_name) if identified_estimand.no_directed_path: logger.warning("No directed path from {0} to {1}.".format(treatment, outcome)) return CausalEstimate( 0, identified_estimand, None, control_value=control_value, treatment_value=treatment_value ) # Check if estimator's target estimand is identified elif identified_estimand.estimands[identifier_name] is None: logger.error("No valid identified estimand available.") return CausalEstimate(None, None, None, control_value=control_value, treatment_value=treatment_value) method.update_input(treatment_value, control_value, target_units) estimate = method.estimate_effect() # Store parameters inside estimate object for refutation methods # TODO: This add_params needs to move to the estimator class # inside estimate_effect and estimate_conditional_effect estimate.add_params( estimand_type=identified_estimand.estimand_type, estimator_class=causal_estimator_class, test_significance=test_significance, evaluate_effect_strength=evaluate_effect_strength, confidence_intervals=confidence_intervals, target_units=target_units, effect_modifiers=effect_modifiers, method_params=method_params, ) return estimate class CausalEstimate: """Class for the estimate object that every causal estimator returns""" def __init__( self, estimate, target_estimand, realized_estimand_expr, control_value, treatment_value, conditional_estimates=None, **kwargs, ): self.value = estimate self.target_estimand = target_estimand self.realized_estimand_expr = realized_estimand_expr self.control_value = control_value self.treatment_value = treatment_value self.conditional_estimates = conditional_estimates self.params = kwargs if self.params is not None: for key, value in self.params.items(): setattr(self, key, value) self.effect_strength = None def add_estimator(self, estimator_instance): self.estimator = estimator_instance def add_effect_strength(self, strength_dict): self.effect_strength = strength_dict def add_params(self, **kwargs): self.params.update(kwargs) def get_confidence_intervals(self, confidence_level=None, method=None, **kwargs): """Get confidence intervals of the obtained estimate. By default, this is done with the help of bootstrapped confidence intervals but can be overridden if the specific estimator implements other methods of estimating confidence intervals. If the method provided is not bootstrap, this function calls the implementation of the specific estimator. :param method: Method for estimating confidence intervals. :param confidence_level: The confidence level of the confidence intervals of the estimate. :param kwargs: Other optional args to be passed to the CI method. :returns: The obtained confidence interval. """ confidence_intervals = self.estimator.estimate_confidence_intervals( estimate_value=self.value, confidence_level=confidence_level, method=method, **kwargs ) return confidence_intervals def get_standard_error(self, method=None, **kwargs): """Get standard error of the obtained estimate. By default, this is done with the help of bootstrapped standard errors but can be overridden if the specific estimator implements other methods of estimating standard error. If the method provided is not bootstrap, this function calls the implementation of the specific estimator. :param method: Method for computing the standard error. :param kwargs: Other optional parameters to be passed to the estimating method. :returns: Standard error of the causal estimate. """ std_error = self.estimator.estimate_std_error(method=method, **kwargs) return std_error def test_stat_significance(self, method=None, **kwargs): """Test statistical significance of the estimate obtained. By default, uses resampling to create a non-parametric significance test. Individual child estimators can implement different methods. If the method name is different from "bootstrap", this function calls the implementation of the child estimator. :param method: Method for checking statistical significance :param kwargs: Other optional parameters to be passed to the estimating method. :returns: p-value from the significance test """ signif_results = self.estimator.test_significance(self.value, method=method, **kwargs) return {"p_value": signif_results["p_value"]} def estimate_conditional_effects( self, effect_modifiers=None, num_quantiles=CausalEstimator.NUM_QUANTILES_TO_DISCRETIZE_CONT_COLS ): """Estimate treatment effect conditioned on given variables. If a numeric effect modifier is provided, it is discretized into quantile bins. If you would like a custom discretization, you can do so yourself: create a new column containing the discretized effect modifier and then include that column's name in the effect_modifier_names argument. :param effect_modifiers: Names of effect modifier variables over which the conditional effects will be estimated. If not provided, defaults to the effect modifiers specified during creation of the CausalEstimator object. :param num_quantiles: The number of quantiles into which a numeric effect modifier variable is discretized. Does not affect any categorical effect modifiers. :returns: A (multi-index) dataframe that provides separate effects for each value of the (discretized) effect modifiers. """ return self.estimator._estimate_conditional_effects( self.estimator._estimate_effect_fn, effect_modifiers, num_quantiles ) def interpret(self, method_name=None, **kwargs): """Interpret the causal estimate. :param method_name: Method used (string) or a list of methods. If None, then the default for the specific estimator is used. :param kwargs:: Optional parameters that are directly passed to the interpreter method. :returns: None """ if method_name is None: method_name = self.estimator.interpret_method method_name_arr = parse_state(method_name) for method in method_name_arr: interpreter = interpreters.get_class_object(method) interpreter(self, **kwargs).interpret() def __str__(self): s = "*** Causal Estimate ***\n" # No estimand was identified (identification failed) if self.target_estimand is None: return "Estimation failed! No relevant identified estimand available for this estimation method." s += "\n## Identified estimand\n{0}".format(self.target_estimand.__str__(only_target_estimand=True)) s += "\n## Realized estimand\n{0}".format(self.realized_estimand_expr) if hasattr(self, "estimator"): s += "\nTarget units: {0}\n".format(self.estimator.target_units_tostr()) s += "\n## Estimate\n" s += "Mean value: {0}\n".format(self.value) s += "" if hasattr(self, "cate_estimates"): s += "Effect estimates: {0}\n".format(self.cate_estimates) if hasattr(self, "estimator"): if self.estimator._significance_test: s += "p-value: {0}\n".format(self.estimator.signif_results_tostr(self.test_stat_significance())) if self.estimator._confidence_intervals: s += "{0}% confidence interval: {1}\n".format( 100 * self.estimator.confidence_level, self.get_confidence_intervals() ) if self.conditional_estimates is not None: s += "### Conditional Estimates\n" s += str(self.conditional_estimates) if self.effect_strength is not None: s += "\n## Effect Strength\n" s += "Change in outcome attributable to treatment: {}\n".format(self.effect_strength["fraction-effect"]) # s += "Variance in outcome explained by treatment: {}\n".format(self.effect_strength["r-squared"]) return s class RealizedEstimand(object): def __init__(self, identified_estimand, estimator_name): self.treatment_variable = identified_estimand.treatment_variable self.outcome_variable = identified_estimand.outcome_variable self.backdoor_variables = identified_estimand.get_backdoor_variables() self.instrumental_variables = identified_estimand.instrumental_variables self.estimand_type = identified_estimand.estimand_type self.estimand_expression = None self.assumptions = None self.estimator_name = estimator_name def update_assumptions(self, estimator_assumptions): self.assumptions = estimator_assumptions def update_estimand_expression(self, estimand_expression): self.estimand_expression = estimand_expression def __str__(self): s = "Realized estimand: {0}\n".format(self.estimator_name) s += "Realized estimand type: {0}\n".format(self.estimand_type) s += "Estimand expression:\n{0}\n".format(sp.pretty(self.estimand_expression)) j = 1 for ass_name, ass_str in self.assumptions.items(): s += "Estimand assumption {0}, {1}: {2}\n".format(j, ass_name, ass_str) j += 1 return s

andresmor-ms

2044d216c322a4b32c6eadce5da7d83463f19c2f

05bfa49dacf0061988c96c6f3e3756219df5422a

actually, to be fully consistent, let's provide X and y. Here y is the outcome variable, provided as `data[outcome_name]` and X would be data.drop(columns=["outcome_name"])

amit-sharma

py-why/dowhy

Functional api/estimate effect function

#### Estimate Effect function * Refactors the estimate effect into a separate function to keep backwards compatibility #### TODO (future PRs): * Add `fit(...)` method to estimators - Move data related parameters from the constructor to the `fit(...)` method * Refactor code to avoid `**kwargs` in `__init__(...)` constructors

2022-10-18 15:49:21+00:00

2022-10-25 17:02:02+00:00

dowhy/causal_estimator.py

import logging from collections import namedtuple import numpy as np import pandas as pd import sympy as sp from sklearn.utils import resample import dowhy.interpreters as interpreters from dowhy.utils.api import parse_state class CausalEstimator: """Base class for an estimator of causal effect. Subclasses implement different estimation methods. All estimation methods are in the package "dowhy.causal_estimators" """ # The default number of simulations for statistical testing DEFAULT_NUMBER_OF_SIMULATIONS_STAT_TEST = 1000 # The default number of simulations to obtain confidence intervals DEFAULT_NUMBER_OF_SIMULATIONS_CI = 100 # The portion of the total size that should be taken each time to find the confidence intervals # 1 is the recommended value # https://ocw.mit.edu/courses/mathematics/18-05-introduction-to-probability-and-statistics-spring-2014/readings/MIT18_05S14_Reading24.pdf # https://projecteuclid.org/download/pdf_1/euclid.ss/1032280214 DEFAULT_SAMPLE_SIZE_FRACTION = 1 # The default Confidence Level DEFAULT_CONFIDENCE_LEVEL = 0.95 # Number of quantiles to discretize continuous columns, for applying groupby NUM_QUANTILES_TO_DISCRETIZE_CONT_COLS = 5 # Prefix to add to temporary categorical variables created after discretization TEMP_CAT_COLUMN_PREFIX = "__categorical__" DEFAULT_NOTIMPLEMENTEDERROR_MSG = "not yet implemented for {0}. If you would this to be implemented in the next version, please raise an issue at https://github.com/microsoft/dowhy/issues" BootstrapEstimates = namedtuple("BootstrapEstimates", ["estimates", "params"]) DEFAULT_INTERPRET_METHOD = ["textual_effect_interpreter"] # std args to be removed from locals() before being passed to args_dict _STD_INIT_ARGS = ("self", "__class__", "args", "kwargs") def __init__( self, data, identified_estimand, treatment, outcome, control_value=0, treatment_value=1, test_significance=False, evaluate_effect_strength=False, confidence_intervals=False, target_units=None, effect_modifiers=None, num_null_simulations=DEFAULT_NUMBER_OF_SIMULATIONS_STAT_TEST, num_simulations=DEFAULT_NUMBER_OF_SIMULATIONS_CI, sample_size_fraction=DEFAULT_SAMPLE_SIZE_FRACTION, confidence_level=DEFAULT_CONFIDENCE_LEVEL, need_conditional_estimates="auto", num_quantiles_to_discretize_cont_cols=NUM_QUANTILES_TO_DISCRETIZE_CONT_COLS, **kwargs, ): """Initializes an estimator with data and names of relevant variables. This method is called from the constructors of its child classes. :param data: data frame containing the data :param identified_estimand: probability expression representing the target identified estimand to estimate. :param treatment: name of the treatment variable :param outcome: name of the outcome variable :param control_value: Value of the treatment in the control group, for effect estimation. If treatment is multi-variate, this can be a list. :param treatment_value: Value of the treatment in the treated group, for effect estimation. If treatment is multi-variate, this can be a list. :param test_significance: Binary flag or a string indicating whether to test significance and by which method. All estimators support test_significance="bootstrap" that estimates a p-value for the obtained estimate using the bootstrap method. Individual estimators can override this to support custom testing methods. The bootstrap method supports an optional parameter, num_null_simulations. If False, no testing is done. If True, significance of the estimate is tested using the custom method if available, otherwise by bootstrap. :param evaluate_effect_strength: (Experimental) whether to evaluate the strength of effect :param confidence_intervals: Binary flag or a string indicating whether the confidence intervals should be computed and which method should be used. All methods support estimation of confidence intervals using the bootstrap method by using the parameter confidence_intervals="bootstrap". The bootstrap method takes in two arguments (num_simulations and sample_size_fraction) that can be optionally specified in the params dictionary. Estimators may also override this to implement their own confidence interval method. If this parameter is False, no confidence intervals are computed. If True, confidence intervals are computed by the estimator's specific method if available, otherwise through bootstrap. :param target_units: The units for which the treatment effect should be estimated. This can be a string for common specifications of target units (namely, "ate", "att" and "atc"). It can also be a lambda function that can be used as an index for the data (pandas DataFrame). Alternatively, it can be a new DataFrame that contains values of the effect_modifiers and effect will be estimated only for this new data. :param effect_modifiers: Variables on which to compute separate effects, or return a heterogeneous effect function. Not all methods support this currently. :param num_null_simulations: The number of simulations for testing the statistical significance of the estimator :param num_simulations: The number of simulations for finding the confidence interval (and/or standard error) for a estimate :param sample_size_fraction: The size of the sample for the bootstrap estimator :param confidence_level: The confidence level of the confidence interval estimate :param need_conditional_estimates: Boolean flag indicating whether conditional estimates should be computed. Defaults to True if there are effect modifiers in the graph :param num_quantiles_to_discretize_cont_cols: The number of quantiles into which a numeric effect modifier is split, to enable estimation of conditional treatment effect over it. :param kwargs: (optional) Additional estimator-specific parameters :returns: an instance of the estimator class. """ self._data = data self._target_estimand = identified_estimand # Currently estimation methods only support univariate treatment and outcome self._treatment_name = treatment self._outcome_name = outcome[0] # assuming one-dimensional outcome self._control_value = control_value self._treatment_value = treatment_value self._significance_test = test_significance self._effect_strength_eval = evaluate_effect_strength self._target_units = target_units self._effect_modifier_names = effect_modifiers self._confidence_intervals = confidence_intervals self._bootstrap_estimates = None # for confidence intervals and std error self._bootstrap_null_estimates = None # for significance test self._effect_modifiers = None self.method_params = kwargs # Setting the default interpret method self.interpret_method = CausalEstimator.DEFAULT_INTERPRET_METHOD self.logger = logging.getLogger(__name__) # Setting treatment and outcome values if self._data is not None: self._treatment = self._data[self._treatment_name] self._outcome = self._data[self._outcome_name] # Now saving the effect modifiers if self._effect_modifier_names: # only add the observed nodes self._effect_modifier_names = [ cname for cname in self._effect_modifier_names if cname in self._data.columns ] if len(self._effect_modifier_names) > 0: self._effect_modifiers = self._data[self._effect_modifier_names] self._effect_modifiers = pd.get_dummies(self._effect_modifiers, drop_first=True) self.logger.debug("Effect modifiers: " + ",".join(self._effect_modifier_names)) else: self._effect_modifier_names = None # Check if some parameters were set, otherwise set to default values self.num_null_simulations = num_null_simulations self.num_simulations = num_simulations self.sample_size_fraction = sample_size_fraction self.confidence_level = confidence_level self.num_quantiles_to_discretize_cont_cols = num_quantiles_to_discretize_cont_cols # Estimate conditional estimates by default self.need_conditional_estimates = ( need_conditional_estimates if need_conditional_estimates != "auto" else bool(self._effect_modifier_names) ) @staticmethod def get_estimator_object(new_data, identified_estimand, estimate): """Create a new estimator of the same type as the one passed in the estimate argument. Creates a new object with new_data and the identified_estimand :param new_data: np.ndarray, pd.Series, pd.DataFrame The newly assigned data on which the estimator should run :param identified_estimand: IdentifiedEstimand An instance of the identified estimand class that provides the information with respect to which causal pathways are employed when the treatment effects the outcome :param estimate: CausalEstimate It is an already existing estimate whose properties we wish to replicate :returns: An instance of the same estimator class that had generated the given estimate. """ estimator_class = estimate.params["estimator_class"] new_estimator = estimator_class( new_data, identified_estimand, identified_estimand.treatment_variable, identified_estimand.outcome_variable, # names of treatment and outcome control_value=estimate.control_value, treatment_value=estimate.treatment_value, test_significance=False, evaluate_effect_strength=False, confidence_intervals=estimate.params["confidence_intervals"], target_units=estimate.params["target_units"], effect_modifiers=estimate.params["effect_modifiers"], **estimate.params["method_params"], ) return new_estimator def _estimate_effect(self): """This method is to be overriden by the child classes, so that they can run the estimation technique of their choice""" raise NotImplementedError( ("Main estimation method is " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG).format(self.__class__) ) def estimate_effect(self): """Base estimation method that calls the estimate_effect method of its calling subclass. Can optionally also test significance and estimate effect strength for any returned estimate. :param self: object instance of class Estimator :returns: A CausalEstimate instance that contains point estimates of average and conditional effects. Based on the parameters provided, it optionally includes confidence intervals, standard errors,statistical significance and other statistical parameters. """ est = self._estimate_effect() est.add_estimator(self) if self._significance_test: self.test_significance(est.value, method=self._significance_test) if self._confidence_intervals: self.estimate_confidence_intervals( est.value, confidence_level=self.confidence_level, method=self._confidence_intervals ) if self._effect_strength_eval: effect_strength_dict = self.evaluate_effect_strength(est) est.add_effect_strength(effect_strength_dict) return est def estimate_effect_naive(self): # TODO Only works for binary treatment df_withtreatment = self._data.loc[self._data[self._treatment_name] == 1] df_notreatment = self._data.loc[self._data[self._treatment_name] == 0] est = np.mean(df_withtreatment[self._outcome_name]) - np.mean(df_notreatment[self._outcome_name]) return CausalEstimate(est, None, None, control_value=0, treatment_value=1) def _estimate_effect_fn(self, data_df): """Function used in conditional effect estimation. This function is to be overridden by each child estimator. The overridden function should take in a dataframe as input and return the estimate for that data. """ raise NotImplementedError( ("Conditional treatment effects are " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG).format( self.__class__ ) ) def _estimate_conditional_effects(self, estimate_effect_fn, effect_modifier_names=None, num_quantiles=None): """Estimate conditional treatment effects. Common method for all estimators that utilizes a specific estimate_effect_fn implemented by each child estimator. If a numeric effect modifier is provided, it is discretized into quantile bins. If you would like a custom discretization, you can do so yourself: create a new column containing the discretized effect modifier and then include that column's name in the effect_modifier_names argument. :param estimate_effect_fn: Function that has a single parameter (a data frame) and returns the treatment effect estimate on that data. :param effect_modifier_names: Names of effect modifier variables over which the conditional effects will be estimated. If not provided, defaults to the effect modifiers specified during creation of the CausalEstimator object. :param num_quantiles: The number of quantiles into which a numeric effect modifier variable is discretized. Does not affect any categorical effect modifiers. :returns: A (multi-index) dataframe that provides separate effects for each value of the (discretized) effect modifiers. """ # Defaulting to class default values if parameters are not provided if effect_modifier_names is None: effect_modifier_names = self._effect_modifier_names if num_quantiles is None: num_quantiles = self.num_quantiles_to_discretize_cont_cols # Checking that there is at least one effect modifier if not effect_modifier_names: raise ValueError("At least one effect modifier should be specified to compute conditional effects.") # Making sure that effect_modifier_names is a list effect_modifier_names = parse_state(effect_modifier_names) if not all(em in self._effect_modifier_names for em in effect_modifier_names): self.logger.warn( "At least one of the provided effect modifiers was not included while fitting the estimator. You may get incorrect results. To resolve, fit the estimator again by providing the updated effect modifiers in estimate_effect()." ) # Making a copy since we are going to be changing effect modifier names effect_modifier_names = effect_modifier_names.copy() prefix = CausalEstimator.TEMP_CAT_COLUMN_PREFIX # For every numeric effect modifier, adding a temp categorical column for i in range(len(effect_modifier_names)): em = effect_modifier_names[i] if pd.api.types.is_numeric_dtype(self._data[em].dtypes): self._data[prefix + str(em)] = pd.qcut(self._data[em], num_quantiles, duplicates="drop") effect_modifier_names[i] = prefix + str(em) # Grouping by effect modifiers and computing effect separately by_effect_mods = self._data.groupby(effect_modifier_names) cond_est_fn = lambda x: self._do(self._treatment_value, x) - self._do(self._control_value, x) conditional_estimates = by_effect_mods.apply(estimate_effect_fn) # Deleting the temporary categorical columns for em in effect_modifier_names: if em.startswith(prefix): self._data.pop(em) return conditional_estimates def _do(self, x, data_df=None): raise NotImplementedError( ("Do-operator is " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG).format(self.__class__) ) def do(self, x, data_df=None): """Method that implements the do-operator. Given a value x for the treatment, returns the expected value of the outcome when the treatment is intervened to a value x. :param x: Value of the treatment :param data_df: Data on which the do-operator is to be applied. :returns: Value of the outcome when treatment is intervened/set to x. """ est = self._do(x, data_df) return est def construct_symbolic_estimator(self, estimand): raise NotImplementedError(("Symbolic estimator string is ").format(self.__class__)) def _generate_bootstrap_estimates(self, num_bootstrap_simulations, sample_size_fraction): """Helper function to generate causal estimates over bootstrapped samples. :param num_bootstrap_simulations: Number of simulations for the bootstrap method. :param sample_size_fraction: Fraction of the dataset to be resampled. :returns: A collections.namedtuple containing a list of bootstrapped estimates and a dictionary containing parameters used for the bootstrap. """ # The array that stores the results of all estimations simulation_results = np.zeros(num_bootstrap_simulations) # Find the sample size the proportion with the population size sample_size = int(sample_size_fraction * len(self._data)) if sample_size > len(self._data): self.logger.warning("WARN: The sample size is greater than the data being sampled") self.logger.info("INFO: The sample size: {}".format(sample_size)) self.logger.info("INFO: The number of simulations: {}".format(num_bootstrap_simulations)) # Perform the set number of simulations for index in range(num_bootstrap_simulations): new_data = resample(self._data, n_samples=sample_size) new_estimator = type(self)( new_data, self._target_estimand, self._target_estimand.treatment_variable, self._target_estimand.outcome_variable, # names of treatment and outcome treatment_value=self._treatment_value, control_value=self._control_value, test_significance=False, evaluate_effect_strength=False, confidence_intervals=False, target_units=self._target_units, effect_modifiers=self._effect_modifier_names, **self.method_params, ) new_effect = new_estimator.estimate_effect() simulation_results[index] = new_effect.value estimates = CausalEstimator.BootstrapEstimates( simulation_results, {"num_simulations": num_bootstrap_simulations, "sample_size_fraction": sample_size_fraction}, ) return estimates def _estimate_confidence_intervals_with_bootstrap( self, estimate_value, confidence_level=None, num_simulations=None, sample_size_fraction=None ): """ Method to compute confidence interval using bootstrapped sampling. :param estimate_value: obtained estimate's value :param confidence_level: The level for which to compute CI (e.g., 95% confidence level translates to confidence_level=0.95) :param num_simulations: The number of simulations to be performed to get the bootstrap confidence intervals. :param sample_size_fraction: The fraction of the dataset to be resampled. :returns: confidence interval at the specified level. For more details on bootstrap or resampling statistics, refer to the following links: https://ocw.mit.edu/courses/mathematics/18-05-introduction-to-probability-and-statistics-spring-2014/readings/MIT18_05S14_Reading24.pdf https://projecteuclid.org/download/pdf_1/euclid.ss/1032280214 """ # Using class default parameters if not specified if num_simulations is None: num_simulations = self.num_simulations if sample_size_fraction is None: sample_size_fraction = self.sample_size_fraction # Checking if bootstrap_estimates are already computed if self._bootstrap_estimates is None: self._bootstrap_estimates = self._generate_bootstrap_estimates(num_simulations, sample_size_fraction) elif CausalEstimator.is_bootstrap_parameter_changed(self._bootstrap_estimates.params, locals()): # Checked if any parameter is changed from the previous std error estimate self._bootstrap_estimates = self._generate_bootstrap_estimates(num_simulations, sample_size_fraction) # Now use the data obtained from the simulations to get the value of the confidence estimates bootstrap_estimates = self._bootstrap_estimates.estimates # Get the variations of each bootstrap estimate and sort bootstrap_variations = [bootstrap_estimate - estimate_value for bootstrap_estimate in bootstrap_estimates] sorted_bootstrap_variations = np.sort(bootstrap_variations) # Now we take the (1- p)th and the (p)th variations, where p is the chosen confidence level upper_bound_index = int((1 - confidence_level) * len(sorted_bootstrap_variations)) lower_bound_index = int(confidence_level * len(sorted_bootstrap_variations)) # Get the lower and upper bounds by subtracting the variations from the estimate lower_bound = estimate_value - sorted_bootstrap_variations[lower_bound_index] upper_bound = estimate_value - sorted_bootstrap_variations[upper_bound_index] return lower_bound, upper_bound def _estimate_confidence_intervals(self, confidence_level=None, method=None, **kwargs): """ This method is to be overriden by the child classes, so that they can run a confidence interval estimation method suited to the specific causal estimator. """ raise NotImplementedError( ( "This method for estimating confidence intervals is " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG + " Meanwhile, you can try the bootstrap method (method='bootstrap') to estimate confidence intervals." ).format(self.__class__) ) def estimate_confidence_intervals(self, estimate_value, confidence_level=None, method=None, **kwargs): """Find the confidence intervals corresponding to any estimator By default, this is done with the help of bootstrapped confidence intervals but can be overridden if the specific estimator implements other methods of estimating confidence intervals. If the method provided is not bootstrap, this function calls the implementation of the specific estimator. :param estimate_value: obtained estimate's value :param method: Method for estimating confidence intervals. :param confidence_level: The confidence level of the confidence intervals of the estimate. :param kwargs: Other optional args to be passed to the CI method. :returns: The obtained confidence interval. """ if method is None: if self._confidence_intervals: method = self._confidence_intervals # this is either True or methodname else: method = "default" confidence_intervals = None if confidence_level is None: confidence_level = self.confidence_level if method == "default" or method is True: # user has not provided any method try: confidence_intervals = self._estimate_confidence_intervals(confidence_level, method=method, **kwargs) except NotImplementedError: confidence_intervals = self._estimate_confidence_intervals_with_bootstrap( estimate_value, confidence_level, **kwargs ) else: if method == "bootstrap": confidence_intervals = self._estimate_confidence_intervals_with_bootstrap( estimate_value, confidence_level, **kwargs ) else: confidence_intervals = self._estimate_confidence_intervals(confidence_level, method=method, **kwargs) return confidence_intervals def _estimate_std_error_with_bootstrap(self, num_simulations=None, sample_size_fraction=None): """Compute standard error using the bootstrap method. Standard error and confidence intervals use the same parameter num_simulations for the number of bootstrap simulations. :param num_simulations: Number of bootstrapped samples. :param sample_size_fraction: Fraction of data to be resampled. :returns: Standard error of the obtained estimate. """ # Use existing params, if new user defined params are not present if num_simulations is None: num_simulations = self.num_simulations if sample_size_fraction is None: sample_size_fraction = self.sample_size_fraction # Checking if bootstrap_estimates are already computed if self._bootstrap_estimates is None: self._bootstrap_estimates = self._generate_bootstrap_estimates(num_simulations, sample_size_fraction) elif CausalEstimator.is_bootstrap_parameter_changed(self._bootstrap_estimates.params, locals()): # Check if any parameter is changed from the previous std error estimate self._bootstrap_estimates = self._generate_bootstrap_estimates(num_simulations, sample_size_fraction) std_error = np.std(self._bootstrap_estimates.estimates) return std_error def _estimate_std_error(self, method=None, **kwargs): """ This method is to be overriden by the child classes, so that they can run a standard error estimation method suited to the specific causal estimator. """ raise NotImplementedError( ( "This method for estimating standard errors is " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG + " Meanwhile, you can try the bootstrap method (method='bootstrap') to estimate standard errors." ).format(self.__class__) ) def estimate_std_error(self, method=None, **kwargs): """Compute standard error of an obtained causal estimate. :param method: Method for computing the standard error. :param kwargs: Other optional parameters to be passed to the estimating method. :returns: Standard error of the causal estimate. """ if method is None: if self._confidence_intervals: method = self._confidence_intervals else: method = "default" std_error = None if method == "default" or method is True: # user has not provided any method try: std_error = self._estimate_std_error(method, **kwargs) except NotImplementedError: std_error = self._estimate_std_error_with_bootstrap(**kwargs) else: if method == "bootstrap": std_error = self._estimate_std_error_with_bootstrap(**kwargs) else: std_error = self._estimate_std_error(method, **kwargs) return std_error def _test_significance_with_bootstrap(self, estimate_value, num_null_simulations=None): """Test statistical significance of an estimate using the bootstrap method. :param estimate_value: Obtained estimate's value :param num_null_simulations: Number of simulations for the null hypothesis :returns: p-value of the statistical significance test. """ # Use existing params, if new user defined params are not present if num_null_simulations is None: num_null_simulations = self.num_null_simulations do_retest = self._bootstrap_null_estimates is None or CausalEstimator.is_bootstrap_parameter_changed( self._bootstrap_null_estimates.params, locals() ) if do_retest: null_estimates = np.zeros(num_null_simulations) for i in range(num_null_simulations): new_outcome = np.random.permutation(self._outcome) new_data = self._data.assign(dummy_outcome=new_outcome) # self._outcome = self._data["dummy_outcome"] new_estimator = type(self)( new_data, self._target_estimand, self._target_estimand.treatment_variable, ("dummy_outcome",), test_significance=False, evaluate_effect_strength=False, confidence_intervals=False, target_units=self._target_units, effect_modifiers=self._effect_modifier_names, **self.method_params, ) new_effect = new_estimator.estimate_effect() null_estimates[i] = new_effect.value self._bootstrap_null_estimates = CausalEstimator.BootstrapEstimates( null_estimates, {"num_null_simulations": num_null_simulations, "sample_size_fraction": 1} ) # Processing the null hypothesis estimates sorted_null_estimates = np.sort(self._bootstrap_null_estimates.estimates) self.logger.debug("Null estimates: {0}".format(sorted_null_estimates)) median_estimate = sorted_null_estimates[int(num_null_simulations / 2)] # Doing a two-sided test if estimate_value > median_estimate: # Being conservative with the p-value reported estimate_index = np.searchsorted(sorted_null_estimates, estimate_value, side="left") p_value = 1 - (estimate_index / num_null_simulations) if estimate_value <= median_estimate: # Being conservative with the p-value reported estimate_index = np.searchsorted(sorted_null_estimates, estimate_value, side="right") p_value = estimate_index / num_null_simulations # If the estimate_index is 0, it depends on the number of simulations if p_value == 0: p_value = (0, 1 / len(sorted_null_estimates)) # a tuple determining the range. elif p_value == 1: p_value = (1 - 1 / len(sorted_null_estimates), 1) signif_dict = {"p_value": p_value} return signif_dict def _test_significance(self, estimate_value, method=None, **kwargs): """ This method is to be overriden by the child classes, so that they can run a significance test suited to the specific causal estimator. """ raise NotImplementedError( ( "This method for testing statistical significance is " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG + " Meanwhile, you can try the bootstrap method (method='bootstrap') to test statistical significance." ).format(self.__class__) ) def test_significance(self, estimate_value, method=None, **kwargs): """Test statistical significance of obtained estimate. By default, uses resampling to create a non-parametric significance test. A general procedure. Individual child estimators can implement different methods. If the method name is different from "bootstrap", this function calls the implementation of the child estimator. :param self: object instance of class Estimator :param estimate_value: obtained estimate's value :param method: Method for checking statistical significance :returns: p-value from the significance test """ if method is None: if self._significance_test: method = self._significance_test # this is either True or methodname else: method = "default" signif_dict = None if method == "default" or method is True: # user has not provided any method try: signif_dict = self._test_significance(estimate_value, method, **kwargs) except NotImplementedError: signif_dict = self._test_significance_with_bootstrap(estimate_value, **kwargs) else: if method == "bootstrap": signif_dict = self._test_significance_with_bootstrap(estimate_value, **kwargs) else: signif_dict = self._test_significance(estimate_value, method, **kwargs) return signif_dict def evaluate_effect_strength(self, estimate): fraction_effect_explained = self._evaluate_effect_strength(estimate, method="fraction-effect") # Need to test r-squared before supporting # effect_r_squared = self._evaluate_effect_strength(estimate, method="r-squared") strength_dict = { "fraction-effect": fraction_effect_explained # 'r-squared': effect_r_squared } return strength_dict def _evaluate_effect_strength(self, estimate, method="fraction-effect"): supported_methods = ["fraction-effect"] if method not in supported_methods: raise NotImplementedError("This method is not supported for evaluating effect strength") if method == "fraction-effect": naive_obs_estimate = self.estimate_effect_naive() self.logger.debug(estimate.value, naive_obs_estimate.value) fraction_effect_explained = estimate.value / naive_obs_estimate.value return fraction_effect_explained # elif method == "r-squared": # outcome_mean = np.mean(self._outcome) # total_variance = np.sum(np.square(self._outcome - outcome_mean)) # Assuming a linear model with one variable: the treatment # Currently only works for continuous y # causal_model = outcome_mean + estimate.value*self._treatment # squared_residual = np.sum(np.square(self._outcome - causal_model)) # r_squared = 1 - (squared_residual/total_variance) # return r_squared else: return None def update_input(self, treatment_value, control_value, target_units): self._control_value = control_value self._treatment_value = treatment_value self._target_units = target_units @staticmethod def is_bootstrap_parameter_changed(bootstrap_estimates_params, given_params): """Check whether parameters of the bootstrap have changed. This is an efficiency method that checks if fresh resampling of the bootstrap samples is required. Returns True if parameters have changed and resampling should be done again. :param bootstrap_estimates_params: A dictionary of parameters for the current bootstrap samples :param given_params: A dictionary of parameters passed by the user :returns: A binary flag denoting whether the parameters are different. """ is_any_parameter_changed = False for prm, val in bootstrap_estimates_params.items(): given_val = given_params.get(prm, None) if given_val is not None and given_val != val: is_any_parameter_changed = True break return is_any_parameter_changed def target_units_tostr(self): s = "" if type(self._target_units) is str: s += self._target_units elif callable(self._target_units): s += "Data subset defined by a function" elif isinstance(self._target_units, pd.DataFrame): s += "Data subset provided as a data frame" return s def signif_results_tostr(self, signif_results): s = "" pval = signif_results["p_value"] if type(pval) is tuple: s += "[{0}, {1}]".format(pval[0], pval[1]) else: s += "{0}".format(pval) return s class CausalEstimate: """Class for the estimate object that every causal estimator returns""" def __init__( self, estimate, target_estimand, realized_estimand_expr, control_value, treatment_value, conditional_estimates=None, **kwargs, ): self.value = estimate self.target_estimand = target_estimand self.realized_estimand_expr = realized_estimand_expr self.control_value = control_value self.treatment_value = treatment_value self.conditional_estimates = conditional_estimates self.params = kwargs if self.params is not None: for key, value in self.params.items(): setattr(self, key, value) self.effect_strength = None def add_estimator(self, estimator_instance): self.estimator = estimator_instance def add_effect_strength(self, strength_dict): self.effect_strength = strength_dict def add_params(self, **kwargs): self.params.update(kwargs) def get_confidence_intervals(self, confidence_level=None, method=None, **kwargs): """Get confidence intervals of the obtained estimate. By default, this is done with the help of bootstrapped confidence intervals but can be overridden if the specific estimator implements other methods of estimating confidence intervals. If the method provided is not bootstrap, this function calls the implementation of the specific estimator. :param method: Method for estimating confidence intervals. :param confidence_level: The confidence level of the confidence intervals of the estimate. :param kwargs: Other optional args to be passed to the CI method. :returns: The obtained confidence interval. """ confidence_intervals = self.estimator.estimate_confidence_intervals( estimate_value=self.value, confidence_level=confidence_level, method=method, **kwargs ) return confidence_intervals def get_standard_error(self, method=None, **kwargs): """Get standard error of the obtained estimate. By default, this is done with the help of bootstrapped standard errors but can be overridden if the specific estimator implements other methods of estimating standard error. If the method provided is not bootstrap, this function calls the implementation of the specific estimator. :param method: Method for computing the standard error. :param kwargs: Other optional parameters to be passed to the estimating method. :returns: Standard error of the causal estimate. """ std_error = self.estimator.estimate_std_error(method=method, **kwargs) return std_error def test_stat_significance(self, method=None, **kwargs): """Test statistical significance of the estimate obtained. By default, uses resampling to create a non-parametric significance test. Individual child estimators can implement different methods. If the method name is different from "bootstrap", this function calls the implementation of the child estimator. :param method: Method for checking statistical significance :param kwargs: Other optional parameters to be passed to the estimating method. :returns: p-value from the significance test """ signif_results = self.estimator.test_significance(self.value, method=method, **kwargs) return {"p_value": signif_results["p_value"]} def estimate_conditional_effects( self, effect_modifiers=None, num_quantiles=CausalEstimator.NUM_QUANTILES_TO_DISCRETIZE_CONT_COLS ): """Estimate treatment effect conditioned on given variables. If a numeric effect modifier is provided, it is discretized into quantile bins. If you would like a custom discretization, you can do so yourself: create a new column containing the discretized effect modifier and then include that column's name in the effect_modifier_names argument. :param effect_modifiers: Names of effect modifier variables over which the conditional effects will be estimated. If not provided, defaults to the effect modifiers specified during creation of the CausalEstimator object. :param num_quantiles: The number of quantiles into which a numeric effect modifier variable is discretized. Does not affect any categorical effect modifiers. :returns: A (multi-index) dataframe that provides separate effects for each value of the (discretized) effect modifiers. """ return self.estimator._estimate_conditional_effects( self.estimator._estimate_effect_fn, effect_modifiers, num_quantiles ) def interpret(self, method_name=None, **kwargs): """Interpret the causal estimate. :param method_name: Method used (string) or a list of methods. If None, then the default for the specific estimator is used. :param kwargs:: Optional parameters that are directly passed to the interpreter method. :returns: None """ if method_name is None: method_name = self.estimator.interpret_method method_name_arr = parse_state(method_name) for method in method_name_arr: interpreter = interpreters.get_class_object(method) interpreter(self, **kwargs).interpret() def __str__(self): s = "*** Causal Estimate ***\n" # No estimand was identified (identification failed) if self.target_estimand is None: return "Estimation failed! No relevant identified estimand available for this estimation method." s += "\n## Identified estimand\n{0}".format(self.target_estimand.__str__(only_target_estimand=True)) s += "\n## Realized estimand\n{0}".format(self.realized_estimand_expr) if hasattr(self, "estimator"): s += "\nTarget units: {0}\n".format(self.estimator.target_units_tostr()) s += "\n## Estimate\n" s += "Mean value: {0}\n".format(self.value) s += "" if hasattr(self, "cate_estimates"): s += "Effect estimates: {0}\n".format(self.cate_estimates) if hasattr(self, "estimator"): if self.estimator._significance_test: s += "p-value: {0}\n".format(self.estimator.signif_results_tostr(self.test_stat_significance())) if self.estimator._confidence_intervals: s += "{0}% confidence interval: {1}\n".format( 100 * self.estimator.confidence_level, self.get_confidence_intervals() ) if self.conditional_estimates is not None: s += "### Conditional Estimates\n" s += str(self.conditional_estimates) if self.effect_strength is not None: s += "\n## Effect Strength\n" s += "Change in outcome attributable to treatment: {}\n".format(self.effect_strength["fraction-effect"]) # s += "Variance in outcome explained by treatment: {}\n".format(self.effect_strength["r-squared"]) return s class RealizedEstimand(object): def __init__(self, identified_estimand, estimator_name): self.treatment_variable = identified_estimand.treatment_variable self.outcome_variable = identified_estimand.outcome_variable self.backdoor_variables = identified_estimand.get_backdoor_variables() self.instrumental_variables = identified_estimand.instrumental_variables self.estimand_type = identified_estimand.estimand_type self.estimand_expression = None self.assumptions = None self.estimator_name = estimator_name def update_assumptions(self, estimator_assumptions): self.assumptions = estimator_assumptions def update_estimand_expression(self, estimand_expression): self.estimand_expression = estimand_expression def __str__(self): s = "Realized estimand: {0}\n".format(self.estimator_name) s += "Realized estimand type: {0}\n".format(self.estimand_type) s += "Estimand expression:\n{0}\n".format(sp.pretty(self.estimand_expression)) j = 1 for ass_name, ass_str in self.assumptions.items(): s += "Estimand assumption {0}, {1}: {2}\n".format(j, ass_name, ass_str) j += 1 return s

import logging from collections import namedtuple from typing import Dict, List, Optional, Union import numpy as np import pandas as pd import sympy as sp from sklearn.utils import resample import dowhy.interpreters as interpreters from dowhy import causal_estimators from dowhy.causal_graph import CausalGraph from dowhy.causal_identifier.identified_estimand import IdentifiedEstimand from dowhy.utils.api import parse_state logger = logging.getLogger(__name__) class CausalEstimator: """Base class for an estimator of causal effect. Subclasses implement different estimation methods. All estimation methods are in the package "dowhy.causal_estimators" """ # The default number of simulations for statistical testing DEFAULT_NUMBER_OF_SIMULATIONS_STAT_TEST = 1000 # The default number of simulations to obtain confidence intervals DEFAULT_NUMBER_OF_SIMULATIONS_CI = 100 # The portion of the total size that should be taken each time to find the confidence intervals # 1 is the recommended value # https://ocw.mit.edu/courses/mathematics/18-05-introduction-to-probability-and-statistics-spring-2014/readings/MIT18_05S14_Reading24.pdf # https://projecteuclid.org/download/pdf_1/euclid.ss/1032280214 DEFAULT_SAMPLE_SIZE_FRACTION = 1 # The default Confidence Level DEFAULT_CONFIDENCE_LEVEL = 0.95 # Number of quantiles to discretize continuous columns, for applying groupby NUM_QUANTILES_TO_DISCRETIZE_CONT_COLS = 5 # Prefix to add to temporary categorical variables created after discretization TEMP_CAT_COLUMN_PREFIX = "__categorical__" DEFAULT_NOTIMPLEMENTEDERROR_MSG = "not yet implemented for {0}. If you would this to be implemented in the next version, please raise an issue at https://github.com/microsoft/dowhy/issues" BootstrapEstimates = namedtuple("BootstrapEstimates", ["estimates", "params"]) DEFAULT_INTERPRET_METHOD = ["textual_effect_interpreter"] # std args to be removed from locals() before being passed to args_dict _STD_INIT_ARGS = ("self", "__class__", "args", "kwargs") def __init__( self, data, identified_estimand, treatment, outcome, control_value=0, treatment_value=1, test_significance=False, evaluate_effect_strength=False, confidence_intervals=False, target_units=None, effect_modifiers=None, num_null_simulations=DEFAULT_NUMBER_OF_SIMULATIONS_STAT_TEST, num_simulations=DEFAULT_NUMBER_OF_SIMULATIONS_CI, sample_size_fraction=DEFAULT_SAMPLE_SIZE_FRACTION, confidence_level=DEFAULT_CONFIDENCE_LEVEL, need_conditional_estimates="auto", num_quantiles_to_discretize_cont_cols=NUM_QUANTILES_TO_DISCRETIZE_CONT_COLS, **kwargs, ): """Initializes an estimator with data and names of relevant variables. This method is called from the constructors of its child classes. :param data: data frame containing the data :param identified_estimand: probability expression representing the target identified estimand to estimate. :param treatment: name of the treatment variable :param outcome: name of the outcome variable :param control_value: Value of the treatment in the control group, for effect estimation. If treatment is multi-variate, this can be a list. :param treatment_value: Value of the treatment in the treated group, for effect estimation. If treatment is multi-variate, this can be a list. :param test_significance: Binary flag or a string indicating whether to test significance and by which method. All estimators support test_significance="bootstrap" that estimates a p-value for the obtained estimate using the bootstrap method. Individual estimators can override this to support custom testing methods. The bootstrap method supports an optional parameter, num_null_simulations. If False, no testing is done. If True, significance of the estimate is tested using the custom method if available, otherwise by bootstrap. :param evaluate_effect_strength: (Experimental) whether to evaluate the strength of effect :param confidence_intervals: Binary flag or a string indicating whether the confidence intervals should be computed and which method should be used. All methods support estimation of confidence intervals using the bootstrap method by using the parameter confidence_intervals="bootstrap". The bootstrap method takes in two arguments (num_simulations and sample_size_fraction) that can be optionally specified in the params dictionary. Estimators may also override this to implement their own confidence interval method. If this parameter is False, no confidence intervals are computed. If True, confidence intervals are computed by the estimator's specific method if available, otherwise through bootstrap. :param target_units: The units for which the treatment effect should be estimated. This can be a string for common specifications of target units (namely, "ate", "att" and "atc"). It can also be a lambda function that can be used as an index for the data (pandas DataFrame). Alternatively, it can be a new DataFrame that contains values of the effect_modifiers and effect will be estimated only for this new data. :param effect_modifiers: Variables on which to compute separate effects, or return a heterogeneous effect function. Not all methods support this currently. :param num_null_simulations: The number of simulations for testing the statistical significance of the estimator :param num_simulations: The number of simulations for finding the confidence interval (and/or standard error) for a estimate :param sample_size_fraction: The size of the sample for the bootstrap estimator :param confidence_level: The confidence level of the confidence interval estimate :param need_conditional_estimates: Boolean flag indicating whether conditional estimates should be computed. Defaults to True if there are effect modifiers in the graph :param num_quantiles_to_discretize_cont_cols: The number of quantiles into which a numeric effect modifier is split, to enable estimation of conditional treatment effect over it. :param kwargs: (optional) Additional estimator-specific parameters :returns: an instance of the estimator class. """ self._data = data self._target_estimand = identified_estimand # Currently estimation methods only support univariate treatment and outcome self._treatment_name = treatment self._outcome_name = outcome[0] # assuming one-dimensional outcome self._control_value = control_value self._treatment_value = treatment_value self._significance_test = test_significance self._effect_strength_eval = evaluate_effect_strength self._target_units = target_units self._effect_modifier_names = effect_modifiers self._confidence_intervals = confidence_intervals self._bootstrap_estimates = None # for confidence intervals and std error self._bootstrap_null_estimates = None # for significance test self._effect_modifiers = None self.method_params = kwargs # Setting the default interpret method self.interpret_method = CausalEstimator.DEFAULT_INTERPRET_METHOD self.logger = logging.getLogger(__name__) # Setting treatment and outcome values if self._data is not None: self._treatment = self._data[self._treatment_name] self._outcome = self._data[self._outcome_name] if self._effect_modifier_names: # only add the observed nodes self._effect_modifier_names = [ cname for cname in self._effect_modifier_names if cname in self._data.columns ] if len(self._effect_modifier_names) > 0: self._effect_modifiers = self._data[self._effect_modifier_names] self._effect_modifiers = pd.get_dummies(self._effect_modifiers, drop_first=True) self.logger.debug("Effect modifiers: " + ",".join(self._effect_modifier_names)) else: self._effect_modifier_names = None # Check if some parameters were set, otherwise set to default values self.num_null_simulations = num_null_simulations self.num_simulations = num_simulations self.sample_size_fraction = sample_size_fraction self.confidence_level = confidence_level self.num_quantiles_to_discretize_cont_cols = num_quantiles_to_discretize_cont_cols # Estimate conditional estimates by default self.need_conditional_estimates = ( need_conditional_estimates if need_conditional_estimates != "auto" else bool(self._effect_modifier_names) ) @staticmethod def get_estimator_object(new_data, identified_estimand, estimate): """Create a new estimator of the same type as the one passed in the estimate argument. Creates a new object with new_data and the identified_estimand :param new_data: np.ndarray, pd.Series, pd.DataFrame The newly assigned data on which the estimator should run :param identified_estimand: IdentifiedEstimand An instance of the identified estimand class that provides the information with respect to which causal pathways are employed when the treatment effects the outcome :param estimate: CausalEstimate It is an already existing estimate whose properties we wish to replicate :returns: An instance of the same estimator class that had generated the given estimate. """ estimator_class = estimate.params["estimator_class"] new_estimator = estimator_class( new_data, identified_estimand, identified_estimand.treatment_variable, identified_estimand.outcome_variable, # names of treatment and outcome control_value=estimate.control_value, treatment_value=estimate.treatment_value, test_significance=False, evaluate_effect_strength=False, confidence_intervals=estimate.params["confidence_intervals"], target_units=estimate.params["target_units"], effect_modifiers=estimate.params["effect_modifiers"], **estimate.params["method_params"] if estimate.params["method_params"] is not None else {}, ) return new_estimator def _estimate_effect(self): """This method is to be overriden by the child classes, so that they can run the estimation technique of their choice""" raise NotImplementedError( ("Main estimation method is " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG).format(self.__class__) ) def estimate_effect(self): """Base estimation method that calls the estimate_effect method of its calling subclass. Can optionally also test significance and estimate effect strength for any returned estimate. :param self: object instance of class Estimator :returns: A CausalEstimate instance that contains point estimates of average and conditional effects. Based on the parameters provided, it optionally includes confidence intervals, standard errors,statistical significance and other statistical parameters. """ est = self._estimate_effect() est.add_estimator(self) if self._significance_test: self.test_significance(est.value, method=self._significance_test) if self._confidence_intervals: self.estimate_confidence_intervals( est.value, confidence_level=self.confidence_level, method=self._confidence_intervals ) if self._effect_strength_eval: effect_strength_dict = self.evaluate_effect_strength(est) est.add_effect_strength(effect_strength_dict) return est def estimate_effect_naive(self): # TODO Only works for binary treatment df_withtreatment = self._data.loc[self._data[self._treatment_name] == 1] df_notreatment = self._data.loc[self._data[self._treatment_name] == 0] est = np.mean(df_withtreatment[self._outcome_name]) - np.mean(df_notreatment[self._outcome_name]) return CausalEstimate(est, None, None, control_value=0, treatment_value=1) def _estimate_effect_fn(self, data_df): """Function used in conditional effect estimation. This function is to be overridden by each child estimator. The overridden function should take in a dataframe as input and return the estimate for that data. """ raise NotImplementedError( ("Conditional treatment effects are " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG).format( self.__class__ ) ) def _estimate_conditional_effects(self, estimate_effect_fn, effect_modifier_names=None, num_quantiles=None): """Estimate conditional treatment effects. Common method for all estimators that utilizes a specific estimate_effect_fn implemented by each child estimator. If a numeric effect modifier is provided, it is discretized into quantile bins. If you would like a custom discretization, you can do so yourself: create a new column containing the discretized effect modifier and then include that column's name in the effect_modifier_names argument. :param estimate_effect_fn: Function that has a single parameter (a data frame) and returns the treatment effect estimate on that data. :param effect_modifier_names: Names of effect modifier variables over which the conditional effects will be estimated. If not provided, defaults to the effect modifiers specified during creation of the CausalEstimator object. :param num_quantiles: The number of quantiles into which a numeric effect modifier variable is discretized. Does not affect any categorical effect modifiers. :returns: A (multi-index) dataframe that provides separate effects for each value of the (discretized) effect modifiers. """ # Defaulting to class default values if parameters are not provided if effect_modifier_names is None: effect_modifier_names = self._effect_modifier_names if num_quantiles is None: num_quantiles = self.num_quantiles_to_discretize_cont_cols # Checking that there is at least one effect modifier if not effect_modifier_names: raise ValueError("At least one effect modifier should be specified to compute conditional effects.") # Making sure that effect_modifier_names is a list effect_modifier_names = parse_state(effect_modifier_names) if not all(em in self._effect_modifier_names for em in effect_modifier_names): self.logger.warn( "At least one of the provided effect modifiers was not included while fitting the estimator. You may get incorrect results. To resolve, fit the estimator again by providing the updated effect modifiers in estimate_effect()." ) # Making a copy since we are going to be changing effect modifier names effect_modifier_names = effect_modifier_names.copy() prefix = CausalEstimator.TEMP_CAT_COLUMN_PREFIX # For every numeric effect modifier, adding a temp categorical column for i in range(len(effect_modifier_names)): em = effect_modifier_names[i] if pd.api.types.is_numeric_dtype(self._data[em].dtypes): self._data[prefix + str(em)] = pd.qcut(self._data[em], num_quantiles, duplicates="drop") effect_modifier_names[i] = prefix + str(em) # Grouping by effect modifiers and computing effect separately by_effect_mods = self._data.groupby(effect_modifier_names) cond_est_fn = lambda x: self._do(self._treatment_value, x) - self._do(self._control_value, x) conditional_estimates = by_effect_mods.apply(estimate_effect_fn) # Deleting the temporary categorical columns for em in effect_modifier_names: if em.startswith(prefix): self._data.pop(em) return conditional_estimates def _do(self, x, data_df=None): raise NotImplementedError( ("Do-operator is " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG).format(self.__class__) ) def do(self, x, data_df=None): """Method that implements the do-operator. Given a value x for the treatment, returns the expected value of the outcome when the treatment is intervened to a value x. :param x: Value of the treatment :param data_df: Data on which the do-operator is to be applied. :returns: Value of the outcome when treatment is intervened/set to x. """ est = self._do(x, data_df) return est def construct_symbolic_estimator(self, estimand): raise NotImplementedError(("Symbolic estimator string is ").format(self.__class__)) def _generate_bootstrap_estimates(self, num_bootstrap_simulations, sample_size_fraction): """Helper function to generate causal estimates over bootstrapped samples. :param num_bootstrap_simulations: Number of simulations for the bootstrap method. :param sample_size_fraction: Fraction of the dataset to be resampled. :returns: A collections.namedtuple containing a list of bootstrapped estimates and a dictionary containing parameters used for the bootstrap. """ # The array that stores the results of all estimations simulation_results = np.zeros(num_bootstrap_simulations) # Find the sample size the proportion with the population size sample_size = int(sample_size_fraction * len(self._data)) if sample_size > len(self._data): self.logger.warning("WARN: The sample size is greater than the data being sampled") self.logger.info("INFO: The sample size: {}".format(sample_size)) self.logger.info("INFO: The number of simulations: {}".format(num_bootstrap_simulations)) # Perform the set number of simulations for index in range(num_bootstrap_simulations): new_data = resample(self._data, n_samples=sample_size) new_estimator = type(self)( new_data, self._target_estimand, self._target_estimand.treatment_variable, self._target_estimand.outcome_variable, # names of treatment and outcome treatment_value=self._treatment_value, control_value=self._control_value, test_significance=False, evaluate_effect_strength=False, confidence_intervals=False, target_units=self._target_units, effect_modifiers=self._effect_modifier_names, **self.method_params, ) new_effect = new_estimator.estimate_effect() simulation_results[index] = new_effect.value estimates = CausalEstimator.BootstrapEstimates( simulation_results, {"num_simulations": num_bootstrap_simulations, "sample_size_fraction": sample_size_fraction}, ) return estimates def _estimate_confidence_intervals_with_bootstrap( self, estimate_value, confidence_level=None, num_simulations=None, sample_size_fraction=None ): """ Method to compute confidence interval using bootstrapped sampling. :param estimate_value: obtained estimate's value :param confidence_level: The level for which to compute CI (e.g., 95% confidence level translates to confidence_level=0.95) :param num_simulations: The number of simulations to be performed to get the bootstrap confidence intervals. :param sample_size_fraction: The fraction of the dataset to be resampled. :returns: confidence interval at the specified level. For more details on bootstrap or resampling statistics, refer to the following links: https://ocw.mit.edu/courses/mathematics/18-05-introduction-to-probability-and-statistics-spring-2014/readings/MIT18_05S14_Reading24.pdf https://projecteuclid.org/download/pdf_1/euclid.ss/1032280214 """ # Using class default parameters if not specified if num_simulations is None: num_simulations = self.num_simulations if sample_size_fraction is None: sample_size_fraction = self.sample_size_fraction # Checking if bootstrap_estimates are already computed if self._bootstrap_estimates is None: self._bootstrap_estimates = self._generate_bootstrap_estimates(num_simulations, sample_size_fraction) elif CausalEstimator.is_bootstrap_parameter_changed(self._bootstrap_estimates.params, locals()): # Checked if any parameter is changed from the previous std error estimate self._bootstrap_estimates = self._generate_bootstrap_estimates(num_simulations, sample_size_fraction) # Now use the data obtained from the simulations to get the value of the confidence estimates bootstrap_estimates = self._bootstrap_estimates.estimates # Get the variations of each bootstrap estimate and sort bootstrap_variations = [bootstrap_estimate - estimate_value for bootstrap_estimate in bootstrap_estimates] sorted_bootstrap_variations = np.sort(bootstrap_variations) # Now we take the (1- p)th and the (p)th variations, where p is the chosen confidence level upper_bound_index = int((1 - confidence_level) * len(sorted_bootstrap_variations)) lower_bound_index = int(confidence_level * len(sorted_bootstrap_variations)) # Get the lower and upper bounds by subtracting the variations from the estimate lower_bound = estimate_value - sorted_bootstrap_variations[lower_bound_index] upper_bound = estimate_value - sorted_bootstrap_variations[upper_bound_index] return lower_bound, upper_bound def _estimate_confidence_intervals(self, confidence_level=None, method=None, **kwargs): """ This method is to be overriden by the child classes, so that they can run a confidence interval estimation method suited to the specific causal estimator. """ raise NotImplementedError( ( "This method for estimating confidence intervals is " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG + " Meanwhile, you can try the bootstrap method (method='bootstrap') to estimate confidence intervals." ).format(self.__class__) ) def estimate_confidence_intervals(self, estimate_value, confidence_level=None, method=None, **kwargs): """Find the confidence intervals corresponding to any estimator By default, this is done with the help of bootstrapped confidence intervals but can be overridden if the specific estimator implements other methods of estimating confidence intervals. If the method provided is not bootstrap, this function calls the implementation of the specific estimator. :param estimate_value: obtained estimate's value :param method: Method for estimating confidence intervals. :param confidence_level: The confidence level of the confidence intervals of the estimate. :param kwargs: Other optional args to be passed to the CI method. :returns: The obtained confidence interval. """ if method is None: if self._confidence_intervals: method = self._confidence_intervals # this is either True or methodname else: method = "default" confidence_intervals = None if confidence_level is None: confidence_level = self.confidence_level if method == "default" or method is True: # user has not provided any method try: confidence_intervals = self._estimate_confidence_intervals(confidence_level, method=method, **kwargs) except NotImplementedError: confidence_intervals = self._estimate_confidence_intervals_with_bootstrap( estimate_value, confidence_level, **kwargs ) else: if method == "bootstrap": confidence_intervals = self._estimate_confidence_intervals_with_bootstrap( estimate_value, confidence_level, **kwargs ) else: confidence_intervals = self._estimate_confidence_intervals(confidence_level, method=method, **kwargs) return confidence_intervals def _estimate_std_error_with_bootstrap(self, num_simulations=None, sample_size_fraction=None): """Compute standard error using the bootstrap method. Standard error and confidence intervals use the same parameter num_simulations for the number of bootstrap simulations. :param num_simulations: Number of bootstrapped samples. :param sample_size_fraction: Fraction of data to be resampled. :returns: Standard error of the obtained estimate. """ # Use existing params, if new user defined params are not present if num_simulations is None: num_simulations = self.num_simulations if sample_size_fraction is None: sample_size_fraction = self.sample_size_fraction # Checking if bootstrap_estimates are already computed if self._bootstrap_estimates is None: self._bootstrap_estimates = self._generate_bootstrap_estimates(num_simulations, sample_size_fraction) elif CausalEstimator.is_bootstrap_parameter_changed(self._bootstrap_estimates.params, locals()): # Check if any parameter is changed from the previous std error estimate self._bootstrap_estimates = self._generate_bootstrap_estimates(num_simulations, sample_size_fraction) std_error = np.std(self._bootstrap_estimates.estimates) return std_error def _estimate_std_error(self, method=None, **kwargs): """ This method is to be overriden by the child classes, so that they can run a standard error estimation method suited to the specific causal estimator. """ raise NotImplementedError( ( "This method for estimating standard errors is " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG + " Meanwhile, you can try the bootstrap method (method='bootstrap') to estimate standard errors." ).format(self.__class__) ) def estimate_std_error(self, method=None, **kwargs): """Compute standard error of an obtained causal estimate. :param method: Method for computing the standard error. :param kwargs: Other optional parameters to be passed to the estimating method. :returns: Standard error of the causal estimate. """ if method is None: if self._confidence_intervals: method = self._confidence_intervals else: method = "default" std_error = None if method == "default" or method is True: # user has not provided any method try: std_error = self._estimate_std_error(method, **kwargs) except NotImplementedError: std_error = self._estimate_std_error_with_bootstrap(**kwargs) else: if method == "bootstrap": std_error = self._estimate_std_error_with_bootstrap(**kwargs) else: std_error = self._estimate_std_error(method, **kwargs) return std_error def _test_significance_with_bootstrap(self, estimate_value, num_null_simulations=None): """Test statistical significance of an estimate using the bootstrap method. :param estimate_value: Obtained estimate's value :param num_null_simulations: Number of simulations for the null hypothesis :returns: p-value of the statistical significance test. """ # Use existing params, if new user defined params are not present if num_null_simulations is None: num_null_simulations = self.num_null_simulations do_retest = self._bootstrap_null_estimates is None or CausalEstimator.is_bootstrap_parameter_changed( self._bootstrap_null_estimates.params, locals() ) if do_retest: null_estimates = np.zeros(num_null_simulations) for i in range(num_null_simulations): new_outcome = np.random.permutation(self._outcome) new_data = self._data.assign(dummy_outcome=new_outcome) # self._outcome = self._data["dummy_outcome"] new_estimator = type(self)( new_data, self._target_estimand, self._target_estimand.treatment_variable, ("dummy_outcome",), test_significance=False, evaluate_effect_strength=False, confidence_intervals=False, target_units=self._target_units, effect_modifiers=self._effect_modifier_names, **self.method_params, ) new_effect = new_estimator.estimate_effect() null_estimates[i] = new_effect.value self._bootstrap_null_estimates = CausalEstimator.BootstrapEstimates( null_estimates, {"num_null_simulations": num_null_simulations, "sample_size_fraction": 1} ) # Processing the null hypothesis estimates sorted_null_estimates = np.sort(self._bootstrap_null_estimates.estimates) self.logger.debug("Null estimates: {0}".format(sorted_null_estimates)) median_estimate = sorted_null_estimates[int(num_null_simulations / 2)] # Doing a two-sided test if estimate_value > median_estimate: # Being conservative with the p-value reported estimate_index = np.searchsorted(sorted_null_estimates, estimate_value, side="left") p_value = 1 - (estimate_index / num_null_simulations) if estimate_value <= median_estimate: # Being conservative with the p-value reported estimate_index = np.searchsorted(sorted_null_estimates, estimate_value, side="right") p_value = estimate_index / num_null_simulations # If the estimate_index is 0, it depends on the number of simulations if p_value == 0: p_value = (0, 1 / len(sorted_null_estimates)) # a tuple determining the range. elif p_value == 1: p_value = (1 - 1 / len(sorted_null_estimates), 1) signif_dict = {"p_value": p_value} return signif_dict def _test_significance(self, estimate_value, method=None, **kwargs): """ This method is to be overriden by the child classes, so that they can run a significance test suited to the specific causal estimator. """ raise NotImplementedError( ( "This method for testing statistical significance is " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG + " Meanwhile, you can try the bootstrap method (method='bootstrap') to test statistical significance." ).format(self.__class__) ) def test_significance(self, estimate_value, method=None, **kwargs): """Test statistical significance of obtained estimate. By default, uses resampling to create a non-parametric significance test. A general procedure. Individual child estimators can implement different methods. If the method name is different from "bootstrap", this function calls the implementation of the child estimator. :param self: object instance of class Estimator :param estimate_value: obtained estimate's value :param method: Method for checking statistical significance :returns: p-value from the significance test """ if method is None: if self._significance_test: method = self._significance_test # this is either True or methodname else: method = "default" signif_dict = None if method == "default" or method is True: # user has not provided any method try: signif_dict = self._test_significance(estimate_value, method, **kwargs) except NotImplementedError: signif_dict = self._test_significance_with_bootstrap(estimate_value, **kwargs) else: if method == "bootstrap": signif_dict = self._test_significance_with_bootstrap(estimate_value, **kwargs) else: signif_dict = self._test_significance(estimate_value, method, **kwargs) return signif_dict def evaluate_effect_strength(self, estimate): fraction_effect_explained = self._evaluate_effect_strength(estimate, method="fraction-effect") # Need to test r-squared before supporting # effect_r_squared = self._evaluate_effect_strength(estimate, method="r-squared") strength_dict = { "fraction-effect": fraction_effect_explained # 'r-squared': effect_r_squared } return strength_dict def _evaluate_effect_strength(self, estimate, method="fraction-effect"): supported_methods = ["fraction-effect"] if method not in supported_methods: raise NotImplementedError("This method is not supported for evaluating effect strength") if method == "fraction-effect": naive_obs_estimate = self.estimate_effect_naive() self.logger.debug(estimate.value, naive_obs_estimate.value) fraction_effect_explained = estimate.value / naive_obs_estimate.value return fraction_effect_explained # elif method == "r-squared": # outcome_mean = np.mean(self._outcome) # total_variance = np.sum(np.square(self._outcome - outcome_mean)) # Assuming a linear model with one variable: the treatment # Currently only works for continuous y # causal_model = outcome_mean + estimate.value*self._treatment # squared_residual = np.sum(np.square(self._outcome - causal_model)) # r_squared = 1 - (squared_residual/total_variance) # return r_squared else: return None def update_input(self, treatment_value, control_value, target_units): self._control_value = control_value self._treatment_value = treatment_value self._target_units = target_units @staticmethod def is_bootstrap_parameter_changed(bootstrap_estimates_params, given_params): """Check whether parameters of the bootstrap have changed. This is an efficiency method that checks if fresh resampling of the bootstrap samples is required. Returns True if parameters have changed and resampling should be done again. :param bootstrap_estimates_params: A dictionary of parameters for the current bootstrap samples :param given_params: A dictionary of parameters passed by the user :returns: A binary flag denoting whether the parameters are different. """ is_any_parameter_changed = False for prm, val in bootstrap_estimates_params.items(): given_val = given_params.get(prm, None) if given_val is not None and given_val != val: is_any_parameter_changed = True break return is_any_parameter_changed def target_units_tostr(self): s = "" if type(self._target_units) is str: s += self._target_units elif callable(self._target_units): s += "Data subset defined by a function" elif isinstance(self._target_units, pd.DataFrame): s += "Data subset provided as a data frame" return s def signif_results_tostr(self, signif_results): s = "" pval = signif_results["p_value"] if type(pval) is tuple: s += "[{0}, {1}]".format(pval[0], pval[1]) else: s += "{0}".format(pval) return s def estimate_effect( treatment: Union[str, List[str]], outcome: Union[str, List[str]], identified_estimand: IdentifiedEstimand, identifier_name: str, method: CausalEstimator, control_value: int = 0, treatment_value: int = 1, test_significance: Optional[bool] = None, evaluate_effect_strength: bool = False, confidence_intervals: bool = False, target_units: str = "ate", effect_modifiers: List[str] = [], fit_estimator: bool = True, method_params: Optional[Dict] = None, ): """Estimate the identified causal effect. Currently requires an explicit method name to be specified. Method names follow the convention of identification method followed by the specific estimation method: "[backdoor/iv].estimation_method_name". Following methods are supported. * Propensity Score Matching: "backdoor.propensity_score_matching" * Propensity Score Stratification: "backdoor.propensity_score_stratification" * Propensity Score-based Inverse Weighting: "backdoor.propensity_score_weighting" * Linear Regression: "backdoor.linear_regression" * Generalized Linear Models (e.g., logistic regression): "backdoor.generalized_linear_model" * Instrumental Variables: "iv.instrumental_variable" * Regression Discontinuity: "iv.regression_discontinuity" In addition, you can directly call any of the EconML estimation methods. The convention is "backdoor.econml.path-to-estimator-class". For example, for the double machine learning estimator ("DML" class) that is located inside "dml" module of EconML, you can use the method name, "backdoor.econml.dml.DML". CausalML estimators can also be called. See `this demo notebook <https://py-why.github.io/dowhy/example_notebooks/dowhy-conditional-treatment-effects.html>`_. :param treatment: Name of the treatment :param outcome: Name of the outcome :param identified_estimand: a probability expression that represents the effect to be estimated. Output of CausalModel.identify_effect method :param method_name: name of the estimation method to be used. :param control_value: Value of the treatment in the control group, for effect estimation. If treatment is multi-variate, this can be a list. :param treatment_value: Value of the treatment in the treated group, for effect estimation. If treatment is multi-variate, this can be a list. :param test_significance: Binary flag on whether to additionally do a statistical signficance test for the estimate. :param evaluate_effect_strength: (Experimental) Binary flag on whether to estimate the relative strength of the treatment's effect. This measure can be used to compare different treatments for the same outcome (by running this method with different treatments sequentially). :param confidence_intervals: (Experimental) Binary flag indicating whether confidence intervals should be computed. :param target_units: (Experimental) The units for which the treatment effect should be estimated. This can be of three types. (1) a string for common specifications of target units (namely, "ate", "att" and "atc"), (2) a lambda function that can be used as an index for the data (pandas DataFrame), or (3) a new DataFrame that contains values of the effect_modifiers and effect will be estimated only for this new data. :param effect_modifiers: Names of effect modifier variables can be (optionally) specified here too, since they do not affect identification. If None, the effect_modifiers from the CausalModel are used. :param fit_estimator: Boolean flag on whether to fit the estimator. Setting it to False is useful to estimate the effect on new data using a previously fitted estimator. :param method_params: Dictionary containing any method-specific parameters. These are passed directly to the estimating method. See the docs for each estimation method for allowed method-specific params. :returns: An instance of the CausalEstimate class, containing the causal effect estimate and other method-dependent information """ treatment = parse_state(treatment) outcome = parse_state(outcome) causal_estimator_class = method.__class__ identified_estimand.set_identifier_method(identifier_name) if identified_estimand.no_directed_path: logger.warning("No directed path from {0} to {1}.".format(treatment, outcome)) return CausalEstimate( 0, identified_estimand, None, control_value=control_value, treatment_value=treatment_value ) # Check if estimator's target estimand is identified elif identified_estimand.estimands[identifier_name] is None: logger.error("No valid identified estimand available.") return CausalEstimate(None, None, None, control_value=control_value, treatment_value=treatment_value) method.update_input(treatment_value, control_value, target_units) estimate = method.estimate_effect() # Store parameters inside estimate object for refutation methods # TODO: This add_params needs to move to the estimator class # inside estimate_effect and estimate_conditional_effect estimate.add_params( estimand_type=identified_estimand.estimand_type, estimator_class=causal_estimator_class, test_significance=test_significance, evaluate_effect_strength=evaluate_effect_strength, confidence_intervals=confidence_intervals, target_units=target_units, effect_modifiers=effect_modifiers, method_params=method_params, ) return estimate class CausalEstimate: """Class for the estimate object that every causal estimator returns""" def __init__( self, estimate, target_estimand, realized_estimand_expr, control_value, treatment_value, conditional_estimates=None, **kwargs, ): self.value = estimate self.target_estimand = target_estimand self.realized_estimand_expr = realized_estimand_expr self.control_value = control_value self.treatment_value = treatment_value self.conditional_estimates = conditional_estimates self.params = kwargs if self.params is not None: for key, value in self.params.items(): setattr(self, key, value) self.effect_strength = None def add_estimator(self, estimator_instance): self.estimator = estimator_instance def add_effect_strength(self, strength_dict): self.effect_strength = strength_dict def add_params(self, **kwargs): self.params.update(kwargs) def get_confidence_intervals(self, confidence_level=None, method=None, **kwargs): """Get confidence intervals of the obtained estimate. By default, this is done with the help of bootstrapped confidence intervals but can be overridden if the specific estimator implements other methods of estimating confidence intervals. If the method provided is not bootstrap, this function calls the implementation of the specific estimator. :param method: Method for estimating confidence intervals. :param confidence_level: The confidence level of the confidence intervals of the estimate. :param kwargs: Other optional args to be passed to the CI method. :returns: The obtained confidence interval. """ confidence_intervals = self.estimator.estimate_confidence_intervals( estimate_value=self.value, confidence_level=confidence_level, method=method, **kwargs ) return confidence_intervals def get_standard_error(self, method=None, **kwargs): """Get standard error of the obtained estimate. By default, this is done with the help of bootstrapped standard errors but can be overridden if the specific estimator implements other methods of estimating standard error. If the method provided is not bootstrap, this function calls the implementation of the specific estimator. :param method: Method for computing the standard error. :param kwargs: Other optional parameters to be passed to the estimating method. :returns: Standard error of the causal estimate. """ std_error = self.estimator.estimate_std_error(method=method, **kwargs) return std_error def test_stat_significance(self, method=None, **kwargs): """Test statistical significance of the estimate obtained. By default, uses resampling to create a non-parametric significance test. Individual child estimators can implement different methods. If the method name is different from "bootstrap", this function calls the implementation of the child estimator. :param method: Method for checking statistical significance :param kwargs: Other optional parameters to be passed to the estimating method. :returns: p-value from the significance test """ signif_results = self.estimator.test_significance(self.value, method=method, **kwargs) return {"p_value": signif_results["p_value"]} def estimate_conditional_effects( self, effect_modifiers=None, num_quantiles=CausalEstimator.NUM_QUANTILES_TO_DISCRETIZE_CONT_COLS ): """Estimate treatment effect conditioned on given variables. If a numeric effect modifier is provided, it is discretized into quantile bins. If you would like a custom discretization, you can do so yourself: create a new column containing the discretized effect modifier and then include that column's name in the effect_modifier_names argument. :param effect_modifiers: Names of effect modifier variables over which the conditional effects will be estimated. If not provided, defaults to the effect modifiers specified during creation of the CausalEstimator object. :param num_quantiles: The number of quantiles into which a numeric effect modifier variable is discretized. Does not affect any categorical effect modifiers. :returns: A (multi-index) dataframe that provides separate effects for each value of the (discretized) effect modifiers. """ return self.estimator._estimate_conditional_effects( self.estimator._estimate_effect_fn, effect_modifiers, num_quantiles ) def interpret(self, method_name=None, **kwargs): """Interpret the causal estimate. :param method_name: Method used (string) or a list of methods. If None, then the default for the specific estimator is used. :param kwargs:: Optional parameters that are directly passed to the interpreter method. :returns: None """ if method_name is None: method_name = self.estimator.interpret_method method_name_arr = parse_state(method_name) for method in method_name_arr: interpreter = interpreters.get_class_object(method) interpreter(self, **kwargs).interpret() def __str__(self): s = "*** Causal Estimate ***\n" # No estimand was identified (identification failed) if self.target_estimand is None: return "Estimation failed! No relevant identified estimand available for this estimation method." s += "\n## Identified estimand\n{0}".format(self.target_estimand.__str__(only_target_estimand=True)) s += "\n## Realized estimand\n{0}".format(self.realized_estimand_expr) if hasattr(self, "estimator"): s += "\nTarget units: {0}\n".format(self.estimator.target_units_tostr()) s += "\n## Estimate\n" s += "Mean value: {0}\n".format(self.value) s += "" if hasattr(self, "cate_estimates"): s += "Effect estimates: {0}\n".format(self.cate_estimates) if hasattr(self, "estimator"): if self.estimator._significance_test: s += "p-value: {0}\n".format(self.estimator.signif_results_tostr(self.test_stat_significance())) if self.estimator._confidence_intervals: s += "{0}% confidence interval: {1}\n".format( 100 * self.estimator.confidence_level, self.get_confidence_intervals() ) if self.conditional_estimates is not None: s += "### Conditional Estimates\n" s += str(self.conditional_estimates) if self.effect_strength is not None: s += "\n## Effect Strength\n" s += "Change in outcome attributable to treatment: {}\n".format(self.effect_strength["fraction-effect"]) # s += "Variance in outcome explained by treatment: {}\n".format(self.effect_strength["r-squared"]) return s class RealizedEstimand(object): def __init__(self, identified_estimand, estimator_name): self.treatment_variable = identified_estimand.treatment_variable self.outcome_variable = identified_estimand.outcome_variable self.backdoor_variables = identified_estimand.get_backdoor_variables() self.instrumental_variables = identified_estimand.instrumental_variables self.estimand_type = identified_estimand.estimand_type self.estimand_expression = None self.assumptions = None self.estimator_name = estimator_name def update_assumptions(self, estimator_assumptions): self.assumptions = estimator_assumptions def update_estimand_expression(self, estimand_expression): self.estimand_expression = estimand_expression def __str__(self): s = "Realized estimand: {0}\n".format(self.estimator_name) s += "Realized estimand type: {0}\n".format(self.estimand_type) s += "Estimand expression:\n{0}\n".format(sp.pretty(self.estimand_expression)) j = 1 for ass_name, ass_str in self.assumptions.items(): s += "Estimand assumption {0}, {1}: {2}\n".format(j, ass_name, ass_str) j += 1 return s

andresmor-ms

2044d216c322a4b32c6eadce5da7d83463f19c2f

05bfa49dacf0061988c96c6f3e3756219df5422a

Right now, this `estimate_effect` should also take fit_estimator param. But the ideal solution later is: ``` if fit_estimate: method.fit() method.effect() ```

amit-sharma

py-why/dowhy

Functional api/estimate effect function

#### Estimate Effect function * Refactors the estimate effect into a separate function to keep backwards compatibility #### TODO (future PRs): * Add `fit(...)` method to estimators - Move data related parameters from the constructor to the `fit(...)` method * Refactor code to avoid `**kwargs` in `__init__(...)` constructors

2022-10-18 15:49:21+00:00

2022-10-25 17:02:02+00:00

dowhy/causal_estimator.py

import logging from collections import namedtuple import numpy as np import pandas as pd import sympy as sp from sklearn.utils import resample import dowhy.interpreters as interpreters from dowhy.utils.api import parse_state class CausalEstimator: """Base class for an estimator of causal effect. Subclasses implement different estimation methods. All estimation methods are in the package "dowhy.causal_estimators" """ # The default number of simulations for statistical testing DEFAULT_NUMBER_OF_SIMULATIONS_STAT_TEST = 1000 # The default number of simulations to obtain confidence intervals DEFAULT_NUMBER_OF_SIMULATIONS_CI = 100 # The portion of the total size that should be taken each time to find the confidence intervals # 1 is the recommended value # https://ocw.mit.edu/courses/mathematics/18-05-introduction-to-probability-and-statistics-spring-2014/readings/MIT18_05S14_Reading24.pdf # https://projecteuclid.org/download/pdf_1/euclid.ss/1032280214 DEFAULT_SAMPLE_SIZE_FRACTION = 1 # The default Confidence Level DEFAULT_CONFIDENCE_LEVEL = 0.95 # Number of quantiles to discretize continuous columns, for applying groupby NUM_QUANTILES_TO_DISCRETIZE_CONT_COLS = 5 # Prefix to add to temporary categorical variables created after discretization TEMP_CAT_COLUMN_PREFIX = "__categorical__" DEFAULT_NOTIMPLEMENTEDERROR_MSG = "not yet implemented for {0}. If you would this to be implemented in the next version, please raise an issue at https://github.com/microsoft/dowhy/issues" BootstrapEstimates = namedtuple("BootstrapEstimates", ["estimates", "params"]) DEFAULT_INTERPRET_METHOD = ["textual_effect_interpreter"] # std args to be removed from locals() before being passed to args_dict _STD_INIT_ARGS = ("self", "__class__", "args", "kwargs") def __init__( self, data, identified_estimand, treatment, outcome, control_value=0, treatment_value=1, test_significance=False, evaluate_effect_strength=False, confidence_intervals=False, target_units=None, effect_modifiers=None, num_null_simulations=DEFAULT_NUMBER_OF_SIMULATIONS_STAT_TEST, num_simulations=DEFAULT_NUMBER_OF_SIMULATIONS_CI, sample_size_fraction=DEFAULT_SAMPLE_SIZE_FRACTION, confidence_level=DEFAULT_CONFIDENCE_LEVEL, need_conditional_estimates="auto", num_quantiles_to_discretize_cont_cols=NUM_QUANTILES_TO_DISCRETIZE_CONT_COLS, **kwargs, ): """Initializes an estimator with data and names of relevant variables. This method is called from the constructors of its child classes. :param data: data frame containing the data :param identified_estimand: probability expression representing the target identified estimand to estimate. :param treatment: name of the treatment variable :param outcome: name of the outcome variable :param control_value: Value of the treatment in the control group, for effect estimation. If treatment is multi-variate, this can be a list. :param treatment_value: Value of the treatment in the treated group, for effect estimation. If treatment is multi-variate, this can be a list. :param test_significance: Binary flag or a string indicating whether to test significance and by which method. All estimators support test_significance="bootstrap" that estimates a p-value for the obtained estimate using the bootstrap method. Individual estimators can override this to support custom testing methods. The bootstrap method supports an optional parameter, num_null_simulations. If False, no testing is done. If True, significance of the estimate is tested using the custom method if available, otherwise by bootstrap. :param evaluate_effect_strength: (Experimental) whether to evaluate the strength of effect :param confidence_intervals: Binary flag or a string indicating whether the confidence intervals should be computed and which method should be used. All methods support estimation of confidence intervals using the bootstrap method by using the parameter confidence_intervals="bootstrap". The bootstrap method takes in two arguments (num_simulations and sample_size_fraction) that can be optionally specified in the params dictionary. Estimators may also override this to implement their own confidence interval method. If this parameter is False, no confidence intervals are computed. If True, confidence intervals are computed by the estimator's specific method if available, otherwise through bootstrap. :param target_units: The units for which the treatment effect should be estimated. This can be a string for common specifications of target units (namely, "ate", "att" and "atc"). It can also be a lambda function that can be used as an index for the data (pandas DataFrame). Alternatively, it can be a new DataFrame that contains values of the effect_modifiers and effect will be estimated only for this new data. :param effect_modifiers: Variables on which to compute separate effects, or return a heterogeneous effect function. Not all methods support this currently. :param num_null_simulations: The number of simulations for testing the statistical significance of the estimator :param num_simulations: The number of simulations for finding the confidence interval (and/or standard error) for a estimate :param sample_size_fraction: The size of the sample for the bootstrap estimator :param confidence_level: The confidence level of the confidence interval estimate :param need_conditional_estimates: Boolean flag indicating whether conditional estimates should be computed. Defaults to True if there are effect modifiers in the graph :param num_quantiles_to_discretize_cont_cols: The number of quantiles into which a numeric effect modifier is split, to enable estimation of conditional treatment effect over it. :param kwargs: (optional) Additional estimator-specific parameters :returns: an instance of the estimator class. """ self._data = data self._target_estimand = identified_estimand # Currently estimation methods only support univariate treatment and outcome self._treatment_name = treatment self._outcome_name = outcome[0] # assuming one-dimensional outcome self._control_value = control_value self._treatment_value = treatment_value self._significance_test = test_significance self._effect_strength_eval = evaluate_effect_strength self._target_units = target_units self._effect_modifier_names = effect_modifiers self._confidence_intervals = confidence_intervals self._bootstrap_estimates = None # for confidence intervals and std error self._bootstrap_null_estimates = None # for significance test self._effect_modifiers = None self.method_params = kwargs # Setting the default interpret method self.interpret_method = CausalEstimator.DEFAULT_INTERPRET_METHOD self.logger = logging.getLogger(__name__) # Setting treatment and outcome values if self._data is not None: self._treatment = self._data[self._treatment_name] self._outcome = self._data[self._outcome_name] # Now saving the effect modifiers if self._effect_modifier_names: # only add the observed nodes self._effect_modifier_names = [ cname for cname in self._effect_modifier_names if cname in self._data.columns ] if len(self._effect_modifier_names) > 0: self._effect_modifiers = self._data[self._effect_modifier_names] self._effect_modifiers = pd.get_dummies(self._effect_modifiers, drop_first=True) self.logger.debug("Effect modifiers: " + ",".join(self._effect_modifier_names)) else: self._effect_modifier_names = None # Check if some parameters were set, otherwise set to default values self.num_null_simulations = num_null_simulations self.num_simulations = num_simulations self.sample_size_fraction = sample_size_fraction self.confidence_level = confidence_level self.num_quantiles_to_discretize_cont_cols = num_quantiles_to_discretize_cont_cols # Estimate conditional estimates by default self.need_conditional_estimates = ( need_conditional_estimates if need_conditional_estimates != "auto" else bool(self._effect_modifier_names) ) @staticmethod def get_estimator_object(new_data, identified_estimand, estimate): """Create a new estimator of the same type as the one passed in the estimate argument. Creates a new object with new_data and the identified_estimand :param new_data: np.ndarray, pd.Series, pd.DataFrame The newly assigned data on which the estimator should run :param identified_estimand: IdentifiedEstimand An instance of the identified estimand class that provides the information with respect to which causal pathways are employed when the treatment effects the outcome :param estimate: CausalEstimate It is an already existing estimate whose properties we wish to replicate :returns: An instance of the same estimator class that had generated the given estimate. """ estimator_class = estimate.params["estimator_class"] new_estimator = estimator_class( new_data, identified_estimand, identified_estimand.treatment_variable, identified_estimand.outcome_variable, # names of treatment and outcome control_value=estimate.control_value, treatment_value=estimate.treatment_value, test_significance=False, evaluate_effect_strength=False, confidence_intervals=estimate.params["confidence_intervals"], target_units=estimate.params["target_units"], effect_modifiers=estimate.params["effect_modifiers"], **estimate.params["method_params"], ) return new_estimator def _estimate_effect(self): """This method is to be overriden by the child classes, so that they can run the estimation technique of their choice""" raise NotImplementedError( ("Main estimation method is " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG).format(self.__class__) ) def estimate_effect(self): """Base estimation method that calls the estimate_effect method of its calling subclass. Can optionally also test significance and estimate effect strength for any returned estimate. :param self: object instance of class Estimator :returns: A CausalEstimate instance that contains point estimates of average and conditional effects. Based on the parameters provided, it optionally includes confidence intervals, standard errors,statistical significance and other statistical parameters. """ est = self._estimate_effect() est.add_estimator(self) if self._significance_test: self.test_significance(est.value, method=self._significance_test) if self._confidence_intervals: self.estimate_confidence_intervals( est.value, confidence_level=self.confidence_level, method=self._confidence_intervals ) if self._effect_strength_eval: effect_strength_dict = self.evaluate_effect_strength(est) est.add_effect_strength(effect_strength_dict) return est def estimate_effect_naive(self): # TODO Only works for binary treatment df_withtreatment = self._data.loc[self._data[self._treatment_name] == 1] df_notreatment = self._data.loc[self._data[self._treatment_name] == 0] est = np.mean(df_withtreatment[self._outcome_name]) - np.mean(df_notreatment[self._outcome_name]) return CausalEstimate(est, None, None, control_value=0, treatment_value=1) def _estimate_effect_fn(self, data_df): """Function used in conditional effect estimation. This function is to be overridden by each child estimator. The overridden function should take in a dataframe as input and return the estimate for that data. """ raise NotImplementedError( ("Conditional treatment effects are " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG).format( self.__class__ ) ) def _estimate_conditional_effects(self, estimate_effect_fn, effect_modifier_names=None, num_quantiles=None): """Estimate conditional treatment effects. Common method for all estimators that utilizes a specific estimate_effect_fn implemented by each child estimator. If a numeric effect modifier is provided, it is discretized into quantile bins. If you would like a custom discretization, you can do so yourself: create a new column containing the discretized effect modifier and then include that column's name in the effect_modifier_names argument. :param estimate_effect_fn: Function that has a single parameter (a data frame) and returns the treatment effect estimate on that data. :param effect_modifier_names: Names of effect modifier variables over which the conditional effects will be estimated. If not provided, defaults to the effect modifiers specified during creation of the CausalEstimator object. :param num_quantiles: The number of quantiles into which a numeric effect modifier variable is discretized. Does not affect any categorical effect modifiers. :returns: A (multi-index) dataframe that provides separate effects for each value of the (discretized) effect modifiers. """ # Defaulting to class default values if parameters are not provided if effect_modifier_names is None: effect_modifier_names = self._effect_modifier_names if num_quantiles is None: num_quantiles = self.num_quantiles_to_discretize_cont_cols # Checking that there is at least one effect modifier if not effect_modifier_names: raise ValueError("At least one effect modifier should be specified to compute conditional effects.") # Making sure that effect_modifier_names is a list effect_modifier_names = parse_state(effect_modifier_names) if not all(em in self._effect_modifier_names for em in effect_modifier_names): self.logger.warn( "At least one of the provided effect modifiers was not included while fitting the estimator. You may get incorrect results. To resolve, fit the estimator again by providing the updated effect modifiers in estimate_effect()." ) # Making a copy since we are going to be changing effect modifier names effect_modifier_names = effect_modifier_names.copy() prefix = CausalEstimator.TEMP_CAT_COLUMN_PREFIX # For every numeric effect modifier, adding a temp categorical column for i in range(len(effect_modifier_names)): em = effect_modifier_names[i] if pd.api.types.is_numeric_dtype(self._data[em].dtypes): self._data[prefix + str(em)] = pd.qcut(self._data[em], num_quantiles, duplicates="drop") effect_modifier_names[i] = prefix + str(em) # Grouping by effect modifiers and computing effect separately by_effect_mods = self._data.groupby(effect_modifier_names) cond_est_fn = lambda x: self._do(self._treatment_value, x) - self._do(self._control_value, x) conditional_estimates = by_effect_mods.apply(estimate_effect_fn) # Deleting the temporary categorical columns for em in effect_modifier_names: if em.startswith(prefix): self._data.pop(em) return conditional_estimates def _do(self, x, data_df=None): raise NotImplementedError( ("Do-operator is " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG).format(self.__class__) ) def do(self, x, data_df=None): """Method that implements the do-operator. Given a value x for the treatment, returns the expected value of the outcome when the treatment is intervened to a value x. :param x: Value of the treatment :param data_df: Data on which the do-operator is to be applied. :returns: Value of the outcome when treatment is intervened/set to x. """ est = self._do(x, data_df) return est def construct_symbolic_estimator(self, estimand): raise NotImplementedError(("Symbolic estimator string is ").format(self.__class__)) def _generate_bootstrap_estimates(self, num_bootstrap_simulations, sample_size_fraction): """Helper function to generate causal estimates over bootstrapped samples. :param num_bootstrap_simulations: Number of simulations for the bootstrap method. :param sample_size_fraction: Fraction of the dataset to be resampled. :returns: A collections.namedtuple containing a list of bootstrapped estimates and a dictionary containing parameters used for the bootstrap. """ # The array that stores the results of all estimations simulation_results = np.zeros(num_bootstrap_simulations) # Find the sample size the proportion with the population size sample_size = int(sample_size_fraction * len(self._data)) if sample_size > len(self._data): self.logger.warning("WARN: The sample size is greater than the data being sampled") self.logger.info("INFO: The sample size: {}".format(sample_size)) self.logger.info("INFO: The number of simulations: {}".format(num_bootstrap_simulations)) # Perform the set number of simulations for index in range(num_bootstrap_simulations): new_data = resample(self._data, n_samples=sample_size) new_estimator = type(self)( new_data, self._target_estimand, self._target_estimand.treatment_variable, self._target_estimand.outcome_variable, # names of treatment and outcome treatment_value=self._treatment_value, control_value=self._control_value, test_significance=False, evaluate_effect_strength=False, confidence_intervals=False, target_units=self._target_units, effect_modifiers=self._effect_modifier_names, **self.method_params, ) new_effect = new_estimator.estimate_effect() simulation_results[index] = new_effect.value estimates = CausalEstimator.BootstrapEstimates( simulation_results, {"num_simulations": num_bootstrap_simulations, "sample_size_fraction": sample_size_fraction}, ) return estimates def _estimate_confidence_intervals_with_bootstrap( self, estimate_value, confidence_level=None, num_simulations=None, sample_size_fraction=None ): """ Method to compute confidence interval using bootstrapped sampling. :param estimate_value: obtained estimate's value :param confidence_level: The level for which to compute CI (e.g., 95% confidence level translates to confidence_level=0.95) :param num_simulations: The number of simulations to be performed to get the bootstrap confidence intervals. :param sample_size_fraction: The fraction of the dataset to be resampled. :returns: confidence interval at the specified level. For more details on bootstrap or resampling statistics, refer to the following links: https://ocw.mit.edu/courses/mathematics/18-05-introduction-to-probability-and-statistics-spring-2014/readings/MIT18_05S14_Reading24.pdf https://projecteuclid.org/download/pdf_1/euclid.ss/1032280214 """ # Using class default parameters if not specified if num_simulations is None: num_simulations = self.num_simulations if sample_size_fraction is None: sample_size_fraction = self.sample_size_fraction # Checking if bootstrap_estimates are already computed if self._bootstrap_estimates is None: self._bootstrap_estimates = self._generate_bootstrap_estimates(num_simulations, sample_size_fraction) elif CausalEstimator.is_bootstrap_parameter_changed(self._bootstrap_estimates.params, locals()): # Checked if any parameter is changed from the previous std error estimate self._bootstrap_estimates = self._generate_bootstrap_estimates(num_simulations, sample_size_fraction) # Now use the data obtained from the simulations to get the value of the confidence estimates bootstrap_estimates = self._bootstrap_estimates.estimates # Get the variations of each bootstrap estimate and sort bootstrap_variations = [bootstrap_estimate - estimate_value for bootstrap_estimate in bootstrap_estimates] sorted_bootstrap_variations = np.sort(bootstrap_variations) # Now we take the (1- p)th and the (p)th variations, where p is the chosen confidence level upper_bound_index = int((1 - confidence_level) * len(sorted_bootstrap_variations)) lower_bound_index = int(confidence_level * len(sorted_bootstrap_variations)) # Get the lower and upper bounds by subtracting the variations from the estimate lower_bound = estimate_value - sorted_bootstrap_variations[lower_bound_index] upper_bound = estimate_value - sorted_bootstrap_variations[upper_bound_index] return lower_bound, upper_bound def _estimate_confidence_intervals(self, confidence_level=None, method=None, **kwargs): """ This method is to be overriden by the child classes, so that they can run a confidence interval estimation method suited to the specific causal estimator. """ raise NotImplementedError( ( "This method for estimating confidence intervals is " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG + " Meanwhile, you can try the bootstrap method (method='bootstrap') to estimate confidence intervals." ).format(self.__class__) ) def estimate_confidence_intervals(self, estimate_value, confidence_level=None, method=None, **kwargs): """Find the confidence intervals corresponding to any estimator By default, this is done with the help of bootstrapped confidence intervals but can be overridden if the specific estimator implements other methods of estimating confidence intervals. If the method provided is not bootstrap, this function calls the implementation of the specific estimator. :param estimate_value: obtained estimate's value :param method: Method for estimating confidence intervals. :param confidence_level: The confidence level of the confidence intervals of the estimate. :param kwargs: Other optional args to be passed to the CI method. :returns: The obtained confidence interval. """ if method is None: if self._confidence_intervals: method = self._confidence_intervals # this is either True or methodname else: method = "default" confidence_intervals = None if confidence_level is None: confidence_level = self.confidence_level if method == "default" or method is True: # user has not provided any method try: confidence_intervals = self._estimate_confidence_intervals(confidence_level, method=method, **kwargs) except NotImplementedError: confidence_intervals = self._estimate_confidence_intervals_with_bootstrap( estimate_value, confidence_level, **kwargs ) else: if method == "bootstrap": confidence_intervals = self._estimate_confidence_intervals_with_bootstrap( estimate_value, confidence_level, **kwargs ) else: confidence_intervals = self._estimate_confidence_intervals(confidence_level, method=method, **kwargs) return confidence_intervals def _estimate_std_error_with_bootstrap(self, num_simulations=None, sample_size_fraction=None): """Compute standard error using the bootstrap method. Standard error and confidence intervals use the same parameter num_simulations for the number of bootstrap simulations. :param num_simulations: Number of bootstrapped samples. :param sample_size_fraction: Fraction of data to be resampled. :returns: Standard error of the obtained estimate. """ # Use existing params, if new user defined params are not present if num_simulations is None: num_simulations = self.num_simulations if sample_size_fraction is None: sample_size_fraction = self.sample_size_fraction # Checking if bootstrap_estimates are already computed if self._bootstrap_estimates is None: self._bootstrap_estimates = self._generate_bootstrap_estimates(num_simulations, sample_size_fraction) elif CausalEstimator.is_bootstrap_parameter_changed(self._bootstrap_estimates.params, locals()): # Check if any parameter is changed from the previous std error estimate self._bootstrap_estimates = self._generate_bootstrap_estimates(num_simulations, sample_size_fraction) std_error = np.std(self._bootstrap_estimates.estimates) return std_error def _estimate_std_error(self, method=None, **kwargs): """ This method is to be overriden by the child classes, so that they can run a standard error estimation method suited to the specific causal estimator. """ raise NotImplementedError( ( "This method for estimating standard errors is " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG + " Meanwhile, you can try the bootstrap method (method='bootstrap') to estimate standard errors." ).format(self.__class__) ) def estimate_std_error(self, method=None, **kwargs): """Compute standard error of an obtained causal estimate. :param method: Method for computing the standard error. :param kwargs: Other optional parameters to be passed to the estimating method. :returns: Standard error of the causal estimate. """ if method is None: if self._confidence_intervals: method = self._confidence_intervals else: method = "default" std_error = None if method == "default" or method is True: # user has not provided any method try: std_error = self._estimate_std_error(method, **kwargs) except NotImplementedError: std_error = self._estimate_std_error_with_bootstrap(**kwargs) else: if method == "bootstrap": std_error = self._estimate_std_error_with_bootstrap(**kwargs) else: std_error = self._estimate_std_error(method, **kwargs) return std_error def _test_significance_with_bootstrap(self, estimate_value, num_null_simulations=None): """Test statistical significance of an estimate using the bootstrap method. :param estimate_value: Obtained estimate's value :param num_null_simulations: Number of simulations for the null hypothesis :returns: p-value of the statistical significance test. """ # Use existing params, if new user defined params are not present if num_null_simulations is None: num_null_simulations = self.num_null_simulations do_retest = self._bootstrap_null_estimates is None or CausalEstimator.is_bootstrap_parameter_changed( self._bootstrap_null_estimates.params, locals() ) if do_retest: null_estimates = np.zeros(num_null_simulations) for i in range(num_null_simulations): new_outcome = np.random.permutation(self._outcome) new_data = self._data.assign(dummy_outcome=new_outcome) # self._outcome = self._data["dummy_outcome"] new_estimator = type(self)( new_data, self._target_estimand, self._target_estimand.treatment_variable, ("dummy_outcome",), test_significance=False, evaluate_effect_strength=False, confidence_intervals=False, target_units=self._target_units, effect_modifiers=self._effect_modifier_names, **self.method_params, ) new_effect = new_estimator.estimate_effect() null_estimates[i] = new_effect.value self._bootstrap_null_estimates = CausalEstimator.BootstrapEstimates( null_estimates, {"num_null_simulations": num_null_simulations, "sample_size_fraction": 1} ) # Processing the null hypothesis estimates sorted_null_estimates = np.sort(self._bootstrap_null_estimates.estimates) self.logger.debug("Null estimates: {0}".format(sorted_null_estimates)) median_estimate = sorted_null_estimates[int(num_null_simulations / 2)] # Doing a two-sided test if estimate_value > median_estimate: # Being conservative with the p-value reported estimate_index = np.searchsorted(sorted_null_estimates, estimate_value, side="left") p_value = 1 - (estimate_index / num_null_simulations) if estimate_value <= median_estimate: # Being conservative with the p-value reported estimate_index = np.searchsorted(sorted_null_estimates, estimate_value, side="right") p_value = estimate_index / num_null_simulations # If the estimate_index is 0, it depends on the number of simulations if p_value == 0: p_value = (0, 1 / len(sorted_null_estimates)) # a tuple determining the range. elif p_value == 1: p_value = (1 - 1 / len(sorted_null_estimates), 1) signif_dict = {"p_value": p_value} return signif_dict def _test_significance(self, estimate_value, method=None, **kwargs): """ This method is to be overriden by the child classes, so that they can run a significance test suited to the specific causal estimator. """ raise NotImplementedError( ( "This method for testing statistical significance is " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG + " Meanwhile, you can try the bootstrap method (method='bootstrap') to test statistical significance." ).format(self.__class__) ) def test_significance(self, estimate_value, method=None, **kwargs): """Test statistical significance of obtained estimate. By default, uses resampling to create a non-parametric significance test. A general procedure. Individual child estimators can implement different methods. If the method name is different from "bootstrap", this function calls the implementation of the child estimator. :param self: object instance of class Estimator :param estimate_value: obtained estimate's value :param method: Method for checking statistical significance :returns: p-value from the significance test """ if method is None: if self._significance_test: method = self._significance_test # this is either True or methodname else: method = "default" signif_dict = None if method == "default" or method is True: # user has not provided any method try: signif_dict = self._test_significance(estimate_value, method, **kwargs) except NotImplementedError: signif_dict = self._test_significance_with_bootstrap(estimate_value, **kwargs) else: if method == "bootstrap": signif_dict = self._test_significance_with_bootstrap(estimate_value, **kwargs) else: signif_dict = self._test_significance(estimate_value, method, **kwargs) return signif_dict def evaluate_effect_strength(self, estimate): fraction_effect_explained = self._evaluate_effect_strength(estimate, method="fraction-effect") # Need to test r-squared before supporting # effect_r_squared = self._evaluate_effect_strength(estimate, method="r-squared") strength_dict = { "fraction-effect": fraction_effect_explained # 'r-squared': effect_r_squared } return strength_dict def _evaluate_effect_strength(self, estimate, method="fraction-effect"): supported_methods = ["fraction-effect"] if method not in supported_methods: raise NotImplementedError("This method is not supported for evaluating effect strength") if method == "fraction-effect": naive_obs_estimate = self.estimate_effect_naive() self.logger.debug(estimate.value, naive_obs_estimate.value) fraction_effect_explained = estimate.value / naive_obs_estimate.value return fraction_effect_explained # elif method == "r-squared": # outcome_mean = np.mean(self._outcome) # total_variance = np.sum(np.square(self._outcome - outcome_mean)) # Assuming a linear model with one variable: the treatment # Currently only works for continuous y # causal_model = outcome_mean + estimate.value*self._treatment # squared_residual = np.sum(np.square(self._outcome - causal_model)) # r_squared = 1 - (squared_residual/total_variance) # return r_squared else: return None def update_input(self, treatment_value, control_value, target_units): self._control_value = control_value self._treatment_value = treatment_value self._target_units = target_units @staticmethod def is_bootstrap_parameter_changed(bootstrap_estimates_params, given_params): """Check whether parameters of the bootstrap have changed. This is an efficiency method that checks if fresh resampling of the bootstrap samples is required. Returns True if parameters have changed and resampling should be done again. :param bootstrap_estimates_params: A dictionary of parameters for the current bootstrap samples :param given_params: A dictionary of parameters passed by the user :returns: A binary flag denoting whether the parameters are different. """ is_any_parameter_changed = False for prm, val in bootstrap_estimates_params.items(): given_val = given_params.get(prm, None) if given_val is not None and given_val != val: is_any_parameter_changed = True break return is_any_parameter_changed def target_units_tostr(self): s = "" if type(self._target_units) is str: s += self._target_units elif callable(self._target_units): s += "Data subset defined by a function" elif isinstance(self._target_units, pd.DataFrame): s += "Data subset provided as a data frame" return s def signif_results_tostr(self, signif_results): s = "" pval = signif_results["p_value"] if type(pval) is tuple: s += "[{0}, {1}]".format(pval[0], pval[1]) else: s += "{0}".format(pval) return s class CausalEstimate: """Class for the estimate object that every causal estimator returns""" def __init__( self, estimate, target_estimand, realized_estimand_expr, control_value, treatment_value, conditional_estimates=None, **kwargs, ): self.value = estimate self.target_estimand = target_estimand self.realized_estimand_expr = realized_estimand_expr self.control_value = control_value self.treatment_value = treatment_value self.conditional_estimates = conditional_estimates self.params = kwargs if self.params is not None: for key, value in self.params.items(): setattr(self, key, value) self.effect_strength = None def add_estimator(self, estimator_instance): self.estimator = estimator_instance def add_effect_strength(self, strength_dict): self.effect_strength = strength_dict def add_params(self, **kwargs): self.params.update(kwargs) def get_confidence_intervals(self, confidence_level=None, method=None, **kwargs): """Get confidence intervals of the obtained estimate. By default, this is done with the help of bootstrapped confidence intervals but can be overridden if the specific estimator implements other methods of estimating confidence intervals. If the method provided is not bootstrap, this function calls the implementation of the specific estimator. :param method: Method for estimating confidence intervals. :param confidence_level: The confidence level of the confidence intervals of the estimate. :param kwargs: Other optional args to be passed to the CI method. :returns: The obtained confidence interval. """ confidence_intervals = self.estimator.estimate_confidence_intervals( estimate_value=self.value, confidence_level=confidence_level, method=method, **kwargs ) return confidence_intervals def get_standard_error(self, method=None, **kwargs): """Get standard error of the obtained estimate. By default, this is done with the help of bootstrapped standard errors but can be overridden if the specific estimator implements other methods of estimating standard error. If the method provided is not bootstrap, this function calls the implementation of the specific estimator. :param method: Method for computing the standard error. :param kwargs: Other optional parameters to be passed to the estimating method. :returns: Standard error of the causal estimate. """ std_error = self.estimator.estimate_std_error(method=method, **kwargs) return std_error def test_stat_significance(self, method=None, **kwargs): """Test statistical significance of the estimate obtained. By default, uses resampling to create a non-parametric significance test. Individual child estimators can implement different methods. If the method name is different from "bootstrap", this function calls the implementation of the child estimator. :param method: Method for checking statistical significance :param kwargs: Other optional parameters to be passed to the estimating method. :returns: p-value from the significance test """ signif_results = self.estimator.test_significance(self.value, method=method, **kwargs) return {"p_value": signif_results["p_value"]} def estimate_conditional_effects( self, effect_modifiers=None, num_quantiles=CausalEstimator.NUM_QUANTILES_TO_DISCRETIZE_CONT_COLS ): """Estimate treatment effect conditioned on given variables. If a numeric effect modifier is provided, it is discretized into quantile bins. If you would like a custom discretization, you can do so yourself: create a new column containing the discretized effect modifier and then include that column's name in the effect_modifier_names argument. :param effect_modifiers: Names of effect modifier variables over which the conditional effects will be estimated. If not provided, defaults to the effect modifiers specified during creation of the CausalEstimator object. :param num_quantiles: The number of quantiles into which a numeric effect modifier variable is discretized. Does not affect any categorical effect modifiers. :returns: A (multi-index) dataframe that provides separate effects for each value of the (discretized) effect modifiers. """ return self.estimator._estimate_conditional_effects( self.estimator._estimate_effect_fn, effect_modifiers, num_quantiles ) def interpret(self, method_name=None, **kwargs): """Interpret the causal estimate. :param method_name: Method used (string) or a list of methods. If None, then the default for the specific estimator is used. :param kwargs:: Optional parameters that are directly passed to the interpreter method. :returns: None """ if method_name is None: method_name = self.estimator.interpret_method method_name_arr = parse_state(method_name) for method in method_name_arr: interpreter = interpreters.get_class_object(method) interpreter(self, **kwargs).interpret() def __str__(self): s = "*** Causal Estimate ***\n" # No estimand was identified (identification failed) if self.target_estimand is None: return "Estimation failed! No relevant identified estimand available for this estimation method." s += "\n## Identified estimand\n{0}".format(self.target_estimand.__str__(only_target_estimand=True)) s += "\n## Realized estimand\n{0}".format(self.realized_estimand_expr) if hasattr(self, "estimator"): s += "\nTarget units: {0}\n".format(self.estimator.target_units_tostr()) s += "\n## Estimate\n" s += "Mean value: {0}\n".format(self.value) s += "" if hasattr(self, "cate_estimates"): s += "Effect estimates: {0}\n".format(self.cate_estimates) if hasattr(self, "estimator"): if self.estimator._significance_test: s += "p-value: {0}\n".format(self.estimator.signif_results_tostr(self.test_stat_significance())) if self.estimator._confidence_intervals: s += "{0}% confidence interval: {1}\n".format( 100 * self.estimator.confidence_level, self.get_confidence_intervals() ) if self.conditional_estimates is not None: s += "### Conditional Estimates\n" s += str(self.conditional_estimates) if self.effect_strength is not None: s += "\n## Effect Strength\n" s += "Change in outcome attributable to treatment: {}\n".format(self.effect_strength["fraction-effect"]) # s += "Variance in outcome explained by treatment: {}\n".format(self.effect_strength["r-squared"]) return s class RealizedEstimand(object): def __init__(self, identified_estimand, estimator_name): self.treatment_variable = identified_estimand.treatment_variable self.outcome_variable = identified_estimand.outcome_variable self.backdoor_variables = identified_estimand.get_backdoor_variables() self.instrumental_variables = identified_estimand.instrumental_variables self.estimand_type = identified_estimand.estimand_type self.estimand_expression = None self.assumptions = None self.estimator_name = estimator_name def update_assumptions(self, estimator_assumptions): self.assumptions = estimator_assumptions def update_estimand_expression(self, estimand_expression): self.estimand_expression = estimand_expression def __str__(self): s = "Realized estimand: {0}\n".format(self.estimator_name) s += "Realized estimand type: {0}\n".format(self.estimand_type) s += "Estimand expression:\n{0}\n".format(sp.pretty(self.estimand_expression)) j = 1 for ass_name, ass_str in self.assumptions.items(): s += "Estimand assumption {0}, {1}: {2}\n".format(j, ass_name, ass_str) j += 1 return s

import logging from collections import namedtuple from typing import Dict, List, Optional, Union import numpy as np import pandas as pd import sympy as sp from sklearn.utils import resample import dowhy.interpreters as interpreters from dowhy import causal_estimators from dowhy.causal_graph import CausalGraph from dowhy.causal_identifier.identified_estimand import IdentifiedEstimand from dowhy.utils.api import parse_state logger = logging.getLogger(__name__) class CausalEstimator: """Base class for an estimator of causal effect. Subclasses implement different estimation methods. All estimation methods are in the package "dowhy.causal_estimators" """ # The default number of simulations for statistical testing DEFAULT_NUMBER_OF_SIMULATIONS_STAT_TEST = 1000 # The default number of simulations to obtain confidence intervals DEFAULT_NUMBER_OF_SIMULATIONS_CI = 100 # The portion of the total size that should be taken each time to find the confidence intervals # 1 is the recommended value # https://ocw.mit.edu/courses/mathematics/18-05-introduction-to-probability-and-statistics-spring-2014/readings/MIT18_05S14_Reading24.pdf # https://projecteuclid.org/download/pdf_1/euclid.ss/1032280214 DEFAULT_SAMPLE_SIZE_FRACTION = 1 # The default Confidence Level DEFAULT_CONFIDENCE_LEVEL = 0.95 # Number of quantiles to discretize continuous columns, for applying groupby NUM_QUANTILES_TO_DISCRETIZE_CONT_COLS = 5 # Prefix to add to temporary categorical variables created after discretization TEMP_CAT_COLUMN_PREFIX = "__categorical__" DEFAULT_NOTIMPLEMENTEDERROR_MSG = "not yet implemented for {0}. If you would this to be implemented in the next version, please raise an issue at https://github.com/microsoft/dowhy/issues" BootstrapEstimates = namedtuple("BootstrapEstimates", ["estimates", "params"]) DEFAULT_INTERPRET_METHOD = ["textual_effect_interpreter"] # std args to be removed from locals() before being passed to args_dict _STD_INIT_ARGS = ("self", "__class__", "args", "kwargs") def __init__( self, data, identified_estimand, treatment, outcome, control_value=0, treatment_value=1, test_significance=False, evaluate_effect_strength=False, confidence_intervals=False, target_units=None, effect_modifiers=None, num_null_simulations=DEFAULT_NUMBER_OF_SIMULATIONS_STAT_TEST, num_simulations=DEFAULT_NUMBER_OF_SIMULATIONS_CI, sample_size_fraction=DEFAULT_SAMPLE_SIZE_FRACTION, confidence_level=DEFAULT_CONFIDENCE_LEVEL, need_conditional_estimates="auto", num_quantiles_to_discretize_cont_cols=NUM_QUANTILES_TO_DISCRETIZE_CONT_COLS, **kwargs, ): """Initializes an estimator with data and names of relevant variables. This method is called from the constructors of its child classes. :param data: data frame containing the data :param identified_estimand: probability expression representing the target identified estimand to estimate. :param treatment: name of the treatment variable :param outcome: name of the outcome variable :param control_value: Value of the treatment in the control group, for effect estimation. If treatment is multi-variate, this can be a list. :param treatment_value: Value of the treatment in the treated group, for effect estimation. If treatment is multi-variate, this can be a list. :param test_significance: Binary flag or a string indicating whether to test significance and by which method. All estimators support test_significance="bootstrap" that estimates a p-value for the obtained estimate using the bootstrap method. Individual estimators can override this to support custom testing methods. The bootstrap method supports an optional parameter, num_null_simulations. If False, no testing is done. If True, significance of the estimate is tested using the custom method if available, otherwise by bootstrap. :param evaluate_effect_strength: (Experimental) whether to evaluate the strength of effect :param confidence_intervals: Binary flag or a string indicating whether the confidence intervals should be computed and which method should be used. All methods support estimation of confidence intervals using the bootstrap method by using the parameter confidence_intervals="bootstrap". The bootstrap method takes in two arguments (num_simulations and sample_size_fraction) that can be optionally specified in the params dictionary. Estimators may also override this to implement their own confidence interval method. If this parameter is False, no confidence intervals are computed. If True, confidence intervals are computed by the estimator's specific method if available, otherwise through bootstrap. :param target_units: The units for which the treatment effect should be estimated. This can be a string for common specifications of target units (namely, "ate", "att" and "atc"). It can also be a lambda function that can be used as an index for the data (pandas DataFrame). Alternatively, it can be a new DataFrame that contains values of the effect_modifiers and effect will be estimated only for this new data. :param effect_modifiers: Variables on which to compute separate effects, or return a heterogeneous effect function. Not all methods support this currently. :param num_null_simulations: The number of simulations for testing the statistical significance of the estimator :param num_simulations: The number of simulations for finding the confidence interval (and/or standard error) for a estimate :param sample_size_fraction: The size of the sample for the bootstrap estimator :param confidence_level: The confidence level of the confidence interval estimate :param need_conditional_estimates: Boolean flag indicating whether conditional estimates should be computed. Defaults to True if there are effect modifiers in the graph :param num_quantiles_to_discretize_cont_cols: The number of quantiles into which a numeric effect modifier is split, to enable estimation of conditional treatment effect over it. :param kwargs: (optional) Additional estimator-specific parameters :returns: an instance of the estimator class. """ self._data = data self._target_estimand = identified_estimand # Currently estimation methods only support univariate treatment and outcome self._treatment_name = treatment self._outcome_name = outcome[0] # assuming one-dimensional outcome self._control_value = control_value self._treatment_value = treatment_value self._significance_test = test_significance self._effect_strength_eval = evaluate_effect_strength self._target_units = target_units self._effect_modifier_names = effect_modifiers self._confidence_intervals = confidence_intervals self._bootstrap_estimates = None # for confidence intervals and std error self._bootstrap_null_estimates = None # for significance test self._effect_modifiers = None self.method_params = kwargs # Setting the default interpret method self.interpret_method = CausalEstimator.DEFAULT_INTERPRET_METHOD self.logger = logging.getLogger(__name__) # Setting treatment and outcome values if self._data is not None: self._treatment = self._data[self._treatment_name] self._outcome = self._data[self._outcome_name] if self._effect_modifier_names: # only add the observed nodes self._effect_modifier_names = [ cname for cname in self._effect_modifier_names if cname in self._data.columns ] if len(self._effect_modifier_names) > 0: self._effect_modifiers = self._data[self._effect_modifier_names] self._effect_modifiers = pd.get_dummies(self._effect_modifiers, drop_first=True) self.logger.debug("Effect modifiers: " + ",".join(self._effect_modifier_names)) else: self._effect_modifier_names = None # Check if some parameters were set, otherwise set to default values self.num_null_simulations = num_null_simulations self.num_simulations = num_simulations self.sample_size_fraction = sample_size_fraction self.confidence_level = confidence_level self.num_quantiles_to_discretize_cont_cols = num_quantiles_to_discretize_cont_cols # Estimate conditional estimates by default self.need_conditional_estimates = ( need_conditional_estimates if need_conditional_estimates != "auto" else bool(self._effect_modifier_names) ) @staticmethod def get_estimator_object(new_data, identified_estimand, estimate): """Create a new estimator of the same type as the one passed in the estimate argument. Creates a new object with new_data and the identified_estimand :param new_data: np.ndarray, pd.Series, pd.DataFrame The newly assigned data on which the estimator should run :param identified_estimand: IdentifiedEstimand An instance of the identified estimand class that provides the information with respect to which causal pathways are employed when the treatment effects the outcome :param estimate: CausalEstimate It is an already existing estimate whose properties we wish to replicate :returns: An instance of the same estimator class that had generated the given estimate. """ estimator_class = estimate.params["estimator_class"] new_estimator = estimator_class( new_data, identified_estimand, identified_estimand.treatment_variable, identified_estimand.outcome_variable, # names of treatment and outcome control_value=estimate.control_value, treatment_value=estimate.treatment_value, test_significance=False, evaluate_effect_strength=False, confidence_intervals=estimate.params["confidence_intervals"], target_units=estimate.params["target_units"], effect_modifiers=estimate.params["effect_modifiers"], **estimate.params["method_params"] if estimate.params["method_params"] is not None else {}, ) return new_estimator def _estimate_effect(self): """This method is to be overriden by the child classes, so that they can run the estimation technique of their choice""" raise NotImplementedError( ("Main estimation method is " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG).format(self.__class__) ) def estimate_effect(self): """Base estimation method that calls the estimate_effect method of its calling subclass. Can optionally also test significance and estimate effect strength for any returned estimate. :param self: object instance of class Estimator :returns: A CausalEstimate instance that contains point estimates of average and conditional effects. Based on the parameters provided, it optionally includes confidence intervals, standard errors,statistical significance and other statistical parameters. """ est = self._estimate_effect() est.add_estimator(self) if self._significance_test: self.test_significance(est.value, method=self._significance_test) if self._confidence_intervals: self.estimate_confidence_intervals( est.value, confidence_level=self.confidence_level, method=self._confidence_intervals ) if self._effect_strength_eval: effect_strength_dict = self.evaluate_effect_strength(est) est.add_effect_strength(effect_strength_dict) return est def estimate_effect_naive(self): # TODO Only works for binary treatment df_withtreatment = self._data.loc[self._data[self._treatment_name] == 1] df_notreatment = self._data.loc[self._data[self._treatment_name] == 0] est = np.mean(df_withtreatment[self._outcome_name]) - np.mean(df_notreatment[self._outcome_name]) return CausalEstimate(est, None, None, control_value=0, treatment_value=1) def _estimate_effect_fn(self, data_df): """Function used in conditional effect estimation. This function is to be overridden by each child estimator. The overridden function should take in a dataframe as input and return the estimate for that data. """ raise NotImplementedError( ("Conditional treatment effects are " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG).format( self.__class__ ) ) def _estimate_conditional_effects(self, estimate_effect_fn, effect_modifier_names=None, num_quantiles=None): """Estimate conditional treatment effects. Common method for all estimators that utilizes a specific estimate_effect_fn implemented by each child estimator. If a numeric effect modifier is provided, it is discretized into quantile bins. If you would like a custom discretization, you can do so yourself: create a new column containing the discretized effect modifier and then include that column's name in the effect_modifier_names argument. :param estimate_effect_fn: Function that has a single parameter (a data frame) and returns the treatment effect estimate on that data. :param effect_modifier_names: Names of effect modifier variables over which the conditional effects will be estimated. If not provided, defaults to the effect modifiers specified during creation of the CausalEstimator object. :param num_quantiles: The number of quantiles into which a numeric effect modifier variable is discretized. Does not affect any categorical effect modifiers. :returns: A (multi-index) dataframe that provides separate effects for each value of the (discretized) effect modifiers. """ # Defaulting to class default values if parameters are not provided if effect_modifier_names is None: effect_modifier_names = self._effect_modifier_names if num_quantiles is None: num_quantiles = self.num_quantiles_to_discretize_cont_cols # Checking that there is at least one effect modifier if not effect_modifier_names: raise ValueError("At least one effect modifier should be specified to compute conditional effects.") # Making sure that effect_modifier_names is a list effect_modifier_names = parse_state(effect_modifier_names) if not all(em in self._effect_modifier_names for em in effect_modifier_names): self.logger.warn( "At least one of the provided effect modifiers was not included while fitting the estimator. You may get incorrect results. To resolve, fit the estimator again by providing the updated effect modifiers in estimate_effect()." ) # Making a copy since we are going to be changing effect modifier names effect_modifier_names = effect_modifier_names.copy() prefix = CausalEstimator.TEMP_CAT_COLUMN_PREFIX # For every numeric effect modifier, adding a temp categorical column for i in range(len(effect_modifier_names)): em = effect_modifier_names[i] if pd.api.types.is_numeric_dtype(self._data[em].dtypes): self._data[prefix + str(em)] = pd.qcut(self._data[em], num_quantiles, duplicates="drop") effect_modifier_names[i] = prefix + str(em) # Grouping by effect modifiers and computing effect separately by_effect_mods = self._data.groupby(effect_modifier_names) cond_est_fn = lambda x: self._do(self._treatment_value, x) - self._do(self._control_value, x) conditional_estimates = by_effect_mods.apply(estimate_effect_fn) # Deleting the temporary categorical columns for em in effect_modifier_names: if em.startswith(prefix): self._data.pop(em) return conditional_estimates def _do(self, x, data_df=None): raise NotImplementedError( ("Do-operator is " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG).format(self.__class__) ) def do(self, x, data_df=None): """Method that implements the do-operator. Given a value x for the treatment, returns the expected value of the outcome when the treatment is intervened to a value x. :param x: Value of the treatment :param data_df: Data on which the do-operator is to be applied. :returns: Value of the outcome when treatment is intervened/set to x. """ est = self._do(x, data_df) return est def construct_symbolic_estimator(self, estimand): raise NotImplementedError(("Symbolic estimator string is ").format(self.__class__)) def _generate_bootstrap_estimates(self, num_bootstrap_simulations, sample_size_fraction): """Helper function to generate causal estimates over bootstrapped samples. :param num_bootstrap_simulations: Number of simulations for the bootstrap method. :param sample_size_fraction: Fraction of the dataset to be resampled. :returns: A collections.namedtuple containing a list of bootstrapped estimates and a dictionary containing parameters used for the bootstrap. """ # The array that stores the results of all estimations simulation_results = np.zeros(num_bootstrap_simulations) # Find the sample size the proportion with the population size sample_size = int(sample_size_fraction * len(self._data)) if sample_size > len(self._data): self.logger.warning("WARN: The sample size is greater than the data being sampled") self.logger.info("INFO: The sample size: {}".format(sample_size)) self.logger.info("INFO: The number of simulations: {}".format(num_bootstrap_simulations)) # Perform the set number of simulations for index in range(num_bootstrap_simulations): new_data = resample(self._data, n_samples=sample_size) new_estimator = type(self)( new_data, self._target_estimand, self._target_estimand.treatment_variable, self._target_estimand.outcome_variable, # names of treatment and outcome treatment_value=self._treatment_value, control_value=self._control_value, test_significance=False, evaluate_effect_strength=False, confidence_intervals=False, target_units=self._target_units, effect_modifiers=self._effect_modifier_names, **self.method_params, ) new_effect = new_estimator.estimate_effect() simulation_results[index] = new_effect.value estimates = CausalEstimator.BootstrapEstimates( simulation_results, {"num_simulations": num_bootstrap_simulations, "sample_size_fraction": sample_size_fraction}, ) return estimates def _estimate_confidence_intervals_with_bootstrap( self, estimate_value, confidence_level=None, num_simulations=None, sample_size_fraction=None ): """ Method to compute confidence interval using bootstrapped sampling. :param estimate_value: obtained estimate's value :param confidence_level: The level for which to compute CI (e.g., 95% confidence level translates to confidence_level=0.95) :param num_simulations: The number of simulations to be performed to get the bootstrap confidence intervals. :param sample_size_fraction: The fraction of the dataset to be resampled. :returns: confidence interval at the specified level. For more details on bootstrap or resampling statistics, refer to the following links: https://ocw.mit.edu/courses/mathematics/18-05-introduction-to-probability-and-statistics-spring-2014/readings/MIT18_05S14_Reading24.pdf https://projecteuclid.org/download/pdf_1/euclid.ss/1032280214 """ # Using class default parameters if not specified if num_simulations is None: num_simulations = self.num_simulations if sample_size_fraction is None: sample_size_fraction = self.sample_size_fraction # Checking if bootstrap_estimates are already computed if self._bootstrap_estimates is None: self._bootstrap_estimates = self._generate_bootstrap_estimates(num_simulations, sample_size_fraction) elif CausalEstimator.is_bootstrap_parameter_changed(self._bootstrap_estimates.params, locals()): # Checked if any parameter is changed from the previous std error estimate self._bootstrap_estimates = self._generate_bootstrap_estimates(num_simulations, sample_size_fraction) # Now use the data obtained from the simulations to get the value of the confidence estimates bootstrap_estimates = self._bootstrap_estimates.estimates # Get the variations of each bootstrap estimate and sort bootstrap_variations = [bootstrap_estimate - estimate_value for bootstrap_estimate in bootstrap_estimates] sorted_bootstrap_variations = np.sort(bootstrap_variations) # Now we take the (1- p)th and the (p)th variations, where p is the chosen confidence level upper_bound_index = int((1 - confidence_level) * len(sorted_bootstrap_variations)) lower_bound_index = int(confidence_level * len(sorted_bootstrap_variations)) # Get the lower and upper bounds by subtracting the variations from the estimate lower_bound = estimate_value - sorted_bootstrap_variations[lower_bound_index] upper_bound = estimate_value - sorted_bootstrap_variations[upper_bound_index] return lower_bound, upper_bound def _estimate_confidence_intervals(self, confidence_level=None, method=None, **kwargs): """ This method is to be overriden by the child classes, so that they can run a confidence interval estimation method suited to the specific causal estimator. """ raise NotImplementedError( ( "This method for estimating confidence intervals is " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG + " Meanwhile, you can try the bootstrap method (method='bootstrap') to estimate confidence intervals." ).format(self.__class__) ) def estimate_confidence_intervals(self, estimate_value, confidence_level=None, method=None, **kwargs): """Find the confidence intervals corresponding to any estimator By default, this is done with the help of bootstrapped confidence intervals but can be overridden if the specific estimator implements other methods of estimating confidence intervals. If the method provided is not bootstrap, this function calls the implementation of the specific estimator. :param estimate_value: obtained estimate's value :param method: Method for estimating confidence intervals. :param confidence_level: The confidence level of the confidence intervals of the estimate. :param kwargs: Other optional args to be passed to the CI method. :returns: The obtained confidence interval. """ if method is None: if self._confidence_intervals: method = self._confidence_intervals # this is either True or methodname else: method = "default" confidence_intervals = None if confidence_level is None: confidence_level = self.confidence_level if method == "default" or method is True: # user has not provided any method try: confidence_intervals = self._estimate_confidence_intervals(confidence_level, method=method, **kwargs) except NotImplementedError: confidence_intervals = self._estimate_confidence_intervals_with_bootstrap( estimate_value, confidence_level, **kwargs ) else: if method == "bootstrap": confidence_intervals = self._estimate_confidence_intervals_with_bootstrap( estimate_value, confidence_level, **kwargs ) else: confidence_intervals = self._estimate_confidence_intervals(confidence_level, method=method, **kwargs) return confidence_intervals def _estimate_std_error_with_bootstrap(self, num_simulations=None, sample_size_fraction=None): """Compute standard error using the bootstrap method. Standard error and confidence intervals use the same parameter num_simulations for the number of bootstrap simulations. :param num_simulations: Number of bootstrapped samples. :param sample_size_fraction: Fraction of data to be resampled. :returns: Standard error of the obtained estimate. """ # Use existing params, if new user defined params are not present if num_simulations is None: num_simulations = self.num_simulations if sample_size_fraction is None: sample_size_fraction = self.sample_size_fraction # Checking if bootstrap_estimates are already computed if self._bootstrap_estimates is None: self._bootstrap_estimates = self._generate_bootstrap_estimates(num_simulations, sample_size_fraction) elif CausalEstimator.is_bootstrap_parameter_changed(self._bootstrap_estimates.params, locals()): # Check if any parameter is changed from the previous std error estimate self._bootstrap_estimates = self._generate_bootstrap_estimates(num_simulations, sample_size_fraction) std_error = np.std(self._bootstrap_estimates.estimates) return std_error def _estimate_std_error(self, method=None, **kwargs): """ This method is to be overriden by the child classes, so that they can run a standard error estimation method suited to the specific causal estimator. """ raise NotImplementedError( ( "This method for estimating standard errors is " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG + " Meanwhile, you can try the bootstrap method (method='bootstrap') to estimate standard errors." ).format(self.__class__) ) def estimate_std_error(self, method=None, **kwargs): """Compute standard error of an obtained causal estimate. :param method: Method for computing the standard error. :param kwargs: Other optional parameters to be passed to the estimating method. :returns: Standard error of the causal estimate. """ if method is None: if self._confidence_intervals: method = self._confidence_intervals else: method = "default" std_error = None if method == "default" or method is True: # user has not provided any method try: std_error = self._estimate_std_error(method, **kwargs) except NotImplementedError: std_error = self._estimate_std_error_with_bootstrap(**kwargs) else: if method == "bootstrap": std_error = self._estimate_std_error_with_bootstrap(**kwargs) else: std_error = self._estimate_std_error(method, **kwargs) return std_error def _test_significance_with_bootstrap(self, estimate_value, num_null_simulations=None): """Test statistical significance of an estimate using the bootstrap method. :param estimate_value: Obtained estimate's value :param num_null_simulations: Number of simulations for the null hypothesis :returns: p-value of the statistical significance test. """ # Use existing params, if new user defined params are not present if num_null_simulations is None: num_null_simulations = self.num_null_simulations do_retest = self._bootstrap_null_estimates is None or CausalEstimator.is_bootstrap_parameter_changed( self._bootstrap_null_estimates.params, locals() ) if do_retest: null_estimates = np.zeros(num_null_simulations) for i in range(num_null_simulations): new_outcome = np.random.permutation(self._outcome) new_data = self._data.assign(dummy_outcome=new_outcome) # self._outcome = self._data["dummy_outcome"] new_estimator = type(self)( new_data, self._target_estimand, self._target_estimand.treatment_variable, ("dummy_outcome",), test_significance=False, evaluate_effect_strength=False, confidence_intervals=False, target_units=self._target_units, effect_modifiers=self._effect_modifier_names, **self.method_params, ) new_effect = new_estimator.estimate_effect() null_estimates[i] = new_effect.value self._bootstrap_null_estimates = CausalEstimator.BootstrapEstimates( null_estimates, {"num_null_simulations": num_null_simulations, "sample_size_fraction": 1} ) # Processing the null hypothesis estimates sorted_null_estimates = np.sort(self._bootstrap_null_estimates.estimates) self.logger.debug("Null estimates: {0}".format(sorted_null_estimates)) median_estimate = sorted_null_estimates[int(num_null_simulations / 2)] # Doing a two-sided test if estimate_value > median_estimate: # Being conservative with the p-value reported estimate_index = np.searchsorted(sorted_null_estimates, estimate_value, side="left") p_value = 1 - (estimate_index / num_null_simulations) if estimate_value <= median_estimate: # Being conservative with the p-value reported estimate_index = np.searchsorted(sorted_null_estimates, estimate_value, side="right") p_value = estimate_index / num_null_simulations # If the estimate_index is 0, it depends on the number of simulations if p_value == 0: p_value = (0, 1 / len(sorted_null_estimates)) # a tuple determining the range. elif p_value == 1: p_value = (1 - 1 / len(sorted_null_estimates), 1) signif_dict = {"p_value": p_value} return signif_dict def _test_significance(self, estimate_value, method=None, **kwargs): """ This method is to be overriden by the child classes, so that they can run a significance test suited to the specific causal estimator. """ raise NotImplementedError( ( "This method for testing statistical significance is " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG + " Meanwhile, you can try the bootstrap method (method='bootstrap') to test statistical significance." ).format(self.__class__) ) def test_significance(self, estimate_value, method=None, **kwargs): """Test statistical significance of obtained estimate. By default, uses resampling to create a non-parametric significance test. A general procedure. Individual child estimators can implement different methods. If the method name is different from "bootstrap", this function calls the implementation of the child estimator. :param self: object instance of class Estimator :param estimate_value: obtained estimate's value :param method: Method for checking statistical significance :returns: p-value from the significance test """ if method is None: if self._significance_test: method = self._significance_test # this is either True or methodname else: method = "default" signif_dict = None if method == "default" or method is True: # user has not provided any method try: signif_dict = self._test_significance(estimate_value, method, **kwargs) except NotImplementedError: signif_dict = self._test_significance_with_bootstrap(estimate_value, **kwargs) else: if method == "bootstrap": signif_dict = self._test_significance_with_bootstrap(estimate_value, **kwargs) else: signif_dict = self._test_significance(estimate_value, method, **kwargs) return signif_dict def evaluate_effect_strength(self, estimate): fraction_effect_explained = self._evaluate_effect_strength(estimate, method="fraction-effect") # Need to test r-squared before supporting # effect_r_squared = self._evaluate_effect_strength(estimate, method="r-squared") strength_dict = { "fraction-effect": fraction_effect_explained # 'r-squared': effect_r_squared } return strength_dict def _evaluate_effect_strength(self, estimate, method="fraction-effect"): supported_methods = ["fraction-effect"] if method not in supported_methods: raise NotImplementedError("This method is not supported for evaluating effect strength") if method == "fraction-effect": naive_obs_estimate = self.estimate_effect_naive() self.logger.debug(estimate.value, naive_obs_estimate.value) fraction_effect_explained = estimate.value / naive_obs_estimate.value return fraction_effect_explained # elif method == "r-squared": # outcome_mean = np.mean(self._outcome) # total_variance = np.sum(np.square(self._outcome - outcome_mean)) # Assuming a linear model with one variable: the treatment # Currently only works for continuous y # causal_model = outcome_mean + estimate.value*self._treatment # squared_residual = np.sum(np.square(self._outcome - causal_model)) # r_squared = 1 - (squared_residual/total_variance) # return r_squared else: return None def update_input(self, treatment_value, control_value, target_units): self._control_value = control_value self._treatment_value = treatment_value self._target_units = target_units @staticmethod def is_bootstrap_parameter_changed(bootstrap_estimates_params, given_params): """Check whether parameters of the bootstrap have changed. This is an efficiency method that checks if fresh resampling of the bootstrap samples is required. Returns True if parameters have changed and resampling should be done again. :param bootstrap_estimates_params: A dictionary of parameters for the current bootstrap samples :param given_params: A dictionary of parameters passed by the user :returns: A binary flag denoting whether the parameters are different. """ is_any_parameter_changed = False for prm, val in bootstrap_estimates_params.items(): given_val = given_params.get(prm, None) if given_val is not None and given_val != val: is_any_parameter_changed = True break return is_any_parameter_changed def target_units_tostr(self): s = "" if type(self._target_units) is str: s += self._target_units elif callable(self._target_units): s += "Data subset defined by a function" elif isinstance(self._target_units, pd.DataFrame): s += "Data subset provided as a data frame" return s def signif_results_tostr(self, signif_results): s = "" pval = signif_results["p_value"] if type(pval) is tuple: s += "[{0}, {1}]".format(pval[0], pval[1]) else: s += "{0}".format(pval) return s def estimate_effect( treatment: Union[str, List[str]], outcome: Union[str, List[str]], identified_estimand: IdentifiedEstimand, identifier_name: str, method: CausalEstimator, control_value: int = 0, treatment_value: int = 1, test_significance: Optional[bool] = None, evaluate_effect_strength: bool = False, confidence_intervals: bool = False, target_units: str = "ate", effect_modifiers: List[str] = [], fit_estimator: bool = True, method_params: Optional[Dict] = None, ): """Estimate the identified causal effect. Currently requires an explicit method name to be specified. Method names follow the convention of identification method followed by the specific estimation method: "[backdoor/iv].estimation_method_name". Following methods are supported. * Propensity Score Matching: "backdoor.propensity_score_matching" * Propensity Score Stratification: "backdoor.propensity_score_stratification" * Propensity Score-based Inverse Weighting: "backdoor.propensity_score_weighting" * Linear Regression: "backdoor.linear_regression" * Generalized Linear Models (e.g., logistic regression): "backdoor.generalized_linear_model" * Instrumental Variables: "iv.instrumental_variable" * Regression Discontinuity: "iv.regression_discontinuity" In addition, you can directly call any of the EconML estimation methods. The convention is "backdoor.econml.path-to-estimator-class". For example, for the double machine learning estimator ("DML" class) that is located inside "dml" module of EconML, you can use the method name, "backdoor.econml.dml.DML". CausalML estimators can also be called. See `this demo notebook <https://py-why.github.io/dowhy/example_notebooks/dowhy-conditional-treatment-effects.html>`_. :param treatment: Name of the treatment :param outcome: Name of the outcome :param identified_estimand: a probability expression that represents the effect to be estimated. Output of CausalModel.identify_effect method :param method_name: name of the estimation method to be used. :param control_value: Value of the treatment in the control group, for effect estimation. If treatment is multi-variate, this can be a list. :param treatment_value: Value of the treatment in the treated group, for effect estimation. If treatment is multi-variate, this can be a list. :param test_significance: Binary flag on whether to additionally do a statistical signficance test for the estimate. :param evaluate_effect_strength: (Experimental) Binary flag on whether to estimate the relative strength of the treatment's effect. This measure can be used to compare different treatments for the same outcome (by running this method with different treatments sequentially). :param confidence_intervals: (Experimental) Binary flag indicating whether confidence intervals should be computed. :param target_units: (Experimental) The units for which the treatment effect should be estimated. This can be of three types. (1) a string for common specifications of target units (namely, "ate", "att" and "atc"), (2) a lambda function that can be used as an index for the data (pandas DataFrame), or (3) a new DataFrame that contains values of the effect_modifiers and effect will be estimated only for this new data. :param effect_modifiers: Names of effect modifier variables can be (optionally) specified here too, since they do not affect identification. If None, the effect_modifiers from the CausalModel are used. :param fit_estimator: Boolean flag on whether to fit the estimator. Setting it to False is useful to estimate the effect on new data using a previously fitted estimator. :param method_params: Dictionary containing any method-specific parameters. These are passed directly to the estimating method. See the docs for each estimation method for allowed method-specific params. :returns: An instance of the CausalEstimate class, containing the causal effect estimate and other method-dependent information """ treatment = parse_state(treatment) outcome = parse_state(outcome) causal_estimator_class = method.__class__ identified_estimand.set_identifier_method(identifier_name) if identified_estimand.no_directed_path: logger.warning("No directed path from {0} to {1}.".format(treatment, outcome)) return CausalEstimate( 0, identified_estimand, None, control_value=control_value, treatment_value=treatment_value ) # Check if estimator's target estimand is identified elif identified_estimand.estimands[identifier_name] is None: logger.error("No valid identified estimand available.") return CausalEstimate(None, None, None, control_value=control_value, treatment_value=treatment_value) method.update_input(treatment_value, control_value, target_units) estimate = method.estimate_effect() # Store parameters inside estimate object for refutation methods # TODO: This add_params needs to move to the estimator class # inside estimate_effect and estimate_conditional_effect estimate.add_params( estimand_type=identified_estimand.estimand_type, estimator_class=causal_estimator_class, test_significance=test_significance, evaluate_effect_strength=evaluate_effect_strength, confidence_intervals=confidence_intervals, target_units=target_units, effect_modifiers=effect_modifiers, method_params=method_params, ) return estimate class CausalEstimate: """Class for the estimate object that every causal estimator returns""" def __init__( self, estimate, target_estimand, realized_estimand_expr, control_value, treatment_value, conditional_estimates=None, **kwargs, ): self.value = estimate self.target_estimand = target_estimand self.realized_estimand_expr = realized_estimand_expr self.control_value = control_value self.treatment_value = treatment_value self.conditional_estimates = conditional_estimates self.params = kwargs if self.params is not None: for key, value in self.params.items(): setattr(self, key, value) self.effect_strength = None def add_estimator(self, estimator_instance): self.estimator = estimator_instance def add_effect_strength(self, strength_dict): self.effect_strength = strength_dict def add_params(self, **kwargs): self.params.update(kwargs) def get_confidence_intervals(self, confidence_level=None, method=None, **kwargs): """Get confidence intervals of the obtained estimate. By default, this is done with the help of bootstrapped confidence intervals but can be overridden if the specific estimator implements other methods of estimating confidence intervals. If the method provided is not bootstrap, this function calls the implementation of the specific estimator. :param method: Method for estimating confidence intervals. :param confidence_level: The confidence level of the confidence intervals of the estimate. :param kwargs: Other optional args to be passed to the CI method. :returns: The obtained confidence interval. """ confidence_intervals = self.estimator.estimate_confidence_intervals( estimate_value=self.value, confidence_level=confidence_level, method=method, **kwargs ) return confidence_intervals def get_standard_error(self, method=None, **kwargs): """Get standard error of the obtained estimate. By default, this is done with the help of bootstrapped standard errors but can be overridden if the specific estimator implements other methods of estimating standard error. If the method provided is not bootstrap, this function calls the implementation of the specific estimator. :param method: Method for computing the standard error. :param kwargs: Other optional parameters to be passed to the estimating method. :returns: Standard error of the causal estimate. """ std_error = self.estimator.estimate_std_error(method=method, **kwargs) return std_error def test_stat_significance(self, method=None, **kwargs): """Test statistical significance of the estimate obtained. By default, uses resampling to create a non-parametric significance test. Individual child estimators can implement different methods. If the method name is different from "bootstrap", this function calls the implementation of the child estimator. :param method: Method for checking statistical significance :param kwargs: Other optional parameters to be passed to the estimating method. :returns: p-value from the significance test """ signif_results = self.estimator.test_significance(self.value, method=method, **kwargs) return {"p_value": signif_results["p_value"]} def estimate_conditional_effects( self, effect_modifiers=None, num_quantiles=CausalEstimator.NUM_QUANTILES_TO_DISCRETIZE_CONT_COLS ): """Estimate treatment effect conditioned on given variables. If a numeric effect modifier is provided, it is discretized into quantile bins. If you would like a custom discretization, you can do so yourself: create a new column containing the discretized effect modifier and then include that column's name in the effect_modifier_names argument. :param effect_modifiers: Names of effect modifier variables over which the conditional effects will be estimated. If not provided, defaults to the effect modifiers specified during creation of the CausalEstimator object. :param num_quantiles: The number of quantiles into which a numeric effect modifier variable is discretized. Does not affect any categorical effect modifiers. :returns: A (multi-index) dataframe that provides separate effects for each value of the (discretized) effect modifiers. """ return self.estimator._estimate_conditional_effects( self.estimator._estimate_effect_fn, effect_modifiers, num_quantiles ) def interpret(self, method_name=None, **kwargs): """Interpret the causal estimate. :param method_name: Method used (string) or a list of methods. If None, then the default for the specific estimator is used. :param kwargs:: Optional parameters that are directly passed to the interpreter method. :returns: None """ if method_name is None: method_name = self.estimator.interpret_method method_name_arr = parse_state(method_name) for method in method_name_arr: interpreter = interpreters.get_class_object(method) interpreter(self, **kwargs).interpret() def __str__(self): s = "*** Causal Estimate ***\n" # No estimand was identified (identification failed) if self.target_estimand is None: return "Estimation failed! No relevant identified estimand available for this estimation method." s += "\n## Identified estimand\n{0}".format(self.target_estimand.__str__(only_target_estimand=True)) s += "\n## Realized estimand\n{0}".format(self.realized_estimand_expr) if hasattr(self, "estimator"): s += "\nTarget units: {0}\n".format(self.estimator.target_units_tostr()) s += "\n## Estimate\n" s += "Mean value: {0}\n".format(self.value) s += "" if hasattr(self, "cate_estimates"): s += "Effect estimates: {0}\n".format(self.cate_estimates) if hasattr(self, "estimator"): if self.estimator._significance_test: s += "p-value: {0}\n".format(self.estimator.signif_results_tostr(self.test_stat_significance())) if self.estimator._confidence_intervals: s += "{0}% confidence interval: {1}\n".format( 100 * self.estimator.confidence_level, self.get_confidence_intervals() ) if self.conditional_estimates is not None: s += "### Conditional Estimates\n" s += str(self.conditional_estimates) if self.effect_strength is not None: s += "\n## Effect Strength\n" s += "Change in outcome attributable to treatment: {}\n".format(self.effect_strength["fraction-effect"]) # s += "Variance in outcome explained by treatment: {}\n".format(self.effect_strength["r-squared"]) return s class RealizedEstimand(object): def __init__(self, identified_estimand, estimator_name): self.treatment_variable = identified_estimand.treatment_variable self.outcome_variable = identified_estimand.outcome_variable self.backdoor_variables = identified_estimand.get_backdoor_variables() self.instrumental_variables = identified_estimand.instrumental_variables self.estimand_type = identified_estimand.estimand_type self.estimand_expression = None self.assumptions = None self.estimator_name = estimator_name def update_assumptions(self, estimator_assumptions): self.assumptions = estimator_assumptions def update_estimand_expression(self, estimand_expression): self.estimand_expression = estimand_expression def __str__(self): s = "Realized estimand: {0}\n".format(self.estimator_name) s += "Realized estimand type: {0}\n".format(self.estimand_type) s += "Estimand expression:\n{0}\n".format(sp.pretty(self.estimand_expression)) j = 1 for ass_name, ass_str in self.assumptions.items(): s += "Estimand assumption {0}, {1}: {2}\n".format(j, ass_name, ass_str) j += 1 return s

andresmor-ms

2044d216c322a4b32c6eadce5da7d83463f19c2f

05bfa49dacf0061988c96c6f3e3756219df5422a

what should be desired functionality for these parameters? test_significance, evaluate_effect_strength, confidence_intervals, effect_modifiers, etc.? Ideally, these should be passed to the estimator. It makes sense if the user does not provide any `method`, so then we can add these parameters when initializing the Estimator class. But if user has provided the estimator object, then it is tricky. One option is to make these fit-related params as optional params to the estimate_effect method of an estimator. The other is to simply update them as we do with `update_input` method. My thinking is that test_signifinance, evaluate_effect_strength confidence_intervals do not belong in the constructor for an estimator. This would involve a refactor of all estimator classes, so it is a big step. What do you think?

amit-sharma

py-why/dowhy

Functional api/estimate effect function

#### Estimate Effect function * Refactors the estimate effect into a separate function to keep backwards compatibility #### TODO (future PRs): * Add `fit(...)` method to estimators - Move data related parameters from the constructor to the `fit(...)` method * Refactor code to avoid `**kwargs` in `__init__(...)` constructors

2022-10-18 15:49:21+00:00

2022-10-25 17:02:02+00:00

dowhy/causal_estimator.py

import logging from collections import namedtuple import numpy as np import pandas as pd import sympy as sp from sklearn.utils import resample import dowhy.interpreters as interpreters from dowhy.utils.api import parse_state class CausalEstimator: """Base class for an estimator of causal effect. Subclasses implement different estimation methods. All estimation methods are in the package "dowhy.causal_estimators" """ # The default number of simulations for statistical testing DEFAULT_NUMBER_OF_SIMULATIONS_STAT_TEST = 1000 # The default number of simulations to obtain confidence intervals DEFAULT_NUMBER_OF_SIMULATIONS_CI = 100 # The portion of the total size that should be taken each time to find the confidence intervals # 1 is the recommended value # https://ocw.mit.edu/courses/mathematics/18-05-introduction-to-probability-and-statistics-spring-2014/readings/MIT18_05S14_Reading24.pdf # https://projecteuclid.org/download/pdf_1/euclid.ss/1032280214 DEFAULT_SAMPLE_SIZE_FRACTION = 1 # The default Confidence Level DEFAULT_CONFIDENCE_LEVEL = 0.95 # Number of quantiles to discretize continuous columns, for applying groupby NUM_QUANTILES_TO_DISCRETIZE_CONT_COLS = 5 # Prefix to add to temporary categorical variables created after discretization TEMP_CAT_COLUMN_PREFIX = "__categorical__" DEFAULT_NOTIMPLEMENTEDERROR_MSG = "not yet implemented for {0}. If you would this to be implemented in the next version, please raise an issue at https://github.com/microsoft/dowhy/issues" BootstrapEstimates = namedtuple("BootstrapEstimates", ["estimates", "params"]) DEFAULT_INTERPRET_METHOD = ["textual_effect_interpreter"] # std args to be removed from locals() before being passed to args_dict _STD_INIT_ARGS = ("self", "__class__", "args", "kwargs") def __init__( self, data, identified_estimand, treatment, outcome, control_value=0, treatment_value=1, test_significance=False, evaluate_effect_strength=False, confidence_intervals=False, target_units=None, effect_modifiers=None, num_null_simulations=DEFAULT_NUMBER_OF_SIMULATIONS_STAT_TEST, num_simulations=DEFAULT_NUMBER_OF_SIMULATIONS_CI, sample_size_fraction=DEFAULT_SAMPLE_SIZE_FRACTION, confidence_level=DEFAULT_CONFIDENCE_LEVEL, need_conditional_estimates="auto", num_quantiles_to_discretize_cont_cols=NUM_QUANTILES_TO_DISCRETIZE_CONT_COLS, **kwargs, ): """Initializes an estimator with data and names of relevant variables. This method is called from the constructors of its child classes. :param data: data frame containing the data :param identified_estimand: probability expression representing the target identified estimand to estimate. :param treatment: name of the treatment variable :param outcome: name of the outcome variable :param control_value: Value of the treatment in the control group, for effect estimation. If treatment is multi-variate, this can be a list. :param treatment_value: Value of the treatment in the treated group, for effect estimation. If treatment is multi-variate, this can be a list. :param test_significance: Binary flag or a string indicating whether to test significance and by which method. All estimators support test_significance="bootstrap" that estimates a p-value for the obtained estimate using the bootstrap method. Individual estimators can override this to support custom testing methods. The bootstrap method supports an optional parameter, num_null_simulations. If False, no testing is done. If True, significance of the estimate is tested using the custom method if available, otherwise by bootstrap. :param evaluate_effect_strength: (Experimental) whether to evaluate the strength of effect :param confidence_intervals: Binary flag or a string indicating whether the confidence intervals should be computed and which method should be used. All methods support estimation of confidence intervals using the bootstrap method by using the parameter confidence_intervals="bootstrap". The bootstrap method takes in two arguments (num_simulations and sample_size_fraction) that can be optionally specified in the params dictionary. Estimators may also override this to implement their own confidence interval method. If this parameter is False, no confidence intervals are computed. If True, confidence intervals are computed by the estimator's specific method if available, otherwise through bootstrap. :param target_units: The units for which the treatment effect should be estimated. This can be a string for common specifications of target units (namely, "ate", "att" and "atc"). It can also be a lambda function that can be used as an index for the data (pandas DataFrame). Alternatively, it can be a new DataFrame that contains values of the effect_modifiers and effect will be estimated only for this new data. :param effect_modifiers: Variables on which to compute separate effects, or return a heterogeneous effect function. Not all methods support this currently. :param num_null_simulations: The number of simulations for testing the statistical significance of the estimator :param num_simulations: The number of simulations for finding the confidence interval (and/or standard error) for a estimate :param sample_size_fraction: The size of the sample for the bootstrap estimator :param confidence_level: The confidence level of the confidence interval estimate :param need_conditional_estimates: Boolean flag indicating whether conditional estimates should be computed. Defaults to True if there are effect modifiers in the graph :param num_quantiles_to_discretize_cont_cols: The number of quantiles into which a numeric effect modifier is split, to enable estimation of conditional treatment effect over it. :param kwargs: (optional) Additional estimator-specific parameters :returns: an instance of the estimator class. """ self._data = data self._target_estimand = identified_estimand # Currently estimation methods only support univariate treatment and outcome self._treatment_name = treatment self._outcome_name = outcome[0] # assuming one-dimensional outcome self._control_value = control_value self._treatment_value = treatment_value self._significance_test = test_significance self._effect_strength_eval = evaluate_effect_strength self._target_units = target_units self._effect_modifier_names = effect_modifiers self._confidence_intervals = confidence_intervals self._bootstrap_estimates = None # for confidence intervals and std error self._bootstrap_null_estimates = None # for significance test self._effect_modifiers = None self.method_params = kwargs # Setting the default interpret method self.interpret_method = CausalEstimator.DEFAULT_INTERPRET_METHOD self.logger = logging.getLogger(__name__) # Setting treatment and outcome values if self._data is not None: self._treatment = self._data[self._treatment_name] self._outcome = self._data[self._outcome_name] # Now saving the effect modifiers if self._effect_modifier_names: # only add the observed nodes self._effect_modifier_names = [ cname for cname in self._effect_modifier_names if cname in self._data.columns ] if len(self._effect_modifier_names) > 0: self._effect_modifiers = self._data[self._effect_modifier_names] self._effect_modifiers = pd.get_dummies(self._effect_modifiers, drop_first=True) self.logger.debug("Effect modifiers: " + ",".join(self._effect_modifier_names)) else: self._effect_modifier_names = None # Check if some parameters were set, otherwise set to default values self.num_null_simulations = num_null_simulations self.num_simulations = num_simulations self.sample_size_fraction = sample_size_fraction self.confidence_level = confidence_level self.num_quantiles_to_discretize_cont_cols = num_quantiles_to_discretize_cont_cols # Estimate conditional estimates by default self.need_conditional_estimates = ( need_conditional_estimates if need_conditional_estimates != "auto" else bool(self._effect_modifier_names) ) @staticmethod def get_estimator_object(new_data, identified_estimand, estimate): """Create a new estimator of the same type as the one passed in the estimate argument. Creates a new object with new_data and the identified_estimand :param new_data: np.ndarray, pd.Series, pd.DataFrame The newly assigned data on which the estimator should run :param identified_estimand: IdentifiedEstimand An instance of the identified estimand class that provides the information with respect to which causal pathways are employed when the treatment effects the outcome :param estimate: CausalEstimate It is an already existing estimate whose properties we wish to replicate :returns: An instance of the same estimator class that had generated the given estimate. """ estimator_class = estimate.params["estimator_class"] new_estimator = estimator_class( new_data, identified_estimand, identified_estimand.treatment_variable, identified_estimand.outcome_variable, # names of treatment and outcome control_value=estimate.control_value, treatment_value=estimate.treatment_value, test_significance=False, evaluate_effect_strength=False, confidence_intervals=estimate.params["confidence_intervals"], target_units=estimate.params["target_units"], effect_modifiers=estimate.params["effect_modifiers"], **estimate.params["method_params"], ) return new_estimator def _estimate_effect(self): """This method is to be overriden by the child classes, so that they can run the estimation technique of their choice""" raise NotImplementedError( ("Main estimation method is " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG).format(self.__class__) ) def estimate_effect(self): """Base estimation method that calls the estimate_effect method of its calling subclass. Can optionally also test significance and estimate effect strength for any returned estimate. :param self: object instance of class Estimator :returns: A CausalEstimate instance that contains point estimates of average and conditional effects. Based on the parameters provided, it optionally includes confidence intervals, standard errors,statistical significance and other statistical parameters. """ est = self._estimate_effect() est.add_estimator(self) if self._significance_test: self.test_significance(est.value, method=self._significance_test) if self._confidence_intervals: self.estimate_confidence_intervals( est.value, confidence_level=self.confidence_level, method=self._confidence_intervals ) if self._effect_strength_eval: effect_strength_dict = self.evaluate_effect_strength(est) est.add_effect_strength(effect_strength_dict) return est def estimate_effect_naive(self): # TODO Only works for binary treatment df_withtreatment = self._data.loc[self._data[self._treatment_name] == 1] df_notreatment = self._data.loc[self._data[self._treatment_name] == 0] est = np.mean(df_withtreatment[self._outcome_name]) - np.mean(df_notreatment[self._outcome_name]) return CausalEstimate(est, None, None, control_value=0, treatment_value=1) def _estimate_effect_fn(self, data_df): """Function used in conditional effect estimation. This function is to be overridden by each child estimator. The overridden function should take in a dataframe as input and return the estimate for that data. """ raise NotImplementedError( ("Conditional treatment effects are " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG).format( self.__class__ ) ) def _estimate_conditional_effects(self, estimate_effect_fn, effect_modifier_names=None, num_quantiles=None): """Estimate conditional treatment effects. Common method for all estimators that utilizes a specific estimate_effect_fn implemented by each child estimator. If a numeric effect modifier is provided, it is discretized into quantile bins. If you would like a custom discretization, you can do so yourself: create a new column containing the discretized effect modifier and then include that column's name in the effect_modifier_names argument. :param estimate_effect_fn: Function that has a single parameter (a data frame) and returns the treatment effect estimate on that data. :param effect_modifier_names: Names of effect modifier variables over which the conditional effects will be estimated. If not provided, defaults to the effect modifiers specified during creation of the CausalEstimator object. :param num_quantiles: The number of quantiles into which a numeric effect modifier variable is discretized. Does not affect any categorical effect modifiers. :returns: A (multi-index) dataframe that provides separate effects for each value of the (discretized) effect modifiers. """ # Defaulting to class default values if parameters are not provided if effect_modifier_names is None: effect_modifier_names = self._effect_modifier_names if num_quantiles is None: num_quantiles = self.num_quantiles_to_discretize_cont_cols # Checking that there is at least one effect modifier if not effect_modifier_names: raise ValueError("At least one effect modifier should be specified to compute conditional effects.") # Making sure that effect_modifier_names is a list effect_modifier_names = parse_state(effect_modifier_names) if not all(em in self._effect_modifier_names for em in effect_modifier_names): self.logger.warn( "At least one of the provided effect modifiers was not included while fitting the estimator. You may get incorrect results. To resolve, fit the estimator again by providing the updated effect modifiers in estimate_effect()." ) # Making a copy since we are going to be changing effect modifier names effect_modifier_names = effect_modifier_names.copy() prefix = CausalEstimator.TEMP_CAT_COLUMN_PREFIX # For every numeric effect modifier, adding a temp categorical column for i in range(len(effect_modifier_names)): em = effect_modifier_names[i] if pd.api.types.is_numeric_dtype(self._data[em].dtypes): self._data[prefix + str(em)] = pd.qcut(self._data[em], num_quantiles, duplicates="drop") effect_modifier_names[i] = prefix + str(em) # Grouping by effect modifiers and computing effect separately by_effect_mods = self._data.groupby(effect_modifier_names) cond_est_fn = lambda x: self._do(self._treatment_value, x) - self._do(self._control_value, x) conditional_estimates = by_effect_mods.apply(estimate_effect_fn) # Deleting the temporary categorical columns for em in effect_modifier_names: if em.startswith(prefix): self._data.pop(em) return conditional_estimates def _do(self, x, data_df=None): raise NotImplementedError( ("Do-operator is " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG).format(self.__class__) ) def do(self, x, data_df=None): """Method that implements the do-operator. Given a value x for the treatment, returns the expected value of the outcome when the treatment is intervened to a value x. :param x: Value of the treatment :param data_df: Data on which the do-operator is to be applied. :returns: Value of the outcome when treatment is intervened/set to x. """ est = self._do(x, data_df) return est def construct_symbolic_estimator(self, estimand): raise NotImplementedError(("Symbolic estimator string is ").format(self.__class__)) def _generate_bootstrap_estimates(self, num_bootstrap_simulations, sample_size_fraction): """Helper function to generate causal estimates over bootstrapped samples. :param num_bootstrap_simulations: Number of simulations for the bootstrap method. :param sample_size_fraction: Fraction of the dataset to be resampled. :returns: A collections.namedtuple containing a list of bootstrapped estimates and a dictionary containing parameters used for the bootstrap. """ # The array that stores the results of all estimations simulation_results = np.zeros(num_bootstrap_simulations) # Find the sample size the proportion with the population size sample_size = int(sample_size_fraction * len(self._data)) if sample_size > len(self._data): self.logger.warning("WARN: The sample size is greater than the data being sampled") self.logger.info("INFO: The sample size: {}".format(sample_size)) self.logger.info("INFO: The number of simulations: {}".format(num_bootstrap_simulations)) # Perform the set number of simulations for index in range(num_bootstrap_simulations): new_data = resample(self._data, n_samples=sample_size) new_estimator = type(self)( new_data, self._target_estimand, self._target_estimand.treatment_variable, self._target_estimand.outcome_variable, # names of treatment and outcome treatment_value=self._treatment_value, control_value=self._control_value, test_significance=False, evaluate_effect_strength=False, confidence_intervals=False, target_units=self._target_units, effect_modifiers=self._effect_modifier_names, **self.method_params, ) new_effect = new_estimator.estimate_effect() simulation_results[index] = new_effect.value estimates = CausalEstimator.BootstrapEstimates( simulation_results, {"num_simulations": num_bootstrap_simulations, "sample_size_fraction": sample_size_fraction}, ) return estimates def _estimate_confidence_intervals_with_bootstrap( self, estimate_value, confidence_level=None, num_simulations=None, sample_size_fraction=None ): """ Method to compute confidence interval using bootstrapped sampling. :param estimate_value: obtained estimate's value :param confidence_level: The level for which to compute CI (e.g., 95% confidence level translates to confidence_level=0.95) :param num_simulations: The number of simulations to be performed to get the bootstrap confidence intervals. :param sample_size_fraction: The fraction of the dataset to be resampled. :returns: confidence interval at the specified level. For more details on bootstrap or resampling statistics, refer to the following links: https://ocw.mit.edu/courses/mathematics/18-05-introduction-to-probability-and-statistics-spring-2014/readings/MIT18_05S14_Reading24.pdf https://projecteuclid.org/download/pdf_1/euclid.ss/1032280214 """ # Using class default parameters if not specified if num_simulations is None: num_simulations = self.num_simulations if sample_size_fraction is None: sample_size_fraction = self.sample_size_fraction # Checking if bootstrap_estimates are already computed if self._bootstrap_estimates is None: self._bootstrap_estimates = self._generate_bootstrap_estimates(num_simulations, sample_size_fraction) elif CausalEstimator.is_bootstrap_parameter_changed(self._bootstrap_estimates.params, locals()): # Checked if any parameter is changed from the previous std error estimate self._bootstrap_estimates = self._generate_bootstrap_estimates(num_simulations, sample_size_fraction) # Now use the data obtained from the simulations to get the value of the confidence estimates bootstrap_estimates = self._bootstrap_estimates.estimates # Get the variations of each bootstrap estimate and sort bootstrap_variations = [bootstrap_estimate - estimate_value for bootstrap_estimate in bootstrap_estimates] sorted_bootstrap_variations = np.sort(bootstrap_variations) # Now we take the (1- p)th and the (p)th variations, where p is the chosen confidence level upper_bound_index = int((1 - confidence_level) * len(sorted_bootstrap_variations)) lower_bound_index = int(confidence_level * len(sorted_bootstrap_variations)) # Get the lower and upper bounds by subtracting the variations from the estimate lower_bound = estimate_value - sorted_bootstrap_variations[lower_bound_index] upper_bound = estimate_value - sorted_bootstrap_variations[upper_bound_index] return lower_bound, upper_bound def _estimate_confidence_intervals(self, confidence_level=None, method=None, **kwargs): """ This method is to be overriden by the child classes, so that they can run a confidence interval estimation method suited to the specific causal estimator. """ raise NotImplementedError( ( "This method for estimating confidence intervals is " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG + " Meanwhile, you can try the bootstrap method (method='bootstrap') to estimate confidence intervals." ).format(self.__class__) ) def estimate_confidence_intervals(self, estimate_value, confidence_level=None, method=None, **kwargs): """Find the confidence intervals corresponding to any estimator By default, this is done with the help of bootstrapped confidence intervals but can be overridden if the specific estimator implements other methods of estimating confidence intervals. If the method provided is not bootstrap, this function calls the implementation of the specific estimator. :param estimate_value: obtained estimate's value :param method: Method for estimating confidence intervals. :param confidence_level: The confidence level of the confidence intervals of the estimate. :param kwargs: Other optional args to be passed to the CI method. :returns: The obtained confidence interval. """ if method is None: if self._confidence_intervals: method = self._confidence_intervals # this is either True or methodname else: method = "default" confidence_intervals = None if confidence_level is None: confidence_level = self.confidence_level if method == "default" or method is True: # user has not provided any method try: confidence_intervals = self._estimate_confidence_intervals(confidence_level, method=method, **kwargs) except NotImplementedError: confidence_intervals = self._estimate_confidence_intervals_with_bootstrap( estimate_value, confidence_level, **kwargs ) else: if method == "bootstrap": confidence_intervals = self._estimate_confidence_intervals_with_bootstrap( estimate_value, confidence_level, **kwargs ) else: confidence_intervals = self._estimate_confidence_intervals(confidence_level, method=method, **kwargs) return confidence_intervals def _estimate_std_error_with_bootstrap(self, num_simulations=None, sample_size_fraction=None): """Compute standard error using the bootstrap method. Standard error and confidence intervals use the same parameter num_simulations for the number of bootstrap simulations. :param num_simulations: Number of bootstrapped samples. :param sample_size_fraction: Fraction of data to be resampled. :returns: Standard error of the obtained estimate. """ # Use existing params, if new user defined params are not present if num_simulations is None: num_simulations = self.num_simulations if sample_size_fraction is None: sample_size_fraction = self.sample_size_fraction # Checking if bootstrap_estimates are already computed if self._bootstrap_estimates is None: self._bootstrap_estimates = self._generate_bootstrap_estimates(num_simulations, sample_size_fraction) elif CausalEstimator.is_bootstrap_parameter_changed(self._bootstrap_estimates.params, locals()): # Check if any parameter is changed from the previous std error estimate self._bootstrap_estimates = self._generate_bootstrap_estimates(num_simulations, sample_size_fraction) std_error = np.std(self._bootstrap_estimates.estimates) return std_error def _estimate_std_error(self, method=None, **kwargs): """ This method is to be overriden by the child classes, so that they can run a standard error estimation method suited to the specific causal estimator. """ raise NotImplementedError( ( "This method for estimating standard errors is " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG + " Meanwhile, you can try the bootstrap method (method='bootstrap') to estimate standard errors." ).format(self.__class__) ) def estimate_std_error(self, method=None, **kwargs): """Compute standard error of an obtained causal estimate. :param method: Method for computing the standard error. :param kwargs: Other optional parameters to be passed to the estimating method. :returns: Standard error of the causal estimate. """ if method is None: if self._confidence_intervals: method = self._confidence_intervals else: method = "default" std_error = None if method == "default" or method is True: # user has not provided any method try: std_error = self._estimate_std_error(method, **kwargs) except NotImplementedError: std_error = self._estimate_std_error_with_bootstrap(**kwargs) else: if method == "bootstrap": std_error = self._estimate_std_error_with_bootstrap(**kwargs) else: std_error = self._estimate_std_error(method, **kwargs) return std_error def _test_significance_with_bootstrap(self, estimate_value, num_null_simulations=None): """Test statistical significance of an estimate using the bootstrap method. :param estimate_value: Obtained estimate's value :param num_null_simulations: Number of simulations for the null hypothesis :returns: p-value of the statistical significance test. """ # Use existing params, if new user defined params are not present if num_null_simulations is None: num_null_simulations = self.num_null_simulations do_retest = self._bootstrap_null_estimates is None or CausalEstimator.is_bootstrap_parameter_changed( self._bootstrap_null_estimates.params, locals() ) if do_retest: null_estimates = np.zeros(num_null_simulations) for i in range(num_null_simulations): new_outcome = np.random.permutation(self._outcome) new_data = self._data.assign(dummy_outcome=new_outcome) # self._outcome = self._data["dummy_outcome"] new_estimator = type(self)( new_data, self._target_estimand, self._target_estimand.treatment_variable, ("dummy_outcome",), test_significance=False, evaluate_effect_strength=False, confidence_intervals=False, target_units=self._target_units, effect_modifiers=self._effect_modifier_names, **self.method_params, ) new_effect = new_estimator.estimate_effect() null_estimates[i] = new_effect.value self._bootstrap_null_estimates = CausalEstimator.BootstrapEstimates( null_estimates, {"num_null_simulations": num_null_simulations, "sample_size_fraction": 1} ) # Processing the null hypothesis estimates sorted_null_estimates = np.sort(self._bootstrap_null_estimates.estimates) self.logger.debug("Null estimates: {0}".format(sorted_null_estimates)) median_estimate = sorted_null_estimates[int(num_null_simulations / 2)] # Doing a two-sided test if estimate_value > median_estimate: # Being conservative with the p-value reported estimate_index = np.searchsorted(sorted_null_estimates, estimate_value, side="left") p_value = 1 - (estimate_index / num_null_simulations) if estimate_value <= median_estimate: # Being conservative with the p-value reported estimate_index = np.searchsorted(sorted_null_estimates, estimate_value, side="right") p_value = estimate_index / num_null_simulations # If the estimate_index is 0, it depends on the number of simulations if p_value == 0: p_value = (0, 1 / len(sorted_null_estimates)) # a tuple determining the range. elif p_value == 1: p_value = (1 - 1 / len(sorted_null_estimates), 1) signif_dict = {"p_value": p_value} return signif_dict def _test_significance(self, estimate_value, method=None, **kwargs): """ This method is to be overriden by the child classes, so that they can run a significance test suited to the specific causal estimator. """ raise NotImplementedError( ( "This method for testing statistical significance is " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG + " Meanwhile, you can try the bootstrap method (method='bootstrap') to test statistical significance." ).format(self.__class__) ) def test_significance(self, estimate_value, method=None, **kwargs): """Test statistical significance of obtained estimate. By default, uses resampling to create a non-parametric significance test. A general procedure. Individual child estimators can implement different methods. If the method name is different from "bootstrap", this function calls the implementation of the child estimator. :param self: object instance of class Estimator :param estimate_value: obtained estimate's value :param method: Method for checking statistical significance :returns: p-value from the significance test """ if method is None: if self._significance_test: method = self._significance_test # this is either True or methodname else: method = "default" signif_dict = None if method == "default" or method is True: # user has not provided any method try: signif_dict = self._test_significance(estimate_value, method, **kwargs) except NotImplementedError: signif_dict = self._test_significance_with_bootstrap(estimate_value, **kwargs) else: if method == "bootstrap": signif_dict = self._test_significance_with_bootstrap(estimate_value, **kwargs) else: signif_dict = self._test_significance(estimate_value, method, **kwargs) return signif_dict def evaluate_effect_strength(self, estimate): fraction_effect_explained = self._evaluate_effect_strength(estimate, method="fraction-effect") # Need to test r-squared before supporting # effect_r_squared = self._evaluate_effect_strength(estimate, method="r-squared") strength_dict = { "fraction-effect": fraction_effect_explained # 'r-squared': effect_r_squared } return strength_dict def _evaluate_effect_strength(self, estimate, method="fraction-effect"): supported_methods = ["fraction-effect"] if method not in supported_methods: raise NotImplementedError("This method is not supported for evaluating effect strength") if method == "fraction-effect": naive_obs_estimate = self.estimate_effect_naive() self.logger.debug(estimate.value, naive_obs_estimate.value) fraction_effect_explained = estimate.value / naive_obs_estimate.value return fraction_effect_explained # elif method == "r-squared": # outcome_mean = np.mean(self._outcome) # total_variance = np.sum(np.square(self._outcome - outcome_mean)) # Assuming a linear model with one variable: the treatment # Currently only works for continuous y # causal_model = outcome_mean + estimate.value*self._treatment # squared_residual = np.sum(np.square(self._outcome - causal_model)) # r_squared = 1 - (squared_residual/total_variance) # return r_squared else: return None def update_input(self, treatment_value, control_value, target_units): self._control_value = control_value self._treatment_value = treatment_value self._target_units = target_units @staticmethod def is_bootstrap_parameter_changed(bootstrap_estimates_params, given_params): """Check whether parameters of the bootstrap have changed. This is an efficiency method that checks if fresh resampling of the bootstrap samples is required. Returns True if parameters have changed and resampling should be done again. :param bootstrap_estimates_params: A dictionary of parameters for the current bootstrap samples :param given_params: A dictionary of parameters passed by the user :returns: A binary flag denoting whether the parameters are different. """ is_any_parameter_changed = False for prm, val in bootstrap_estimates_params.items(): given_val = given_params.get(prm, None) if given_val is not None and given_val != val: is_any_parameter_changed = True break return is_any_parameter_changed def target_units_tostr(self): s = "" if type(self._target_units) is str: s += self._target_units elif callable(self._target_units): s += "Data subset defined by a function" elif isinstance(self._target_units, pd.DataFrame): s += "Data subset provided as a data frame" return s def signif_results_tostr(self, signif_results): s = "" pval = signif_results["p_value"] if type(pval) is tuple: s += "[{0}, {1}]".format(pval[0], pval[1]) else: s += "{0}".format(pval) return s class CausalEstimate: """Class for the estimate object that every causal estimator returns""" def __init__( self, estimate, target_estimand, realized_estimand_expr, control_value, treatment_value, conditional_estimates=None, **kwargs, ): self.value = estimate self.target_estimand = target_estimand self.realized_estimand_expr = realized_estimand_expr self.control_value = control_value self.treatment_value = treatment_value self.conditional_estimates = conditional_estimates self.params = kwargs if self.params is not None: for key, value in self.params.items(): setattr(self, key, value) self.effect_strength = None def add_estimator(self, estimator_instance): self.estimator = estimator_instance def add_effect_strength(self, strength_dict): self.effect_strength = strength_dict def add_params(self, **kwargs): self.params.update(kwargs) def get_confidence_intervals(self, confidence_level=None, method=None, **kwargs): """Get confidence intervals of the obtained estimate. By default, this is done with the help of bootstrapped confidence intervals but can be overridden if the specific estimator implements other methods of estimating confidence intervals. If the method provided is not bootstrap, this function calls the implementation of the specific estimator. :param method: Method for estimating confidence intervals. :param confidence_level: The confidence level of the confidence intervals of the estimate. :param kwargs: Other optional args to be passed to the CI method. :returns: The obtained confidence interval. """ confidence_intervals = self.estimator.estimate_confidence_intervals( estimate_value=self.value, confidence_level=confidence_level, method=method, **kwargs ) return confidence_intervals def get_standard_error(self, method=None, **kwargs): """Get standard error of the obtained estimate. By default, this is done with the help of bootstrapped standard errors but can be overridden if the specific estimator implements other methods of estimating standard error. If the method provided is not bootstrap, this function calls the implementation of the specific estimator. :param method: Method for computing the standard error. :param kwargs: Other optional parameters to be passed to the estimating method. :returns: Standard error of the causal estimate. """ std_error = self.estimator.estimate_std_error(method=method, **kwargs) return std_error def test_stat_significance(self, method=None, **kwargs): """Test statistical significance of the estimate obtained. By default, uses resampling to create a non-parametric significance test. Individual child estimators can implement different methods. If the method name is different from "bootstrap", this function calls the implementation of the child estimator. :param method: Method for checking statistical significance :param kwargs: Other optional parameters to be passed to the estimating method. :returns: p-value from the significance test """ signif_results = self.estimator.test_significance(self.value, method=method, **kwargs) return {"p_value": signif_results["p_value"]} def estimate_conditional_effects( self, effect_modifiers=None, num_quantiles=CausalEstimator.NUM_QUANTILES_TO_DISCRETIZE_CONT_COLS ): """Estimate treatment effect conditioned on given variables. If a numeric effect modifier is provided, it is discretized into quantile bins. If you would like a custom discretization, you can do so yourself: create a new column containing the discretized effect modifier and then include that column's name in the effect_modifier_names argument. :param effect_modifiers: Names of effect modifier variables over which the conditional effects will be estimated. If not provided, defaults to the effect modifiers specified during creation of the CausalEstimator object. :param num_quantiles: The number of quantiles into which a numeric effect modifier variable is discretized. Does not affect any categorical effect modifiers. :returns: A (multi-index) dataframe that provides separate effects for each value of the (discretized) effect modifiers. """ return self.estimator._estimate_conditional_effects( self.estimator._estimate_effect_fn, effect_modifiers, num_quantiles ) def interpret(self, method_name=None, **kwargs): """Interpret the causal estimate. :param method_name: Method used (string) or a list of methods. If None, then the default for the specific estimator is used. :param kwargs:: Optional parameters that are directly passed to the interpreter method. :returns: None """ if method_name is None: method_name = self.estimator.interpret_method method_name_arr = parse_state(method_name) for method in method_name_arr: interpreter = interpreters.get_class_object(method) interpreter(self, **kwargs).interpret() def __str__(self): s = "*** Causal Estimate ***\n" # No estimand was identified (identification failed) if self.target_estimand is None: return "Estimation failed! No relevant identified estimand available for this estimation method." s += "\n## Identified estimand\n{0}".format(self.target_estimand.__str__(only_target_estimand=True)) s += "\n## Realized estimand\n{0}".format(self.realized_estimand_expr) if hasattr(self, "estimator"): s += "\nTarget units: {0}\n".format(self.estimator.target_units_tostr()) s += "\n## Estimate\n" s += "Mean value: {0}\n".format(self.value) s += "" if hasattr(self, "cate_estimates"): s += "Effect estimates: {0}\n".format(self.cate_estimates) if hasattr(self, "estimator"): if self.estimator._significance_test: s += "p-value: {0}\n".format(self.estimator.signif_results_tostr(self.test_stat_significance())) if self.estimator._confidence_intervals: s += "{0}% confidence interval: {1}\n".format( 100 * self.estimator.confidence_level, self.get_confidence_intervals() ) if self.conditional_estimates is not None: s += "### Conditional Estimates\n" s += str(self.conditional_estimates) if self.effect_strength is not None: s += "\n## Effect Strength\n" s += "Change in outcome attributable to treatment: {}\n".format(self.effect_strength["fraction-effect"]) # s += "Variance in outcome explained by treatment: {}\n".format(self.effect_strength["r-squared"]) return s class RealizedEstimand(object): def __init__(self, identified_estimand, estimator_name): self.treatment_variable = identified_estimand.treatment_variable self.outcome_variable = identified_estimand.outcome_variable self.backdoor_variables = identified_estimand.get_backdoor_variables() self.instrumental_variables = identified_estimand.instrumental_variables self.estimand_type = identified_estimand.estimand_type self.estimand_expression = None self.assumptions = None self.estimator_name = estimator_name def update_assumptions(self, estimator_assumptions): self.assumptions = estimator_assumptions def update_estimand_expression(self, estimand_expression): self.estimand_expression = estimand_expression def __str__(self): s = "Realized estimand: {0}\n".format(self.estimator_name) s += "Realized estimand type: {0}\n".format(self.estimand_type) s += "Estimand expression:\n{0}\n".format(sp.pretty(self.estimand_expression)) j = 1 for ass_name, ass_str in self.assumptions.items(): s += "Estimand assumption {0}, {1}: {2}\n".format(j, ass_name, ass_str) j += 1 return s

import logging from collections import namedtuple from typing import Dict, List, Optional, Union import numpy as np import pandas as pd import sympy as sp from sklearn.utils import resample import dowhy.interpreters as interpreters from dowhy import causal_estimators from dowhy.causal_graph import CausalGraph from dowhy.causal_identifier.identified_estimand import IdentifiedEstimand from dowhy.utils.api import parse_state logger = logging.getLogger(__name__) class CausalEstimator: """Base class for an estimator of causal effect. Subclasses implement different estimation methods. All estimation methods are in the package "dowhy.causal_estimators" """ # The default number of simulations for statistical testing DEFAULT_NUMBER_OF_SIMULATIONS_STAT_TEST = 1000 # The default number of simulations to obtain confidence intervals DEFAULT_NUMBER_OF_SIMULATIONS_CI = 100 # The portion of the total size that should be taken each time to find the confidence intervals # 1 is the recommended value # https://ocw.mit.edu/courses/mathematics/18-05-introduction-to-probability-and-statistics-spring-2014/readings/MIT18_05S14_Reading24.pdf # https://projecteuclid.org/download/pdf_1/euclid.ss/1032280214 DEFAULT_SAMPLE_SIZE_FRACTION = 1 # The default Confidence Level DEFAULT_CONFIDENCE_LEVEL = 0.95 # Number of quantiles to discretize continuous columns, for applying groupby NUM_QUANTILES_TO_DISCRETIZE_CONT_COLS = 5 # Prefix to add to temporary categorical variables created after discretization TEMP_CAT_COLUMN_PREFIX = "__categorical__" DEFAULT_NOTIMPLEMENTEDERROR_MSG = "not yet implemented for {0}. If you would this to be implemented in the next version, please raise an issue at https://github.com/microsoft/dowhy/issues" BootstrapEstimates = namedtuple("BootstrapEstimates", ["estimates", "params"]) DEFAULT_INTERPRET_METHOD = ["textual_effect_interpreter"] # std args to be removed from locals() before being passed to args_dict _STD_INIT_ARGS = ("self", "__class__", "args", "kwargs") def __init__( self, data, identified_estimand, treatment, outcome, control_value=0, treatment_value=1, test_significance=False, evaluate_effect_strength=False, confidence_intervals=False, target_units=None, effect_modifiers=None, num_null_simulations=DEFAULT_NUMBER_OF_SIMULATIONS_STAT_TEST, num_simulations=DEFAULT_NUMBER_OF_SIMULATIONS_CI, sample_size_fraction=DEFAULT_SAMPLE_SIZE_FRACTION, confidence_level=DEFAULT_CONFIDENCE_LEVEL, need_conditional_estimates="auto", num_quantiles_to_discretize_cont_cols=NUM_QUANTILES_TO_DISCRETIZE_CONT_COLS, **kwargs, ): """Initializes an estimator with data and names of relevant variables. This method is called from the constructors of its child classes. :param data: data frame containing the data :param identified_estimand: probability expression representing the target identified estimand to estimate. :param treatment: name of the treatment variable :param outcome: name of the outcome variable :param control_value: Value of the treatment in the control group, for effect estimation. If treatment is multi-variate, this can be a list. :param treatment_value: Value of the treatment in the treated group, for effect estimation. If treatment is multi-variate, this can be a list. :param test_significance: Binary flag or a string indicating whether to test significance and by which method. All estimators support test_significance="bootstrap" that estimates a p-value for the obtained estimate using the bootstrap method. Individual estimators can override this to support custom testing methods. The bootstrap method supports an optional parameter, num_null_simulations. If False, no testing is done. If True, significance of the estimate is tested using the custom method if available, otherwise by bootstrap. :param evaluate_effect_strength: (Experimental) whether to evaluate the strength of effect :param confidence_intervals: Binary flag or a string indicating whether the confidence intervals should be computed and which method should be used. All methods support estimation of confidence intervals using the bootstrap method by using the parameter confidence_intervals="bootstrap". The bootstrap method takes in two arguments (num_simulations and sample_size_fraction) that can be optionally specified in the params dictionary. Estimators may also override this to implement their own confidence interval method. If this parameter is False, no confidence intervals are computed. If True, confidence intervals are computed by the estimator's specific method if available, otherwise through bootstrap. :param target_units: The units for which the treatment effect should be estimated. This can be a string for common specifications of target units (namely, "ate", "att" and "atc"). It can also be a lambda function that can be used as an index for the data (pandas DataFrame). Alternatively, it can be a new DataFrame that contains values of the effect_modifiers and effect will be estimated only for this new data. :param effect_modifiers: Variables on which to compute separate effects, or return a heterogeneous effect function. Not all methods support this currently. :param num_null_simulations: The number of simulations for testing the statistical significance of the estimator :param num_simulations: The number of simulations for finding the confidence interval (and/or standard error) for a estimate :param sample_size_fraction: The size of the sample for the bootstrap estimator :param confidence_level: The confidence level of the confidence interval estimate :param need_conditional_estimates: Boolean flag indicating whether conditional estimates should be computed. Defaults to True if there are effect modifiers in the graph :param num_quantiles_to_discretize_cont_cols: The number of quantiles into which a numeric effect modifier is split, to enable estimation of conditional treatment effect over it. :param kwargs: (optional) Additional estimator-specific parameters :returns: an instance of the estimator class. """ self._data = data self._target_estimand = identified_estimand # Currently estimation methods only support univariate treatment and outcome self._treatment_name = treatment self._outcome_name = outcome[0] # assuming one-dimensional outcome self._control_value = control_value self._treatment_value = treatment_value self._significance_test = test_significance self._effect_strength_eval = evaluate_effect_strength self._target_units = target_units self._effect_modifier_names = effect_modifiers self._confidence_intervals = confidence_intervals self._bootstrap_estimates = None # for confidence intervals and std error self._bootstrap_null_estimates = None # for significance test self._effect_modifiers = None self.method_params = kwargs # Setting the default interpret method self.interpret_method = CausalEstimator.DEFAULT_INTERPRET_METHOD self.logger = logging.getLogger(__name__) # Setting treatment and outcome values if self._data is not None: self._treatment = self._data[self._treatment_name] self._outcome = self._data[self._outcome_name] if self._effect_modifier_names: # only add the observed nodes self._effect_modifier_names = [ cname for cname in self._effect_modifier_names if cname in self._data.columns ] if len(self._effect_modifier_names) > 0: self._effect_modifiers = self._data[self._effect_modifier_names] self._effect_modifiers = pd.get_dummies(self._effect_modifiers, drop_first=True) self.logger.debug("Effect modifiers: " + ",".join(self._effect_modifier_names)) else: self._effect_modifier_names = None # Check if some parameters were set, otherwise set to default values self.num_null_simulations = num_null_simulations self.num_simulations = num_simulations self.sample_size_fraction = sample_size_fraction self.confidence_level = confidence_level self.num_quantiles_to_discretize_cont_cols = num_quantiles_to_discretize_cont_cols # Estimate conditional estimates by default self.need_conditional_estimates = ( need_conditional_estimates if need_conditional_estimates != "auto" else bool(self._effect_modifier_names) ) @staticmethod def get_estimator_object(new_data, identified_estimand, estimate): """Create a new estimator of the same type as the one passed in the estimate argument. Creates a new object with new_data and the identified_estimand :param new_data: np.ndarray, pd.Series, pd.DataFrame The newly assigned data on which the estimator should run :param identified_estimand: IdentifiedEstimand An instance of the identified estimand class that provides the information with respect to which causal pathways are employed when the treatment effects the outcome :param estimate: CausalEstimate It is an already existing estimate whose properties we wish to replicate :returns: An instance of the same estimator class that had generated the given estimate. """ estimator_class = estimate.params["estimator_class"] new_estimator = estimator_class( new_data, identified_estimand, identified_estimand.treatment_variable, identified_estimand.outcome_variable, # names of treatment and outcome control_value=estimate.control_value, treatment_value=estimate.treatment_value, test_significance=False, evaluate_effect_strength=False, confidence_intervals=estimate.params["confidence_intervals"], target_units=estimate.params["target_units"], effect_modifiers=estimate.params["effect_modifiers"], **estimate.params["method_params"] if estimate.params["method_params"] is not None else {}, ) return new_estimator def _estimate_effect(self): """This method is to be overriden by the child classes, so that they can run the estimation technique of their choice""" raise NotImplementedError( ("Main estimation method is " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG).format(self.__class__) ) def estimate_effect(self): """Base estimation method that calls the estimate_effect method of its calling subclass. Can optionally also test significance and estimate effect strength for any returned estimate. :param self: object instance of class Estimator :returns: A CausalEstimate instance that contains point estimates of average and conditional effects. Based on the parameters provided, it optionally includes confidence intervals, standard errors,statistical significance and other statistical parameters. """ est = self._estimate_effect() est.add_estimator(self) if self._significance_test: self.test_significance(est.value, method=self._significance_test) if self._confidence_intervals: self.estimate_confidence_intervals( est.value, confidence_level=self.confidence_level, method=self._confidence_intervals ) if self._effect_strength_eval: effect_strength_dict = self.evaluate_effect_strength(est) est.add_effect_strength(effect_strength_dict) return est def estimate_effect_naive(self): # TODO Only works for binary treatment df_withtreatment = self._data.loc[self._data[self._treatment_name] == 1] df_notreatment = self._data.loc[self._data[self._treatment_name] == 0] est = np.mean(df_withtreatment[self._outcome_name]) - np.mean(df_notreatment[self._outcome_name]) return CausalEstimate(est, None, None, control_value=0, treatment_value=1) def _estimate_effect_fn(self, data_df): """Function used in conditional effect estimation. This function is to be overridden by each child estimator. The overridden function should take in a dataframe as input and return the estimate for that data. """ raise NotImplementedError( ("Conditional treatment effects are " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG).format( self.__class__ ) ) def _estimate_conditional_effects(self, estimate_effect_fn, effect_modifier_names=None, num_quantiles=None): """Estimate conditional treatment effects. Common method for all estimators that utilizes a specific estimate_effect_fn implemented by each child estimator. If a numeric effect modifier is provided, it is discretized into quantile bins. If you would like a custom discretization, you can do so yourself: create a new column containing the discretized effect modifier and then include that column's name in the effect_modifier_names argument. :param estimate_effect_fn: Function that has a single parameter (a data frame) and returns the treatment effect estimate on that data. :param effect_modifier_names: Names of effect modifier variables over which the conditional effects will be estimated. If not provided, defaults to the effect modifiers specified during creation of the CausalEstimator object. :param num_quantiles: The number of quantiles into which a numeric effect modifier variable is discretized. Does not affect any categorical effect modifiers. :returns: A (multi-index) dataframe that provides separate effects for each value of the (discretized) effect modifiers. """ # Defaulting to class default values if parameters are not provided if effect_modifier_names is None: effect_modifier_names = self._effect_modifier_names if num_quantiles is None: num_quantiles = self.num_quantiles_to_discretize_cont_cols # Checking that there is at least one effect modifier if not effect_modifier_names: raise ValueError("At least one effect modifier should be specified to compute conditional effects.") # Making sure that effect_modifier_names is a list effect_modifier_names = parse_state(effect_modifier_names) if not all(em in self._effect_modifier_names for em in effect_modifier_names): self.logger.warn( "At least one of the provided effect modifiers was not included while fitting the estimator. You may get incorrect results. To resolve, fit the estimator again by providing the updated effect modifiers in estimate_effect()." ) # Making a copy since we are going to be changing effect modifier names effect_modifier_names = effect_modifier_names.copy() prefix = CausalEstimator.TEMP_CAT_COLUMN_PREFIX # For every numeric effect modifier, adding a temp categorical column for i in range(len(effect_modifier_names)): em = effect_modifier_names[i] if pd.api.types.is_numeric_dtype(self._data[em].dtypes): self._data[prefix + str(em)] = pd.qcut(self._data[em], num_quantiles, duplicates="drop") effect_modifier_names[i] = prefix + str(em) # Grouping by effect modifiers and computing effect separately by_effect_mods = self._data.groupby(effect_modifier_names) cond_est_fn = lambda x: self._do(self._treatment_value, x) - self._do(self._control_value, x) conditional_estimates = by_effect_mods.apply(estimate_effect_fn) # Deleting the temporary categorical columns for em in effect_modifier_names: if em.startswith(prefix): self._data.pop(em) return conditional_estimates def _do(self, x, data_df=None): raise NotImplementedError( ("Do-operator is " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG).format(self.__class__) ) def do(self, x, data_df=None): """Method that implements the do-operator. Given a value x for the treatment, returns the expected value of the outcome when the treatment is intervened to a value x. :param x: Value of the treatment :param data_df: Data on which the do-operator is to be applied. :returns: Value of the outcome when treatment is intervened/set to x. """ est = self._do(x, data_df) return est def construct_symbolic_estimator(self, estimand): raise NotImplementedError(("Symbolic estimator string is ").format(self.__class__)) def _generate_bootstrap_estimates(self, num_bootstrap_simulations, sample_size_fraction): """Helper function to generate causal estimates over bootstrapped samples. :param num_bootstrap_simulations: Number of simulations for the bootstrap method. :param sample_size_fraction: Fraction of the dataset to be resampled. :returns: A collections.namedtuple containing a list of bootstrapped estimates and a dictionary containing parameters used for the bootstrap. """ # The array that stores the results of all estimations simulation_results = np.zeros(num_bootstrap_simulations) # Find the sample size the proportion with the population size sample_size = int(sample_size_fraction * len(self._data)) if sample_size > len(self._data): self.logger.warning("WARN: The sample size is greater than the data being sampled") self.logger.info("INFO: The sample size: {}".format(sample_size)) self.logger.info("INFO: The number of simulations: {}".format(num_bootstrap_simulations)) # Perform the set number of simulations for index in range(num_bootstrap_simulations): new_data = resample(self._data, n_samples=sample_size) new_estimator = type(self)( new_data, self._target_estimand, self._target_estimand.treatment_variable, self._target_estimand.outcome_variable, # names of treatment and outcome treatment_value=self._treatment_value, control_value=self._control_value, test_significance=False, evaluate_effect_strength=False, confidence_intervals=False, target_units=self._target_units, effect_modifiers=self._effect_modifier_names, **self.method_params, ) new_effect = new_estimator.estimate_effect() simulation_results[index] = new_effect.value estimates = CausalEstimator.BootstrapEstimates( simulation_results, {"num_simulations": num_bootstrap_simulations, "sample_size_fraction": sample_size_fraction}, ) return estimates def _estimate_confidence_intervals_with_bootstrap( self, estimate_value, confidence_level=None, num_simulations=None, sample_size_fraction=None ): """ Method to compute confidence interval using bootstrapped sampling. :param estimate_value: obtained estimate's value :param confidence_level: The level for which to compute CI (e.g., 95% confidence level translates to confidence_level=0.95) :param num_simulations: The number of simulations to be performed to get the bootstrap confidence intervals. :param sample_size_fraction: The fraction of the dataset to be resampled. :returns: confidence interval at the specified level. For more details on bootstrap or resampling statistics, refer to the following links: https://ocw.mit.edu/courses/mathematics/18-05-introduction-to-probability-and-statistics-spring-2014/readings/MIT18_05S14_Reading24.pdf https://projecteuclid.org/download/pdf_1/euclid.ss/1032280214 """ # Using class default parameters if not specified if num_simulations is None: num_simulations = self.num_simulations if sample_size_fraction is None: sample_size_fraction = self.sample_size_fraction # Checking if bootstrap_estimates are already computed if self._bootstrap_estimates is None: self._bootstrap_estimates = self._generate_bootstrap_estimates(num_simulations, sample_size_fraction) elif CausalEstimator.is_bootstrap_parameter_changed(self._bootstrap_estimates.params, locals()): # Checked if any parameter is changed from the previous std error estimate self._bootstrap_estimates = self._generate_bootstrap_estimates(num_simulations, sample_size_fraction) # Now use the data obtained from the simulations to get the value of the confidence estimates bootstrap_estimates = self._bootstrap_estimates.estimates # Get the variations of each bootstrap estimate and sort bootstrap_variations = [bootstrap_estimate - estimate_value for bootstrap_estimate in bootstrap_estimates] sorted_bootstrap_variations = np.sort(bootstrap_variations) # Now we take the (1- p)th and the (p)th variations, where p is the chosen confidence level upper_bound_index = int((1 - confidence_level) * len(sorted_bootstrap_variations)) lower_bound_index = int(confidence_level * len(sorted_bootstrap_variations)) # Get the lower and upper bounds by subtracting the variations from the estimate lower_bound = estimate_value - sorted_bootstrap_variations[lower_bound_index] upper_bound = estimate_value - sorted_bootstrap_variations[upper_bound_index] return lower_bound, upper_bound def _estimate_confidence_intervals(self, confidence_level=None, method=None, **kwargs): """ This method is to be overriden by the child classes, so that they can run a confidence interval estimation method suited to the specific causal estimator. """ raise NotImplementedError( ( "This method for estimating confidence intervals is " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG + " Meanwhile, you can try the bootstrap method (method='bootstrap') to estimate confidence intervals." ).format(self.__class__) ) def estimate_confidence_intervals(self, estimate_value, confidence_level=None, method=None, **kwargs): """Find the confidence intervals corresponding to any estimator By default, this is done with the help of bootstrapped confidence intervals but can be overridden if the specific estimator implements other methods of estimating confidence intervals. If the method provided is not bootstrap, this function calls the implementation of the specific estimator. :param estimate_value: obtained estimate's value :param method: Method for estimating confidence intervals. :param confidence_level: The confidence level of the confidence intervals of the estimate. :param kwargs: Other optional args to be passed to the CI method. :returns: The obtained confidence interval. """ if method is None: if self._confidence_intervals: method = self._confidence_intervals # this is either True or methodname else: method = "default" confidence_intervals = None if confidence_level is None: confidence_level = self.confidence_level if method == "default" or method is True: # user has not provided any method try: confidence_intervals = self._estimate_confidence_intervals(confidence_level, method=method, **kwargs) except NotImplementedError: confidence_intervals = self._estimate_confidence_intervals_with_bootstrap( estimate_value, confidence_level, **kwargs ) else: if method == "bootstrap": confidence_intervals = self._estimate_confidence_intervals_with_bootstrap( estimate_value, confidence_level, **kwargs ) else: confidence_intervals = self._estimate_confidence_intervals(confidence_level, method=method, **kwargs) return confidence_intervals def _estimate_std_error_with_bootstrap(self, num_simulations=None, sample_size_fraction=None): """Compute standard error using the bootstrap method. Standard error and confidence intervals use the same parameter num_simulations for the number of bootstrap simulations. :param num_simulations: Number of bootstrapped samples. :param sample_size_fraction: Fraction of data to be resampled. :returns: Standard error of the obtained estimate. """ # Use existing params, if new user defined params are not present if num_simulations is None: num_simulations = self.num_simulations if sample_size_fraction is None: sample_size_fraction = self.sample_size_fraction # Checking if bootstrap_estimates are already computed if self._bootstrap_estimates is None: self._bootstrap_estimates = self._generate_bootstrap_estimates(num_simulations, sample_size_fraction) elif CausalEstimator.is_bootstrap_parameter_changed(self._bootstrap_estimates.params, locals()): # Check if any parameter is changed from the previous std error estimate self._bootstrap_estimates = self._generate_bootstrap_estimates(num_simulations, sample_size_fraction) std_error = np.std(self._bootstrap_estimates.estimates) return std_error def _estimate_std_error(self, method=None, **kwargs): """ This method is to be overriden by the child classes, so that they can run a standard error estimation method suited to the specific causal estimator. """ raise NotImplementedError( ( "This method for estimating standard errors is " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG + " Meanwhile, you can try the bootstrap method (method='bootstrap') to estimate standard errors." ).format(self.__class__) ) def estimate_std_error(self, method=None, **kwargs): """Compute standard error of an obtained causal estimate. :param method: Method for computing the standard error. :param kwargs: Other optional parameters to be passed to the estimating method. :returns: Standard error of the causal estimate. """ if method is None: if self._confidence_intervals: method = self._confidence_intervals else: method = "default" std_error = None if method == "default" or method is True: # user has not provided any method try: std_error = self._estimate_std_error(method, **kwargs) except NotImplementedError: std_error = self._estimate_std_error_with_bootstrap(**kwargs) else: if method == "bootstrap": std_error = self._estimate_std_error_with_bootstrap(**kwargs) else: std_error = self._estimate_std_error(method, **kwargs) return std_error def _test_significance_with_bootstrap(self, estimate_value, num_null_simulations=None): """Test statistical significance of an estimate using the bootstrap method. :param estimate_value: Obtained estimate's value :param num_null_simulations: Number of simulations for the null hypothesis :returns: p-value of the statistical significance test. """ # Use existing params, if new user defined params are not present if num_null_simulations is None: num_null_simulations = self.num_null_simulations do_retest = self._bootstrap_null_estimates is None or CausalEstimator.is_bootstrap_parameter_changed( self._bootstrap_null_estimates.params, locals() ) if do_retest: null_estimates = np.zeros(num_null_simulations) for i in range(num_null_simulations): new_outcome = np.random.permutation(self._outcome) new_data = self._data.assign(dummy_outcome=new_outcome) # self._outcome = self._data["dummy_outcome"] new_estimator = type(self)( new_data, self._target_estimand, self._target_estimand.treatment_variable, ("dummy_outcome",), test_significance=False, evaluate_effect_strength=False, confidence_intervals=False, target_units=self._target_units, effect_modifiers=self._effect_modifier_names, **self.method_params, ) new_effect = new_estimator.estimate_effect() null_estimates[i] = new_effect.value self._bootstrap_null_estimates = CausalEstimator.BootstrapEstimates( null_estimates, {"num_null_simulations": num_null_simulations, "sample_size_fraction": 1} ) # Processing the null hypothesis estimates sorted_null_estimates = np.sort(self._bootstrap_null_estimates.estimates) self.logger.debug("Null estimates: {0}".format(sorted_null_estimates)) median_estimate = sorted_null_estimates[int(num_null_simulations / 2)] # Doing a two-sided test if estimate_value > median_estimate: # Being conservative with the p-value reported estimate_index = np.searchsorted(sorted_null_estimates, estimate_value, side="left") p_value = 1 - (estimate_index / num_null_simulations) if estimate_value <= median_estimate: # Being conservative with the p-value reported estimate_index = np.searchsorted(sorted_null_estimates, estimate_value, side="right") p_value = estimate_index / num_null_simulations # If the estimate_index is 0, it depends on the number of simulations if p_value == 0: p_value = (0, 1 / len(sorted_null_estimates)) # a tuple determining the range. elif p_value == 1: p_value = (1 - 1 / len(sorted_null_estimates), 1) signif_dict = {"p_value": p_value} return signif_dict def _test_significance(self, estimate_value, method=None, **kwargs): """ This method is to be overriden by the child classes, so that they can run a significance test suited to the specific causal estimator. """ raise NotImplementedError( ( "This method for testing statistical significance is " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG + " Meanwhile, you can try the bootstrap method (method='bootstrap') to test statistical significance." ).format(self.__class__) ) def test_significance(self, estimate_value, method=None, **kwargs): """Test statistical significance of obtained estimate. By default, uses resampling to create a non-parametric significance test. A general procedure. Individual child estimators can implement different methods. If the method name is different from "bootstrap", this function calls the implementation of the child estimator. :param self: object instance of class Estimator :param estimate_value: obtained estimate's value :param method: Method for checking statistical significance :returns: p-value from the significance test """ if method is None: if self._significance_test: method = self._significance_test # this is either True or methodname else: method = "default" signif_dict = None if method == "default" or method is True: # user has not provided any method try: signif_dict = self._test_significance(estimate_value, method, **kwargs) except NotImplementedError: signif_dict = self._test_significance_with_bootstrap(estimate_value, **kwargs) else: if method == "bootstrap": signif_dict = self._test_significance_with_bootstrap(estimate_value, **kwargs) else: signif_dict = self._test_significance(estimate_value, method, **kwargs) return signif_dict def evaluate_effect_strength(self, estimate): fraction_effect_explained = self._evaluate_effect_strength(estimate, method="fraction-effect") # Need to test r-squared before supporting # effect_r_squared = self._evaluate_effect_strength(estimate, method="r-squared") strength_dict = { "fraction-effect": fraction_effect_explained # 'r-squared': effect_r_squared } return strength_dict def _evaluate_effect_strength(self, estimate, method="fraction-effect"): supported_methods = ["fraction-effect"] if method not in supported_methods: raise NotImplementedError("This method is not supported for evaluating effect strength") if method == "fraction-effect": naive_obs_estimate = self.estimate_effect_naive() self.logger.debug(estimate.value, naive_obs_estimate.value) fraction_effect_explained = estimate.value / naive_obs_estimate.value return fraction_effect_explained # elif method == "r-squared": # outcome_mean = np.mean(self._outcome) # total_variance = np.sum(np.square(self._outcome - outcome_mean)) # Assuming a linear model with one variable: the treatment # Currently only works for continuous y # causal_model = outcome_mean + estimate.value*self._treatment # squared_residual = np.sum(np.square(self._outcome - causal_model)) # r_squared = 1 - (squared_residual/total_variance) # return r_squared else: return None def update_input(self, treatment_value, control_value, target_units): self._control_value = control_value self._treatment_value = treatment_value self._target_units = target_units @staticmethod def is_bootstrap_parameter_changed(bootstrap_estimates_params, given_params): """Check whether parameters of the bootstrap have changed. This is an efficiency method that checks if fresh resampling of the bootstrap samples is required. Returns True if parameters have changed and resampling should be done again. :param bootstrap_estimates_params: A dictionary of parameters for the current bootstrap samples :param given_params: A dictionary of parameters passed by the user :returns: A binary flag denoting whether the parameters are different. """ is_any_parameter_changed = False for prm, val in bootstrap_estimates_params.items(): given_val = given_params.get(prm, None) if given_val is not None and given_val != val: is_any_parameter_changed = True break return is_any_parameter_changed def target_units_tostr(self): s = "" if type(self._target_units) is str: s += self._target_units elif callable(self._target_units): s += "Data subset defined by a function" elif isinstance(self._target_units, pd.DataFrame): s += "Data subset provided as a data frame" return s def signif_results_tostr(self, signif_results): s = "" pval = signif_results["p_value"] if type(pval) is tuple: s += "[{0}, {1}]".format(pval[0], pval[1]) else: s += "{0}".format(pval) return s def estimate_effect( treatment: Union[str, List[str]], outcome: Union[str, List[str]], identified_estimand: IdentifiedEstimand, identifier_name: str, method: CausalEstimator, control_value: int = 0, treatment_value: int = 1, test_significance: Optional[bool] = None, evaluate_effect_strength: bool = False, confidence_intervals: bool = False, target_units: str = "ate", effect_modifiers: List[str] = [], fit_estimator: bool = True, method_params: Optional[Dict] = None, ): """Estimate the identified causal effect. Currently requires an explicit method name to be specified. Method names follow the convention of identification method followed by the specific estimation method: "[backdoor/iv].estimation_method_name". Following methods are supported. * Propensity Score Matching: "backdoor.propensity_score_matching" * Propensity Score Stratification: "backdoor.propensity_score_stratification" * Propensity Score-based Inverse Weighting: "backdoor.propensity_score_weighting" * Linear Regression: "backdoor.linear_regression" * Generalized Linear Models (e.g., logistic regression): "backdoor.generalized_linear_model" * Instrumental Variables: "iv.instrumental_variable" * Regression Discontinuity: "iv.regression_discontinuity" In addition, you can directly call any of the EconML estimation methods. The convention is "backdoor.econml.path-to-estimator-class". For example, for the double machine learning estimator ("DML" class) that is located inside "dml" module of EconML, you can use the method name, "backdoor.econml.dml.DML". CausalML estimators can also be called. See `this demo notebook <https://py-why.github.io/dowhy/example_notebooks/dowhy-conditional-treatment-effects.html>`_. :param treatment: Name of the treatment :param outcome: Name of the outcome :param identified_estimand: a probability expression that represents the effect to be estimated. Output of CausalModel.identify_effect method :param method_name: name of the estimation method to be used. :param control_value: Value of the treatment in the control group, for effect estimation. If treatment is multi-variate, this can be a list. :param treatment_value: Value of the treatment in the treated group, for effect estimation. If treatment is multi-variate, this can be a list. :param test_significance: Binary flag on whether to additionally do a statistical signficance test for the estimate. :param evaluate_effect_strength: (Experimental) Binary flag on whether to estimate the relative strength of the treatment's effect. This measure can be used to compare different treatments for the same outcome (by running this method with different treatments sequentially). :param confidence_intervals: (Experimental) Binary flag indicating whether confidence intervals should be computed. :param target_units: (Experimental) The units for which the treatment effect should be estimated. This can be of three types. (1) a string for common specifications of target units (namely, "ate", "att" and "atc"), (2) a lambda function that can be used as an index for the data (pandas DataFrame), or (3) a new DataFrame that contains values of the effect_modifiers and effect will be estimated only for this new data. :param effect_modifiers: Names of effect modifier variables can be (optionally) specified here too, since they do not affect identification. If None, the effect_modifiers from the CausalModel are used. :param fit_estimator: Boolean flag on whether to fit the estimator. Setting it to False is useful to estimate the effect on new data using a previously fitted estimator. :param method_params: Dictionary containing any method-specific parameters. These are passed directly to the estimating method. See the docs for each estimation method for allowed method-specific params. :returns: An instance of the CausalEstimate class, containing the causal effect estimate and other method-dependent information """ treatment = parse_state(treatment) outcome = parse_state(outcome) causal_estimator_class = method.__class__ identified_estimand.set_identifier_method(identifier_name) if identified_estimand.no_directed_path: logger.warning("No directed path from {0} to {1}.".format(treatment, outcome)) return CausalEstimate( 0, identified_estimand, None, control_value=control_value, treatment_value=treatment_value ) # Check if estimator's target estimand is identified elif identified_estimand.estimands[identifier_name] is None: logger.error("No valid identified estimand available.") return CausalEstimate(None, None, None, control_value=control_value, treatment_value=treatment_value) method.update_input(treatment_value, control_value, target_units) estimate = method.estimate_effect() # Store parameters inside estimate object for refutation methods # TODO: This add_params needs to move to the estimator class # inside estimate_effect and estimate_conditional_effect estimate.add_params( estimand_type=identified_estimand.estimand_type, estimator_class=causal_estimator_class, test_significance=test_significance, evaluate_effect_strength=evaluate_effect_strength, confidence_intervals=confidence_intervals, target_units=target_units, effect_modifiers=effect_modifiers, method_params=method_params, ) return estimate class CausalEstimate: """Class for the estimate object that every causal estimator returns""" def __init__( self, estimate, target_estimand, realized_estimand_expr, control_value, treatment_value, conditional_estimates=None, **kwargs, ): self.value = estimate self.target_estimand = target_estimand self.realized_estimand_expr = realized_estimand_expr self.control_value = control_value self.treatment_value = treatment_value self.conditional_estimates = conditional_estimates self.params = kwargs if self.params is not None: for key, value in self.params.items(): setattr(self, key, value) self.effect_strength = None def add_estimator(self, estimator_instance): self.estimator = estimator_instance def add_effect_strength(self, strength_dict): self.effect_strength = strength_dict def add_params(self, **kwargs): self.params.update(kwargs) def get_confidence_intervals(self, confidence_level=None, method=None, **kwargs): """Get confidence intervals of the obtained estimate. By default, this is done with the help of bootstrapped confidence intervals but can be overridden if the specific estimator implements other methods of estimating confidence intervals. If the method provided is not bootstrap, this function calls the implementation of the specific estimator. :param method: Method for estimating confidence intervals. :param confidence_level: The confidence level of the confidence intervals of the estimate. :param kwargs: Other optional args to be passed to the CI method. :returns: The obtained confidence interval. """ confidence_intervals = self.estimator.estimate_confidence_intervals( estimate_value=self.value, confidence_level=confidence_level, method=method, **kwargs ) return confidence_intervals def get_standard_error(self, method=None, **kwargs): """Get standard error of the obtained estimate. By default, this is done with the help of bootstrapped standard errors but can be overridden if the specific estimator implements other methods of estimating standard error. If the method provided is not bootstrap, this function calls the implementation of the specific estimator. :param method: Method for computing the standard error. :param kwargs: Other optional parameters to be passed to the estimating method. :returns: Standard error of the causal estimate. """ std_error = self.estimator.estimate_std_error(method=method, **kwargs) return std_error def test_stat_significance(self, method=None, **kwargs): """Test statistical significance of the estimate obtained. By default, uses resampling to create a non-parametric significance test. Individual child estimators can implement different methods. If the method name is different from "bootstrap", this function calls the implementation of the child estimator. :param method: Method for checking statistical significance :param kwargs: Other optional parameters to be passed to the estimating method. :returns: p-value from the significance test """ signif_results = self.estimator.test_significance(self.value, method=method, **kwargs) return {"p_value": signif_results["p_value"]} def estimate_conditional_effects( self, effect_modifiers=None, num_quantiles=CausalEstimator.NUM_QUANTILES_TO_DISCRETIZE_CONT_COLS ): """Estimate treatment effect conditioned on given variables. If a numeric effect modifier is provided, it is discretized into quantile bins. If you would like a custom discretization, you can do so yourself: create a new column containing the discretized effect modifier and then include that column's name in the effect_modifier_names argument. :param effect_modifiers: Names of effect modifier variables over which the conditional effects will be estimated. If not provided, defaults to the effect modifiers specified during creation of the CausalEstimator object. :param num_quantiles: The number of quantiles into which a numeric effect modifier variable is discretized. Does not affect any categorical effect modifiers. :returns: A (multi-index) dataframe that provides separate effects for each value of the (discretized) effect modifiers. """ return self.estimator._estimate_conditional_effects( self.estimator._estimate_effect_fn, effect_modifiers, num_quantiles ) def interpret(self, method_name=None, **kwargs): """Interpret the causal estimate. :param method_name: Method used (string) or a list of methods. If None, then the default for the specific estimator is used. :param kwargs:: Optional parameters that are directly passed to the interpreter method. :returns: None """ if method_name is None: method_name = self.estimator.interpret_method method_name_arr = parse_state(method_name) for method in method_name_arr: interpreter = interpreters.get_class_object(method) interpreter(self, **kwargs).interpret() def __str__(self): s = "*** Causal Estimate ***\n" # No estimand was identified (identification failed) if self.target_estimand is None: return "Estimation failed! No relevant identified estimand available for this estimation method." s += "\n## Identified estimand\n{0}".format(self.target_estimand.__str__(only_target_estimand=True)) s += "\n## Realized estimand\n{0}".format(self.realized_estimand_expr) if hasattr(self, "estimator"): s += "\nTarget units: {0}\n".format(self.estimator.target_units_tostr()) s += "\n## Estimate\n" s += "Mean value: {0}\n".format(self.value) s += "" if hasattr(self, "cate_estimates"): s += "Effect estimates: {0}\n".format(self.cate_estimates) if hasattr(self, "estimator"): if self.estimator._significance_test: s += "p-value: {0}\n".format(self.estimator.signif_results_tostr(self.test_stat_significance())) if self.estimator._confidence_intervals: s += "{0}% confidence interval: {1}\n".format( 100 * self.estimator.confidence_level, self.get_confidence_intervals() ) if self.conditional_estimates is not None: s += "### Conditional Estimates\n" s += str(self.conditional_estimates) if self.effect_strength is not None: s += "\n## Effect Strength\n" s += "Change in outcome attributable to treatment: {}\n".format(self.effect_strength["fraction-effect"]) # s += "Variance in outcome explained by treatment: {}\n".format(self.effect_strength["r-squared"]) return s class RealizedEstimand(object): def __init__(self, identified_estimand, estimator_name): self.treatment_variable = identified_estimand.treatment_variable self.outcome_variable = identified_estimand.outcome_variable self.backdoor_variables = identified_estimand.get_backdoor_variables() self.instrumental_variables = identified_estimand.instrumental_variables self.estimand_type = identified_estimand.estimand_type self.estimand_expression = None self.assumptions = None self.estimator_name = estimator_name def update_assumptions(self, estimator_assumptions): self.assumptions = estimator_assumptions def update_estimand_expression(self, estimand_expression): self.estimand_expression = estimand_expression def __str__(self): s = "Realized estimand: {0}\n".format(self.estimator_name) s += "Realized estimand type: {0}\n".format(self.estimand_type) s += "Estimand expression:\n{0}\n".format(sp.pretty(self.estimand_expression)) j = 1 for ass_name, ass_str in self.assumptions.items(): s += "Estimand assumption {0}, {1}: {2}\n".format(j, ass_name, ass_str) j += 1 return s

andresmor-ms

2044d216c322a4b32c6eadce5da7d83463f19c2f

05bfa49dacf0061988c96c6f3e3756219df5422a

I'll add this in a future PR when I start to refactor all the estimator objects

andresmor-ms

py-why/dowhy

Functional api/estimate effect function

#### Estimate Effect function * Refactors the estimate effect into a separate function to keep backwards compatibility #### TODO (future PRs): * Add `fit(...)` method to estimators - Move data related parameters from the constructor to the `fit(...)` method * Refactor code to avoid `**kwargs` in `__init__(...)` constructors

2022-10-18 15:49:21+00:00

2022-10-25 17:02:02+00:00

dowhy/causal_estimator.py

import logging from collections import namedtuple import numpy as np import pandas as pd import sympy as sp from sklearn.utils import resample import dowhy.interpreters as interpreters from dowhy.utils.api import parse_state class CausalEstimator: """Base class for an estimator of causal effect. Subclasses implement different estimation methods. All estimation methods are in the package "dowhy.causal_estimators" """ # The default number of simulations for statistical testing DEFAULT_NUMBER_OF_SIMULATIONS_STAT_TEST = 1000 # The default number of simulations to obtain confidence intervals DEFAULT_NUMBER_OF_SIMULATIONS_CI = 100 # The portion of the total size that should be taken each time to find the confidence intervals # 1 is the recommended value # https://ocw.mit.edu/courses/mathematics/18-05-introduction-to-probability-and-statistics-spring-2014/readings/MIT18_05S14_Reading24.pdf # https://projecteuclid.org/download/pdf_1/euclid.ss/1032280214 DEFAULT_SAMPLE_SIZE_FRACTION = 1 # The default Confidence Level DEFAULT_CONFIDENCE_LEVEL = 0.95 # Number of quantiles to discretize continuous columns, for applying groupby NUM_QUANTILES_TO_DISCRETIZE_CONT_COLS = 5 # Prefix to add to temporary categorical variables created after discretization TEMP_CAT_COLUMN_PREFIX = "__categorical__" DEFAULT_NOTIMPLEMENTEDERROR_MSG = "not yet implemented for {0}. If you would this to be implemented in the next version, please raise an issue at https://github.com/microsoft/dowhy/issues" BootstrapEstimates = namedtuple("BootstrapEstimates", ["estimates", "params"]) DEFAULT_INTERPRET_METHOD = ["textual_effect_interpreter"] # std args to be removed from locals() before being passed to args_dict _STD_INIT_ARGS = ("self", "__class__", "args", "kwargs") def __init__( self, data, identified_estimand, treatment, outcome, control_value=0, treatment_value=1, test_significance=False, evaluate_effect_strength=False, confidence_intervals=False, target_units=None, effect_modifiers=None, num_null_simulations=DEFAULT_NUMBER_OF_SIMULATIONS_STAT_TEST, num_simulations=DEFAULT_NUMBER_OF_SIMULATIONS_CI, sample_size_fraction=DEFAULT_SAMPLE_SIZE_FRACTION, confidence_level=DEFAULT_CONFIDENCE_LEVEL, need_conditional_estimates="auto", num_quantiles_to_discretize_cont_cols=NUM_QUANTILES_TO_DISCRETIZE_CONT_COLS, **kwargs, ): """Initializes an estimator with data and names of relevant variables. This method is called from the constructors of its child classes. :param data: data frame containing the data :param identified_estimand: probability expression representing the target identified estimand to estimate. :param treatment: name of the treatment variable :param outcome: name of the outcome variable :param control_value: Value of the treatment in the control group, for effect estimation. If treatment is multi-variate, this can be a list. :param treatment_value: Value of the treatment in the treated group, for effect estimation. If treatment is multi-variate, this can be a list. :param test_significance: Binary flag or a string indicating whether to test significance and by which method. All estimators support test_significance="bootstrap" that estimates a p-value for the obtained estimate using the bootstrap method. Individual estimators can override this to support custom testing methods. The bootstrap method supports an optional parameter, num_null_simulations. If False, no testing is done. If True, significance of the estimate is tested using the custom method if available, otherwise by bootstrap. :param evaluate_effect_strength: (Experimental) whether to evaluate the strength of effect :param confidence_intervals: Binary flag or a string indicating whether the confidence intervals should be computed and which method should be used. All methods support estimation of confidence intervals using the bootstrap method by using the parameter confidence_intervals="bootstrap". The bootstrap method takes in two arguments (num_simulations and sample_size_fraction) that can be optionally specified in the params dictionary. Estimators may also override this to implement their own confidence interval method. If this parameter is False, no confidence intervals are computed. If True, confidence intervals are computed by the estimator's specific method if available, otherwise through bootstrap. :param target_units: The units for which the treatment effect should be estimated. This can be a string for common specifications of target units (namely, "ate", "att" and "atc"). It can also be a lambda function that can be used as an index for the data (pandas DataFrame). Alternatively, it can be a new DataFrame that contains values of the effect_modifiers and effect will be estimated only for this new data. :param effect_modifiers: Variables on which to compute separate effects, or return a heterogeneous effect function. Not all methods support this currently. :param num_null_simulations: The number of simulations for testing the statistical significance of the estimator :param num_simulations: The number of simulations for finding the confidence interval (and/or standard error) for a estimate :param sample_size_fraction: The size of the sample for the bootstrap estimator :param confidence_level: The confidence level of the confidence interval estimate :param need_conditional_estimates: Boolean flag indicating whether conditional estimates should be computed. Defaults to True if there are effect modifiers in the graph :param num_quantiles_to_discretize_cont_cols: The number of quantiles into which a numeric effect modifier is split, to enable estimation of conditional treatment effect over it. :param kwargs: (optional) Additional estimator-specific parameters :returns: an instance of the estimator class. """ self._data = data self._target_estimand = identified_estimand # Currently estimation methods only support univariate treatment and outcome self._treatment_name = treatment self._outcome_name = outcome[0] # assuming one-dimensional outcome self._control_value = control_value self._treatment_value = treatment_value self._significance_test = test_significance self._effect_strength_eval = evaluate_effect_strength self._target_units = target_units self._effect_modifier_names = effect_modifiers self._confidence_intervals = confidence_intervals self._bootstrap_estimates = None # for confidence intervals and std error self._bootstrap_null_estimates = None # for significance test self._effect_modifiers = None self.method_params = kwargs # Setting the default interpret method self.interpret_method = CausalEstimator.DEFAULT_INTERPRET_METHOD self.logger = logging.getLogger(__name__) # Setting treatment and outcome values if self._data is not None: self._treatment = self._data[self._treatment_name] self._outcome = self._data[self._outcome_name] # Now saving the effect modifiers if self._effect_modifier_names: # only add the observed nodes self._effect_modifier_names = [ cname for cname in self._effect_modifier_names if cname in self._data.columns ] if len(self._effect_modifier_names) > 0: self._effect_modifiers = self._data[self._effect_modifier_names] self._effect_modifiers = pd.get_dummies(self._effect_modifiers, drop_first=True) self.logger.debug("Effect modifiers: " + ",".join(self._effect_modifier_names)) else: self._effect_modifier_names = None # Check if some parameters were set, otherwise set to default values self.num_null_simulations = num_null_simulations self.num_simulations = num_simulations self.sample_size_fraction = sample_size_fraction self.confidence_level = confidence_level self.num_quantiles_to_discretize_cont_cols = num_quantiles_to_discretize_cont_cols # Estimate conditional estimates by default self.need_conditional_estimates = ( need_conditional_estimates if need_conditional_estimates != "auto" else bool(self._effect_modifier_names) ) @staticmethod def get_estimator_object(new_data, identified_estimand, estimate): """Create a new estimator of the same type as the one passed in the estimate argument. Creates a new object with new_data and the identified_estimand :param new_data: np.ndarray, pd.Series, pd.DataFrame The newly assigned data on which the estimator should run :param identified_estimand: IdentifiedEstimand An instance of the identified estimand class that provides the information with respect to which causal pathways are employed when the treatment effects the outcome :param estimate: CausalEstimate It is an already existing estimate whose properties we wish to replicate :returns: An instance of the same estimator class that had generated the given estimate. """ estimator_class = estimate.params["estimator_class"] new_estimator = estimator_class( new_data, identified_estimand, identified_estimand.treatment_variable, identified_estimand.outcome_variable, # names of treatment and outcome control_value=estimate.control_value, treatment_value=estimate.treatment_value, test_significance=False, evaluate_effect_strength=False, confidence_intervals=estimate.params["confidence_intervals"], target_units=estimate.params["target_units"], effect_modifiers=estimate.params["effect_modifiers"], **estimate.params["method_params"], ) return new_estimator def _estimate_effect(self): """This method is to be overriden by the child classes, so that they can run the estimation technique of their choice""" raise NotImplementedError( ("Main estimation method is " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG).format(self.__class__) ) def estimate_effect(self): """Base estimation method that calls the estimate_effect method of its calling subclass. Can optionally also test significance and estimate effect strength for any returned estimate. :param self: object instance of class Estimator :returns: A CausalEstimate instance that contains point estimates of average and conditional effects. Based on the parameters provided, it optionally includes confidence intervals, standard errors,statistical significance and other statistical parameters. """ est = self._estimate_effect() est.add_estimator(self) if self._significance_test: self.test_significance(est.value, method=self._significance_test) if self._confidence_intervals: self.estimate_confidence_intervals( est.value, confidence_level=self.confidence_level, method=self._confidence_intervals ) if self._effect_strength_eval: effect_strength_dict = self.evaluate_effect_strength(est) est.add_effect_strength(effect_strength_dict) return est def estimate_effect_naive(self): # TODO Only works for binary treatment df_withtreatment = self._data.loc[self._data[self._treatment_name] == 1] df_notreatment = self._data.loc[self._data[self._treatment_name] == 0] est = np.mean(df_withtreatment[self._outcome_name]) - np.mean(df_notreatment[self._outcome_name]) return CausalEstimate(est, None, None, control_value=0, treatment_value=1) def _estimate_effect_fn(self, data_df): """Function used in conditional effect estimation. This function is to be overridden by each child estimator. The overridden function should take in a dataframe as input and return the estimate for that data. """ raise NotImplementedError( ("Conditional treatment effects are " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG).format( self.__class__ ) ) def _estimate_conditional_effects(self, estimate_effect_fn, effect_modifier_names=None, num_quantiles=None): """Estimate conditional treatment effects. Common method for all estimators that utilizes a specific estimate_effect_fn implemented by each child estimator. If a numeric effect modifier is provided, it is discretized into quantile bins. If you would like a custom discretization, you can do so yourself: create a new column containing the discretized effect modifier and then include that column's name in the effect_modifier_names argument. :param estimate_effect_fn: Function that has a single parameter (a data frame) and returns the treatment effect estimate on that data. :param effect_modifier_names: Names of effect modifier variables over which the conditional effects will be estimated. If not provided, defaults to the effect modifiers specified during creation of the CausalEstimator object. :param num_quantiles: The number of quantiles into which a numeric effect modifier variable is discretized. Does not affect any categorical effect modifiers. :returns: A (multi-index) dataframe that provides separate effects for each value of the (discretized) effect modifiers. """ # Defaulting to class default values if parameters are not provided if effect_modifier_names is None: effect_modifier_names = self._effect_modifier_names if num_quantiles is None: num_quantiles = self.num_quantiles_to_discretize_cont_cols # Checking that there is at least one effect modifier if not effect_modifier_names: raise ValueError("At least one effect modifier should be specified to compute conditional effects.") # Making sure that effect_modifier_names is a list effect_modifier_names = parse_state(effect_modifier_names) if not all(em in self._effect_modifier_names for em in effect_modifier_names): self.logger.warn( "At least one of the provided effect modifiers was not included while fitting the estimator. You may get incorrect results. To resolve, fit the estimator again by providing the updated effect modifiers in estimate_effect()." ) # Making a copy since we are going to be changing effect modifier names effect_modifier_names = effect_modifier_names.copy() prefix = CausalEstimator.TEMP_CAT_COLUMN_PREFIX # For every numeric effect modifier, adding a temp categorical column for i in range(len(effect_modifier_names)): em = effect_modifier_names[i] if pd.api.types.is_numeric_dtype(self._data[em].dtypes): self._data[prefix + str(em)] = pd.qcut(self._data[em], num_quantiles, duplicates="drop") effect_modifier_names[i] = prefix + str(em) # Grouping by effect modifiers and computing effect separately by_effect_mods = self._data.groupby(effect_modifier_names) cond_est_fn = lambda x: self._do(self._treatment_value, x) - self._do(self._control_value, x) conditional_estimates = by_effect_mods.apply(estimate_effect_fn) # Deleting the temporary categorical columns for em in effect_modifier_names: if em.startswith(prefix): self._data.pop(em) return conditional_estimates def _do(self, x, data_df=None): raise NotImplementedError( ("Do-operator is " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG).format(self.__class__) ) def do(self, x, data_df=None): """Method that implements the do-operator. Given a value x for the treatment, returns the expected value of the outcome when the treatment is intervened to a value x. :param x: Value of the treatment :param data_df: Data on which the do-operator is to be applied. :returns: Value of the outcome when treatment is intervened/set to x. """ est = self._do(x, data_df) return est def construct_symbolic_estimator(self, estimand): raise NotImplementedError(("Symbolic estimator string is ").format(self.__class__)) def _generate_bootstrap_estimates(self, num_bootstrap_simulations, sample_size_fraction): """Helper function to generate causal estimates over bootstrapped samples. :param num_bootstrap_simulations: Number of simulations for the bootstrap method. :param sample_size_fraction: Fraction of the dataset to be resampled. :returns: A collections.namedtuple containing a list of bootstrapped estimates and a dictionary containing parameters used for the bootstrap. """ # The array that stores the results of all estimations simulation_results = np.zeros(num_bootstrap_simulations) # Find the sample size the proportion with the population size sample_size = int(sample_size_fraction * len(self._data)) if sample_size > len(self._data): self.logger.warning("WARN: The sample size is greater than the data being sampled") self.logger.info("INFO: The sample size: {}".format(sample_size)) self.logger.info("INFO: The number of simulations: {}".format(num_bootstrap_simulations)) # Perform the set number of simulations for index in range(num_bootstrap_simulations): new_data = resample(self._data, n_samples=sample_size) new_estimator = type(self)( new_data, self._target_estimand, self._target_estimand.treatment_variable, self._target_estimand.outcome_variable, # names of treatment and outcome treatment_value=self._treatment_value, control_value=self._control_value, test_significance=False, evaluate_effect_strength=False, confidence_intervals=False, target_units=self._target_units, effect_modifiers=self._effect_modifier_names, **self.method_params, ) new_effect = new_estimator.estimate_effect() simulation_results[index] = new_effect.value estimates = CausalEstimator.BootstrapEstimates( simulation_results, {"num_simulations": num_bootstrap_simulations, "sample_size_fraction": sample_size_fraction}, ) return estimates def _estimate_confidence_intervals_with_bootstrap( self, estimate_value, confidence_level=None, num_simulations=None, sample_size_fraction=None ): """ Method to compute confidence interval using bootstrapped sampling. :param estimate_value: obtained estimate's value :param confidence_level: The level for which to compute CI (e.g., 95% confidence level translates to confidence_level=0.95) :param num_simulations: The number of simulations to be performed to get the bootstrap confidence intervals. :param sample_size_fraction: The fraction of the dataset to be resampled. :returns: confidence interval at the specified level. For more details on bootstrap or resampling statistics, refer to the following links: https://ocw.mit.edu/courses/mathematics/18-05-introduction-to-probability-and-statistics-spring-2014/readings/MIT18_05S14_Reading24.pdf https://projecteuclid.org/download/pdf_1/euclid.ss/1032280214 """ # Using class default parameters if not specified if num_simulations is None: num_simulations = self.num_simulations if sample_size_fraction is None: sample_size_fraction = self.sample_size_fraction # Checking if bootstrap_estimates are already computed if self._bootstrap_estimates is None: self._bootstrap_estimates = self._generate_bootstrap_estimates(num_simulations, sample_size_fraction) elif CausalEstimator.is_bootstrap_parameter_changed(self._bootstrap_estimates.params, locals()): # Checked if any parameter is changed from the previous std error estimate self._bootstrap_estimates = self._generate_bootstrap_estimates(num_simulations, sample_size_fraction) # Now use the data obtained from the simulations to get the value of the confidence estimates bootstrap_estimates = self._bootstrap_estimates.estimates # Get the variations of each bootstrap estimate and sort bootstrap_variations = [bootstrap_estimate - estimate_value for bootstrap_estimate in bootstrap_estimates] sorted_bootstrap_variations = np.sort(bootstrap_variations) # Now we take the (1- p)th and the (p)th variations, where p is the chosen confidence level upper_bound_index = int((1 - confidence_level) * len(sorted_bootstrap_variations)) lower_bound_index = int(confidence_level * len(sorted_bootstrap_variations)) # Get the lower and upper bounds by subtracting the variations from the estimate lower_bound = estimate_value - sorted_bootstrap_variations[lower_bound_index] upper_bound = estimate_value - sorted_bootstrap_variations[upper_bound_index] return lower_bound, upper_bound def _estimate_confidence_intervals(self, confidence_level=None, method=None, **kwargs): """ This method is to be overriden by the child classes, so that they can run a confidence interval estimation method suited to the specific causal estimator. """ raise NotImplementedError( ( "This method for estimating confidence intervals is " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG + " Meanwhile, you can try the bootstrap method (method='bootstrap') to estimate confidence intervals." ).format(self.__class__) ) def estimate_confidence_intervals(self, estimate_value, confidence_level=None, method=None, **kwargs): """Find the confidence intervals corresponding to any estimator By default, this is done with the help of bootstrapped confidence intervals but can be overridden if the specific estimator implements other methods of estimating confidence intervals. If the method provided is not bootstrap, this function calls the implementation of the specific estimator. :param estimate_value: obtained estimate's value :param method: Method for estimating confidence intervals. :param confidence_level: The confidence level of the confidence intervals of the estimate. :param kwargs: Other optional args to be passed to the CI method. :returns: The obtained confidence interval. """ if method is None: if self._confidence_intervals: method = self._confidence_intervals # this is either True or methodname else: method = "default" confidence_intervals = None if confidence_level is None: confidence_level = self.confidence_level if method == "default" or method is True: # user has not provided any method try: confidence_intervals = self._estimate_confidence_intervals(confidence_level, method=method, **kwargs) except NotImplementedError: confidence_intervals = self._estimate_confidence_intervals_with_bootstrap( estimate_value, confidence_level, **kwargs ) else: if method == "bootstrap": confidence_intervals = self._estimate_confidence_intervals_with_bootstrap( estimate_value, confidence_level, **kwargs ) else: confidence_intervals = self._estimate_confidence_intervals(confidence_level, method=method, **kwargs) return confidence_intervals def _estimate_std_error_with_bootstrap(self, num_simulations=None, sample_size_fraction=None): """Compute standard error using the bootstrap method. Standard error and confidence intervals use the same parameter num_simulations for the number of bootstrap simulations. :param num_simulations: Number of bootstrapped samples. :param sample_size_fraction: Fraction of data to be resampled. :returns: Standard error of the obtained estimate. """ # Use existing params, if new user defined params are not present if num_simulations is None: num_simulations = self.num_simulations if sample_size_fraction is None: sample_size_fraction = self.sample_size_fraction # Checking if bootstrap_estimates are already computed if self._bootstrap_estimates is None: self._bootstrap_estimates = self._generate_bootstrap_estimates(num_simulations, sample_size_fraction) elif CausalEstimator.is_bootstrap_parameter_changed(self._bootstrap_estimates.params, locals()): # Check if any parameter is changed from the previous std error estimate self._bootstrap_estimates = self._generate_bootstrap_estimates(num_simulations, sample_size_fraction) std_error = np.std(self._bootstrap_estimates.estimates) return std_error def _estimate_std_error(self, method=None, **kwargs): """ This method is to be overriden by the child classes, so that they can run a standard error estimation method suited to the specific causal estimator. """ raise NotImplementedError( ( "This method for estimating standard errors is " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG + " Meanwhile, you can try the bootstrap method (method='bootstrap') to estimate standard errors." ).format(self.__class__) ) def estimate_std_error(self, method=None, **kwargs): """Compute standard error of an obtained causal estimate. :param method: Method for computing the standard error. :param kwargs: Other optional parameters to be passed to the estimating method. :returns: Standard error of the causal estimate. """ if method is None: if self._confidence_intervals: method = self._confidence_intervals else: method = "default" std_error = None if method == "default" or method is True: # user has not provided any method try: std_error = self._estimate_std_error(method, **kwargs) except NotImplementedError: std_error = self._estimate_std_error_with_bootstrap(**kwargs) else: if method == "bootstrap": std_error = self._estimate_std_error_with_bootstrap(**kwargs) else: std_error = self._estimate_std_error(method, **kwargs) return std_error def _test_significance_with_bootstrap(self, estimate_value, num_null_simulations=None): """Test statistical significance of an estimate using the bootstrap method. :param estimate_value: Obtained estimate's value :param num_null_simulations: Number of simulations for the null hypothesis :returns: p-value of the statistical significance test. """ # Use existing params, if new user defined params are not present if num_null_simulations is None: num_null_simulations = self.num_null_simulations do_retest = self._bootstrap_null_estimates is None or CausalEstimator.is_bootstrap_parameter_changed( self._bootstrap_null_estimates.params, locals() ) if do_retest: null_estimates = np.zeros(num_null_simulations) for i in range(num_null_simulations): new_outcome = np.random.permutation(self._outcome) new_data = self._data.assign(dummy_outcome=new_outcome) # self._outcome = self._data["dummy_outcome"] new_estimator = type(self)( new_data, self._target_estimand, self._target_estimand.treatment_variable, ("dummy_outcome",), test_significance=False, evaluate_effect_strength=False, confidence_intervals=False, target_units=self._target_units, effect_modifiers=self._effect_modifier_names, **self.method_params, ) new_effect = new_estimator.estimate_effect() null_estimates[i] = new_effect.value self._bootstrap_null_estimates = CausalEstimator.BootstrapEstimates( null_estimates, {"num_null_simulations": num_null_simulations, "sample_size_fraction": 1} ) # Processing the null hypothesis estimates sorted_null_estimates = np.sort(self._bootstrap_null_estimates.estimates) self.logger.debug("Null estimates: {0}".format(sorted_null_estimates)) median_estimate = sorted_null_estimates[int(num_null_simulations / 2)] # Doing a two-sided test if estimate_value > median_estimate: # Being conservative with the p-value reported estimate_index = np.searchsorted(sorted_null_estimates, estimate_value, side="left") p_value = 1 - (estimate_index / num_null_simulations) if estimate_value <= median_estimate: # Being conservative with the p-value reported estimate_index = np.searchsorted(sorted_null_estimates, estimate_value, side="right") p_value = estimate_index / num_null_simulations # If the estimate_index is 0, it depends on the number of simulations if p_value == 0: p_value = (0, 1 / len(sorted_null_estimates)) # a tuple determining the range. elif p_value == 1: p_value = (1 - 1 / len(sorted_null_estimates), 1) signif_dict = {"p_value": p_value} return signif_dict def _test_significance(self, estimate_value, method=None, **kwargs): """ This method is to be overriden by the child classes, so that they can run a significance test suited to the specific causal estimator. """ raise NotImplementedError( ( "This method for testing statistical significance is " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG + " Meanwhile, you can try the bootstrap method (method='bootstrap') to test statistical significance." ).format(self.__class__) ) def test_significance(self, estimate_value, method=None, **kwargs): """Test statistical significance of obtained estimate. By default, uses resampling to create a non-parametric significance test. A general procedure. Individual child estimators can implement different methods. If the method name is different from "bootstrap", this function calls the implementation of the child estimator. :param self: object instance of class Estimator :param estimate_value: obtained estimate's value :param method: Method for checking statistical significance :returns: p-value from the significance test """ if method is None: if self._significance_test: method = self._significance_test # this is either True or methodname else: method = "default" signif_dict = None if method == "default" or method is True: # user has not provided any method try: signif_dict = self._test_significance(estimate_value, method, **kwargs) except NotImplementedError: signif_dict = self._test_significance_with_bootstrap(estimate_value, **kwargs) else: if method == "bootstrap": signif_dict = self._test_significance_with_bootstrap(estimate_value, **kwargs) else: signif_dict = self._test_significance(estimate_value, method, **kwargs) return signif_dict def evaluate_effect_strength(self, estimate): fraction_effect_explained = self._evaluate_effect_strength(estimate, method="fraction-effect") # Need to test r-squared before supporting # effect_r_squared = self._evaluate_effect_strength(estimate, method="r-squared") strength_dict = { "fraction-effect": fraction_effect_explained # 'r-squared': effect_r_squared } return strength_dict def _evaluate_effect_strength(self, estimate, method="fraction-effect"): supported_methods = ["fraction-effect"] if method not in supported_methods: raise NotImplementedError("This method is not supported for evaluating effect strength") if method == "fraction-effect": naive_obs_estimate = self.estimate_effect_naive() self.logger.debug(estimate.value, naive_obs_estimate.value) fraction_effect_explained = estimate.value / naive_obs_estimate.value return fraction_effect_explained # elif method == "r-squared": # outcome_mean = np.mean(self._outcome) # total_variance = np.sum(np.square(self._outcome - outcome_mean)) # Assuming a linear model with one variable: the treatment # Currently only works for continuous y # causal_model = outcome_mean + estimate.value*self._treatment # squared_residual = np.sum(np.square(self._outcome - causal_model)) # r_squared = 1 - (squared_residual/total_variance) # return r_squared else: return None def update_input(self, treatment_value, control_value, target_units): self._control_value = control_value self._treatment_value = treatment_value self._target_units = target_units @staticmethod def is_bootstrap_parameter_changed(bootstrap_estimates_params, given_params): """Check whether parameters of the bootstrap have changed. This is an efficiency method that checks if fresh resampling of the bootstrap samples is required. Returns True if parameters have changed and resampling should be done again. :param bootstrap_estimates_params: A dictionary of parameters for the current bootstrap samples :param given_params: A dictionary of parameters passed by the user :returns: A binary flag denoting whether the parameters are different. """ is_any_parameter_changed = False for prm, val in bootstrap_estimates_params.items(): given_val = given_params.get(prm, None) if given_val is not None and given_val != val: is_any_parameter_changed = True break return is_any_parameter_changed def target_units_tostr(self): s = "" if type(self._target_units) is str: s += self._target_units elif callable(self._target_units): s += "Data subset defined by a function" elif isinstance(self._target_units, pd.DataFrame): s += "Data subset provided as a data frame" return s def signif_results_tostr(self, signif_results): s = "" pval = signif_results["p_value"] if type(pval) is tuple: s += "[{0}, {1}]".format(pval[0], pval[1]) else: s += "{0}".format(pval) return s class CausalEstimate: """Class for the estimate object that every causal estimator returns""" def __init__( self, estimate, target_estimand, realized_estimand_expr, control_value, treatment_value, conditional_estimates=None, **kwargs, ): self.value = estimate self.target_estimand = target_estimand self.realized_estimand_expr = realized_estimand_expr self.control_value = control_value self.treatment_value = treatment_value self.conditional_estimates = conditional_estimates self.params = kwargs if self.params is not None: for key, value in self.params.items(): setattr(self, key, value) self.effect_strength = None def add_estimator(self, estimator_instance): self.estimator = estimator_instance def add_effect_strength(self, strength_dict): self.effect_strength = strength_dict def add_params(self, **kwargs): self.params.update(kwargs) def get_confidence_intervals(self, confidence_level=None, method=None, **kwargs): """Get confidence intervals of the obtained estimate. By default, this is done with the help of bootstrapped confidence intervals but can be overridden if the specific estimator implements other methods of estimating confidence intervals. If the method provided is not bootstrap, this function calls the implementation of the specific estimator. :param method: Method for estimating confidence intervals. :param confidence_level: The confidence level of the confidence intervals of the estimate. :param kwargs: Other optional args to be passed to the CI method. :returns: The obtained confidence interval. """ confidence_intervals = self.estimator.estimate_confidence_intervals( estimate_value=self.value, confidence_level=confidence_level, method=method, **kwargs ) return confidence_intervals def get_standard_error(self, method=None, **kwargs): """Get standard error of the obtained estimate. By default, this is done with the help of bootstrapped standard errors but can be overridden if the specific estimator implements other methods of estimating standard error. If the method provided is not bootstrap, this function calls the implementation of the specific estimator. :param method: Method for computing the standard error. :param kwargs: Other optional parameters to be passed to the estimating method. :returns: Standard error of the causal estimate. """ std_error = self.estimator.estimate_std_error(method=method, **kwargs) return std_error def test_stat_significance(self, method=None, **kwargs): """Test statistical significance of the estimate obtained. By default, uses resampling to create a non-parametric significance test. Individual child estimators can implement different methods. If the method name is different from "bootstrap", this function calls the implementation of the child estimator. :param method: Method for checking statistical significance :param kwargs: Other optional parameters to be passed to the estimating method. :returns: p-value from the significance test """ signif_results = self.estimator.test_significance(self.value, method=method, **kwargs) return {"p_value": signif_results["p_value"]} def estimate_conditional_effects( self, effect_modifiers=None, num_quantiles=CausalEstimator.NUM_QUANTILES_TO_DISCRETIZE_CONT_COLS ): """Estimate treatment effect conditioned on given variables. If a numeric effect modifier is provided, it is discretized into quantile bins. If you would like a custom discretization, you can do so yourself: create a new column containing the discretized effect modifier and then include that column's name in the effect_modifier_names argument. :param effect_modifiers: Names of effect modifier variables over which the conditional effects will be estimated. If not provided, defaults to the effect modifiers specified during creation of the CausalEstimator object. :param num_quantiles: The number of quantiles into which a numeric effect modifier variable is discretized. Does not affect any categorical effect modifiers. :returns: A (multi-index) dataframe that provides separate effects for each value of the (discretized) effect modifiers. """ return self.estimator._estimate_conditional_effects( self.estimator._estimate_effect_fn, effect_modifiers, num_quantiles ) def interpret(self, method_name=None, **kwargs): """Interpret the causal estimate. :param method_name: Method used (string) or a list of methods. If None, then the default for the specific estimator is used. :param kwargs:: Optional parameters that are directly passed to the interpreter method. :returns: None """ if method_name is None: method_name = self.estimator.interpret_method method_name_arr = parse_state(method_name) for method in method_name_arr: interpreter = interpreters.get_class_object(method) interpreter(self, **kwargs).interpret() def __str__(self): s = "*** Causal Estimate ***\n" # No estimand was identified (identification failed) if self.target_estimand is None: return "Estimation failed! No relevant identified estimand available for this estimation method." s += "\n## Identified estimand\n{0}".format(self.target_estimand.__str__(only_target_estimand=True)) s += "\n## Realized estimand\n{0}".format(self.realized_estimand_expr) if hasattr(self, "estimator"): s += "\nTarget units: {0}\n".format(self.estimator.target_units_tostr()) s += "\n## Estimate\n" s += "Mean value: {0}\n".format(self.value) s += "" if hasattr(self, "cate_estimates"): s += "Effect estimates: {0}\n".format(self.cate_estimates) if hasattr(self, "estimator"): if self.estimator._significance_test: s += "p-value: {0}\n".format(self.estimator.signif_results_tostr(self.test_stat_significance())) if self.estimator._confidence_intervals: s += "{0}% confidence interval: {1}\n".format( 100 * self.estimator.confidence_level, self.get_confidence_intervals() ) if self.conditional_estimates is not None: s += "### Conditional Estimates\n" s += str(self.conditional_estimates) if self.effect_strength is not None: s += "\n## Effect Strength\n" s += "Change in outcome attributable to treatment: {}\n".format(self.effect_strength["fraction-effect"]) # s += "Variance in outcome explained by treatment: {}\n".format(self.effect_strength["r-squared"]) return s class RealizedEstimand(object): def __init__(self, identified_estimand, estimator_name): self.treatment_variable = identified_estimand.treatment_variable self.outcome_variable = identified_estimand.outcome_variable self.backdoor_variables = identified_estimand.get_backdoor_variables() self.instrumental_variables = identified_estimand.instrumental_variables self.estimand_type = identified_estimand.estimand_type self.estimand_expression = None self.assumptions = None self.estimator_name = estimator_name def update_assumptions(self, estimator_assumptions): self.assumptions = estimator_assumptions def update_estimand_expression(self, estimand_expression): self.estimand_expression = estimand_expression def __str__(self): s = "Realized estimand: {0}\n".format(self.estimator_name) s += "Realized estimand type: {0}\n".format(self.estimand_type) s += "Estimand expression:\n{0}\n".format(sp.pretty(self.estimand_expression)) j = 1 for ass_name, ass_str in self.assumptions.items(): s += "Estimand assumption {0}, {1}: {2}\n".format(j, ass_name, ass_str) j += 1 return s

import logging from collections import namedtuple from typing import Dict, List, Optional, Union import numpy as np import pandas as pd import sympy as sp from sklearn.utils import resample import dowhy.interpreters as interpreters from dowhy import causal_estimators from dowhy.causal_graph import CausalGraph from dowhy.causal_identifier.identified_estimand import IdentifiedEstimand from dowhy.utils.api import parse_state logger = logging.getLogger(__name__) class CausalEstimator: """Base class for an estimator of causal effect. Subclasses implement different estimation methods. All estimation methods are in the package "dowhy.causal_estimators" """ # The default number of simulations for statistical testing DEFAULT_NUMBER_OF_SIMULATIONS_STAT_TEST = 1000 # The default number of simulations to obtain confidence intervals DEFAULT_NUMBER_OF_SIMULATIONS_CI = 100 # The portion of the total size that should be taken each time to find the confidence intervals # 1 is the recommended value # https://ocw.mit.edu/courses/mathematics/18-05-introduction-to-probability-and-statistics-spring-2014/readings/MIT18_05S14_Reading24.pdf # https://projecteuclid.org/download/pdf_1/euclid.ss/1032280214 DEFAULT_SAMPLE_SIZE_FRACTION = 1 # The default Confidence Level DEFAULT_CONFIDENCE_LEVEL = 0.95 # Number of quantiles to discretize continuous columns, for applying groupby NUM_QUANTILES_TO_DISCRETIZE_CONT_COLS = 5 # Prefix to add to temporary categorical variables created after discretization TEMP_CAT_COLUMN_PREFIX = "__categorical__" DEFAULT_NOTIMPLEMENTEDERROR_MSG = "not yet implemented for {0}. If you would this to be implemented in the next version, please raise an issue at https://github.com/microsoft/dowhy/issues" BootstrapEstimates = namedtuple("BootstrapEstimates", ["estimates", "params"]) DEFAULT_INTERPRET_METHOD = ["textual_effect_interpreter"] # std args to be removed from locals() before being passed to args_dict _STD_INIT_ARGS = ("self", "__class__", "args", "kwargs") def __init__( self, data, identified_estimand, treatment, outcome, control_value=0, treatment_value=1, test_significance=False, evaluate_effect_strength=False, confidence_intervals=False, target_units=None, effect_modifiers=None, num_null_simulations=DEFAULT_NUMBER_OF_SIMULATIONS_STAT_TEST, num_simulations=DEFAULT_NUMBER_OF_SIMULATIONS_CI, sample_size_fraction=DEFAULT_SAMPLE_SIZE_FRACTION, confidence_level=DEFAULT_CONFIDENCE_LEVEL, need_conditional_estimates="auto", num_quantiles_to_discretize_cont_cols=NUM_QUANTILES_TO_DISCRETIZE_CONT_COLS, **kwargs, ): """Initializes an estimator with data and names of relevant variables. This method is called from the constructors of its child classes. :param data: data frame containing the data :param identified_estimand: probability expression representing the target identified estimand to estimate. :param treatment: name of the treatment variable :param outcome: name of the outcome variable :param control_value: Value of the treatment in the control group, for effect estimation. If treatment is multi-variate, this can be a list. :param treatment_value: Value of the treatment in the treated group, for effect estimation. If treatment is multi-variate, this can be a list. :param test_significance: Binary flag or a string indicating whether to test significance and by which method. All estimators support test_significance="bootstrap" that estimates a p-value for the obtained estimate using the bootstrap method. Individual estimators can override this to support custom testing methods. The bootstrap method supports an optional parameter, num_null_simulations. If False, no testing is done. If True, significance of the estimate is tested using the custom method if available, otherwise by bootstrap. :param evaluate_effect_strength: (Experimental) whether to evaluate the strength of effect :param confidence_intervals: Binary flag or a string indicating whether the confidence intervals should be computed and which method should be used. All methods support estimation of confidence intervals using the bootstrap method by using the parameter confidence_intervals="bootstrap". The bootstrap method takes in two arguments (num_simulations and sample_size_fraction) that can be optionally specified in the params dictionary. Estimators may also override this to implement their own confidence interval method. If this parameter is False, no confidence intervals are computed. If True, confidence intervals are computed by the estimator's specific method if available, otherwise through bootstrap. :param target_units: The units for which the treatment effect should be estimated. This can be a string for common specifications of target units (namely, "ate", "att" and "atc"). It can also be a lambda function that can be used as an index for the data (pandas DataFrame). Alternatively, it can be a new DataFrame that contains values of the effect_modifiers and effect will be estimated only for this new data. :param effect_modifiers: Variables on which to compute separate effects, or return a heterogeneous effect function. Not all methods support this currently. :param num_null_simulations: The number of simulations for testing the statistical significance of the estimator :param num_simulations: The number of simulations for finding the confidence interval (and/or standard error) for a estimate :param sample_size_fraction: The size of the sample for the bootstrap estimator :param confidence_level: The confidence level of the confidence interval estimate :param need_conditional_estimates: Boolean flag indicating whether conditional estimates should be computed. Defaults to True if there are effect modifiers in the graph :param num_quantiles_to_discretize_cont_cols: The number of quantiles into which a numeric effect modifier is split, to enable estimation of conditional treatment effect over it. :param kwargs: (optional) Additional estimator-specific parameters :returns: an instance of the estimator class. """ self._data = data self._target_estimand = identified_estimand # Currently estimation methods only support univariate treatment and outcome self._treatment_name = treatment self._outcome_name = outcome[0] # assuming one-dimensional outcome self._control_value = control_value self._treatment_value = treatment_value self._significance_test = test_significance self._effect_strength_eval = evaluate_effect_strength self._target_units = target_units self._effect_modifier_names = effect_modifiers self._confidence_intervals = confidence_intervals self._bootstrap_estimates = None # for confidence intervals and std error self._bootstrap_null_estimates = None # for significance test self._effect_modifiers = None self.method_params = kwargs # Setting the default interpret method self.interpret_method = CausalEstimator.DEFAULT_INTERPRET_METHOD self.logger = logging.getLogger(__name__) # Setting treatment and outcome values if self._data is not None: self._treatment = self._data[self._treatment_name] self._outcome = self._data[self._outcome_name] if self._effect_modifier_names: # only add the observed nodes self._effect_modifier_names = [ cname for cname in self._effect_modifier_names if cname in self._data.columns ] if len(self._effect_modifier_names) > 0: self._effect_modifiers = self._data[self._effect_modifier_names] self._effect_modifiers = pd.get_dummies(self._effect_modifiers, drop_first=True) self.logger.debug("Effect modifiers: " + ",".join(self._effect_modifier_names)) else: self._effect_modifier_names = None # Check if some parameters were set, otherwise set to default values self.num_null_simulations = num_null_simulations self.num_simulations = num_simulations self.sample_size_fraction = sample_size_fraction self.confidence_level = confidence_level self.num_quantiles_to_discretize_cont_cols = num_quantiles_to_discretize_cont_cols # Estimate conditional estimates by default self.need_conditional_estimates = ( need_conditional_estimates if need_conditional_estimates != "auto" else bool(self._effect_modifier_names) ) @staticmethod def get_estimator_object(new_data, identified_estimand, estimate): """Create a new estimator of the same type as the one passed in the estimate argument. Creates a new object with new_data and the identified_estimand :param new_data: np.ndarray, pd.Series, pd.DataFrame The newly assigned data on which the estimator should run :param identified_estimand: IdentifiedEstimand An instance of the identified estimand class that provides the information with respect to which causal pathways are employed when the treatment effects the outcome :param estimate: CausalEstimate It is an already existing estimate whose properties we wish to replicate :returns: An instance of the same estimator class that had generated the given estimate. """ estimator_class = estimate.params["estimator_class"] new_estimator = estimator_class( new_data, identified_estimand, identified_estimand.treatment_variable, identified_estimand.outcome_variable, # names of treatment and outcome control_value=estimate.control_value, treatment_value=estimate.treatment_value, test_significance=False, evaluate_effect_strength=False, confidence_intervals=estimate.params["confidence_intervals"], target_units=estimate.params["target_units"], effect_modifiers=estimate.params["effect_modifiers"], **estimate.params["method_params"] if estimate.params["method_params"] is not None else {}, ) return new_estimator def _estimate_effect(self): """This method is to be overriden by the child classes, so that they can run the estimation technique of their choice""" raise NotImplementedError( ("Main estimation method is " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG).format(self.__class__) ) def estimate_effect(self): """Base estimation method that calls the estimate_effect method of its calling subclass. Can optionally also test significance and estimate effect strength for any returned estimate. :param self: object instance of class Estimator :returns: A CausalEstimate instance that contains point estimates of average and conditional effects. Based on the parameters provided, it optionally includes confidence intervals, standard errors,statistical significance and other statistical parameters. """ est = self._estimate_effect() est.add_estimator(self) if self._significance_test: self.test_significance(est.value, method=self._significance_test) if self._confidence_intervals: self.estimate_confidence_intervals( est.value, confidence_level=self.confidence_level, method=self._confidence_intervals ) if self._effect_strength_eval: effect_strength_dict = self.evaluate_effect_strength(est) est.add_effect_strength(effect_strength_dict) return est def estimate_effect_naive(self): # TODO Only works for binary treatment df_withtreatment = self._data.loc[self._data[self._treatment_name] == 1] df_notreatment = self._data.loc[self._data[self._treatment_name] == 0] est = np.mean(df_withtreatment[self._outcome_name]) - np.mean(df_notreatment[self._outcome_name]) return CausalEstimate(est, None, None, control_value=0, treatment_value=1) def _estimate_effect_fn(self, data_df): """Function used in conditional effect estimation. This function is to be overridden by each child estimator. The overridden function should take in a dataframe as input and return the estimate for that data. """ raise NotImplementedError( ("Conditional treatment effects are " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG).format( self.__class__ ) ) def _estimate_conditional_effects(self, estimate_effect_fn, effect_modifier_names=None, num_quantiles=None): """Estimate conditional treatment effects. Common method for all estimators that utilizes a specific estimate_effect_fn implemented by each child estimator. If a numeric effect modifier is provided, it is discretized into quantile bins. If you would like a custom discretization, you can do so yourself: create a new column containing the discretized effect modifier and then include that column's name in the effect_modifier_names argument. :param estimate_effect_fn: Function that has a single parameter (a data frame) and returns the treatment effect estimate on that data. :param effect_modifier_names: Names of effect modifier variables over which the conditional effects will be estimated. If not provided, defaults to the effect modifiers specified during creation of the CausalEstimator object. :param num_quantiles: The number of quantiles into which a numeric effect modifier variable is discretized. Does not affect any categorical effect modifiers. :returns: A (multi-index) dataframe that provides separate effects for each value of the (discretized) effect modifiers. """ # Defaulting to class default values if parameters are not provided if effect_modifier_names is None: effect_modifier_names = self._effect_modifier_names if num_quantiles is None: num_quantiles = self.num_quantiles_to_discretize_cont_cols # Checking that there is at least one effect modifier if not effect_modifier_names: raise ValueError("At least one effect modifier should be specified to compute conditional effects.") # Making sure that effect_modifier_names is a list effect_modifier_names = parse_state(effect_modifier_names) if not all(em in self._effect_modifier_names for em in effect_modifier_names): self.logger.warn( "At least one of the provided effect modifiers was not included while fitting the estimator. You may get incorrect results. To resolve, fit the estimator again by providing the updated effect modifiers in estimate_effect()." ) # Making a copy since we are going to be changing effect modifier names effect_modifier_names = effect_modifier_names.copy() prefix = CausalEstimator.TEMP_CAT_COLUMN_PREFIX # For every numeric effect modifier, adding a temp categorical column for i in range(len(effect_modifier_names)): em = effect_modifier_names[i] if pd.api.types.is_numeric_dtype(self._data[em].dtypes): self._data[prefix + str(em)] = pd.qcut(self._data[em], num_quantiles, duplicates="drop") effect_modifier_names[i] = prefix + str(em) # Grouping by effect modifiers and computing effect separately by_effect_mods = self._data.groupby(effect_modifier_names) cond_est_fn = lambda x: self._do(self._treatment_value, x) - self._do(self._control_value, x) conditional_estimates = by_effect_mods.apply(estimate_effect_fn) # Deleting the temporary categorical columns for em in effect_modifier_names: if em.startswith(prefix): self._data.pop(em) return conditional_estimates def _do(self, x, data_df=None): raise NotImplementedError( ("Do-operator is " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG).format(self.__class__) ) def do(self, x, data_df=None): """Method that implements the do-operator. Given a value x for the treatment, returns the expected value of the outcome when the treatment is intervened to a value x. :param x: Value of the treatment :param data_df: Data on which the do-operator is to be applied. :returns: Value of the outcome when treatment is intervened/set to x. """ est = self._do(x, data_df) return est def construct_symbolic_estimator(self, estimand): raise NotImplementedError(("Symbolic estimator string is ").format(self.__class__)) def _generate_bootstrap_estimates(self, num_bootstrap_simulations, sample_size_fraction): """Helper function to generate causal estimates over bootstrapped samples. :param num_bootstrap_simulations: Number of simulations for the bootstrap method. :param sample_size_fraction: Fraction of the dataset to be resampled. :returns: A collections.namedtuple containing a list of bootstrapped estimates and a dictionary containing parameters used for the bootstrap. """ # The array that stores the results of all estimations simulation_results = np.zeros(num_bootstrap_simulations) # Find the sample size the proportion with the population size sample_size = int(sample_size_fraction * len(self._data)) if sample_size > len(self._data): self.logger.warning("WARN: The sample size is greater than the data being sampled") self.logger.info("INFO: The sample size: {}".format(sample_size)) self.logger.info("INFO: The number of simulations: {}".format(num_bootstrap_simulations)) # Perform the set number of simulations for index in range(num_bootstrap_simulations): new_data = resample(self._data, n_samples=sample_size) new_estimator = type(self)( new_data, self._target_estimand, self._target_estimand.treatment_variable, self._target_estimand.outcome_variable, # names of treatment and outcome treatment_value=self._treatment_value, control_value=self._control_value, test_significance=False, evaluate_effect_strength=False, confidence_intervals=False, target_units=self._target_units, effect_modifiers=self._effect_modifier_names, **self.method_params, ) new_effect = new_estimator.estimate_effect() simulation_results[index] = new_effect.value estimates = CausalEstimator.BootstrapEstimates( simulation_results, {"num_simulations": num_bootstrap_simulations, "sample_size_fraction": sample_size_fraction}, ) return estimates def _estimate_confidence_intervals_with_bootstrap( self, estimate_value, confidence_level=None, num_simulations=None, sample_size_fraction=None ): """ Method to compute confidence interval using bootstrapped sampling. :param estimate_value: obtained estimate's value :param confidence_level: The level for which to compute CI (e.g., 95% confidence level translates to confidence_level=0.95) :param num_simulations: The number of simulations to be performed to get the bootstrap confidence intervals. :param sample_size_fraction: The fraction of the dataset to be resampled. :returns: confidence interval at the specified level. For more details on bootstrap or resampling statistics, refer to the following links: https://ocw.mit.edu/courses/mathematics/18-05-introduction-to-probability-and-statistics-spring-2014/readings/MIT18_05S14_Reading24.pdf https://projecteuclid.org/download/pdf_1/euclid.ss/1032280214 """ # Using class default parameters if not specified if num_simulations is None: num_simulations = self.num_simulations if sample_size_fraction is None: sample_size_fraction = self.sample_size_fraction # Checking if bootstrap_estimates are already computed if self._bootstrap_estimates is None: self._bootstrap_estimates = self._generate_bootstrap_estimates(num_simulations, sample_size_fraction) elif CausalEstimator.is_bootstrap_parameter_changed(self._bootstrap_estimates.params, locals()): # Checked if any parameter is changed from the previous std error estimate self._bootstrap_estimates = self._generate_bootstrap_estimates(num_simulations, sample_size_fraction) # Now use the data obtained from the simulations to get the value of the confidence estimates bootstrap_estimates = self._bootstrap_estimates.estimates # Get the variations of each bootstrap estimate and sort bootstrap_variations = [bootstrap_estimate - estimate_value for bootstrap_estimate in bootstrap_estimates] sorted_bootstrap_variations = np.sort(bootstrap_variations) # Now we take the (1- p)th and the (p)th variations, where p is the chosen confidence level upper_bound_index = int((1 - confidence_level) * len(sorted_bootstrap_variations)) lower_bound_index = int(confidence_level * len(sorted_bootstrap_variations)) # Get the lower and upper bounds by subtracting the variations from the estimate lower_bound = estimate_value - sorted_bootstrap_variations[lower_bound_index] upper_bound = estimate_value - sorted_bootstrap_variations[upper_bound_index] return lower_bound, upper_bound def _estimate_confidence_intervals(self, confidence_level=None, method=None, **kwargs): """ This method is to be overriden by the child classes, so that they can run a confidence interval estimation method suited to the specific causal estimator. """ raise NotImplementedError( ( "This method for estimating confidence intervals is " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG + " Meanwhile, you can try the bootstrap method (method='bootstrap') to estimate confidence intervals." ).format(self.__class__) ) def estimate_confidence_intervals(self, estimate_value, confidence_level=None, method=None, **kwargs): """Find the confidence intervals corresponding to any estimator By default, this is done with the help of bootstrapped confidence intervals but can be overridden if the specific estimator implements other methods of estimating confidence intervals. If the method provided is not bootstrap, this function calls the implementation of the specific estimator. :param estimate_value: obtained estimate's value :param method: Method for estimating confidence intervals. :param confidence_level: The confidence level of the confidence intervals of the estimate. :param kwargs: Other optional args to be passed to the CI method. :returns: The obtained confidence interval. """ if method is None: if self._confidence_intervals: method = self._confidence_intervals # this is either True or methodname else: method = "default" confidence_intervals = None if confidence_level is None: confidence_level = self.confidence_level if method == "default" or method is True: # user has not provided any method try: confidence_intervals = self._estimate_confidence_intervals(confidence_level, method=method, **kwargs) except NotImplementedError: confidence_intervals = self._estimate_confidence_intervals_with_bootstrap( estimate_value, confidence_level, **kwargs ) else: if method == "bootstrap": confidence_intervals = self._estimate_confidence_intervals_with_bootstrap( estimate_value, confidence_level, **kwargs ) else: confidence_intervals = self._estimate_confidence_intervals(confidence_level, method=method, **kwargs) return confidence_intervals def _estimate_std_error_with_bootstrap(self, num_simulations=None, sample_size_fraction=None): """Compute standard error using the bootstrap method. Standard error and confidence intervals use the same parameter num_simulations for the number of bootstrap simulations. :param num_simulations: Number of bootstrapped samples. :param sample_size_fraction: Fraction of data to be resampled. :returns: Standard error of the obtained estimate. """ # Use existing params, if new user defined params are not present if num_simulations is None: num_simulations = self.num_simulations if sample_size_fraction is None: sample_size_fraction = self.sample_size_fraction # Checking if bootstrap_estimates are already computed if self._bootstrap_estimates is None: self._bootstrap_estimates = self._generate_bootstrap_estimates(num_simulations, sample_size_fraction) elif CausalEstimator.is_bootstrap_parameter_changed(self._bootstrap_estimates.params, locals()): # Check if any parameter is changed from the previous std error estimate self._bootstrap_estimates = self._generate_bootstrap_estimates(num_simulations, sample_size_fraction) std_error = np.std(self._bootstrap_estimates.estimates) return std_error def _estimate_std_error(self, method=None, **kwargs): """ This method is to be overriden by the child classes, so that they can run a standard error estimation method suited to the specific causal estimator. """ raise NotImplementedError( ( "This method for estimating standard errors is " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG + " Meanwhile, you can try the bootstrap method (method='bootstrap') to estimate standard errors." ).format(self.__class__) ) def estimate_std_error(self, method=None, **kwargs): """Compute standard error of an obtained causal estimate. :param method: Method for computing the standard error. :param kwargs: Other optional parameters to be passed to the estimating method. :returns: Standard error of the causal estimate. """ if method is None: if self._confidence_intervals: method = self._confidence_intervals else: method = "default" std_error = None if method == "default" or method is True: # user has not provided any method try: std_error = self._estimate_std_error(method, **kwargs) except NotImplementedError: std_error = self._estimate_std_error_with_bootstrap(**kwargs) else: if method == "bootstrap": std_error = self._estimate_std_error_with_bootstrap(**kwargs) else: std_error = self._estimate_std_error(method, **kwargs) return std_error def _test_significance_with_bootstrap(self, estimate_value, num_null_simulations=None): """Test statistical significance of an estimate using the bootstrap method. :param estimate_value: Obtained estimate's value :param num_null_simulations: Number of simulations for the null hypothesis :returns: p-value of the statistical significance test. """ # Use existing params, if new user defined params are not present if num_null_simulations is None: num_null_simulations = self.num_null_simulations do_retest = self._bootstrap_null_estimates is None or CausalEstimator.is_bootstrap_parameter_changed( self._bootstrap_null_estimates.params, locals() ) if do_retest: null_estimates = np.zeros(num_null_simulations) for i in range(num_null_simulations): new_outcome = np.random.permutation(self._outcome) new_data = self._data.assign(dummy_outcome=new_outcome) # self._outcome = self._data["dummy_outcome"] new_estimator = type(self)( new_data, self._target_estimand, self._target_estimand.treatment_variable, ("dummy_outcome",), test_significance=False, evaluate_effect_strength=False, confidence_intervals=False, target_units=self._target_units, effect_modifiers=self._effect_modifier_names, **self.method_params, ) new_effect = new_estimator.estimate_effect() null_estimates[i] = new_effect.value self._bootstrap_null_estimates = CausalEstimator.BootstrapEstimates( null_estimates, {"num_null_simulations": num_null_simulations, "sample_size_fraction": 1} ) # Processing the null hypothesis estimates sorted_null_estimates = np.sort(self._bootstrap_null_estimates.estimates) self.logger.debug("Null estimates: {0}".format(sorted_null_estimates)) median_estimate = sorted_null_estimates[int(num_null_simulations / 2)] # Doing a two-sided test if estimate_value > median_estimate: # Being conservative with the p-value reported estimate_index = np.searchsorted(sorted_null_estimates, estimate_value, side="left") p_value = 1 - (estimate_index / num_null_simulations) if estimate_value <= median_estimate: # Being conservative with the p-value reported estimate_index = np.searchsorted(sorted_null_estimates, estimate_value, side="right") p_value = estimate_index / num_null_simulations # If the estimate_index is 0, it depends on the number of simulations if p_value == 0: p_value = (0, 1 / len(sorted_null_estimates)) # a tuple determining the range. elif p_value == 1: p_value = (1 - 1 / len(sorted_null_estimates), 1) signif_dict = {"p_value": p_value} return signif_dict def _test_significance(self, estimate_value, method=None, **kwargs): """ This method is to be overriden by the child classes, so that they can run a significance test suited to the specific causal estimator. """ raise NotImplementedError( ( "This method for testing statistical significance is " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG + " Meanwhile, you can try the bootstrap method (method='bootstrap') to test statistical significance." ).format(self.__class__) ) def test_significance(self, estimate_value, method=None, **kwargs): """Test statistical significance of obtained estimate. By default, uses resampling to create a non-parametric significance test. A general procedure. Individual child estimators can implement different methods. If the method name is different from "bootstrap", this function calls the implementation of the child estimator. :param self: object instance of class Estimator :param estimate_value: obtained estimate's value :param method: Method for checking statistical significance :returns: p-value from the significance test """ if method is None: if self._significance_test: method = self._significance_test # this is either True or methodname else: method = "default" signif_dict = None if method == "default" or method is True: # user has not provided any method try: signif_dict = self._test_significance(estimate_value, method, **kwargs) except NotImplementedError: signif_dict = self._test_significance_with_bootstrap(estimate_value, **kwargs) else: if method == "bootstrap": signif_dict = self._test_significance_with_bootstrap(estimate_value, **kwargs) else: signif_dict = self._test_significance(estimate_value, method, **kwargs) return signif_dict def evaluate_effect_strength(self, estimate): fraction_effect_explained = self._evaluate_effect_strength(estimate, method="fraction-effect") # Need to test r-squared before supporting # effect_r_squared = self._evaluate_effect_strength(estimate, method="r-squared") strength_dict = { "fraction-effect": fraction_effect_explained # 'r-squared': effect_r_squared } return strength_dict def _evaluate_effect_strength(self, estimate, method="fraction-effect"): supported_methods = ["fraction-effect"] if method not in supported_methods: raise NotImplementedError("This method is not supported for evaluating effect strength") if method == "fraction-effect": naive_obs_estimate = self.estimate_effect_naive() self.logger.debug(estimate.value, naive_obs_estimate.value) fraction_effect_explained = estimate.value / naive_obs_estimate.value return fraction_effect_explained # elif method == "r-squared": # outcome_mean = np.mean(self._outcome) # total_variance = np.sum(np.square(self._outcome - outcome_mean)) # Assuming a linear model with one variable: the treatment # Currently only works for continuous y # causal_model = outcome_mean + estimate.value*self._treatment # squared_residual = np.sum(np.square(self._outcome - causal_model)) # r_squared = 1 - (squared_residual/total_variance) # return r_squared else: return None def update_input(self, treatment_value, control_value, target_units): self._control_value = control_value self._treatment_value = treatment_value self._target_units = target_units @staticmethod def is_bootstrap_parameter_changed(bootstrap_estimates_params, given_params): """Check whether parameters of the bootstrap have changed. This is an efficiency method that checks if fresh resampling of the bootstrap samples is required. Returns True if parameters have changed and resampling should be done again. :param bootstrap_estimates_params: A dictionary of parameters for the current bootstrap samples :param given_params: A dictionary of parameters passed by the user :returns: A binary flag denoting whether the parameters are different. """ is_any_parameter_changed = False for prm, val in bootstrap_estimates_params.items(): given_val = given_params.get(prm, None) if given_val is not None and given_val != val: is_any_parameter_changed = True break return is_any_parameter_changed def target_units_tostr(self): s = "" if type(self._target_units) is str: s += self._target_units elif callable(self._target_units): s += "Data subset defined by a function" elif isinstance(self._target_units, pd.DataFrame): s += "Data subset provided as a data frame" return s def signif_results_tostr(self, signif_results): s = "" pval = signif_results["p_value"] if type(pval) is tuple: s += "[{0}, {1}]".format(pval[0], pval[1]) else: s += "{0}".format(pval) return s def estimate_effect( treatment: Union[str, List[str]], outcome: Union[str, List[str]], identified_estimand: IdentifiedEstimand, identifier_name: str, method: CausalEstimator, control_value: int = 0, treatment_value: int = 1, test_significance: Optional[bool] = None, evaluate_effect_strength: bool = False, confidence_intervals: bool = False, target_units: str = "ate", effect_modifiers: List[str] = [], fit_estimator: bool = True, method_params: Optional[Dict] = None, ): """Estimate the identified causal effect. Currently requires an explicit method name to be specified. Method names follow the convention of identification method followed by the specific estimation method: "[backdoor/iv].estimation_method_name". Following methods are supported. * Propensity Score Matching: "backdoor.propensity_score_matching" * Propensity Score Stratification: "backdoor.propensity_score_stratification" * Propensity Score-based Inverse Weighting: "backdoor.propensity_score_weighting" * Linear Regression: "backdoor.linear_regression" * Generalized Linear Models (e.g., logistic regression): "backdoor.generalized_linear_model" * Instrumental Variables: "iv.instrumental_variable" * Regression Discontinuity: "iv.regression_discontinuity" In addition, you can directly call any of the EconML estimation methods. The convention is "backdoor.econml.path-to-estimator-class". For example, for the double machine learning estimator ("DML" class) that is located inside "dml" module of EconML, you can use the method name, "backdoor.econml.dml.DML". CausalML estimators can also be called. See `this demo notebook <https://py-why.github.io/dowhy/example_notebooks/dowhy-conditional-treatment-effects.html>`_. :param treatment: Name of the treatment :param outcome: Name of the outcome :param identified_estimand: a probability expression that represents the effect to be estimated. Output of CausalModel.identify_effect method :param method_name: name of the estimation method to be used. :param control_value: Value of the treatment in the control group, for effect estimation. If treatment is multi-variate, this can be a list. :param treatment_value: Value of the treatment in the treated group, for effect estimation. If treatment is multi-variate, this can be a list. :param test_significance: Binary flag on whether to additionally do a statistical signficance test for the estimate. :param evaluate_effect_strength: (Experimental) Binary flag on whether to estimate the relative strength of the treatment's effect. This measure can be used to compare different treatments for the same outcome (by running this method with different treatments sequentially). :param confidence_intervals: (Experimental) Binary flag indicating whether confidence intervals should be computed. :param target_units: (Experimental) The units for which the treatment effect should be estimated. This can be of three types. (1) a string for common specifications of target units (namely, "ate", "att" and "atc"), (2) a lambda function that can be used as an index for the data (pandas DataFrame), or (3) a new DataFrame that contains values of the effect_modifiers and effect will be estimated only for this new data. :param effect_modifiers: Names of effect modifier variables can be (optionally) specified here too, since they do not affect identification. If None, the effect_modifiers from the CausalModel are used. :param fit_estimator: Boolean flag on whether to fit the estimator. Setting it to False is useful to estimate the effect on new data using a previously fitted estimator. :param method_params: Dictionary containing any method-specific parameters. These are passed directly to the estimating method. See the docs for each estimation method for allowed method-specific params. :returns: An instance of the CausalEstimate class, containing the causal effect estimate and other method-dependent information """ treatment = parse_state(treatment) outcome = parse_state(outcome) causal_estimator_class = method.__class__ identified_estimand.set_identifier_method(identifier_name) if identified_estimand.no_directed_path: logger.warning("No directed path from {0} to {1}.".format(treatment, outcome)) return CausalEstimate( 0, identified_estimand, None, control_value=control_value, treatment_value=treatment_value ) # Check if estimator's target estimand is identified elif identified_estimand.estimands[identifier_name] is None: logger.error("No valid identified estimand available.") return CausalEstimate(None, None, None, control_value=control_value, treatment_value=treatment_value) method.update_input(treatment_value, control_value, target_units) estimate = method.estimate_effect() # Store parameters inside estimate object for refutation methods # TODO: This add_params needs to move to the estimator class # inside estimate_effect and estimate_conditional_effect estimate.add_params( estimand_type=identified_estimand.estimand_type, estimator_class=causal_estimator_class, test_significance=test_significance, evaluate_effect_strength=evaluate_effect_strength, confidence_intervals=confidence_intervals, target_units=target_units, effect_modifiers=effect_modifiers, method_params=method_params, ) return estimate class CausalEstimate: """Class for the estimate object that every causal estimator returns""" def __init__( self, estimate, target_estimand, realized_estimand_expr, control_value, treatment_value, conditional_estimates=None, **kwargs, ): self.value = estimate self.target_estimand = target_estimand self.realized_estimand_expr = realized_estimand_expr self.control_value = control_value self.treatment_value = treatment_value self.conditional_estimates = conditional_estimates self.params = kwargs if self.params is not None: for key, value in self.params.items(): setattr(self, key, value) self.effect_strength = None def add_estimator(self, estimator_instance): self.estimator = estimator_instance def add_effect_strength(self, strength_dict): self.effect_strength = strength_dict def add_params(self, **kwargs): self.params.update(kwargs) def get_confidence_intervals(self, confidence_level=None, method=None, **kwargs): """Get confidence intervals of the obtained estimate. By default, this is done with the help of bootstrapped confidence intervals but can be overridden if the specific estimator implements other methods of estimating confidence intervals. If the method provided is not bootstrap, this function calls the implementation of the specific estimator. :param method: Method for estimating confidence intervals. :param confidence_level: The confidence level of the confidence intervals of the estimate. :param kwargs: Other optional args to be passed to the CI method. :returns: The obtained confidence interval. """ confidence_intervals = self.estimator.estimate_confidence_intervals( estimate_value=self.value, confidence_level=confidence_level, method=method, **kwargs ) return confidence_intervals def get_standard_error(self, method=None, **kwargs): """Get standard error of the obtained estimate. By default, this is done with the help of bootstrapped standard errors but can be overridden if the specific estimator implements other methods of estimating standard error. If the method provided is not bootstrap, this function calls the implementation of the specific estimator. :param method: Method for computing the standard error. :param kwargs: Other optional parameters to be passed to the estimating method. :returns: Standard error of the causal estimate. """ std_error = self.estimator.estimate_std_error(method=method, **kwargs) return std_error def test_stat_significance(self, method=None, **kwargs): """Test statistical significance of the estimate obtained. By default, uses resampling to create a non-parametric significance test. Individual child estimators can implement different methods. If the method name is different from "bootstrap", this function calls the implementation of the child estimator. :param method: Method for checking statistical significance :param kwargs: Other optional parameters to be passed to the estimating method. :returns: p-value from the significance test """ signif_results = self.estimator.test_significance(self.value, method=method, **kwargs) return {"p_value": signif_results["p_value"]} def estimate_conditional_effects( self, effect_modifiers=None, num_quantiles=CausalEstimator.NUM_QUANTILES_TO_DISCRETIZE_CONT_COLS ): """Estimate treatment effect conditioned on given variables. If a numeric effect modifier is provided, it is discretized into quantile bins. If you would like a custom discretization, you can do so yourself: create a new column containing the discretized effect modifier and then include that column's name in the effect_modifier_names argument. :param effect_modifiers: Names of effect modifier variables over which the conditional effects will be estimated. If not provided, defaults to the effect modifiers specified during creation of the CausalEstimator object. :param num_quantiles: The number of quantiles into which a numeric effect modifier variable is discretized. Does not affect any categorical effect modifiers. :returns: A (multi-index) dataframe that provides separate effects for each value of the (discretized) effect modifiers. """ return self.estimator._estimate_conditional_effects( self.estimator._estimate_effect_fn, effect_modifiers, num_quantiles ) def interpret(self, method_name=None, **kwargs): """Interpret the causal estimate. :param method_name: Method used (string) or a list of methods. If None, then the default for the specific estimator is used. :param kwargs:: Optional parameters that are directly passed to the interpreter method. :returns: None """ if method_name is None: method_name = self.estimator.interpret_method method_name_arr = parse_state(method_name) for method in method_name_arr: interpreter = interpreters.get_class_object(method) interpreter(self, **kwargs).interpret() def __str__(self): s = "*** Causal Estimate ***\n" # No estimand was identified (identification failed) if self.target_estimand is None: return "Estimation failed! No relevant identified estimand available for this estimation method." s += "\n## Identified estimand\n{0}".format(self.target_estimand.__str__(only_target_estimand=True)) s += "\n## Realized estimand\n{0}".format(self.realized_estimand_expr) if hasattr(self, "estimator"): s += "\nTarget units: {0}\n".format(self.estimator.target_units_tostr()) s += "\n## Estimate\n" s += "Mean value: {0}\n".format(self.value) s += "" if hasattr(self, "cate_estimates"): s += "Effect estimates: {0}\n".format(self.cate_estimates) if hasattr(self, "estimator"): if self.estimator._significance_test: s += "p-value: {0}\n".format(self.estimator.signif_results_tostr(self.test_stat_significance())) if self.estimator._confidence_intervals: s += "{0}% confidence interval: {1}\n".format( 100 * self.estimator.confidence_level, self.get_confidence_intervals() ) if self.conditional_estimates is not None: s += "### Conditional Estimates\n" s += str(self.conditional_estimates) if self.effect_strength is not None: s += "\n## Effect Strength\n" s += "Change in outcome attributable to treatment: {}\n".format(self.effect_strength["fraction-effect"]) # s += "Variance in outcome explained by treatment: {}\n".format(self.effect_strength["r-squared"]) return s class RealizedEstimand(object): def __init__(self, identified_estimand, estimator_name): self.treatment_variable = identified_estimand.treatment_variable self.outcome_variable = identified_estimand.outcome_variable self.backdoor_variables = identified_estimand.get_backdoor_variables() self.instrumental_variables = identified_estimand.instrumental_variables self.estimand_type = identified_estimand.estimand_type self.estimand_expression = None self.assumptions = None self.estimator_name = estimator_name def update_assumptions(self, estimator_assumptions): self.assumptions = estimator_assumptions def update_estimand_expression(self, estimand_expression): self.estimand_expression = estimand_expression def __str__(self): s = "Realized estimand: {0}\n".format(self.estimator_name) s += "Realized estimand type: {0}\n".format(self.estimand_type) s += "Estimand expression:\n{0}\n".format(sp.pretty(self.estimand_expression)) j = 1 for ass_name, ass_str in self.assumptions.items(): s += "Estimand assumption {0}, {1}: {2}\n".format(j, ass_name, ass_str) j += 1 return s

andresmor-ms

2044d216c322a4b32c6eadce5da7d83463f19c2f

05bfa49dacf0061988c96c6f3e3756219df5422a

Agree, I'll do this when I refactor all the estimator objects in a future PR, that's why I decided to leave it as it currently is

andresmor-ms

py-why/dowhy

Functional api/estimate effect function

#### Estimate Effect function * Refactors the estimate effect into a separate function to keep backwards compatibility #### TODO (future PRs): * Add `fit(...)` method to estimators - Move data related parameters from the constructor to the `fit(...)` method * Refactor code to avoid `**kwargs` in `__init__(...)` constructors

2022-10-18 15:49:21+00:00

2022-10-25 17:02:02+00:00

dowhy/causal_estimator.py

import logging from collections import namedtuple import numpy as np import pandas as pd import sympy as sp from sklearn.utils import resample import dowhy.interpreters as interpreters from dowhy.utils.api import parse_state class CausalEstimator: """Base class for an estimator of causal effect. Subclasses implement different estimation methods. All estimation methods are in the package "dowhy.causal_estimators" """ # The default number of simulations for statistical testing DEFAULT_NUMBER_OF_SIMULATIONS_STAT_TEST = 1000 # The default number of simulations to obtain confidence intervals DEFAULT_NUMBER_OF_SIMULATIONS_CI = 100 # The portion of the total size that should be taken each time to find the confidence intervals # 1 is the recommended value # https://ocw.mit.edu/courses/mathematics/18-05-introduction-to-probability-and-statistics-spring-2014/readings/MIT18_05S14_Reading24.pdf # https://projecteuclid.org/download/pdf_1/euclid.ss/1032280214 DEFAULT_SAMPLE_SIZE_FRACTION = 1 # The default Confidence Level DEFAULT_CONFIDENCE_LEVEL = 0.95 # Number of quantiles to discretize continuous columns, for applying groupby NUM_QUANTILES_TO_DISCRETIZE_CONT_COLS = 5 # Prefix to add to temporary categorical variables created after discretization TEMP_CAT_COLUMN_PREFIX = "__categorical__" DEFAULT_NOTIMPLEMENTEDERROR_MSG = "not yet implemented for {0}. If you would this to be implemented in the next version, please raise an issue at https://github.com/microsoft/dowhy/issues" BootstrapEstimates = namedtuple("BootstrapEstimates", ["estimates", "params"]) DEFAULT_INTERPRET_METHOD = ["textual_effect_interpreter"] # std args to be removed from locals() before being passed to args_dict _STD_INIT_ARGS = ("self", "__class__", "args", "kwargs") def __init__( self, data, identified_estimand, treatment, outcome, control_value=0, treatment_value=1, test_significance=False, evaluate_effect_strength=False, confidence_intervals=False, target_units=None, effect_modifiers=None, num_null_simulations=DEFAULT_NUMBER_OF_SIMULATIONS_STAT_TEST, num_simulations=DEFAULT_NUMBER_OF_SIMULATIONS_CI, sample_size_fraction=DEFAULT_SAMPLE_SIZE_FRACTION, confidence_level=DEFAULT_CONFIDENCE_LEVEL, need_conditional_estimates="auto", num_quantiles_to_discretize_cont_cols=NUM_QUANTILES_TO_DISCRETIZE_CONT_COLS, **kwargs, ): """Initializes an estimator with data and names of relevant variables. This method is called from the constructors of its child classes. :param data: data frame containing the data :param identified_estimand: probability expression representing the target identified estimand to estimate. :param treatment: name of the treatment variable :param outcome: name of the outcome variable :param control_value: Value of the treatment in the control group, for effect estimation. If treatment is multi-variate, this can be a list. :param treatment_value: Value of the treatment in the treated group, for effect estimation. If treatment is multi-variate, this can be a list. :param test_significance: Binary flag or a string indicating whether to test significance and by which method. All estimators support test_significance="bootstrap" that estimates a p-value for the obtained estimate using the bootstrap method. Individual estimators can override this to support custom testing methods. The bootstrap method supports an optional parameter, num_null_simulations. If False, no testing is done. If True, significance of the estimate is tested using the custom method if available, otherwise by bootstrap. :param evaluate_effect_strength: (Experimental) whether to evaluate the strength of effect :param confidence_intervals: Binary flag or a string indicating whether the confidence intervals should be computed and which method should be used. All methods support estimation of confidence intervals using the bootstrap method by using the parameter confidence_intervals="bootstrap". The bootstrap method takes in two arguments (num_simulations and sample_size_fraction) that can be optionally specified in the params dictionary. Estimators may also override this to implement their own confidence interval method. If this parameter is False, no confidence intervals are computed. If True, confidence intervals are computed by the estimator's specific method if available, otherwise through bootstrap. :param target_units: The units for which the treatment effect should be estimated. This can be a string for common specifications of target units (namely, "ate", "att" and "atc"). It can also be a lambda function that can be used as an index for the data (pandas DataFrame). Alternatively, it can be a new DataFrame that contains values of the effect_modifiers and effect will be estimated only for this new data. :param effect_modifiers: Variables on which to compute separate effects, or return a heterogeneous effect function. Not all methods support this currently. :param num_null_simulations: The number of simulations for testing the statistical significance of the estimator :param num_simulations: The number of simulations for finding the confidence interval (and/or standard error) for a estimate :param sample_size_fraction: The size of the sample for the bootstrap estimator :param confidence_level: The confidence level of the confidence interval estimate :param need_conditional_estimates: Boolean flag indicating whether conditional estimates should be computed. Defaults to True if there are effect modifiers in the graph :param num_quantiles_to_discretize_cont_cols: The number of quantiles into which a numeric effect modifier is split, to enable estimation of conditional treatment effect over it. :param kwargs: (optional) Additional estimator-specific parameters :returns: an instance of the estimator class. """ self._data = data self._target_estimand = identified_estimand # Currently estimation methods only support univariate treatment and outcome self._treatment_name = treatment self._outcome_name = outcome[0] # assuming one-dimensional outcome self._control_value = control_value self._treatment_value = treatment_value self._significance_test = test_significance self._effect_strength_eval = evaluate_effect_strength self._target_units = target_units self._effect_modifier_names = effect_modifiers self._confidence_intervals = confidence_intervals self._bootstrap_estimates = None # for confidence intervals and std error self._bootstrap_null_estimates = None # for significance test self._effect_modifiers = None self.method_params = kwargs # Setting the default interpret method self.interpret_method = CausalEstimator.DEFAULT_INTERPRET_METHOD self.logger = logging.getLogger(__name__) # Setting treatment and outcome values if self._data is not None: self._treatment = self._data[self._treatment_name] self._outcome = self._data[self._outcome_name] # Now saving the effect modifiers if self._effect_modifier_names: # only add the observed nodes self._effect_modifier_names = [ cname for cname in self._effect_modifier_names if cname in self._data.columns ] if len(self._effect_modifier_names) > 0: self._effect_modifiers = self._data[self._effect_modifier_names] self._effect_modifiers = pd.get_dummies(self._effect_modifiers, drop_first=True) self.logger.debug("Effect modifiers: " + ",".join(self._effect_modifier_names)) else: self._effect_modifier_names = None # Check if some parameters were set, otherwise set to default values self.num_null_simulations = num_null_simulations self.num_simulations = num_simulations self.sample_size_fraction = sample_size_fraction self.confidence_level = confidence_level self.num_quantiles_to_discretize_cont_cols = num_quantiles_to_discretize_cont_cols # Estimate conditional estimates by default self.need_conditional_estimates = ( need_conditional_estimates if need_conditional_estimates != "auto" else bool(self._effect_modifier_names) ) @staticmethod def get_estimator_object(new_data, identified_estimand, estimate): """Create a new estimator of the same type as the one passed in the estimate argument. Creates a new object with new_data and the identified_estimand :param new_data: np.ndarray, pd.Series, pd.DataFrame The newly assigned data on which the estimator should run :param identified_estimand: IdentifiedEstimand An instance of the identified estimand class that provides the information with respect to which causal pathways are employed when the treatment effects the outcome :param estimate: CausalEstimate It is an already existing estimate whose properties we wish to replicate :returns: An instance of the same estimator class that had generated the given estimate. """ estimator_class = estimate.params["estimator_class"] new_estimator = estimator_class( new_data, identified_estimand, identified_estimand.treatment_variable, identified_estimand.outcome_variable, # names of treatment and outcome control_value=estimate.control_value, treatment_value=estimate.treatment_value, test_significance=False, evaluate_effect_strength=False, confidence_intervals=estimate.params["confidence_intervals"], target_units=estimate.params["target_units"], effect_modifiers=estimate.params["effect_modifiers"], **estimate.params["method_params"], ) return new_estimator def _estimate_effect(self): """This method is to be overriden by the child classes, so that they can run the estimation technique of their choice""" raise NotImplementedError( ("Main estimation method is " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG).format(self.__class__) ) def estimate_effect(self): """Base estimation method that calls the estimate_effect method of its calling subclass. Can optionally also test significance and estimate effect strength for any returned estimate. :param self: object instance of class Estimator :returns: A CausalEstimate instance that contains point estimates of average and conditional effects. Based on the parameters provided, it optionally includes confidence intervals, standard errors,statistical significance and other statistical parameters. """ est = self._estimate_effect() est.add_estimator(self) if self._significance_test: self.test_significance(est.value, method=self._significance_test) if self._confidence_intervals: self.estimate_confidence_intervals( est.value, confidence_level=self.confidence_level, method=self._confidence_intervals ) if self._effect_strength_eval: effect_strength_dict = self.evaluate_effect_strength(est) est.add_effect_strength(effect_strength_dict) return est def estimate_effect_naive(self): # TODO Only works for binary treatment df_withtreatment = self._data.loc[self._data[self._treatment_name] == 1] df_notreatment = self._data.loc[self._data[self._treatment_name] == 0] est = np.mean(df_withtreatment[self._outcome_name]) - np.mean(df_notreatment[self._outcome_name]) return CausalEstimate(est, None, None, control_value=0, treatment_value=1) def _estimate_effect_fn(self, data_df): """Function used in conditional effect estimation. This function is to be overridden by each child estimator. The overridden function should take in a dataframe as input and return the estimate for that data. """ raise NotImplementedError( ("Conditional treatment effects are " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG).format( self.__class__ ) ) def _estimate_conditional_effects(self, estimate_effect_fn, effect_modifier_names=None, num_quantiles=None): """Estimate conditional treatment effects. Common method for all estimators that utilizes a specific estimate_effect_fn implemented by each child estimator. If a numeric effect modifier is provided, it is discretized into quantile bins. If you would like a custom discretization, you can do so yourself: create a new column containing the discretized effect modifier and then include that column's name in the effect_modifier_names argument. :param estimate_effect_fn: Function that has a single parameter (a data frame) and returns the treatment effect estimate on that data. :param effect_modifier_names: Names of effect modifier variables over which the conditional effects will be estimated. If not provided, defaults to the effect modifiers specified during creation of the CausalEstimator object. :param num_quantiles: The number of quantiles into which a numeric effect modifier variable is discretized. Does not affect any categorical effect modifiers. :returns: A (multi-index) dataframe that provides separate effects for each value of the (discretized) effect modifiers. """ # Defaulting to class default values if parameters are not provided if effect_modifier_names is None: effect_modifier_names = self._effect_modifier_names if num_quantiles is None: num_quantiles = self.num_quantiles_to_discretize_cont_cols # Checking that there is at least one effect modifier if not effect_modifier_names: raise ValueError("At least one effect modifier should be specified to compute conditional effects.") # Making sure that effect_modifier_names is a list effect_modifier_names = parse_state(effect_modifier_names) if not all(em in self._effect_modifier_names for em in effect_modifier_names): self.logger.warn( "At least one of the provided effect modifiers was not included while fitting the estimator. You may get incorrect results. To resolve, fit the estimator again by providing the updated effect modifiers in estimate_effect()." ) # Making a copy since we are going to be changing effect modifier names effect_modifier_names = effect_modifier_names.copy() prefix = CausalEstimator.TEMP_CAT_COLUMN_PREFIX # For every numeric effect modifier, adding a temp categorical column for i in range(len(effect_modifier_names)): em = effect_modifier_names[i] if pd.api.types.is_numeric_dtype(self._data[em].dtypes): self._data[prefix + str(em)] = pd.qcut(self._data[em], num_quantiles, duplicates="drop") effect_modifier_names[i] = prefix + str(em) # Grouping by effect modifiers and computing effect separately by_effect_mods = self._data.groupby(effect_modifier_names) cond_est_fn = lambda x: self._do(self._treatment_value, x) - self._do(self._control_value, x) conditional_estimates = by_effect_mods.apply(estimate_effect_fn) # Deleting the temporary categorical columns for em in effect_modifier_names: if em.startswith(prefix): self._data.pop(em) return conditional_estimates def _do(self, x, data_df=None): raise NotImplementedError( ("Do-operator is " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG).format(self.__class__) ) def do(self, x, data_df=None): """Method that implements the do-operator. Given a value x for the treatment, returns the expected value of the outcome when the treatment is intervened to a value x. :param x: Value of the treatment :param data_df: Data on which the do-operator is to be applied. :returns: Value of the outcome when treatment is intervened/set to x. """ est = self._do(x, data_df) return est def construct_symbolic_estimator(self, estimand): raise NotImplementedError(("Symbolic estimator string is ").format(self.__class__)) def _generate_bootstrap_estimates(self, num_bootstrap_simulations, sample_size_fraction): """Helper function to generate causal estimates over bootstrapped samples. :param num_bootstrap_simulations: Number of simulations for the bootstrap method. :param sample_size_fraction: Fraction of the dataset to be resampled. :returns: A collections.namedtuple containing a list of bootstrapped estimates and a dictionary containing parameters used for the bootstrap. """ # The array that stores the results of all estimations simulation_results = np.zeros(num_bootstrap_simulations) # Find the sample size the proportion with the population size sample_size = int(sample_size_fraction * len(self._data)) if sample_size > len(self._data): self.logger.warning("WARN: The sample size is greater than the data being sampled") self.logger.info("INFO: The sample size: {}".format(sample_size)) self.logger.info("INFO: The number of simulations: {}".format(num_bootstrap_simulations)) # Perform the set number of simulations for index in range(num_bootstrap_simulations): new_data = resample(self._data, n_samples=sample_size) new_estimator = type(self)( new_data, self._target_estimand, self._target_estimand.treatment_variable, self._target_estimand.outcome_variable, # names of treatment and outcome treatment_value=self._treatment_value, control_value=self._control_value, test_significance=False, evaluate_effect_strength=False, confidence_intervals=False, target_units=self._target_units, effect_modifiers=self._effect_modifier_names, **self.method_params, ) new_effect = new_estimator.estimate_effect() simulation_results[index] = new_effect.value estimates = CausalEstimator.BootstrapEstimates( simulation_results, {"num_simulations": num_bootstrap_simulations, "sample_size_fraction": sample_size_fraction}, ) return estimates def _estimate_confidence_intervals_with_bootstrap( self, estimate_value, confidence_level=None, num_simulations=None, sample_size_fraction=None ): """ Method to compute confidence interval using bootstrapped sampling. :param estimate_value: obtained estimate's value :param confidence_level: The level for which to compute CI (e.g., 95% confidence level translates to confidence_level=0.95) :param num_simulations: The number of simulations to be performed to get the bootstrap confidence intervals. :param sample_size_fraction: The fraction of the dataset to be resampled. :returns: confidence interval at the specified level. For more details on bootstrap or resampling statistics, refer to the following links: https://ocw.mit.edu/courses/mathematics/18-05-introduction-to-probability-and-statistics-spring-2014/readings/MIT18_05S14_Reading24.pdf https://projecteuclid.org/download/pdf_1/euclid.ss/1032280214 """ # Using class default parameters if not specified if num_simulations is None: num_simulations = self.num_simulations if sample_size_fraction is None: sample_size_fraction = self.sample_size_fraction # Checking if bootstrap_estimates are already computed if self._bootstrap_estimates is None: self._bootstrap_estimates = self._generate_bootstrap_estimates(num_simulations, sample_size_fraction) elif CausalEstimator.is_bootstrap_parameter_changed(self._bootstrap_estimates.params, locals()): # Checked if any parameter is changed from the previous std error estimate self._bootstrap_estimates = self._generate_bootstrap_estimates(num_simulations, sample_size_fraction) # Now use the data obtained from the simulations to get the value of the confidence estimates bootstrap_estimates = self._bootstrap_estimates.estimates # Get the variations of each bootstrap estimate and sort bootstrap_variations = [bootstrap_estimate - estimate_value for bootstrap_estimate in bootstrap_estimates] sorted_bootstrap_variations = np.sort(bootstrap_variations) # Now we take the (1- p)th and the (p)th variations, where p is the chosen confidence level upper_bound_index = int((1 - confidence_level) * len(sorted_bootstrap_variations)) lower_bound_index = int(confidence_level * len(sorted_bootstrap_variations)) # Get the lower and upper bounds by subtracting the variations from the estimate lower_bound = estimate_value - sorted_bootstrap_variations[lower_bound_index] upper_bound = estimate_value - sorted_bootstrap_variations[upper_bound_index] return lower_bound, upper_bound def _estimate_confidence_intervals(self, confidence_level=None, method=None, **kwargs): """ This method is to be overriden by the child classes, so that they can run a confidence interval estimation method suited to the specific causal estimator. """ raise NotImplementedError( ( "This method for estimating confidence intervals is " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG + " Meanwhile, you can try the bootstrap method (method='bootstrap') to estimate confidence intervals." ).format(self.__class__) ) def estimate_confidence_intervals(self, estimate_value, confidence_level=None, method=None, **kwargs): """Find the confidence intervals corresponding to any estimator By default, this is done with the help of bootstrapped confidence intervals but can be overridden if the specific estimator implements other methods of estimating confidence intervals. If the method provided is not bootstrap, this function calls the implementation of the specific estimator. :param estimate_value: obtained estimate's value :param method: Method for estimating confidence intervals. :param confidence_level: The confidence level of the confidence intervals of the estimate. :param kwargs: Other optional args to be passed to the CI method. :returns: The obtained confidence interval. """ if method is None: if self._confidence_intervals: method = self._confidence_intervals # this is either True or methodname else: method = "default" confidence_intervals = None if confidence_level is None: confidence_level = self.confidence_level if method == "default" or method is True: # user has not provided any method try: confidence_intervals = self._estimate_confidence_intervals(confidence_level, method=method, **kwargs) except NotImplementedError: confidence_intervals = self._estimate_confidence_intervals_with_bootstrap( estimate_value, confidence_level, **kwargs ) else: if method == "bootstrap": confidence_intervals = self._estimate_confidence_intervals_with_bootstrap( estimate_value, confidence_level, **kwargs ) else: confidence_intervals = self._estimate_confidence_intervals(confidence_level, method=method, **kwargs) return confidence_intervals def _estimate_std_error_with_bootstrap(self, num_simulations=None, sample_size_fraction=None): """Compute standard error using the bootstrap method. Standard error and confidence intervals use the same parameter num_simulations for the number of bootstrap simulations. :param num_simulations: Number of bootstrapped samples. :param sample_size_fraction: Fraction of data to be resampled. :returns: Standard error of the obtained estimate. """ # Use existing params, if new user defined params are not present if num_simulations is None: num_simulations = self.num_simulations if sample_size_fraction is None: sample_size_fraction = self.sample_size_fraction # Checking if bootstrap_estimates are already computed if self._bootstrap_estimates is None: self._bootstrap_estimates = self._generate_bootstrap_estimates(num_simulations, sample_size_fraction) elif CausalEstimator.is_bootstrap_parameter_changed(self._bootstrap_estimates.params, locals()): # Check if any parameter is changed from the previous std error estimate self._bootstrap_estimates = self._generate_bootstrap_estimates(num_simulations, sample_size_fraction) std_error = np.std(self._bootstrap_estimates.estimates) return std_error def _estimate_std_error(self, method=None, **kwargs): """ This method is to be overriden by the child classes, so that they can run a standard error estimation method suited to the specific causal estimator. """ raise NotImplementedError( ( "This method for estimating standard errors is " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG + " Meanwhile, you can try the bootstrap method (method='bootstrap') to estimate standard errors." ).format(self.__class__) ) def estimate_std_error(self, method=None, **kwargs): """Compute standard error of an obtained causal estimate. :param method: Method for computing the standard error. :param kwargs: Other optional parameters to be passed to the estimating method. :returns: Standard error of the causal estimate. """ if method is None: if self._confidence_intervals: method = self._confidence_intervals else: method = "default" std_error = None if method == "default" or method is True: # user has not provided any method try: std_error = self._estimate_std_error(method, **kwargs) except NotImplementedError: std_error = self._estimate_std_error_with_bootstrap(**kwargs) else: if method == "bootstrap": std_error = self._estimate_std_error_with_bootstrap(**kwargs) else: std_error = self._estimate_std_error(method, **kwargs) return std_error def _test_significance_with_bootstrap(self, estimate_value, num_null_simulations=None): """Test statistical significance of an estimate using the bootstrap method. :param estimate_value: Obtained estimate's value :param num_null_simulations: Number of simulations for the null hypothesis :returns: p-value of the statistical significance test. """ # Use existing params, if new user defined params are not present if num_null_simulations is None: num_null_simulations = self.num_null_simulations do_retest = self._bootstrap_null_estimates is None or CausalEstimator.is_bootstrap_parameter_changed( self._bootstrap_null_estimates.params, locals() ) if do_retest: null_estimates = np.zeros(num_null_simulations) for i in range(num_null_simulations): new_outcome = np.random.permutation(self._outcome) new_data = self._data.assign(dummy_outcome=new_outcome) # self._outcome = self._data["dummy_outcome"] new_estimator = type(self)( new_data, self._target_estimand, self._target_estimand.treatment_variable, ("dummy_outcome",), test_significance=False, evaluate_effect_strength=False, confidence_intervals=False, target_units=self._target_units, effect_modifiers=self._effect_modifier_names, **self.method_params, ) new_effect = new_estimator.estimate_effect() null_estimates[i] = new_effect.value self._bootstrap_null_estimates = CausalEstimator.BootstrapEstimates( null_estimates, {"num_null_simulations": num_null_simulations, "sample_size_fraction": 1} ) # Processing the null hypothesis estimates sorted_null_estimates = np.sort(self._bootstrap_null_estimates.estimates) self.logger.debug("Null estimates: {0}".format(sorted_null_estimates)) median_estimate = sorted_null_estimates[int(num_null_simulations / 2)] # Doing a two-sided test if estimate_value > median_estimate: # Being conservative with the p-value reported estimate_index = np.searchsorted(sorted_null_estimates, estimate_value, side="left") p_value = 1 - (estimate_index / num_null_simulations) if estimate_value <= median_estimate: # Being conservative with the p-value reported estimate_index = np.searchsorted(sorted_null_estimates, estimate_value, side="right") p_value = estimate_index / num_null_simulations # If the estimate_index is 0, it depends on the number of simulations if p_value == 0: p_value = (0, 1 / len(sorted_null_estimates)) # a tuple determining the range. elif p_value == 1: p_value = (1 - 1 / len(sorted_null_estimates), 1) signif_dict = {"p_value": p_value} return signif_dict def _test_significance(self, estimate_value, method=None, **kwargs): """ This method is to be overriden by the child classes, so that they can run a significance test suited to the specific causal estimator. """ raise NotImplementedError( ( "This method for testing statistical significance is " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG + " Meanwhile, you can try the bootstrap method (method='bootstrap') to test statistical significance." ).format(self.__class__) ) def test_significance(self, estimate_value, method=None, **kwargs): """Test statistical significance of obtained estimate. By default, uses resampling to create a non-parametric significance test. A general procedure. Individual child estimators can implement different methods. If the method name is different from "bootstrap", this function calls the implementation of the child estimator. :param self: object instance of class Estimator :param estimate_value: obtained estimate's value :param method: Method for checking statistical significance :returns: p-value from the significance test """ if method is None: if self._significance_test: method = self._significance_test # this is either True or methodname else: method = "default" signif_dict = None if method == "default" or method is True: # user has not provided any method try: signif_dict = self._test_significance(estimate_value, method, **kwargs) except NotImplementedError: signif_dict = self._test_significance_with_bootstrap(estimate_value, **kwargs) else: if method == "bootstrap": signif_dict = self._test_significance_with_bootstrap(estimate_value, **kwargs) else: signif_dict = self._test_significance(estimate_value, method, **kwargs) return signif_dict def evaluate_effect_strength(self, estimate): fraction_effect_explained = self._evaluate_effect_strength(estimate, method="fraction-effect") # Need to test r-squared before supporting # effect_r_squared = self._evaluate_effect_strength(estimate, method="r-squared") strength_dict = { "fraction-effect": fraction_effect_explained # 'r-squared': effect_r_squared } return strength_dict def _evaluate_effect_strength(self, estimate, method="fraction-effect"): supported_methods = ["fraction-effect"] if method not in supported_methods: raise NotImplementedError("This method is not supported for evaluating effect strength") if method == "fraction-effect": naive_obs_estimate = self.estimate_effect_naive() self.logger.debug(estimate.value, naive_obs_estimate.value) fraction_effect_explained = estimate.value / naive_obs_estimate.value return fraction_effect_explained # elif method == "r-squared": # outcome_mean = np.mean(self._outcome) # total_variance = np.sum(np.square(self._outcome - outcome_mean)) # Assuming a linear model with one variable: the treatment # Currently only works for continuous y # causal_model = outcome_mean + estimate.value*self._treatment # squared_residual = np.sum(np.square(self._outcome - causal_model)) # r_squared = 1 - (squared_residual/total_variance) # return r_squared else: return None def update_input(self, treatment_value, control_value, target_units): self._control_value = control_value self._treatment_value = treatment_value self._target_units = target_units @staticmethod def is_bootstrap_parameter_changed(bootstrap_estimates_params, given_params): """Check whether parameters of the bootstrap have changed. This is an efficiency method that checks if fresh resampling of the bootstrap samples is required. Returns True if parameters have changed and resampling should be done again. :param bootstrap_estimates_params: A dictionary of parameters for the current bootstrap samples :param given_params: A dictionary of parameters passed by the user :returns: A binary flag denoting whether the parameters are different. """ is_any_parameter_changed = False for prm, val in bootstrap_estimates_params.items(): given_val = given_params.get(prm, None) if given_val is not None and given_val != val: is_any_parameter_changed = True break return is_any_parameter_changed def target_units_tostr(self): s = "" if type(self._target_units) is str: s += self._target_units elif callable(self._target_units): s += "Data subset defined by a function" elif isinstance(self._target_units, pd.DataFrame): s += "Data subset provided as a data frame" return s def signif_results_tostr(self, signif_results): s = "" pval = signif_results["p_value"] if type(pval) is tuple: s += "[{0}, {1}]".format(pval[0], pval[1]) else: s += "{0}".format(pval) return s class CausalEstimate: """Class for the estimate object that every causal estimator returns""" def __init__( self, estimate, target_estimand, realized_estimand_expr, control_value, treatment_value, conditional_estimates=None, **kwargs, ): self.value = estimate self.target_estimand = target_estimand self.realized_estimand_expr = realized_estimand_expr self.control_value = control_value self.treatment_value = treatment_value self.conditional_estimates = conditional_estimates self.params = kwargs if self.params is not None: for key, value in self.params.items(): setattr(self, key, value) self.effect_strength = None def add_estimator(self, estimator_instance): self.estimator = estimator_instance def add_effect_strength(self, strength_dict): self.effect_strength = strength_dict def add_params(self, **kwargs): self.params.update(kwargs) def get_confidence_intervals(self, confidence_level=None, method=None, **kwargs): """Get confidence intervals of the obtained estimate. By default, this is done with the help of bootstrapped confidence intervals but can be overridden if the specific estimator implements other methods of estimating confidence intervals. If the method provided is not bootstrap, this function calls the implementation of the specific estimator. :param method: Method for estimating confidence intervals. :param confidence_level: The confidence level of the confidence intervals of the estimate. :param kwargs: Other optional args to be passed to the CI method. :returns: The obtained confidence interval. """ confidence_intervals = self.estimator.estimate_confidence_intervals( estimate_value=self.value, confidence_level=confidence_level, method=method, **kwargs ) return confidence_intervals def get_standard_error(self, method=None, **kwargs): """Get standard error of the obtained estimate. By default, this is done with the help of bootstrapped standard errors but can be overridden if the specific estimator implements other methods of estimating standard error. If the method provided is not bootstrap, this function calls the implementation of the specific estimator. :param method: Method for computing the standard error. :param kwargs: Other optional parameters to be passed to the estimating method. :returns: Standard error of the causal estimate. """ std_error = self.estimator.estimate_std_error(method=method, **kwargs) return std_error def test_stat_significance(self, method=None, **kwargs): """Test statistical significance of the estimate obtained. By default, uses resampling to create a non-parametric significance test. Individual child estimators can implement different methods. If the method name is different from "bootstrap", this function calls the implementation of the child estimator. :param method: Method for checking statistical significance :param kwargs: Other optional parameters to be passed to the estimating method. :returns: p-value from the significance test """ signif_results = self.estimator.test_significance(self.value, method=method, **kwargs) return {"p_value": signif_results["p_value"]} def estimate_conditional_effects( self, effect_modifiers=None, num_quantiles=CausalEstimator.NUM_QUANTILES_TO_DISCRETIZE_CONT_COLS ): """Estimate treatment effect conditioned on given variables. If a numeric effect modifier is provided, it is discretized into quantile bins. If you would like a custom discretization, you can do so yourself: create a new column containing the discretized effect modifier and then include that column's name in the effect_modifier_names argument. :param effect_modifiers: Names of effect modifier variables over which the conditional effects will be estimated. If not provided, defaults to the effect modifiers specified during creation of the CausalEstimator object. :param num_quantiles: The number of quantiles into which a numeric effect modifier variable is discretized. Does not affect any categorical effect modifiers. :returns: A (multi-index) dataframe that provides separate effects for each value of the (discretized) effect modifiers. """ return self.estimator._estimate_conditional_effects( self.estimator._estimate_effect_fn, effect_modifiers, num_quantiles ) def interpret(self, method_name=None, **kwargs): """Interpret the causal estimate. :param method_name: Method used (string) or a list of methods. If None, then the default for the specific estimator is used. :param kwargs:: Optional parameters that are directly passed to the interpreter method. :returns: None """ if method_name is None: method_name = self.estimator.interpret_method method_name_arr = parse_state(method_name) for method in method_name_arr: interpreter = interpreters.get_class_object(method) interpreter(self, **kwargs).interpret() def __str__(self): s = "*** Causal Estimate ***\n" # No estimand was identified (identification failed) if self.target_estimand is None: return "Estimation failed! No relevant identified estimand available for this estimation method." s += "\n## Identified estimand\n{0}".format(self.target_estimand.__str__(only_target_estimand=True)) s += "\n## Realized estimand\n{0}".format(self.realized_estimand_expr) if hasattr(self, "estimator"): s += "\nTarget units: {0}\n".format(self.estimator.target_units_tostr()) s += "\n## Estimate\n" s += "Mean value: {0}\n".format(self.value) s += "" if hasattr(self, "cate_estimates"): s += "Effect estimates: {0}\n".format(self.cate_estimates) if hasattr(self, "estimator"): if self.estimator._significance_test: s += "p-value: {0}\n".format(self.estimator.signif_results_tostr(self.test_stat_significance())) if self.estimator._confidence_intervals: s += "{0}% confidence interval: {1}\n".format( 100 * self.estimator.confidence_level, self.get_confidence_intervals() ) if self.conditional_estimates is not None: s += "### Conditional Estimates\n" s += str(self.conditional_estimates) if self.effect_strength is not None: s += "\n## Effect Strength\n" s += "Change in outcome attributable to treatment: {}\n".format(self.effect_strength["fraction-effect"]) # s += "Variance in outcome explained by treatment: {}\n".format(self.effect_strength["r-squared"]) return s class RealizedEstimand(object): def __init__(self, identified_estimand, estimator_name): self.treatment_variable = identified_estimand.treatment_variable self.outcome_variable = identified_estimand.outcome_variable self.backdoor_variables = identified_estimand.get_backdoor_variables() self.instrumental_variables = identified_estimand.instrumental_variables self.estimand_type = identified_estimand.estimand_type self.estimand_expression = None self.assumptions = None self.estimator_name = estimator_name def update_assumptions(self, estimator_assumptions): self.assumptions = estimator_assumptions def update_estimand_expression(self, estimand_expression): self.estimand_expression = estimand_expression def __str__(self): s = "Realized estimand: {0}\n".format(self.estimator_name) s += "Realized estimand type: {0}\n".format(self.estimand_type) s += "Estimand expression:\n{0}\n".format(sp.pretty(self.estimand_expression)) j = 1 for ass_name, ass_str in self.assumptions.items(): s += "Estimand assumption {0}, {1}: {2}\n".format(j, ass_name, ass_str) j += 1 return s

import logging from collections import namedtuple from typing import Dict, List, Optional, Union import numpy as np import pandas as pd import sympy as sp from sklearn.utils import resample import dowhy.interpreters as interpreters from dowhy import causal_estimators from dowhy.causal_graph import CausalGraph from dowhy.causal_identifier.identified_estimand import IdentifiedEstimand from dowhy.utils.api import parse_state logger = logging.getLogger(__name__) class CausalEstimator: """Base class for an estimator of causal effect. Subclasses implement different estimation methods. All estimation methods are in the package "dowhy.causal_estimators" """ # The default number of simulations for statistical testing DEFAULT_NUMBER_OF_SIMULATIONS_STAT_TEST = 1000 # The default number of simulations to obtain confidence intervals DEFAULT_NUMBER_OF_SIMULATIONS_CI = 100 # The portion of the total size that should be taken each time to find the confidence intervals # 1 is the recommended value # https://ocw.mit.edu/courses/mathematics/18-05-introduction-to-probability-and-statistics-spring-2014/readings/MIT18_05S14_Reading24.pdf # https://projecteuclid.org/download/pdf_1/euclid.ss/1032280214 DEFAULT_SAMPLE_SIZE_FRACTION = 1 # The default Confidence Level DEFAULT_CONFIDENCE_LEVEL = 0.95 # Number of quantiles to discretize continuous columns, for applying groupby NUM_QUANTILES_TO_DISCRETIZE_CONT_COLS = 5 # Prefix to add to temporary categorical variables created after discretization TEMP_CAT_COLUMN_PREFIX = "__categorical__" DEFAULT_NOTIMPLEMENTEDERROR_MSG = "not yet implemented for {0}. If you would this to be implemented in the next version, please raise an issue at https://github.com/microsoft/dowhy/issues" BootstrapEstimates = namedtuple("BootstrapEstimates", ["estimates", "params"]) DEFAULT_INTERPRET_METHOD = ["textual_effect_interpreter"] # std args to be removed from locals() before being passed to args_dict _STD_INIT_ARGS = ("self", "__class__", "args", "kwargs") def __init__( self, data, identified_estimand, treatment, outcome, control_value=0, treatment_value=1, test_significance=False, evaluate_effect_strength=False, confidence_intervals=False, target_units=None, effect_modifiers=None, num_null_simulations=DEFAULT_NUMBER_OF_SIMULATIONS_STAT_TEST, num_simulations=DEFAULT_NUMBER_OF_SIMULATIONS_CI, sample_size_fraction=DEFAULT_SAMPLE_SIZE_FRACTION, confidence_level=DEFAULT_CONFIDENCE_LEVEL, need_conditional_estimates="auto", num_quantiles_to_discretize_cont_cols=NUM_QUANTILES_TO_DISCRETIZE_CONT_COLS, **kwargs, ): """Initializes an estimator with data and names of relevant variables. This method is called from the constructors of its child classes. :param data: data frame containing the data :param identified_estimand: probability expression representing the target identified estimand to estimate. :param treatment: name of the treatment variable :param outcome: name of the outcome variable :param control_value: Value of the treatment in the control group, for effect estimation. If treatment is multi-variate, this can be a list. :param treatment_value: Value of the treatment in the treated group, for effect estimation. If treatment is multi-variate, this can be a list. :param test_significance: Binary flag or a string indicating whether to test significance and by which method. All estimators support test_significance="bootstrap" that estimates a p-value for the obtained estimate using the bootstrap method. Individual estimators can override this to support custom testing methods. The bootstrap method supports an optional parameter, num_null_simulations. If False, no testing is done. If True, significance of the estimate is tested using the custom method if available, otherwise by bootstrap. :param evaluate_effect_strength: (Experimental) whether to evaluate the strength of effect :param confidence_intervals: Binary flag or a string indicating whether the confidence intervals should be computed and which method should be used. All methods support estimation of confidence intervals using the bootstrap method by using the parameter confidence_intervals="bootstrap". The bootstrap method takes in two arguments (num_simulations and sample_size_fraction) that can be optionally specified in the params dictionary. Estimators may also override this to implement their own confidence interval method. If this parameter is False, no confidence intervals are computed. If True, confidence intervals are computed by the estimator's specific method if available, otherwise through bootstrap. :param target_units: The units for which the treatment effect should be estimated. This can be a string for common specifications of target units (namely, "ate", "att" and "atc"). It can also be a lambda function that can be used as an index for the data (pandas DataFrame). Alternatively, it can be a new DataFrame that contains values of the effect_modifiers and effect will be estimated only for this new data. :param effect_modifiers: Variables on which to compute separate effects, or return a heterogeneous effect function. Not all methods support this currently. :param num_null_simulations: The number of simulations for testing the statistical significance of the estimator :param num_simulations: The number of simulations for finding the confidence interval (and/or standard error) for a estimate :param sample_size_fraction: The size of the sample for the bootstrap estimator :param confidence_level: The confidence level of the confidence interval estimate :param need_conditional_estimates: Boolean flag indicating whether conditional estimates should be computed. Defaults to True if there are effect modifiers in the graph :param num_quantiles_to_discretize_cont_cols: The number of quantiles into which a numeric effect modifier is split, to enable estimation of conditional treatment effect over it. :param kwargs: (optional) Additional estimator-specific parameters :returns: an instance of the estimator class. """ self._data = data self._target_estimand = identified_estimand # Currently estimation methods only support univariate treatment and outcome self._treatment_name = treatment self._outcome_name = outcome[0] # assuming one-dimensional outcome self._control_value = control_value self._treatment_value = treatment_value self._significance_test = test_significance self._effect_strength_eval = evaluate_effect_strength self._target_units = target_units self._effect_modifier_names = effect_modifiers self._confidence_intervals = confidence_intervals self._bootstrap_estimates = None # for confidence intervals and std error self._bootstrap_null_estimates = None # for significance test self._effect_modifiers = None self.method_params = kwargs # Setting the default interpret method self.interpret_method = CausalEstimator.DEFAULT_INTERPRET_METHOD self.logger = logging.getLogger(__name__) # Setting treatment and outcome values if self._data is not None: self._treatment = self._data[self._treatment_name] self._outcome = self._data[self._outcome_name] if self._effect_modifier_names: # only add the observed nodes self._effect_modifier_names = [ cname for cname in self._effect_modifier_names if cname in self._data.columns ] if len(self._effect_modifier_names) > 0: self._effect_modifiers = self._data[self._effect_modifier_names] self._effect_modifiers = pd.get_dummies(self._effect_modifiers, drop_first=True) self.logger.debug("Effect modifiers: " + ",".join(self._effect_modifier_names)) else: self._effect_modifier_names = None # Check if some parameters were set, otherwise set to default values self.num_null_simulations = num_null_simulations self.num_simulations = num_simulations self.sample_size_fraction = sample_size_fraction self.confidence_level = confidence_level self.num_quantiles_to_discretize_cont_cols = num_quantiles_to_discretize_cont_cols # Estimate conditional estimates by default self.need_conditional_estimates = ( need_conditional_estimates if need_conditional_estimates != "auto" else bool(self._effect_modifier_names) ) @staticmethod def get_estimator_object(new_data, identified_estimand, estimate): """Create a new estimator of the same type as the one passed in the estimate argument. Creates a new object with new_data and the identified_estimand :param new_data: np.ndarray, pd.Series, pd.DataFrame The newly assigned data on which the estimator should run :param identified_estimand: IdentifiedEstimand An instance of the identified estimand class that provides the information with respect to which causal pathways are employed when the treatment effects the outcome :param estimate: CausalEstimate It is an already existing estimate whose properties we wish to replicate :returns: An instance of the same estimator class that had generated the given estimate. """ estimator_class = estimate.params["estimator_class"] new_estimator = estimator_class( new_data, identified_estimand, identified_estimand.treatment_variable, identified_estimand.outcome_variable, # names of treatment and outcome control_value=estimate.control_value, treatment_value=estimate.treatment_value, test_significance=False, evaluate_effect_strength=False, confidence_intervals=estimate.params["confidence_intervals"], target_units=estimate.params["target_units"], effect_modifiers=estimate.params["effect_modifiers"], **estimate.params["method_params"] if estimate.params["method_params"] is not None else {}, ) return new_estimator def _estimate_effect(self): """This method is to be overriden by the child classes, so that they can run the estimation technique of their choice""" raise NotImplementedError( ("Main estimation method is " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG).format(self.__class__) ) def estimate_effect(self): """Base estimation method that calls the estimate_effect method of its calling subclass. Can optionally also test significance and estimate effect strength for any returned estimate. :param self: object instance of class Estimator :returns: A CausalEstimate instance that contains point estimates of average and conditional effects. Based on the parameters provided, it optionally includes confidence intervals, standard errors,statistical significance and other statistical parameters. """ est = self._estimate_effect() est.add_estimator(self) if self._significance_test: self.test_significance(est.value, method=self._significance_test) if self._confidence_intervals: self.estimate_confidence_intervals( est.value, confidence_level=self.confidence_level, method=self._confidence_intervals ) if self._effect_strength_eval: effect_strength_dict = self.evaluate_effect_strength(est) est.add_effect_strength(effect_strength_dict) return est def estimate_effect_naive(self): # TODO Only works for binary treatment df_withtreatment = self._data.loc[self._data[self._treatment_name] == 1] df_notreatment = self._data.loc[self._data[self._treatment_name] == 0] est = np.mean(df_withtreatment[self._outcome_name]) - np.mean(df_notreatment[self._outcome_name]) return CausalEstimate(est, None, None, control_value=0, treatment_value=1) def _estimate_effect_fn(self, data_df): """Function used in conditional effect estimation. This function is to be overridden by each child estimator. The overridden function should take in a dataframe as input and return the estimate for that data. """ raise NotImplementedError( ("Conditional treatment effects are " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG).format( self.__class__ ) ) def _estimate_conditional_effects(self, estimate_effect_fn, effect_modifier_names=None, num_quantiles=None): """Estimate conditional treatment effects. Common method for all estimators that utilizes a specific estimate_effect_fn implemented by each child estimator. If a numeric effect modifier is provided, it is discretized into quantile bins. If you would like a custom discretization, you can do so yourself: create a new column containing the discretized effect modifier and then include that column's name in the effect_modifier_names argument. :param estimate_effect_fn: Function that has a single parameter (a data frame) and returns the treatment effect estimate on that data. :param effect_modifier_names: Names of effect modifier variables over which the conditional effects will be estimated. If not provided, defaults to the effect modifiers specified during creation of the CausalEstimator object. :param num_quantiles: The number of quantiles into which a numeric effect modifier variable is discretized. Does not affect any categorical effect modifiers. :returns: A (multi-index) dataframe that provides separate effects for each value of the (discretized) effect modifiers. """ # Defaulting to class default values if parameters are not provided if effect_modifier_names is None: effect_modifier_names = self._effect_modifier_names if num_quantiles is None: num_quantiles = self.num_quantiles_to_discretize_cont_cols # Checking that there is at least one effect modifier if not effect_modifier_names: raise ValueError("At least one effect modifier should be specified to compute conditional effects.") # Making sure that effect_modifier_names is a list effect_modifier_names = parse_state(effect_modifier_names) if not all(em in self._effect_modifier_names for em in effect_modifier_names): self.logger.warn( "At least one of the provided effect modifiers was not included while fitting the estimator. You may get incorrect results. To resolve, fit the estimator again by providing the updated effect modifiers in estimate_effect()." ) # Making a copy since we are going to be changing effect modifier names effect_modifier_names = effect_modifier_names.copy() prefix = CausalEstimator.TEMP_CAT_COLUMN_PREFIX # For every numeric effect modifier, adding a temp categorical column for i in range(len(effect_modifier_names)): em = effect_modifier_names[i] if pd.api.types.is_numeric_dtype(self._data[em].dtypes): self._data[prefix + str(em)] = pd.qcut(self._data[em], num_quantiles, duplicates="drop") effect_modifier_names[i] = prefix + str(em) # Grouping by effect modifiers and computing effect separately by_effect_mods = self._data.groupby(effect_modifier_names) cond_est_fn = lambda x: self._do(self._treatment_value, x) - self._do(self._control_value, x) conditional_estimates = by_effect_mods.apply(estimate_effect_fn) # Deleting the temporary categorical columns for em in effect_modifier_names: if em.startswith(prefix): self._data.pop(em) return conditional_estimates def _do(self, x, data_df=None): raise NotImplementedError( ("Do-operator is " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG).format(self.__class__) ) def do(self, x, data_df=None): """Method that implements the do-operator. Given a value x for the treatment, returns the expected value of the outcome when the treatment is intervened to a value x. :param x: Value of the treatment :param data_df: Data on which the do-operator is to be applied. :returns: Value of the outcome when treatment is intervened/set to x. """ est = self._do(x, data_df) return est def construct_symbolic_estimator(self, estimand): raise NotImplementedError(("Symbolic estimator string is ").format(self.__class__)) def _generate_bootstrap_estimates(self, num_bootstrap_simulations, sample_size_fraction): """Helper function to generate causal estimates over bootstrapped samples. :param num_bootstrap_simulations: Number of simulations for the bootstrap method. :param sample_size_fraction: Fraction of the dataset to be resampled. :returns: A collections.namedtuple containing a list of bootstrapped estimates and a dictionary containing parameters used for the bootstrap. """ # The array that stores the results of all estimations simulation_results = np.zeros(num_bootstrap_simulations) # Find the sample size the proportion with the population size sample_size = int(sample_size_fraction * len(self._data)) if sample_size > len(self._data): self.logger.warning("WARN: The sample size is greater than the data being sampled") self.logger.info("INFO: The sample size: {}".format(sample_size)) self.logger.info("INFO: The number of simulations: {}".format(num_bootstrap_simulations)) # Perform the set number of simulations for index in range(num_bootstrap_simulations): new_data = resample(self._data, n_samples=sample_size) new_estimator = type(self)( new_data, self._target_estimand, self._target_estimand.treatment_variable, self._target_estimand.outcome_variable, # names of treatment and outcome treatment_value=self._treatment_value, control_value=self._control_value, test_significance=False, evaluate_effect_strength=False, confidence_intervals=False, target_units=self._target_units, effect_modifiers=self._effect_modifier_names, **self.method_params, ) new_effect = new_estimator.estimate_effect() simulation_results[index] = new_effect.value estimates = CausalEstimator.BootstrapEstimates( simulation_results, {"num_simulations": num_bootstrap_simulations, "sample_size_fraction": sample_size_fraction}, ) return estimates def _estimate_confidence_intervals_with_bootstrap( self, estimate_value, confidence_level=None, num_simulations=None, sample_size_fraction=None ): """ Method to compute confidence interval using bootstrapped sampling. :param estimate_value: obtained estimate's value :param confidence_level: The level for which to compute CI (e.g., 95% confidence level translates to confidence_level=0.95) :param num_simulations: The number of simulations to be performed to get the bootstrap confidence intervals. :param sample_size_fraction: The fraction of the dataset to be resampled. :returns: confidence interval at the specified level. For more details on bootstrap or resampling statistics, refer to the following links: https://ocw.mit.edu/courses/mathematics/18-05-introduction-to-probability-and-statistics-spring-2014/readings/MIT18_05S14_Reading24.pdf https://projecteuclid.org/download/pdf_1/euclid.ss/1032280214 """ # Using class default parameters if not specified if num_simulations is None: num_simulations = self.num_simulations if sample_size_fraction is None: sample_size_fraction = self.sample_size_fraction # Checking if bootstrap_estimates are already computed if self._bootstrap_estimates is None: self._bootstrap_estimates = self._generate_bootstrap_estimates(num_simulations, sample_size_fraction) elif CausalEstimator.is_bootstrap_parameter_changed(self._bootstrap_estimates.params, locals()): # Checked if any parameter is changed from the previous std error estimate self._bootstrap_estimates = self._generate_bootstrap_estimates(num_simulations, sample_size_fraction) # Now use the data obtained from the simulations to get the value of the confidence estimates bootstrap_estimates = self._bootstrap_estimates.estimates # Get the variations of each bootstrap estimate and sort bootstrap_variations = [bootstrap_estimate - estimate_value for bootstrap_estimate in bootstrap_estimates] sorted_bootstrap_variations = np.sort(bootstrap_variations) # Now we take the (1- p)th and the (p)th variations, where p is the chosen confidence level upper_bound_index = int((1 - confidence_level) * len(sorted_bootstrap_variations)) lower_bound_index = int(confidence_level * len(sorted_bootstrap_variations)) # Get the lower and upper bounds by subtracting the variations from the estimate lower_bound = estimate_value - sorted_bootstrap_variations[lower_bound_index] upper_bound = estimate_value - sorted_bootstrap_variations[upper_bound_index] return lower_bound, upper_bound def _estimate_confidence_intervals(self, confidence_level=None, method=None, **kwargs): """ This method is to be overriden by the child classes, so that they can run a confidence interval estimation method suited to the specific causal estimator. """ raise NotImplementedError( ( "This method for estimating confidence intervals is " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG + " Meanwhile, you can try the bootstrap method (method='bootstrap') to estimate confidence intervals." ).format(self.__class__) ) def estimate_confidence_intervals(self, estimate_value, confidence_level=None, method=None, **kwargs): """Find the confidence intervals corresponding to any estimator By default, this is done with the help of bootstrapped confidence intervals but can be overridden if the specific estimator implements other methods of estimating confidence intervals. If the method provided is not bootstrap, this function calls the implementation of the specific estimator. :param estimate_value: obtained estimate's value :param method: Method for estimating confidence intervals. :param confidence_level: The confidence level of the confidence intervals of the estimate. :param kwargs: Other optional args to be passed to the CI method. :returns: The obtained confidence interval. """ if method is None: if self._confidence_intervals: method = self._confidence_intervals # this is either True or methodname else: method = "default" confidence_intervals = None if confidence_level is None: confidence_level = self.confidence_level if method == "default" or method is True: # user has not provided any method try: confidence_intervals = self._estimate_confidence_intervals(confidence_level, method=method, **kwargs) except NotImplementedError: confidence_intervals = self._estimate_confidence_intervals_with_bootstrap( estimate_value, confidence_level, **kwargs ) else: if method == "bootstrap": confidence_intervals = self._estimate_confidence_intervals_with_bootstrap( estimate_value, confidence_level, **kwargs ) else: confidence_intervals = self._estimate_confidence_intervals(confidence_level, method=method, **kwargs) return confidence_intervals def _estimate_std_error_with_bootstrap(self, num_simulations=None, sample_size_fraction=None): """Compute standard error using the bootstrap method. Standard error and confidence intervals use the same parameter num_simulations for the number of bootstrap simulations. :param num_simulations: Number of bootstrapped samples. :param sample_size_fraction: Fraction of data to be resampled. :returns: Standard error of the obtained estimate. """ # Use existing params, if new user defined params are not present if num_simulations is None: num_simulations = self.num_simulations if sample_size_fraction is None: sample_size_fraction = self.sample_size_fraction # Checking if bootstrap_estimates are already computed if self._bootstrap_estimates is None: self._bootstrap_estimates = self._generate_bootstrap_estimates(num_simulations, sample_size_fraction) elif CausalEstimator.is_bootstrap_parameter_changed(self._bootstrap_estimates.params, locals()): # Check if any parameter is changed from the previous std error estimate self._bootstrap_estimates = self._generate_bootstrap_estimates(num_simulations, sample_size_fraction) std_error = np.std(self._bootstrap_estimates.estimates) return std_error def _estimate_std_error(self, method=None, **kwargs): """ This method is to be overriden by the child classes, so that they can run a standard error estimation method suited to the specific causal estimator. """ raise NotImplementedError( ( "This method for estimating standard errors is " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG + " Meanwhile, you can try the bootstrap method (method='bootstrap') to estimate standard errors." ).format(self.__class__) ) def estimate_std_error(self, method=None, **kwargs): """Compute standard error of an obtained causal estimate. :param method: Method for computing the standard error. :param kwargs: Other optional parameters to be passed to the estimating method. :returns: Standard error of the causal estimate. """ if method is None: if self._confidence_intervals: method = self._confidence_intervals else: method = "default" std_error = None if method == "default" or method is True: # user has not provided any method try: std_error = self._estimate_std_error(method, **kwargs) except NotImplementedError: std_error = self._estimate_std_error_with_bootstrap(**kwargs) else: if method == "bootstrap": std_error = self._estimate_std_error_with_bootstrap(**kwargs) else: std_error = self._estimate_std_error(method, **kwargs) return std_error def _test_significance_with_bootstrap(self, estimate_value, num_null_simulations=None): """Test statistical significance of an estimate using the bootstrap method. :param estimate_value: Obtained estimate's value :param num_null_simulations: Number of simulations for the null hypothesis :returns: p-value of the statistical significance test. """ # Use existing params, if new user defined params are not present if num_null_simulations is None: num_null_simulations = self.num_null_simulations do_retest = self._bootstrap_null_estimates is None or CausalEstimator.is_bootstrap_parameter_changed( self._bootstrap_null_estimates.params, locals() ) if do_retest: null_estimates = np.zeros(num_null_simulations) for i in range(num_null_simulations): new_outcome = np.random.permutation(self._outcome) new_data = self._data.assign(dummy_outcome=new_outcome) # self._outcome = self._data["dummy_outcome"] new_estimator = type(self)( new_data, self._target_estimand, self._target_estimand.treatment_variable, ("dummy_outcome",), test_significance=False, evaluate_effect_strength=False, confidence_intervals=False, target_units=self._target_units, effect_modifiers=self._effect_modifier_names, **self.method_params, ) new_effect = new_estimator.estimate_effect() null_estimates[i] = new_effect.value self._bootstrap_null_estimates = CausalEstimator.BootstrapEstimates( null_estimates, {"num_null_simulations": num_null_simulations, "sample_size_fraction": 1} ) # Processing the null hypothesis estimates sorted_null_estimates = np.sort(self._bootstrap_null_estimates.estimates) self.logger.debug("Null estimates: {0}".format(sorted_null_estimates)) median_estimate = sorted_null_estimates[int(num_null_simulations / 2)] # Doing a two-sided test if estimate_value > median_estimate: # Being conservative with the p-value reported estimate_index = np.searchsorted(sorted_null_estimates, estimate_value, side="left") p_value = 1 - (estimate_index / num_null_simulations) if estimate_value <= median_estimate: # Being conservative with the p-value reported estimate_index = np.searchsorted(sorted_null_estimates, estimate_value, side="right") p_value = estimate_index / num_null_simulations # If the estimate_index is 0, it depends on the number of simulations if p_value == 0: p_value = (0, 1 / len(sorted_null_estimates)) # a tuple determining the range. elif p_value == 1: p_value = (1 - 1 / len(sorted_null_estimates), 1) signif_dict = {"p_value": p_value} return signif_dict def _test_significance(self, estimate_value, method=None, **kwargs): """ This method is to be overriden by the child classes, so that they can run a significance test suited to the specific causal estimator. """ raise NotImplementedError( ( "This method for testing statistical significance is " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG + " Meanwhile, you can try the bootstrap method (method='bootstrap') to test statistical significance." ).format(self.__class__) ) def test_significance(self, estimate_value, method=None, **kwargs): """Test statistical significance of obtained estimate. By default, uses resampling to create a non-parametric significance test. A general procedure. Individual child estimators can implement different methods. If the method name is different from "bootstrap", this function calls the implementation of the child estimator. :param self: object instance of class Estimator :param estimate_value: obtained estimate's value :param method: Method for checking statistical significance :returns: p-value from the significance test """ if method is None: if self._significance_test: method = self._significance_test # this is either True or methodname else: method = "default" signif_dict = None if method == "default" or method is True: # user has not provided any method try: signif_dict = self._test_significance(estimate_value, method, **kwargs) except NotImplementedError: signif_dict = self._test_significance_with_bootstrap(estimate_value, **kwargs) else: if method == "bootstrap": signif_dict = self._test_significance_with_bootstrap(estimate_value, **kwargs) else: signif_dict = self._test_significance(estimate_value, method, **kwargs) return signif_dict def evaluate_effect_strength(self, estimate): fraction_effect_explained = self._evaluate_effect_strength(estimate, method="fraction-effect") # Need to test r-squared before supporting # effect_r_squared = self._evaluate_effect_strength(estimate, method="r-squared") strength_dict = { "fraction-effect": fraction_effect_explained # 'r-squared': effect_r_squared } return strength_dict def _evaluate_effect_strength(self, estimate, method="fraction-effect"): supported_methods = ["fraction-effect"] if method not in supported_methods: raise NotImplementedError("This method is not supported for evaluating effect strength") if method == "fraction-effect": naive_obs_estimate = self.estimate_effect_naive() self.logger.debug(estimate.value, naive_obs_estimate.value) fraction_effect_explained = estimate.value / naive_obs_estimate.value return fraction_effect_explained # elif method == "r-squared": # outcome_mean = np.mean(self._outcome) # total_variance = np.sum(np.square(self._outcome - outcome_mean)) # Assuming a linear model with one variable: the treatment # Currently only works for continuous y # causal_model = outcome_mean + estimate.value*self._treatment # squared_residual = np.sum(np.square(self._outcome - causal_model)) # r_squared = 1 - (squared_residual/total_variance) # return r_squared else: return None def update_input(self, treatment_value, control_value, target_units): self._control_value = control_value self._treatment_value = treatment_value self._target_units = target_units @staticmethod def is_bootstrap_parameter_changed(bootstrap_estimates_params, given_params): """Check whether parameters of the bootstrap have changed. This is an efficiency method that checks if fresh resampling of the bootstrap samples is required. Returns True if parameters have changed and resampling should be done again. :param bootstrap_estimates_params: A dictionary of parameters for the current bootstrap samples :param given_params: A dictionary of parameters passed by the user :returns: A binary flag denoting whether the parameters are different. """ is_any_parameter_changed = False for prm, val in bootstrap_estimates_params.items(): given_val = given_params.get(prm, None) if given_val is not None and given_val != val: is_any_parameter_changed = True break return is_any_parameter_changed def target_units_tostr(self): s = "" if type(self._target_units) is str: s += self._target_units elif callable(self._target_units): s += "Data subset defined by a function" elif isinstance(self._target_units, pd.DataFrame): s += "Data subset provided as a data frame" return s def signif_results_tostr(self, signif_results): s = "" pval = signif_results["p_value"] if type(pval) is tuple: s += "[{0}, {1}]".format(pval[0], pval[1]) else: s += "{0}".format(pval) return s def estimate_effect( treatment: Union[str, List[str]], outcome: Union[str, List[str]], identified_estimand: IdentifiedEstimand, identifier_name: str, method: CausalEstimator, control_value: int = 0, treatment_value: int = 1, test_significance: Optional[bool] = None, evaluate_effect_strength: bool = False, confidence_intervals: bool = False, target_units: str = "ate", effect_modifiers: List[str] = [], fit_estimator: bool = True, method_params: Optional[Dict] = None, ): """Estimate the identified causal effect. Currently requires an explicit method name to be specified. Method names follow the convention of identification method followed by the specific estimation method: "[backdoor/iv].estimation_method_name". Following methods are supported. * Propensity Score Matching: "backdoor.propensity_score_matching" * Propensity Score Stratification: "backdoor.propensity_score_stratification" * Propensity Score-based Inverse Weighting: "backdoor.propensity_score_weighting" * Linear Regression: "backdoor.linear_regression" * Generalized Linear Models (e.g., logistic regression): "backdoor.generalized_linear_model" * Instrumental Variables: "iv.instrumental_variable" * Regression Discontinuity: "iv.regression_discontinuity" In addition, you can directly call any of the EconML estimation methods. The convention is "backdoor.econml.path-to-estimator-class". For example, for the double machine learning estimator ("DML" class) that is located inside "dml" module of EconML, you can use the method name, "backdoor.econml.dml.DML". CausalML estimators can also be called. See `this demo notebook <https://py-why.github.io/dowhy/example_notebooks/dowhy-conditional-treatment-effects.html>`_. :param treatment: Name of the treatment :param outcome: Name of the outcome :param identified_estimand: a probability expression that represents the effect to be estimated. Output of CausalModel.identify_effect method :param method_name: name of the estimation method to be used. :param control_value: Value of the treatment in the control group, for effect estimation. If treatment is multi-variate, this can be a list. :param treatment_value: Value of the treatment in the treated group, for effect estimation. If treatment is multi-variate, this can be a list. :param test_significance: Binary flag on whether to additionally do a statistical signficance test for the estimate. :param evaluate_effect_strength: (Experimental) Binary flag on whether to estimate the relative strength of the treatment's effect. This measure can be used to compare different treatments for the same outcome (by running this method with different treatments sequentially). :param confidence_intervals: (Experimental) Binary flag indicating whether confidence intervals should be computed. :param target_units: (Experimental) The units for which the treatment effect should be estimated. This can be of three types. (1) a string for common specifications of target units (namely, "ate", "att" and "atc"), (2) a lambda function that can be used as an index for the data (pandas DataFrame), or (3) a new DataFrame that contains values of the effect_modifiers and effect will be estimated only for this new data. :param effect_modifiers: Names of effect modifier variables can be (optionally) specified here too, since they do not affect identification. If None, the effect_modifiers from the CausalModel are used. :param fit_estimator: Boolean flag on whether to fit the estimator. Setting it to False is useful to estimate the effect on new data using a previously fitted estimator. :param method_params: Dictionary containing any method-specific parameters. These are passed directly to the estimating method. See the docs for each estimation method for allowed method-specific params. :returns: An instance of the CausalEstimate class, containing the causal effect estimate and other method-dependent information """ treatment = parse_state(treatment) outcome = parse_state(outcome) causal_estimator_class = method.__class__ identified_estimand.set_identifier_method(identifier_name) if identified_estimand.no_directed_path: logger.warning("No directed path from {0} to {1}.".format(treatment, outcome)) return CausalEstimate( 0, identified_estimand, None, control_value=control_value, treatment_value=treatment_value ) # Check if estimator's target estimand is identified elif identified_estimand.estimands[identifier_name] is None: logger.error("No valid identified estimand available.") return CausalEstimate(None, None, None, control_value=control_value, treatment_value=treatment_value) method.update_input(treatment_value, control_value, target_units) estimate = method.estimate_effect() # Store parameters inside estimate object for refutation methods # TODO: This add_params needs to move to the estimator class # inside estimate_effect and estimate_conditional_effect estimate.add_params( estimand_type=identified_estimand.estimand_type, estimator_class=causal_estimator_class, test_significance=test_significance, evaluate_effect_strength=evaluate_effect_strength, confidence_intervals=confidence_intervals, target_units=target_units, effect_modifiers=effect_modifiers, method_params=method_params, ) return estimate class CausalEstimate: """Class for the estimate object that every causal estimator returns""" def __init__( self, estimate, target_estimand, realized_estimand_expr, control_value, treatment_value, conditional_estimates=None, **kwargs, ): self.value = estimate self.target_estimand = target_estimand self.realized_estimand_expr = realized_estimand_expr self.control_value = control_value self.treatment_value = treatment_value self.conditional_estimates = conditional_estimates self.params = kwargs if self.params is not None: for key, value in self.params.items(): setattr(self, key, value) self.effect_strength = None def add_estimator(self, estimator_instance): self.estimator = estimator_instance def add_effect_strength(self, strength_dict): self.effect_strength = strength_dict def add_params(self, **kwargs): self.params.update(kwargs) def get_confidence_intervals(self, confidence_level=None, method=None, **kwargs): """Get confidence intervals of the obtained estimate. By default, this is done with the help of bootstrapped confidence intervals but can be overridden if the specific estimator implements other methods of estimating confidence intervals. If the method provided is not bootstrap, this function calls the implementation of the specific estimator. :param method: Method for estimating confidence intervals. :param confidence_level: The confidence level of the confidence intervals of the estimate. :param kwargs: Other optional args to be passed to the CI method. :returns: The obtained confidence interval. """ confidence_intervals = self.estimator.estimate_confidence_intervals( estimate_value=self.value, confidence_level=confidence_level, method=method, **kwargs ) return confidence_intervals def get_standard_error(self, method=None, **kwargs): """Get standard error of the obtained estimate. By default, this is done with the help of bootstrapped standard errors but can be overridden if the specific estimator implements other methods of estimating standard error. If the method provided is not bootstrap, this function calls the implementation of the specific estimator. :param method: Method for computing the standard error. :param kwargs: Other optional parameters to be passed to the estimating method. :returns: Standard error of the causal estimate. """ std_error = self.estimator.estimate_std_error(method=method, **kwargs) return std_error def test_stat_significance(self, method=None, **kwargs): """Test statistical significance of the estimate obtained. By default, uses resampling to create a non-parametric significance test. Individual child estimators can implement different methods. If the method name is different from "bootstrap", this function calls the implementation of the child estimator. :param method: Method for checking statistical significance :param kwargs: Other optional parameters to be passed to the estimating method. :returns: p-value from the significance test """ signif_results = self.estimator.test_significance(self.value, method=method, **kwargs) return {"p_value": signif_results["p_value"]} def estimate_conditional_effects( self, effect_modifiers=None, num_quantiles=CausalEstimator.NUM_QUANTILES_TO_DISCRETIZE_CONT_COLS ): """Estimate treatment effect conditioned on given variables. If a numeric effect modifier is provided, it is discretized into quantile bins. If you would like a custom discretization, you can do so yourself: create a new column containing the discretized effect modifier and then include that column's name in the effect_modifier_names argument. :param effect_modifiers: Names of effect modifier variables over which the conditional effects will be estimated. If not provided, defaults to the effect modifiers specified during creation of the CausalEstimator object. :param num_quantiles: The number of quantiles into which a numeric effect modifier variable is discretized. Does not affect any categorical effect modifiers. :returns: A (multi-index) dataframe that provides separate effects for each value of the (discretized) effect modifiers. """ return self.estimator._estimate_conditional_effects( self.estimator._estimate_effect_fn, effect_modifiers, num_quantiles ) def interpret(self, method_name=None, **kwargs): """Interpret the causal estimate. :param method_name: Method used (string) or a list of methods. If None, then the default for the specific estimator is used. :param kwargs:: Optional parameters that are directly passed to the interpreter method. :returns: None """ if method_name is None: method_name = self.estimator.interpret_method method_name_arr = parse_state(method_name) for method in method_name_arr: interpreter = interpreters.get_class_object(method) interpreter(self, **kwargs).interpret() def __str__(self): s = "*** Causal Estimate ***\n" # No estimand was identified (identification failed) if self.target_estimand is None: return "Estimation failed! No relevant identified estimand available for this estimation method." s += "\n## Identified estimand\n{0}".format(self.target_estimand.__str__(only_target_estimand=True)) s += "\n## Realized estimand\n{0}".format(self.realized_estimand_expr) if hasattr(self, "estimator"): s += "\nTarget units: {0}\n".format(self.estimator.target_units_tostr()) s += "\n## Estimate\n" s += "Mean value: {0}\n".format(self.value) s += "" if hasattr(self, "cate_estimates"): s += "Effect estimates: {0}\n".format(self.cate_estimates) if hasattr(self, "estimator"): if self.estimator._significance_test: s += "p-value: {0}\n".format(self.estimator.signif_results_tostr(self.test_stat_significance())) if self.estimator._confidence_intervals: s += "{0}% confidence interval: {1}\n".format( 100 * self.estimator.confidence_level, self.get_confidence_intervals() ) if self.conditional_estimates is not None: s += "### Conditional Estimates\n" s += str(self.conditional_estimates) if self.effect_strength is not None: s += "\n## Effect Strength\n" s += "Change in outcome attributable to treatment: {}\n".format(self.effect_strength["fraction-effect"]) # s += "Variance in outcome explained by treatment: {}\n".format(self.effect_strength["r-squared"]) return s class RealizedEstimand(object): def __init__(self, identified_estimand, estimator_name): self.treatment_variable = identified_estimand.treatment_variable self.outcome_variable = identified_estimand.outcome_variable self.backdoor_variables = identified_estimand.get_backdoor_variables() self.instrumental_variables = identified_estimand.instrumental_variables self.estimand_type = identified_estimand.estimand_type self.estimand_expression = None self.assumptions = None self.estimator_name = estimator_name def update_assumptions(self, estimator_assumptions): self.assumptions = estimator_assumptions def update_estimand_expression(self, estimand_expression): self.estimand_expression = estimand_expression def __str__(self): s = "Realized estimand: {0}\n".format(self.estimator_name) s += "Realized estimand type: {0}\n".format(self.estimand_type) s += "Estimand expression:\n{0}\n".format(sp.pretty(self.estimand_expression)) j = 1 for ass_name, ass_str in self.assumptions.items(): s += "Estimand assumption {0}, {1}: {2}\n".format(j, ass_name, ass_str) j += 1 return s

andresmor-ms

2044d216c322a4b32c6eadce5da7d83463f19c2f

05bfa49dacf0061988c96c6f3e3756219df5422a

I think we should move those params into the estimator object, so when initializing it the user can provide those, when I start refactoring the estimators we can find where's the best place for each parameter

andresmor-ms

py-why/dowhy

Functional api/estimate effect function

#### Estimate Effect function * Refactors the estimate effect into a separate function to keep backwards compatibility #### TODO (future PRs): * Add `fit(...)` method to estimators - Move data related parameters from the constructor to the `fit(...)` method * Refactor code to avoid `**kwargs` in `__init__(...)` constructors

2022-10-18 15:49:21+00:00

2022-10-25 17:02:02+00:00

dowhy/causal_model.py

""" Module containing the main model class for the dowhy package. """ import logging from itertools import combinations from sympy import init_printing import dowhy.causal_estimators as causal_estimators import dowhy.causal_refuters as causal_refuters import dowhy.graph_learners as graph_learners import dowhy.utils.cli_helpers as cli from dowhy.causal_estimator import CausalEstimate from dowhy.causal_graph import CausalGraph from dowhy.causal_identifier import AutoIdentifier, BackdoorAdjustment, IDIdentifier from dowhy.causal_identifier.identify_effect import EstimandType from dowhy.causal_refuters.graph_refuter import GraphRefuter from dowhy.utils.api import parse_state init_printing() # To display symbolic math symbols class CausalModel: """Main class for storing the causal model state.""" def __init__( self, data, treatment, outcome, graph=None, common_causes=None, instruments=None, effect_modifiers=None, estimand_type="nonparametric-ate", proceed_when_unidentifiable=False, missing_nodes_as_confounders=False, identify_vars=False, **kwargs, ): """Initialize data and create a causal graph instance. Assigns treatment and outcome variables. Also checks and finds the common causes and instruments for treatment and outcome. At least one of graph, common_causes or instruments must be provided. If none of these variables are provided, then learn_graph() can be used later. :param data: a pandas dataframe containing treatment, outcome and other variables. :param treatment: name of the treatment variable :param outcome: name of the outcome variable :param graph: path to DOT file containing a DAG or a string containing a DAG specification in DOT format :param common_causes: names of common causes of treatment and _outcome. Only used when graph is None. :param instruments: names of instrumental variables for the effect of treatment on outcome. Only used when graph is None. :param effect_modifiers: names of variables that can modify the treatment effect. If not provided, then the causal graph is used to find the effect modifiers. Estimators will return multiple different estimates based on each value of effect_modifiers. :param estimand_type: the type of estimand requested (currently only "nonparametric-ate" is supported). In the future, may support other specific parametric forms of identification. :param proceed_when_unidentifiable: does the identification proceed by ignoring potential unobserved confounders. Binary flag. :param missing_nodes_as_confounders: Binary flag indicating whether variables in the dataframe that are not included in the causal graph, should be automatically included as confounder nodes. :param identify_vars: Variable deciding whether to compute common causes, instruments and effect modifiers while initializing the class. identify_vars should be set to False when user is providing common_causes, instruments or effect modifiers on their own(otherwise the identify_vars code can override the user provided values). Also it does not make sense if no graph is given. :returns: an instance of CausalModel class """ self._data = data self._treatment = parse_state(treatment) self._outcome = parse_state(outcome) self._effect_modifiers = parse_state(effect_modifiers) self._estimand_type = estimand_type self._proceed_when_unidentifiable = proceed_when_unidentifiable self._missing_nodes_as_confounders = missing_nodes_as_confounders self.logger = logging.getLogger(__name__) if graph is None: self.logger.warning("Causal Graph not provided. DoWhy will construct a graph based on data inputs.") self._common_causes = parse_state(common_causes) self._instruments = parse_state(instruments) if common_causes is not None and instruments is not None: self._graph = CausalGraph( self._treatment, self._outcome, common_cause_names=self._common_causes, instrument_names=self._instruments, effect_modifier_names=self._effect_modifiers, observed_node_names=self._data.columns.tolist(), ) elif common_causes is not None: self._graph = CausalGraph( self._treatment, self._outcome, common_cause_names=self._common_causes, effect_modifier_names=self._effect_modifiers, observed_node_names=self._data.columns.tolist(), ) elif instruments is not None: self._graph = CausalGraph( self._treatment, self._outcome, instrument_names=self._instruments, effect_modifier_names=self._effect_modifiers, observed_node_names=self._data.columns.tolist(), ) else: self.logger.warning( "Relevant variables to build causal graph not provided. You may want to use the learn_graph() function to construct the causal graph." ) self._graph = CausalGraph( self._treatment, self._outcome, effect_modifier_names=self._effect_modifiers, observed_node_names=self._data.columns.tolist(), ) else: self.init_graph(graph=graph, identify_vars=identify_vars) self._other_variables = kwargs self.summary() def init_graph(self, graph, identify_vars): """ Initialize self._graph using graph provided by the user. """ # Create causal graph object self._graph = CausalGraph( self._treatment, self._outcome, graph, effect_modifier_names=self._effect_modifiers, observed_node_names=self._data.columns.tolist(), missing_nodes_as_confounders=self._missing_nodes_as_confounders, ) if identify_vars: self._common_causes = self._graph.get_common_causes(self._treatment, self._outcome) self._instruments = self._graph.get_instruments(self._treatment, self._outcome) # Sometimes, effect modifiers from the graph may not match those provided by the user. # (Because some effect modifiers may also be common causes) # In such cases, the user-provided modifiers are used. # If no effect modifiers are provided, then the ones from the graph are used. if self._effect_modifiers is None or not self._effect_modifiers: self._effect_modifiers = self._graph.get_effect_modifiers(self._treatment, self._outcome) def get_common_causes(self): self._common_causes = self._graph.get_common_causes(self._treatment, self._outcome) return self._common_causes def get_instruments(self): self._instruments = self._graph.get_instruments(self._treatment, self._outcome) return self._instruments def get_effect_modifiers(self): self._effect_modifiers = self._graph.get_effect_modifiers(self._treatment, self._outcome) return self._effect_modifiers def learn_graph(self, method_name="cdt.causality.graph.LiNGAM", *args, **kwargs): """ Learn causal graph from the data. This function takes the method name as input and initializes the causal graph object using the learnt graph. :param self: instance of the CausalModel class (or its subclass) :param method_name: Exact method name of the object to be imported from the concerned library. :returns: an instance of the CausalGraph class initialized with the learned graph. """ # Import causal discovery class str_arr = method_name.split(".", maxsplit=1) library_name = str_arr[0] causal_discovery_class = graph_learners.get_discovery_class_object(library_name) model = causal_discovery_class(self._data, method_name, *args, **kwargs) graph = model.learn_graph() # Initialize causal graph object self.init_graph(graph=graph) return self._graph def identify_effect( self, estimand_type=None, method_name="default", proceed_when_unidentifiable=None, optimize_backdoor=False ): """Identify the causal effect to be estimated, using properties of the causal graph. :param method_name: Method name for identification algorithm. ("id-algorithm" or "default") :param proceed_when_unidentifiable: Binary flag indicating whether identification should proceed in the presence of (potential) unobserved confounders. :returns: a probability expression (estimand) for the causal effect if identified, else NULL """ if proceed_when_unidentifiable is None: proceed_when_unidentifiable = self._proceed_when_unidentifiable if estimand_type is None: estimand_type = self._estimand_type estimand_type = EstimandType(estimand_type) if method_name == "id-algorithm": identifier = IDIdentifier() else: identifier = AutoIdentifier( estimand_type=estimand_type, backdoor_adjustment=BackdoorAdjustment(method_name), proceed_when_unidentifiable=proceed_when_unidentifiable, optimize_backdoor=optimize_backdoor, ) identified_estimand = identifier.identify_effect( graph=self._graph, treatment_name=self._treatment, outcome_name=self._outcome ) self.identifier = identifier return identified_estimand def estimate_effect( self, identified_estimand, method_name=None, control_value=0, treatment_value=1, test_significance=None, evaluate_effect_strength=False, confidence_intervals=False, target_units="ate", effect_modifiers=None, fit_estimator=True, method_params=None, ): """Estimate the identified causal effect. Currently requires an explicit method name to be specified. Method names follow the convention of identification method followed by the specific estimation method: "[backdoor/iv].estimation_method_name". Following methods are supported. * Propensity Score Matching: "backdoor.propensity_score_matching" * Propensity Score Stratification: "backdoor.propensity_score_stratification" * Propensity Score-based Inverse Weighting: "backdoor.propensity_score_weighting" * Linear Regression: "backdoor.linear_regression" * Generalized Linear Models (e.g., logistic regression): "backdoor.generalized_linear_model" * Instrumental Variables: "iv.instrumental_variable" * Regression Discontinuity: "iv.regression_discontinuity" In addition, you can directly call any of the EconML estimation methods. The convention is "backdoor.econml.path-to-estimator-class". For example, for the double machine learning estimator ("DML" class) that is located inside "dml" module of EconML, you can use the method name, "backdoor.econml.dml.DML". CausalML estimators can also be called. See `this demo notebook <https://py-why.github.io/dowhy/example_notebooks/dowhy-conditional-treatment-effects.html>`_. :param identified_estimand: a probability expression that represents the effect to be estimated. Output of CausalModel.identify_effect method :param method_name: name of the estimation method to be used. :param control_value: Value of the treatment in the control group, for effect estimation. If treatment is multi-variate, this can be a list. :param treatment_value: Value of the treatment in the treated group, for effect estimation. If treatment is multi-variate, this can be a list. :param test_significance: Binary flag on whether to additionally do a statistical signficance test for the estimate. :param evaluate_effect_strength: (Experimental) Binary flag on whether to estimate the relative strength of the treatment's effect. This measure can be used to compare different treatments for the same outcome (by running this method with different treatments sequentially). :param confidence_intervals: (Experimental) Binary flag indicating whether confidence intervals should be computed. :param target_units: (Experimental) The units for which the treatment effect should be estimated. This can be of three types. (1) a string for common specifications of target units (namely, "ate", "att" and "atc"), (2) a lambda function that can be used as an index for the data (pandas DataFrame), or (3) a new DataFrame that contains values of the effect_modifiers and effect will be estimated only for this new data. :param effect_modifiers: Names of effect modifier variables can be (optionally) specified here too, since they do not affect identification. If None, the effect_modifiers from the CausalModel are used. :param fit_estimator: Boolean flag on whether to fit the estimator. Setting it to False is useful to estimate the effect on new data using a previously fitted estimator. :param method_params: Dictionary containing any method-specific parameters. These are passed directly to the estimating method. See the docs for each estimation method for allowed method-specific params. :returns: An instance of the CausalEstimate class, containing the causal effect estimate and other method-dependent information """ if effect_modifiers is None: if self._effect_modifiers is None or len(self._effect_modifiers) == 0: effect_modifiers = self.get_effect_modifiers() else: effect_modifiers = self._effect_modifiers if fit_estimator: if method_name is None: # TODO add propensity score as default backdoor method, iv as default iv method, add an informational message to show which method has been selected. pass else: # TODO add dowhy as a prefix to all dowhy estimators num_components = len(method_name.split(".")) str_arr = method_name.split(".", maxsplit=1) identifier_name = str_arr[0] estimator_name = str_arr[1] identified_estimand.set_identifier_method(identifier_name) # This is done as all dowhy estimators have two parts and external ones have two or more parts if num_components > 2: estimator_package = estimator_name.split(".")[0] if estimator_package == "dowhy": # For updated dowhy methods estimator_method = estimator_name.split(".", maxsplit=1)[ 1 ] # discard dowhy from the full package name causal_estimator_class = causal_estimators.get_class_object(estimator_method + "_estimator") else: third_party_estimator_package = estimator_package causal_estimator_class = causal_estimators.get_class_object( third_party_estimator_package, estimator_name ) if method_params is None: method_params = {} # Define the third-party estimation method to be used method_params[third_party_estimator_package + "_methodname"] = estimator_name else: # For older dowhy methods self.logger.info(estimator_name) # Process the dowhy estimators causal_estimator_class = causal_estimators.get_class_object(estimator_name + "_estimator") if identified_estimand.no_directed_path: self.logger.warning("No directed path from {0} to {1}.".format(self._treatment, self._outcome)) return CausalEstimate( 0, identified_estimand, None, control_value=control_value, treatment_value=treatment_value ) # Check if estimator's target estimand is identified elif identified_estimand.estimands[identifier_name] is None: self.logger.error("No valid identified estimand available.") return CausalEstimate(None, None, None, control_value=control_value, treatment_value=treatment_value) else: if method_params is not None and (num_components <= 2 or estimator_package == "dowhy"): extra_args = method_params.get("init_params", {}) else: extra_args = {} if method_params is None: method_params = {} self.causal_estimator = causal_estimator_class( self._data, identified_estimand, self._treatment, self._outcome, # names of treatment and outcome control_value=control_value, treatment_value=treatment_value, test_significance=test_significance, evaluate_effect_strength=evaluate_effect_strength, confidence_intervals=confidence_intervals, target_units=target_units, effect_modifiers=effect_modifiers, **method_params, **extra_args, ) else: # Estimator had been computed in a previous call assert self.causal_estimator is not None causal_estimator_class = self.causal_estimator.__class__ self.causal_estimator.update_input(treatment_value, control_value, target_units) estimate = self.causal_estimator.estimate_effect() # Store parameters inside estimate object for refutation methods # TODO: This add_params needs to move to the estimator class # inside estimate_effect and estimate_conditional_effect estimate.add_params( estimand_type=identified_estimand.estimand_type, estimator_class=causal_estimator_class, test_significance=test_significance, evaluate_effect_strength=evaluate_effect_strength, confidence_intervals=confidence_intervals, target_units=target_units, effect_modifiers=effect_modifiers, method_params=method_params, ) return estimate def do(self, x, identified_estimand, method_name=None, fit_estimator=True, method_params=None): """Do operator for estimating values of the outcome after intervening on treatment. :param x: interventional value of the treatment variable :param identified_estimand: a probability expression that represents the effect to be estimated. Output of CausalModel.identify_effect method :param method_name: any of the estimation method to be used. See docs for estimate_effect method for a list of supported estimation methods. :param fit_estimator: Boolean flag on whether to fit the estimator. Setting it to False is useful to compute the do-operation on new data using a previously fitted estimator. :param method_params: Dictionary containing any method-specific parameters. These are passed directly to the estimating method. :returns: an instance of the CausalEstimate class, containing the causal effect estimate and other method-dependent information """ if method_name is None: pass else: str_arr = method_name.split(".", maxsplit=1) identifier_name = str_arr[0] estimator_name = str_arr[1] identified_estimand.set_identifier_method(identifier_name) causal_estimator_class = causal_estimators.get_class_object(estimator_name + "_estimator") # Check if estimator's target estimand is identified if identified_estimand.estimands[identifier_name] is None: self.logger.warning("No valid identified estimand for using instrumental variables method") estimate = CausalEstimate(None, None, None, None, None) else: if fit_estimator: # Note that while the name of the variable is the same, # "self.causal_estimator", this estimator takes in less # parameters than the same from the # estimate_effect code. It is not advisable to use the # estimator from this function to call estimate_effect # with fit_estimator=False. self.causal_estimator = causal_estimator_class( self._data, identified_estimand, self._treatment, self._outcome, test_significance=False, **method_params, ) else: # Estimator had been computed in a previous call assert self.causal_estimator is not None try: estimate = self.causal_estimator.do(x) except NotImplementedError: self.logger.error("Do Operation not implemented or not supported for this estimator.") raise NotImplementedError return estimate def refute_estimate(self, estimand, estimate, method_name=None, show_progress_bar=False, **kwargs): """Refute an estimated causal effect. If method_name is provided, uses the provided method. In the future, we may support automatic selection of suitable refutation tests. Following refutation methods are supported. * Adding a randomly-generated confounder: "random_common_cause" * Adding a confounder that is associated with both treatment and outcome: "add_unobserved_common_cause" * Replacing the treatment with a placebo (random) variable): "placebo_treatment_refuter" * Removing a random subset of the data: "data_subset_refuter" :param estimand: target estimand, an instance of the IdentifiedEstimand class (typically, the output of identify_effect) :param estimate: estimate to be refuted, an instance of the CausalEstimate class (typically, the output of estimate_effect) :param method_name: name of the refutation method :param show_progress_bar: Boolean flag on whether to show a progress bar :param kwargs: (optional) additional arguments that are passed directly to the refutation method. Can specify a random seed here to ensure reproducible results ('random_seed' parameter). For method-specific parameters, consult the documentation for the specific method. All refutation methods are in the causal_refuters subpackage. :returns: an instance of the RefuteResult class """ if estimate is None or estimate.value is None: self.logger.error("Aborting refutation! No estimate is provided.") raise ValueError("Aborting refutation! No valid estimate is provided.") if method_name is None: pass else: refuter_class = causal_refuters.get_class_object(method_name) refuter = refuter_class(self._data, identified_estimand=estimand, estimate=estimate, **kwargs) res = refuter.refute_estimate(show_progress_bar) return res def view_model(self, layout="dot", size=(8, 6), file_name="causal_model"): """View the causal DAG. :param layout: string specifying the layout of the graph. :param size: tuple (x, y) specifying the width and height of the figure in inches. :param file_name: string specifying the file name for the saved causal graph png. :returns: a visualization of the graph """ self._graph.view_graph(layout, size, file_name) def interpret(self, method_name=None, **kwargs): """Interpret the causal model. :param method_name: method used for interpreting the model. If None, then default interpreter is chosen that describes the model summary and shows the associated causal graph. :param kwargs:: Optional parameters that are directly passed to the interpreter method. :returns: None """ if method_name is None: self.summary(print_to_stdout=True) self.view_model() return method_name_arr = parse_state(method_name) import dowhy.interpreters as interpreters for method in method_name_arr: interpreter = interpreters.get_class_object(method) interpreter(self, **kwargs).interpret() def summary(self, print_to_stdout=False): """Print a text summary of the model. :returns: a string containining the summary """ summary_text = "Model to find the causal effect of treatment {0} on outcome {1}".format( self._treatment, self._outcome ) self.logger.info(summary_text) if print_to_stdout: print(summary_text) return summary_text def refute_graph(self, k=1, independence_test=None, independence_constraints=None): """ Check if the dependencies in input graph matches with the dataset - ( X ⫫ Y ) | Z where X and Y are considered as singleton sets currently Z can have multiple variables :param k: number of covariates in set Z :param independence_test: dictionary containing methods to test conditional independece in data :param independence_constraints: list of implications to be test input by the user in the format [(x,y,(z1,z2)), (x,y, (z3,)) ] : returns: an instance of GraphRefuter class """ if independence_test is not None: test_for_continuous = independence_test["test_for_continuous"] test_for_discrete = independence_test["test_for_discrete"] refuter = GraphRefuter( data=self._data, method_name_continuous=test_for_continuous, method_name_discrete=test_for_discrete ) else: refuter = GraphRefuter(data=self._data) if independence_constraints is None: all_nodes = list(self._graph.get_all_nodes(include_unobserved=False)) num_nodes = len(all_nodes) array_indices = list(range(0, num_nodes)) all_possible_combinations = list( combinations(array_indices, 2) ) # Generating sets of indices of size 2 for different x and y conditional_independences = [] self.logger.info("The followed conditional independences are true for the input graph") for combination in all_possible_combinations: # Iterate over the unique 2-sized sets [x,y] i = combination[0] j = combination[1] a = all_nodes[i] b = all_nodes[j] if i < j: temp_arr = all_nodes[:i] + all_nodes[i + 1 : j] + all_nodes[j + 1 :] else: temp_arr = all_nodes[:j] + all_nodes[j + 1 : i] + all_nodes[i + 1 :] k_sized_lists = list(combinations(temp_arr, k)) for k_list in k_sized_lists: if self._graph.check_dseparation([str(a)], [str(b)], k_list) == True: self.logger.info(" %s and %s are CI given %s ", a, b, k_list) conditional_independences.append([a, b, k_list]) independence_constraints = conditional_independences res = refuter.refute_model(independence_constraints=independence_constraints) self.logger.info(refuter._refutation_passed) return res

""" Module containing the main model class for the dowhy package. """ import logging from itertools import combinations from sympy import init_printing import dowhy.causal_estimators as causal_estimators import dowhy.causal_refuters as causal_refuters import dowhy.graph_learners as graph_learners import dowhy.utils.cli_helpers as cli from dowhy.causal_estimator import CausalEstimate, estimate_effect from dowhy.causal_graph import CausalGraph from dowhy.causal_identifier import AutoIdentifier, BackdoorAdjustment, IDIdentifier from dowhy.causal_identifier.identify_effect import EstimandType from dowhy.causal_refuters.graph_refuter import GraphRefuter from dowhy.utils.api import parse_state init_printing() # To display symbolic math symbols class CausalModel: """Main class for storing the causal model state.""" def __init__( self, data, treatment, outcome, graph=None, common_causes=None, instruments=None, effect_modifiers=None, estimand_type="nonparametric-ate", proceed_when_unidentifiable=False, missing_nodes_as_confounders=False, identify_vars=False, **kwargs, ): """Initialize data and create a causal graph instance. Assigns treatment and outcome variables. Also checks and finds the common causes and instruments for treatment and outcome. At least one of graph, common_causes or instruments must be provided. If none of these variables are provided, then learn_graph() can be used later. :param data: a pandas dataframe containing treatment, outcome and other variables. :param treatment: name of the treatment variable :param outcome: name of the outcome variable :param graph: path to DOT file containing a DAG or a string containing a DAG specification in DOT format :param common_causes: names of common causes of treatment and _outcome. Only used when graph is None. :param instruments: names of instrumental variables for the effect of treatment on outcome. Only used when graph is None. :param effect_modifiers: names of variables that can modify the treatment effect. If not provided, then the causal graph is used to find the effect modifiers. Estimators will return multiple different estimates based on each value of effect_modifiers. :param estimand_type: the type of estimand requested (currently only "nonparametric-ate" is supported). In the future, may support other specific parametric forms of identification. :param proceed_when_unidentifiable: does the identification proceed by ignoring potential unobserved confounders. Binary flag. :param missing_nodes_as_confounders: Binary flag indicating whether variables in the dataframe that are not included in the causal graph, should be automatically included as confounder nodes. :param identify_vars: Variable deciding whether to compute common causes, instruments and effect modifiers while initializing the class. identify_vars should be set to False when user is providing common_causes, instruments or effect modifiers on their own(otherwise the identify_vars code can override the user provided values). Also it does not make sense if no graph is given. :returns: an instance of CausalModel class """ self._data = data self._treatment = parse_state(treatment) self._outcome = parse_state(outcome) self._effect_modifiers = parse_state(effect_modifiers) self._estimand_type = estimand_type self._proceed_when_unidentifiable = proceed_when_unidentifiable self._missing_nodes_as_confounders = missing_nodes_as_confounders self.logger = logging.getLogger(__name__) if graph is None: self.logger.warning("Causal Graph not provided. DoWhy will construct a graph based on data inputs.") self._common_causes = parse_state(common_causes) self._instruments = parse_state(instruments) if common_causes is not None and instruments is not None: self._graph = CausalGraph( self._treatment, self._outcome, common_cause_names=self._common_causes, instrument_names=self._instruments, effect_modifier_names=self._effect_modifiers, observed_node_names=self._data.columns.tolist(), ) elif common_causes is not None: self._graph = CausalGraph( self._treatment, self._outcome, common_cause_names=self._common_causes, effect_modifier_names=self._effect_modifiers, observed_node_names=self._data.columns.tolist(), ) elif instruments is not None: self._graph = CausalGraph( self._treatment, self._outcome, instrument_names=self._instruments, effect_modifier_names=self._effect_modifiers, observed_node_names=self._data.columns.tolist(), ) else: self.logger.warning( "Relevant variables to build causal graph not provided. You may want to use the learn_graph() function to construct the causal graph." ) self._graph = CausalGraph( self._treatment, self._outcome, effect_modifier_names=self._effect_modifiers, observed_node_names=self._data.columns.tolist(), ) else: self.init_graph(graph=graph, identify_vars=identify_vars) self._other_variables = kwargs self.summary() def init_graph(self, graph, identify_vars): """ Initialize self._graph using graph provided by the user. """ # Create causal graph object self._graph = CausalGraph( self._treatment, self._outcome, graph, effect_modifier_names=self._effect_modifiers, observed_node_names=self._data.columns.tolist(), missing_nodes_as_confounders=self._missing_nodes_as_confounders, ) if identify_vars: self._common_causes = self._graph.get_common_causes(self._treatment, self._outcome) self._instruments = self._graph.get_instruments(self._treatment, self._outcome) # Sometimes, effect modifiers from the graph may not match those provided by the user. # (Because some effect modifiers may also be common causes) # In such cases, the user-provided modifiers are used. # If no effect modifiers are provided, then the ones from the graph are used. if self._effect_modifiers is None or not self._effect_modifiers: self._effect_modifiers = self._graph.get_effect_modifiers(self._treatment, self._outcome) def get_common_causes(self): self._common_causes = self._graph.get_common_causes(self._treatment, self._outcome) return self._common_causes def get_instruments(self): self._instruments = self._graph.get_instruments(self._treatment, self._outcome) return self._instruments def get_effect_modifiers(self): self._effect_modifiers = self._graph.get_effect_modifiers(self._treatment, self._outcome) return self._effect_modifiers def learn_graph(self, method_name="cdt.causality.graph.LiNGAM", *args, **kwargs): """ Learn causal graph from the data. This function takes the method name as input and initializes the causal graph object using the learnt graph. :param self: instance of the CausalModel class (or its subclass) :param method_name: Exact method name of the object to be imported from the concerned library. :returns: an instance of the CausalGraph class initialized with the learned graph. """ # Import causal discovery class str_arr = method_name.split(".", maxsplit=1) library_name = str_arr[0] causal_discovery_class = graph_learners.get_discovery_class_object(library_name) model = causal_discovery_class(self._data, method_name, *args, **kwargs) graph = model.learn_graph() # Initialize causal graph object self.init_graph(graph=graph) return self._graph def identify_effect( self, estimand_type=None, method_name="default", proceed_when_unidentifiable=None, optimize_backdoor=False ): """Identify the causal effect to be estimated, using properties of the causal graph. :param method_name: Method name for identification algorithm. ("id-algorithm" or "default") :param proceed_when_unidentifiable: Binary flag indicating whether identification should proceed in the presence of (potential) unobserved confounders. :returns: a probability expression (estimand) for the causal effect if identified, else NULL """ if proceed_when_unidentifiable is None: proceed_when_unidentifiable = self._proceed_when_unidentifiable if estimand_type is None: estimand_type = self._estimand_type estimand_type = EstimandType(estimand_type) if method_name == "id-algorithm": identifier = IDIdentifier() else: identifier = AutoIdentifier( estimand_type=estimand_type, backdoor_adjustment=BackdoorAdjustment(method_name), proceed_when_unidentifiable=proceed_when_unidentifiable, optimize_backdoor=optimize_backdoor, ) identified_estimand = identifier.identify_effect( graph=self._graph, treatment_name=self._treatment, outcome_name=self._outcome ) self.identifier = identifier return identified_estimand def estimate_effect( self, identified_estimand, method_name=None, control_value=0, treatment_value=1, test_significance=None, evaluate_effect_strength=False, confidence_intervals=False, target_units="ate", effect_modifiers=None, fit_estimator=True, method_params=None, ): """Estimate the identified causal effect. Currently requires an explicit method name to be specified. Method names follow the convention of identification method followed by the specific estimation method: "[backdoor/iv].estimation_method_name". Following methods are supported. * Propensity Score Matching: "backdoor.propensity_score_matching" * Propensity Score Stratification: "backdoor.propensity_score_stratification" * Propensity Score-based Inverse Weighting: "backdoor.propensity_score_weighting" * Linear Regression: "backdoor.linear_regression" * Generalized Linear Models (e.g., logistic regression): "backdoor.generalized_linear_model" * Instrumental Variables: "iv.instrumental_variable" * Regression Discontinuity: "iv.regression_discontinuity" In addition, you can directly call any of the EconML estimation methods. The convention is "backdoor.econml.path-to-estimator-class". For example, for the double machine learning estimator ("DML" class) that is located inside "dml" module of EconML, you can use the method name, "backdoor.econml.dml.DML". CausalML estimators can also be called. See `this demo notebook <https://py-why.github.io/dowhy/example_notebooks/dowhy-conditional-treatment-effects.html>`_. :param identified_estimand: a probability expression that represents the effect to be estimated. Output of CausalModel.identify_effect method :param method_name: name of the estimation method to be used. :param control_value: Value of the treatment in the control group, for effect estimation. If treatment is multi-variate, this can be a list. :param treatment_value: Value of the treatment in the treated group, for effect estimation. If treatment is multi-variate, this can be a list. :param test_significance: Binary flag on whether to additionally do a statistical signficance test for the estimate. :param evaluate_effect_strength: (Experimental) Binary flag on whether to estimate the relative strength of the treatment's effect. This measure can be used to compare different treatments for the same outcome (by running this method with different treatments sequentially). :param confidence_intervals: (Experimental) Binary flag indicating whether confidence intervals should be computed. :param target_units: (Experimental) The units for which the treatment effect should be estimated. This can be of three types. (1) a string for common specifications of target units (namely, "ate", "att" and "atc"), (2) a lambda function that can be used as an index for the data (pandas DataFrame), or (3) a new DataFrame that contains values of the effect_modifiers and effect will be estimated only for this new data. :param effect_modifiers: Names of effect modifier variables can be (optionally) specified here too, since they do not affect identification. If None, the effect_modifiers from the CausalModel are used. :param fit_estimator: Boolean flag on whether to fit the estimator. Setting it to False is useful to estimate the effect on new data using a previously fitted estimator. :param method_params: Dictionary containing any method-specific parameters. These are passed directly to the estimating method. See the docs for each estimation method for allowed method-specific params. :returns: An instance of the CausalEstimate class, containing the causal effect estimate and other method-dependent information """ if effect_modifiers is None or len(effect_modifiers) == 0: effect_modifiers = self._graph.get_effect_modifiers(self._treatment, self._outcome) if method_name is None: # TODO add propensity score as default backdoor method, iv as default iv method, add an informational message to show which method has been selected. pass else: # TODO add dowhy as a prefix to all dowhy estimators num_components = len(method_name.split(".")) str_arr = method_name.split(".", maxsplit=1) identifier_name = str_arr[0] estimator_name = str_arr[1] # This is done as all dowhy estimators have two parts and external ones have two or more parts if num_components > 2: estimator_package = estimator_name.split(".")[0] if estimator_package == "dowhy": # For updated dowhy methods estimator_method = estimator_name.split(".", maxsplit=1)[ 1 ] # discard dowhy from the full package name causal_estimator_class = causal_estimators.get_class_object(estimator_method + "_estimator") else: third_party_estimator_package = estimator_package causal_estimator_class = causal_estimators.get_class_object( third_party_estimator_package, estimator_name ) if method_params is None: method_params = {} # Define the third-party estimation method to be used method_params[third_party_estimator_package + "_methodname"] = estimator_name else: # For older dowhy methods self.logger.info(estimator_name) # Process the dowhy estimators causal_estimator_class = causal_estimators.get_class_object(estimator_name + "_estimator") if method_params is not None and (num_components <= 2 or estimator_package == "dowhy"): extra_args = method_params.get("init_params", {}) else: extra_args = {} if method_params is None: method_params = {} identified_estimand.set_identifier_method(identifier_name) causal_estimator = causal_estimator_class( self._data, identified_estimand, self._treatment, self._outcome, # names of treatment and outcome control_value=control_value, treatment_value=treatment_value, test_significance=test_significance, evaluate_effect_strength=evaluate_effect_strength, confidence_intervals=confidence_intervals, target_units=target_units, effect_modifiers=effect_modifiers, **method_params, **extra_args, ) return estimate_effect( self._treatment, self._outcome, identified_estimand, identifier_name, causal_estimator, control_value, treatment_value, test_significance, evaluate_effect_strength, confidence_intervals, target_units, effect_modifiers, fit_estimator, method_params, ) def do(self, x, identified_estimand, method_name=None, fit_estimator=True, method_params=None): """Do operator for estimating values of the outcome after intervening on treatment. :param x: interventional value of the treatment variable :param identified_estimand: a probability expression that represents the effect to be estimated. Output of CausalModel.identify_effect method :param method_name: any of the estimation method to be used. See docs for estimate_effect method for a list of supported estimation methods. :param fit_estimator: Boolean flag on whether to fit the estimator. Setting it to False is useful to compute the do-operation on new data using a previously fitted estimator. :param method_params: Dictionary containing any method-specific parameters. These are passed directly to the estimating method. :returns: an instance of the CausalEstimate class, containing the causal effect estimate and other method-dependent information """ if method_name is None: pass else: str_arr = method_name.split(".", maxsplit=1) identifier_name = str_arr[0] estimator_name = str_arr[1] identified_estimand.set_identifier_method(identifier_name) causal_estimator_class = causal_estimators.get_class_object(estimator_name + "_estimator") # Check if estimator's target estimand is identified if identified_estimand.estimands[identifier_name] is None: self.logger.warning("No valid identified estimand for using instrumental variables method") estimate = CausalEstimate(None, None, None, None, None) else: if fit_estimator: # Note that while the name of the variable is the same, # "self.causal_estimator", this estimator takes in less # parameters than the same from the # estimate_effect code. It is not advisable to use the # estimator from this function to call estimate_effect # with fit_estimator=False. self.causal_estimator = causal_estimator_class( self._data, identified_estimand, self._treatment, self._outcome, test_significance=False, **method_params, ) else: # Estimator had been computed in a previous call assert self.causal_estimator is not None try: estimate = self.causal_estimator.do(x) except NotImplementedError: self.logger.error("Do Operation not implemented or not supported for this estimator.") raise NotImplementedError return estimate def refute_estimate(self, estimand, estimate, method_name=None, show_progress_bar=False, **kwargs): """Refute an estimated causal effect. If method_name is provided, uses the provided method. In the future, we may support automatic selection of suitable refutation tests. Following refutation methods are supported. * Adding a randomly-generated confounder: "random_common_cause" * Adding a confounder that is associated with both treatment and outcome: "add_unobserved_common_cause" * Replacing the treatment with a placebo (random) variable): "placebo_treatment_refuter" * Removing a random subset of the data: "data_subset_refuter" :param estimand: target estimand, an instance of the IdentifiedEstimand class (typically, the output of identify_effect) :param estimate: estimate to be refuted, an instance of the CausalEstimate class (typically, the output of estimate_effect) :param method_name: name of the refutation method :param show_progress_bar: Boolean flag on whether to show a progress bar :param kwargs: (optional) additional arguments that are passed directly to the refutation method. Can specify a random seed here to ensure reproducible results ('random_seed' parameter). For method-specific parameters, consult the documentation for the specific method. All refutation methods are in the causal_refuters subpackage. :returns: an instance of the RefuteResult class """ if estimate is None or estimate.value is None: self.logger.error("Aborting refutation! No estimate is provided.") raise ValueError("Aborting refutation! No valid estimate is provided.") if method_name is None: pass else: refuter_class = causal_refuters.get_class_object(method_name) refuter = refuter_class(self._data, identified_estimand=estimand, estimate=estimate, **kwargs) res = refuter.refute_estimate(show_progress_bar) return res def view_model(self, layout="dot", size=(8, 6), file_name="causal_model"): """View the causal DAG. :param layout: string specifying the layout of the graph. :param size: tuple (x, y) specifying the width and height of the figure in inches. :param file_name: string specifying the file name for the saved causal graph png. :returns: a visualization of the graph """ self._graph.view_graph(layout, size, file_name) def interpret(self, method_name=None, **kwargs): """Interpret the causal model. :param method_name: method used for interpreting the model. If None, then default interpreter is chosen that describes the model summary and shows the associated causal graph. :param kwargs:: Optional parameters that are directly passed to the interpreter method. :returns: None """ if method_name is None: self.summary(print_to_stdout=True) self.view_model() return method_name_arr = parse_state(method_name) import dowhy.interpreters as interpreters for method in method_name_arr: interpreter = interpreters.get_class_object(method) interpreter(self, **kwargs).interpret() def summary(self, print_to_stdout=False): """Print a text summary of the model. :returns: a string containining the summary """ summary_text = "Model to find the causal effect of treatment {0} on outcome {1}".format( self._treatment, self._outcome ) self.logger.info(summary_text) if print_to_stdout: print(summary_text) return summary_text def refute_graph(self, k=1, independence_test=None, independence_constraints=None): """ Check if the dependencies in input graph matches with the dataset - ( X ⫫ Y ) | Z where X and Y are considered as singleton sets currently Z can have multiple variables :param k: number of covariates in set Z :param independence_test: dictionary containing methods to test conditional independece in data :param independence_constraints: list of implications to be test input by the user in the format [(x,y,(z1,z2)), (x,y, (z3,)) ] : returns: an instance of GraphRefuter class """ if independence_test is not None: test_for_continuous = independence_test["test_for_continuous"] test_for_discrete = independence_test["test_for_discrete"] refuter = GraphRefuter( data=self._data, method_name_continuous=test_for_continuous, method_name_discrete=test_for_discrete ) else: refuter = GraphRefuter(data=self._data) if independence_constraints is None: all_nodes = list(self._graph.get_all_nodes(include_unobserved=False)) num_nodes = len(all_nodes) array_indices = list(range(0, num_nodes)) all_possible_combinations = list( combinations(array_indices, 2) ) # Generating sets of indices of size 2 for different x and y conditional_independences = [] self.logger.info("The followed conditional independences are true for the input graph") for combination in all_possible_combinations: # Iterate over the unique 2-sized sets [x,y] i = combination[0] j = combination[1] a = all_nodes[i] b = all_nodes[j] if i < j: temp_arr = all_nodes[:i] + all_nodes[i + 1 : j] + all_nodes[j + 1 :] else: temp_arr = all_nodes[:j] + all_nodes[j + 1 : i] + all_nodes[i + 1 :] k_sized_lists = list(combinations(temp_arr, k)) for k_list in k_sized_lists: if self._graph.check_dseparation([str(a)], [str(b)], k_list) == True: self.logger.info(" %s and %s are CI given %s ", a, b, k_list) conditional_independences.append([a, b, k_list]) independence_constraints = conditional_independences res = refuter.refute_model(independence_constraints=independence_constraints) self.logger.info(refuter._refutation_passed) return res

andresmor-ms

2044d216c322a4b32c6eadce5da7d83463f19c2f

05bfa49dacf0061988c96c6f3e3756219df5422a

there is a repetition of parameters, e.g., "test_signficance", "treatment_value" in both estimator and estimate_effect method. We need to decide where each parameter goes. I suggest that `target_units`, `control_value`, `treatment_value` belong to the `effect` method of an Estimator. One can call effect multiple times setting different values of these without changing the fitted estimator. ``

amit-sharma

py-why/dowhy

Functional api/estimate effect function

#### Estimate Effect function * Refactors the estimate effect into a separate function to keep backwards compatibility #### TODO (future PRs): * Add `fit(...)` method to estimators - Move data related parameters from the constructor to the `fit(...)` method * Refactor code to avoid `**kwargs` in `__init__(...)` constructors

2022-10-18 15:49:21+00:00

2022-10-25 17:02:02+00:00

dowhy/causal_model.py

""" Module containing the main model class for the dowhy package. """ import logging from itertools import combinations from sympy import init_printing import dowhy.causal_estimators as causal_estimators import dowhy.causal_refuters as causal_refuters import dowhy.graph_learners as graph_learners import dowhy.utils.cli_helpers as cli from dowhy.causal_estimator import CausalEstimate from dowhy.causal_graph import CausalGraph from dowhy.causal_identifier import AutoIdentifier, BackdoorAdjustment, IDIdentifier from dowhy.causal_identifier.identify_effect import EstimandType from dowhy.causal_refuters.graph_refuter import GraphRefuter from dowhy.utils.api import parse_state init_printing() # To display symbolic math symbols class CausalModel: """Main class for storing the causal model state.""" def __init__( self, data, treatment, outcome, graph=None, common_causes=None, instruments=None, effect_modifiers=None, estimand_type="nonparametric-ate", proceed_when_unidentifiable=False, missing_nodes_as_confounders=False, identify_vars=False, **kwargs, ): """Initialize data and create a causal graph instance. Assigns treatment and outcome variables. Also checks and finds the common causes and instruments for treatment and outcome. At least one of graph, common_causes or instruments must be provided. If none of these variables are provided, then learn_graph() can be used later. :param data: a pandas dataframe containing treatment, outcome and other variables. :param treatment: name of the treatment variable :param outcome: name of the outcome variable :param graph: path to DOT file containing a DAG or a string containing a DAG specification in DOT format :param common_causes: names of common causes of treatment and _outcome. Only used when graph is None. :param instruments: names of instrumental variables for the effect of treatment on outcome. Only used when graph is None. :param effect_modifiers: names of variables that can modify the treatment effect. If not provided, then the causal graph is used to find the effect modifiers. Estimators will return multiple different estimates based on each value of effect_modifiers. :param estimand_type: the type of estimand requested (currently only "nonparametric-ate" is supported). In the future, may support other specific parametric forms of identification. :param proceed_when_unidentifiable: does the identification proceed by ignoring potential unobserved confounders. Binary flag. :param missing_nodes_as_confounders: Binary flag indicating whether variables in the dataframe that are not included in the causal graph, should be automatically included as confounder nodes. :param identify_vars: Variable deciding whether to compute common causes, instruments and effect modifiers while initializing the class. identify_vars should be set to False when user is providing common_causes, instruments or effect modifiers on their own(otherwise the identify_vars code can override the user provided values). Also it does not make sense if no graph is given. :returns: an instance of CausalModel class """ self._data = data self._treatment = parse_state(treatment) self._outcome = parse_state(outcome) self._effect_modifiers = parse_state(effect_modifiers) self._estimand_type = estimand_type self._proceed_when_unidentifiable = proceed_when_unidentifiable self._missing_nodes_as_confounders = missing_nodes_as_confounders self.logger = logging.getLogger(__name__) if graph is None: self.logger.warning("Causal Graph not provided. DoWhy will construct a graph based on data inputs.") self._common_causes = parse_state(common_causes) self._instruments = parse_state(instruments) if common_causes is not None and instruments is not None: self._graph = CausalGraph( self._treatment, self._outcome, common_cause_names=self._common_causes, instrument_names=self._instruments, effect_modifier_names=self._effect_modifiers, observed_node_names=self._data.columns.tolist(), ) elif common_causes is not None: self._graph = CausalGraph( self._treatment, self._outcome, common_cause_names=self._common_causes, effect_modifier_names=self._effect_modifiers, observed_node_names=self._data.columns.tolist(), ) elif instruments is not None: self._graph = CausalGraph( self._treatment, self._outcome, instrument_names=self._instruments, effect_modifier_names=self._effect_modifiers, observed_node_names=self._data.columns.tolist(), ) else: self.logger.warning( "Relevant variables to build causal graph not provided. You may want to use the learn_graph() function to construct the causal graph." ) self._graph = CausalGraph( self._treatment, self._outcome, effect_modifier_names=self._effect_modifiers, observed_node_names=self._data.columns.tolist(), ) else: self.init_graph(graph=graph, identify_vars=identify_vars) self._other_variables = kwargs self.summary() def init_graph(self, graph, identify_vars): """ Initialize self._graph using graph provided by the user. """ # Create causal graph object self._graph = CausalGraph( self._treatment, self._outcome, graph, effect_modifier_names=self._effect_modifiers, observed_node_names=self._data.columns.tolist(), missing_nodes_as_confounders=self._missing_nodes_as_confounders, ) if identify_vars: self._common_causes = self._graph.get_common_causes(self._treatment, self._outcome) self._instruments = self._graph.get_instruments(self._treatment, self._outcome) # Sometimes, effect modifiers from the graph may not match those provided by the user. # (Because some effect modifiers may also be common causes) # In such cases, the user-provided modifiers are used. # If no effect modifiers are provided, then the ones from the graph are used. if self._effect_modifiers is None or not self._effect_modifiers: self._effect_modifiers = self._graph.get_effect_modifiers(self._treatment, self._outcome) def get_common_causes(self): self._common_causes = self._graph.get_common_causes(self._treatment, self._outcome) return self._common_causes def get_instruments(self): self._instruments = self._graph.get_instruments(self._treatment, self._outcome) return self._instruments def get_effect_modifiers(self): self._effect_modifiers = self._graph.get_effect_modifiers(self._treatment, self._outcome) return self._effect_modifiers def learn_graph(self, method_name="cdt.causality.graph.LiNGAM", *args, **kwargs): """ Learn causal graph from the data. This function takes the method name as input and initializes the causal graph object using the learnt graph. :param self: instance of the CausalModel class (or its subclass) :param method_name: Exact method name of the object to be imported from the concerned library. :returns: an instance of the CausalGraph class initialized with the learned graph. """ # Import causal discovery class str_arr = method_name.split(".", maxsplit=1) library_name = str_arr[0] causal_discovery_class = graph_learners.get_discovery_class_object(library_name) model = causal_discovery_class(self._data, method_name, *args, **kwargs) graph = model.learn_graph() # Initialize causal graph object self.init_graph(graph=graph) return self._graph def identify_effect( self, estimand_type=None, method_name="default", proceed_when_unidentifiable=None, optimize_backdoor=False ): """Identify the causal effect to be estimated, using properties of the causal graph. :param method_name: Method name for identification algorithm. ("id-algorithm" or "default") :param proceed_when_unidentifiable: Binary flag indicating whether identification should proceed in the presence of (potential) unobserved confounders. :returns: a probability expression (estimand) for the causal effect if identified, else NULL """ if proceed_when_unidentifiable is None: proceed_when_unidentifiable = self._proceed_when_unidentifiable if estimand_type is None: estimand_type = self._estimand_type estimand_type = EstimandType(estimand_type) if method_name == "id-algorithm": identifier = IDIdentifier() else: identifier = AutoIdentifier( estimand_type=estimand_type, backdoor_adjustment=BackdoorAdjustment(method_name), proceed_when_unidentifiable=proceed_when_unidentifiable, optimize_backdoor=optimize_backdoor, ) identified_estimand = identifier.identify_effect( graph=self._graph, treatment_name=self._treatment, outcome_name=self._outcome ) self.identifier = identifier return identified_estimand def estimate_effect( self, identified_estimand, method_name=None, control_value=0, treatment_value=1, test_significance=None, evaluate_effect_strength=False, confidence_intervals=False, target_units="ate", effect_modifiers=None, fit_estimator=True, method_params=None, ): """Estimate the identified causal effect. Currently requires an explicit method name to be specified. Method names follow the convention of identification method followed by the specific estimation method: "[backdoor/iv].estimation_method_name". Following methods are supported. * Propensity Score Matching: "backdoor.propensity_score_matching" * Propensity Score Stratification: "backdoor.propensity_score_stratification" * Propensity Score-based Inverse Weighting: "backdoor.propensity_score_weighting" * Linear Regression: "backdoor.linear_regression" * Generalized Linear Models (e.g., logistic regression): "backdoor.generalized_linear_model" * Instrumental Variables: "iv.instrumental_variable" * Regression Discontinuity: "iv.regression_discontinuity" In addition, you can directly call any of the EconML estimation methods. The convention is "backdoor.econml.path-to-estimator-class". For example, for the double machine learning estimator ("DML" class) that is located inside "dml" module of EconML, you can use the method name, "backdoor.econml.dml.DML". CausalML estimators can also be called. See `this demo notebook <https://py-why.github.io/dowhy/example_notebooks/dowhy-conditional-treatment-effects.html>`_. :param identified_estimand: a probability expression that represents the effect to be estimated. Output of CausalModel.identify_effect method :param method_name: name of the estimation method to be used. :param control_value: Value of the treatment in the control group, for effect estimation. If treatment is multi-variate, this can be a list. :param treatment_value: Value of the treatment in the treated group, for effect estimation. If treatment is multi-variate, this can be a list. :param test_significance: Binary flag on whether to additionally do a statistical signficance test for the estimate. :param evaluate_effect_strength: (Experimental) Binary flag on whether to estimate the relative strength of the treatment's effect. This measure can be used to compare different treatments for the same outcome (by running this method with different treatments sequentially). :param confidence_intervals: (Experimental) Binary flag indicating whether confidence intervals should be computed. :param target_units: (Experimental) The units for which the treatment effect should be estimated. This can be of three types. (1) a string for common specifications of target units (namely, "ate", "att" and "atc"), (2) a lambda function that can be used as an index for the data (pandas DataFrame), or (3) a new DataFrame that contains values of the effect_modifiers and effect will be estimated only for this new data. :param effect_modifiers: Names of effect modifier variables can be (optionally) specified here too, since they do not affect identification. If None, the effect_modifiers from the CausalModel are used. :param fit_estimator: Boolean flag on whether to fit the estimator. Setting it to False is useful to estimate the effect on new data using a previously fitted estimator. :param method_params: Dictionary containing any method-specific parameters. These are passed directly to the estimating method. See the docs for each estimation method for allowed method-specific params. :returns: An instance of the CausalEstimate class, containing the causal effect estimate and other method-dependent information """ if effect_modifiers is None: if self._effect_modifiers is None or len(self._effect_modifiers) == 0: effect_modifiers = self.get_effect_modifiers() else: effect_modifiers = self._effect_modifiers if fit_estimator: if method_name is None: # TODO add propensity score as default backdoor method, iv as default iv method, add an informational message to show which method has been selected. pass else: # TODO add dowhy as a prefix to all dowhy estimators num_components = len(method_name.split(".")) str_arr = method_name.split(".", maxsplit=1) identifier_name = str_arr[0] estimator_name = str_arr[1] identified_estimand.set_identifier_method(identifier_name) # This is done as all dowhy estimators have two parts and external ones have two or more parts if num_components > 2: estimator_package = estimator_name.split(".")[0] if estimator_package == "dowhy": # For updated dowhy methods estimator_method = estimator_name.split(".", maxsplit=1)[ 1 ] # discard dowhy from the full package name causal_estimator_class = causal_estimators.get_class_object(estimator_method + "_estimator") else: third_party_estimator_package = estimator_package causal_estimator_class = causal_estimators.get_class_object( third_party_estimator_package, estimator_name ) if method_params is None: method_params = {} # Define the third-party estimation method to be used method_params[third_party_estimator_package + "_methodname"] = estimator_name else: # For older dowhy methods self.logger.info(estimator_name) # Process the dowhy estimators causal_estimator_class = causal_estimators.get_class_object(estimator_name + "_estimator") if identified_estimand.no_directed_path: self.logger.warning("No directed path from {0} to {1}.".format(self._treatment, self._outcome)) return CausalEstimate( 0, identified_estimand, None, control_value=control_value, treatment_value=treatment_value ) # Check if estimator's target estimand is identified elif identified_estimand.estimands[identifier_name] is None: self.logger.error("No valid identified estimand available.") return CausalEstimate(None, None, None, control_value=control_value, treatment_value=treatment_value) else: if method_params is not None and (num_components <= 2 or estimator_package == "dowhy"): extra_args = method_params.get("init_params", {}) else: extra_args = {} if method_params is None: method_params = {} self.causal_estimator = causal_estimator_class( self._data, identified_estimand, self._treatment, self._outcome, # names of treatment and outcome control_value=control_value, treatment_value=treatment_value, test_significance=test_significance, evaluate_effect_strength=evaluate_effect_strength, confidence_intervals=confidence_intervals, target_units=target_units, effect_modifiers=effect_modifiers, **method_params, **extra_args, ) else: # Estimator had been computed in a previous call assert self.causal_estimator is not None causal_estimator_class = self.causal_estimator.__class__ self.causal_estimator.update_input(treatment_value, control_value, target_units) estimate = self.causal_estimator.estimate_effect() # Store parameters inside estimate object for refutation methods # TODO: This add_params needs to move to the estimator class # inside estimate_effect and estimate_conditional_effect estimate.add_params( estimand_type=identified_estimand.estimand_type, estimator_class=causal_estimator_class, test_significance=test_significance, evaluate_effect_strength=evaluate_effect_strength, confidence_intervals=confidence_intervals, target_units=target_units, effect_modifiers=effect_modifiers, method_params=method_params, ) return estimate def do(self, x, identified_estimand, method_name=None, fit_estimator=True, method_params=None): """Do operator for estimating values of the outcome after intervening on treatment. :param x: interventional value of the treatment variable :param identified_estimand: a probability expression that represents the effect to be estimated. Output of CausalModel.identify_effect method :param method_name: any of the estimation method to be used. See docs for estimate_effect method for a list of supported estimation methods. :param fit_estimator: Boolean flag on whether to fit the estimator. Setting it to False is useful to compute the do-operation on new data using a previously fitted estimator. :param method_params: Dictionary containing any method-specific parameters. These are passed directly to the estimating method. :returns: an instance of the CausalEstimate class, containing the causal effect estimate and other method-dependent information """ if method_name is None: pass else: str_arr = method_name.split(".", maxsplit=1) identifier_name = str_arr[0] estimator_name = str_arr[1] identified_estimand.set_identifier_method(identifier_name) causal_estimator_class = causal_estimators.get_class_object(estimator_name + "_estimator") # Check if estimator's target estimand is identified if identified_estimand.estimands[identifier_name] is None: self.logger.warning("No valid identified estimand for using instrumental variables method") estimate = CausalEstimate(None, None, None, None, None) else: if fit_estimator: # Note that while the name of the variable is the same, # "self.causal_estimator", this estimator takes in less # parameters than the same from the # estimate_effect code. It is not advisable to use the # estimator from this function to call estimate_effect # with fit_estimator=False. self.causal_estimator = causal_estimator_class( self._data, identified_estimand, self._treatment, self._outcome, test_significance=False, **method_params, ) else: # Estimator had been computed in a previous call assert self.causal_estimator is not None try: estimate = self.causal_estimator.do(x) except NotImplementedError: self.logger.error("Do Operation not implemented or not supported for this estimator.") raise NotImplementedError return estimate def refute_estimate(self, estimand, estimate, method_name=None, show_progress_bar=False, **kwargs): """Refute an estimated causal effect. If method_name is provided, uses the provided method. In the future, we may support automatic selection of suitable refutation tests. Following refutation methods are supported. * Adding a randomly-generated confounder: "random_common_cause" * Adding a confounder that is associated with both treatment and outcome: "add_unobserved_common_cause" * Replacing the treatment with a placebo (random) variable): "placebo_treatment_refuter" * Removing a random subset of the data: "data_subset_refuter" :param estimand: target estimand, an instance of the IdentifiedEstimand class (typically, the output of identify_effect) :param estimate: estimate to be refuted, an instance of the CausalEstimate class (typically, the output of estimate_effect) :param method_name: name of the refutation method :param show_progress_bar: Boolean flag on whether to show a progress bar :param kwargs: (optional) additional arguments that are passed directly to the refutation method. Can specify a random seed here to ensure reproducible results ('random_seed' parameter). For method-specific parameters, consult the documentation for the specific method. All refutation methods are in the causal_refuters subpackage. :returns: an instance of the RefuteResult class """ if estimate is None or estimate.value is None: self.logger.error("Aborting refutation! No estimate is provided.") raise ValueError("Aborting refutation! No valid estimate is provided.") if method_name is None: pass else: refuter_class = causal_refuters.get_class_object(method_name) refuter = refuter_class(self._data, identified_estimand=estimand, estimate=estimate, **kwargs) res = refuter.refute_estimate(show_progress_bar) return res def view_model(self, layout="dot", size=(8, 6), file_name="causal_model"): """View the causal DAG. :param layout: string specifying the layout of the graph. :param size: tuple (x, y) specifying the width and height of the figure in inches. :param file_name: string specifying the file name for the saved causal graph png. :returns: a visualization of the graph """ self._graph.view_graph(layout, size, file_name) def interpret(self, method_name=None, **kwargs): """Interpret the causal model. :param method_name: method used for interpreting the model. If None, then default interpreter is chosen that describes the model summary and shows the associated causal graph. :param kwargs:: Optional parameters that are directly passed to the interpreter method. :returns: None """ if method_name is None: self.summary(print_to_stdout=True) self.view_model() return method_name_arr = parse_state(method_name) import dowhy.interpreters as interpreters for method in method_name_arr: interpreter = interpreters.get_class_object(method) interpreter(self, **kwargs).interpret() def summary(self, print_to_stdout=False): """Print a text summary of the model. :returns: a string containining the summary """ summary_text = "Model to find the causal effect of treatment {0} on outcome {1}".format( self._treatment, self._outcome ) self.logger.info(summary_text) if print_to_stdout: print(summary_text) return summary_text def refute_graph(self, k=1, independence_test=None, independence_constraints=None): """ Check if the dependencies in input graph matches with the dataset - ( X ⫫ Y ) | Z where X and Y are considered as singleton sets currently Z can have multiple variables :param k: number of covariates in set Z :param independence_test: dictionary containing methods to test conditional independece in data :param independence_constraints: list of implications to be test input by the user in the format [(x,y,(z1,z2)), (x,y, (z3,)) ] : returns: an instance of GraphRefuter class """ if independence_test is not None: test_for_continuous = independence_test["test_for_continuous"] test_for_discrete = independence_test["test_for_discrete"] refuter = GraphRefuter( data=self._data, method_name_continuous=test_for_continuous, method_name_discrete=test_for_discrete ) else: refuter = GraphRefuter(data=self._data) if independence_constraints is None: all_nodes = list(self._graph.get_all_nodes(include_unobserved=False)) num_nodes = len(all_nodes) array_indices = list(range(0, num_nodes)) all_possible_combinations = list( combinations(array_indices, 2) ) # Generating sets of indices of size 2 for different x and y conditional_independences = [] self.logger.info("The followed conditional independences are true for the input graph") for combination in all_possible_combinations: # Iterate over the unique 2-sized sets [x,y] i = combination[0] j = combination[1] a = all_nodes[i] b = all_nodes[j] if i < j: temp_arr = all_nodes[:i] + all_nodes[i + 1 : j] + all_nodes[j + 1 :] else: temp_arr = all_nodes[:j] + all_nodes[j + 1 : i] + all_nodes[i + 1 :] k_sized_lists = list(combinations(temp_arr, k)) for k_list in k_sized_lists: if self._graph.check_dseparation([str(a)], [str(b)], k_list) == True: self.logger.info(" %s and %s are CI given %s ", a, b, k_list) conditional_independences.append([a, b, k_list]) independence_constraints = conditional_independences res = refuter.refute_model(independence_constraints=independence_constraints) self.logger.info(refuter._refutation_passed) return res

""" Module containing the main model class for the dowhy package. """ import logging from itertools import combinations from sympy import init_printing import dowhy.causal_estimators as causal_estimators import dowhy.causal_refuters as causal_refuters import dowhy.graph_learners as graph_learners import dowhy.utils.cli_helpers as cli from dowhy.causal_estimator import CausalEstimate, estimate_effect from dowhy.causal_graph import CausalGraph from dowhy.causal_identifier import AutoIdentifier, BackdoorAdjustment, IDIdentifier from dowhy.causal_identifier.identify_effect import EstimandType from dowhy.causal_refuters.graph_refuter import GraphRefuter from dowhy.utils.api import parse_state init_printing() # To display symbolic math symbols class CausalModel: """Main class for storing the causal model state.""" def __init__( self, data, treatment, outcome, graph=None, common_causes=None, instruments=None, effect_modifiers=None, estimand_type="nonparametric-ate", proceed_when_unidentifiable=False, missing_nodes_as_confounders=False, identify_vars=False, **kwargs, ): """Initialize data and create a causal graph instance. Assigns treatment and outcome variables. Also checks and finds the common causes and instruments for treatment and outcome. At least one of graph, common_causes or instruments must be provided. If none of these variables are provided, then learn_graph() can be used later. :param data: a pandas dataframe containing treatment, outcome and other variables. :param treatment: name of the treatment variable :param outcome: name of the outcome variable :param graph: path to DOT file containing a DAG or a string containing a DAG specification in DOT format :param common_causes: names of common causes of treatment and _outcome. Only used when graph is None. :param instruments: names of instrumental variables for the effect of treatment on outcome. Only used when graph is None. :param effect_modifiers: names of variables that can modify the treatment effect. If not provided, then the causal graph is used to find the effect modifiers. Estimators will return multiple different estimates based on each value of effect_modifiers. :param estimand_type: the type of estimand requested (currently only "nonparametric-ate" is supported). In the future, may support other specific parametric forms of identification. :param proceed_when_unidentifiable: does the identification proceed by ignoring potential unobserved confounders. Binary flag. :param missing_nodes_as_confounders: Binary flag indicating whether variables in the dataframe that are not included in the causal graph, should be automatically included as confounder nodes. :param identify_vars: Variable deciding whether to compute common causes, instruments and effect modifiers while initializing the class. identify_vars should be set to False when user is providing common_causes, instruments or effect modifiers on their own(otherwise the identify_vars code can override the user provided values). Also it does not make sense if no graph is given. :returns: an instance of CausalModel class """ self._data = data self._treatment = parse_state(treatment) self._outcome = parse_state(outcome) self._effect_modifiers = parse_state(effect_modifiers) self._estimand_type = estimand_type self._proceed_when_unidentifiable = proceed_when_unidentifiable self._missing_nodes_as_confounders = missing_nodes_as_confounders self.logger = logging.getLogger(__name__) if graph is None: self.logger.warning("Causal Graph not provided. DoWhy will construct a graph based on data inputs.") self._common_causes = parse_state(common_causes) self._instruments = parse_state(instruments) if common_causes is not None and instruments is not None: self._graph = CausalGraph( self._treatment, self._outcome, common_cause_names=self._common_causes, instrument_names=self._instruments, effect_modifier_names=self._effect_modifiers, observed_node_names=self._data.columns.tolist(), ) elif common_causes is not None: self._graph = CausalGraph( self._treatment, self._outcome, common_cause_names=self._common_causes, effect_modifier_names=self._effect_modifiers, observed_node_names=self._data.columns.tolist(), ) elif instruments is not None: self._graph = CausalGraph( self._treatment, self._outcome, instrument_names=self._instruments, effect_modifier_names=self._effect_modifiers, observed_node_names=self._data.columns.tolist(), ) else: self.logger.warning( "Relevant variables to build causal graph not provided. You may want to use the learn_graph() function to construct the causal graph." ) self._graph = CausalGraph( self._treatment, self._outcome, effect_modifier_names=self._effect_modifiers, observed_node_names=self._data.columns.tolist(), ) else: self.init_graph(graph=graph, identify_vars=identify_vars) self._other_variables = kwargs self.summary() def init_graph(self, graph, identify_vars): """ Initialize self._graph using graph provided by the user. """ # Create causal graph object self._graph = CausalGraph( self._treatment, self._outcome, graph, effect_modifier_names=self._effect_modifiers, observed_node_names=self._data.columns.tolist(), missing_nodes_as_confounders=self._missing_nodes_as_confounders, ) if identify_vars: self._common_causes = self._graph.get_common_causes(self._treatment, self._outcome) self._instruments = self._graph.get_instruments(self._treatment, self._outcome) # Sometimes, effect modifiers from the graph may not match those provided by the user. # (Because some effect modifiers may also be common causes) # In such cases, the user-provided modifiers are used. # If no effect modifiers are provided, then the ones from the graph are used. if self._effect_modifiers is None or not self._effect_modifiers: self._effect_modifiers = self._graph.get_effect_modifiers(self._treatment, self._outcome) def get_common_causes(self): self._common_causes = self._graph.get_common_causes(self._treatment, self._outcome) return self._common_causes def get_instruments(self): self._instruments = self._graph.get_instruments(self._treatment, self._outcome) return self._instruments def get_effect_modifiers(self): self._effect_modifiers = self._graph.get_effect_modifiers(self._treatment, self._outcome) return self._effect_modifiers def learn_graph(self, method_name="cdt.causality.graph.LiNGAM", *args, **kwargs): """ Learn causal graph from the data. This function takes the method name as input and initializes the causal graph object using the learnt graph. :param self: instance of the CausalModel class (or its subclass) :param method_name: Exact method name of the object to be imported from the concerned library. :returns: an instance of the CausalGraph class initialized with the learned graph. """ # Import causal discovery class str_arr = method_name.split(".", maxsplit=1) library_name = str_arr[0] causal_discovery_class = graph_learners.get_discovery_class_object(library_name) model = causal_discovery_class(self._data, method_name, *args, **kwargs) graph = model.learn_graph() # Initialize causal graph object self.init_graph(graph=graph) return self._graph def identify_effect( self, estimand_type=None, method_name="default", proceed_when_unidentifiable=None, optimize_backdoor=False ): """Identify the causal effect to be estimated, using properties of the causal graph. :param method_name: Method name for identification algorithm. ("id-algorithm" or "default") :param proceed_when_unidentifiable: Binary flag indicating whether identification should proceed in the presence of (potential) unobserved confounders. :returns: a probability expression (estimand) for the causal effect if identified, else NULL """ if proceed_when_unidentifiable is None: proceed_when_unidentifiable = self._proceed_when_unidentifiable if estimand_type is None: estimand_type = self._estimand_type estimand_type = EstimandType(estimand_type) if method_name == "id-algorithm": identifier = IDIdentifier() else: identifier = AutoIdentifier( estimand_type=estimand_type, backdoor_adjustment=BackdoorAdjustment(method_name), proceed_when_unidentifiable=proceed_when_unidentifiable, optimize_backdoor=optimize_backdoor, ) identified_estimand = identifier.identify_effect( graph=self._graph, treatment_name=self._treatment, outcome_name=self._outcome ) self.identifier = identifier return identified_estimand def estimate_effect( self, identified_estimand, method_name=None, control_value=0, treatment_value=1, test_significance=None, evaluate_effect_strength=False, confidence_intervals=False, target_units="ate", effect_modifiers=None, fit_estimator=True, method_params=None, ): """Estimate the identified causal effect. Currently requires an explicit method name to be specified. Method names follow the convention of identification method followed by the specific estimation method: "[backdoor/iv].estimation_method_name". Following methods are supported. * Propensity Score Matching: "backdoor.propensity_score_matching" * Propensity Score Stratification: "backdoor.propensity_score_stratification" * Propensity Score-based Inverse Weighting: "backdoor.propensity_score_weighting" * Linear Regression: "backdoor.linear_regression" * Generalized Linear Models (e.g., logistic regression): "backdoor.generalized_linear_model" * Instrumental Variables: "iv.instrumental_variable" * Regression Discontinuity: "iv.regression_discontinuity" In addition, you can directly call any of the EconML estimation methods. The convention is "backdoor.econml.path-to-estimator-class". For example, for the double machine learning estimator ("DML" class) that is located inside "dml" module of EconML, you can use the method name, "backdoor.econml.dml.DML". CausalML estimators can also be called. See `this demo notebook <https://py-why.github.io/dowhy/example_notebooks/dowhy-conditional-treatment-effects.html>`_. :param identified_estimand: a probability expression that represents the effect to be estimated. Output of CausalModel.identify_effect method :param method_name: name of the estimation method to be used. :param control_value: Value of the treatment in the control group, for effect estimation. If treatment is multi-variate, this can be a list. :param treatment_value: Value of the treatment in the treated group, for effect estimation. If treatment is multi-variate, this can be a list. :param test_significance: Binary flag on whether to additionally do a statistical signficance test for the estimate. :param evaluate_effect_strength: (Experimental) Binary flag on whether to estimate the relative strength of the treatment's effect. This measure can be used to compare different treatments for the same outcome (by running this method with different treatments sequentially). :param confidence_intervals: (Experimental) Binary flag indicating whether confidence intervals should be computed. :param target_units: (Experimental) The units for which the treatment effect should be estimated. This can be of three types. (1) a string for common specifications of target units (namely, "ate", "att" and "atc"), (2) a lambda function that can be used as an index for the data (pandas DataFrame), or (3) a new DataFrame that contains values of the effect_modifiers and effect will be estimated only for this new data. :param effect_modifiers: Names of effect modifier variables can be (optionally) specified here too, since they do not affect identification. If None, the effect_modifiers from the CausalModel are used. :param fit_estimator: Boolean flag on whether to fit the estimator. Setting it to False is useful to estimate the effect on new data using a previously fitted estimator. :param method_params: Dictionary containing any method-specific parameters. These are passed directly to the estimating method. See the docs for each estimation method for allowed method-specific params. :returns: An instance of the CausalEstimate class, containing the causal effect estimate and other method-dependent information """ if effect_modifiers is None or len(effect_modifiers) == 0: effect_modifiers = self._graph.get_effect_modifiers(self._treatment, self._outcome) if method_name is None: # TODO add propensity score as default backdoor method, iv as default iv method, add an informational message to show which method has been selected. pass else: # TODO add dowhy as a prefix to all dowhy estimators num_components = len(method_name.split(".")) str_arr = method_name.split(".", maxsplit=1) identifier_name = str_arr[0] estimator_name = str_arr[1] # This is done as all dowhy estimators have two parts and external ones have two or more parts if num_components > 2: estimator_package = estimator_name.split(".")[0] if estimator_package == "dowhy": # For updated dowhy methods estimator_method = estimator_name.split(".", maxsplit=1)[ 1 ] # discard dowhy from the full package name causal_estimator_class = causal_estimators.get_class_object(estimator_method + "_estimator") else: third_party_estimator_package = estimator_package causal_estimator_class = causal_estimators.get_class_object( third_party_estimator_package, estimator_name ) if method_params is None: method_params = {} # Define the third-party estimation method to be used method_params[third_party_estimator_package + "_methodname"] = estimator_name else: # For older dowhy methods self.logger.info(estimator_name) # Process the dowhy estimators causal_estimator_class = causal_estimators.get_class_object(estimator_name + "_estimator") if method_params is not None and (num_components <= 2 or estimator_package == "dowhy"): extra_args = method_params.get("init_params", {}) else: extra_args = {} if method_params is None: method_params = {} identified_estimand.set_identifier_method(identifier_name) causal_estimator = causal_estimator_class( self._data, identified_estimand, self._treatment, self._outcome, # names of treatment and outcome control_value=control_value, treatment_value=treatment_value, test_significance=test_significance, evaluate_effect_strength=evaluate_effect_strength, confidence_intervals=confidence_intervals, target_units=target_units, effect_modifiers=effect_modifiers, **method_params, **extra_args, ) return estimate_effect( self._treatment, self._outcome, identified_estimand, identifier_name, causal_estimator, control_value, treatment_value, test_significance, evaluate_effect_strength, confidence_intervals, target_units, effect_modifiers, fit_estimator, method_params, ) def do(self, x, identified_estimand, method_name=None, fit_estimator=True, method_params=None): """Do operator for estimating values of the outcome after intervening on treatment. :param x: interventional value of the treatment variable :param identified_estimand: a probability expression that represents the effect to be estimated. Output of CausalModel.identify_effect method :param method_name: any of the estimation method to be used. See docs for estimate_effect method for a list of supported estimation methods. :param fit_estimator: Boolean flag on whether to fit the estimator. Setting it to False is useful to compute the do-operation on new data using a previously fitted estimator. :param method_params: Dictionary containing any method-specific parameters. These are passed directly to the estimating method. :returns: an instance of the CausalEstimate class, containing the causal effect estimate and other method-dependent information """ if method_name is None: pass else: str_arr = method_name.split(".", maxsplit=1) identifier_name = str_arr[0] estimator_name = str_arr[1] identified_estimand.set_identifier_method(identifier_name) causal_estimator_class = causal_estimators.get_class_object(estimator_name + "_estimator") # Check if estimator's target estimand is identified if identified_estimand.estimands[identifier_name] is None: self.logger.warning("No valid identified estimand for using instrumental variables method") estimate = CausalEstimate(None, None, None, None, None) else: if fit_estimator: # Note that while the name of the variable is the same, # "self.causal_estimator", this estimator takes in less # parameters than the same from the # estimate_effect code. It is not advisable to use the # estimator from this function to call estimate_effect # with fit_estimator=False. self.causal_estimator = causal_estimator_class( self._data, identified_estimand, self._treatment, self._outcome, test_significance=False, **method_params, ) else: # Estimator had been computed in a previous call assert self.causal_estimator is not None try: estimate = self.causal_estimator.do(x) except NotImplementedError: self.logger.error("Do Operation not implemented or not supported for this estimator.") raise NotImplementedError return estimate def refute_estimate(self, estimand, estimate, method_name=None, show_progress_bar=False, **kwargs): """Refute an estimated causal effect. If method_name is provided, uses the provided method. In the future, we may support automatic selection of suitable refutation tests. Following refutation methods are supported. * Adding a randomly-generated confounder: "random_common_cause" * Adding a confounder that is associated with both treatment and outcome: "add_unobserved_common_cause" * Replacing the treatment with a placebo (random) variable): "placebo_treatment_refuter" * Removing a random subset of the data: "data_subset_refuter" :param estimand: target estimand, an instance of the IdentifiedEstimand class (typically, the output of identify_effect) :param estimate: estimate to be refuted, an instance of the CausalEstimate class (typically, the output of estimate_effect) :param method_name: name of the refutation method :param show_progress_bar: Boolean flag on whether to show a progress bar :param kwargs: (optional) additional arguments that are passed directly to the refutation method. Can specify a random seed here to ensure reproducible results ('random_seed' parameter). For method-specific parameters, consult the documentation for the specific method. All refutation methods are in the causal_refuters subpackage. :returns: an instance of the RefuteResult class """ if estimate is None or estimate.value is None: self.logger.error("Aborting refutation! No estimate is provided.") raise ValueError("Aborting refutation! No valid estimate is provided.") if method_name is None: pass else: refuter_class = causal_refuters.get_class_object(method_name) refuter = refuter_class(self._data, identified_estimand=estimand, estimate=estimate, **kwargs) res = refuter.refute_estimate(show_progress_bar) return res def view_model(self, layout="dot", size=(8, 6), file_name="causal_model"): """View the causal DAG. :param layout: string specifying the layout of the graph. :param size: tuple (x, y) specifying the width and height of the figure in inches. :param file_name: string specifying the file name for the saved causal graph png. :returns: a visualization of the graph """ self._graph.view_graph(layout, size, file_name) def interpret(self, method_name=None, **kwargs): """Interpret the causal model. :param method_name: method used for interpreting the model. If None, then default interpreter is chosen that describes the model summary and shows the associated causal graph. :param kwargs:: Optional parameters that are directly passed to the interpreter method. :returns: None """ if method_name is None: self.summary(print_to_stdout=True) self.view_model() return method_name_arr = parse_state(method_name) import dowhy.interpreters as interpreters for method in method_name_arr: interpreter = interpreters.get_class_object(method) interpreter(self, **kwargs).interpret() def summary(self, print_to_stdout=False): """Print a text summary of the model. :returns: a string containining the summary """ summary_text = "Model to find the causal effect of treatment {0} on outcome {1}".format( self._treatment, self._outcome ) self.logger.info(summary_text) if print_to_stdout: print(summary_text) return summary_text def refute_graph(self, k=1, independence_test=None, independence_constraints=None): """ Check if the dependencies in input graph matches with the dataset - ( X ⫫ Y ) | Z where X and Y are considered as singleton sets currently Z can have multiple variables :param k: number of covariates in set Z :param independence_test: dictionary containing methods to test conditional independece in data :param independence_constraints: list of implications to be test input by the user in the format [(x,y,(z1,z2)), (x,y, (z3,)) ] : returns: an instance of GraphRefuter class """ if independence_test is not None: test_for_continuous = independence_test["test_for_continuous"] test_for_discrete = independence_test["test_for_discrete"] refuter = GraphRefuter( data=self._data, method_name_continuous=test_for_continuous, method_name_discrete=test_for_discrete ) else: refuter = GraphRefuter(data=self._data) if independence_constraints is None: all_nodes = list(self._graph.get_all_nodes(include_unobserved=False)) num_nodes = len(all_nodes) array_indices = list(range(0, num_nodes)) all_possible_combinations = list( combinations(array_indices, 2) ) # Generating sets of indices of size 2 for different x and y conditional_independences = [] self.logger.info("The followed conditional independences are true for the input graph") for combination in all_possible_combinations: # Iterate over the unique 2-sized sets [x,y] i = combination[0] j = combination[1] a = all_nodes[i] b = all_nodes[j] if i < j: temp_arr = all_nodes[:i] + all_nodes[i + 1 : j] + all_nodes[j + 1 :] else: temp_arr = all_nodes[:j] + all_nodes[j + 1 : i] + all_nodes[i + 1 :] k_sized_lists = list(combinations(temp_arr, k)) for k_list in k_sized_lists: if self._graph.check_dseparation([str(a)], [str(b)], k_list) == True: self.logger.info(" %s and %s are CI given %s ", a, b, k_list) conditional_independences.append([a, b, k_list]) independence_constraints = conditional_independences res = refuter.refute_model(independence_constraints=independence_constraints) self.logger.info(refuter._refutation_passed) return res

andresmor-ms

2044d216c322a4b32c6eadce5da7d83463f19c2f

05bfa49dacf0061988c96c6f3e3756219df5422a

Got it, will take it into account for the PR where i refactor the estimator objects

andresmor-ms

py-why/dowhy

Functional api/refute estimate

* Refactor refuters into functions * Rename functional_api notebook for clarity * Add return types to identify_estimate * Update `__init__.py` for imports * Add joblib for bootstrap refuter * Create `refute_estimate` function * Add types for refuter parameters & return types

2022-10-04 16:18:49+00:00

2022-10-07 04:30:22+00:00

dowhy/causal_identifier/auto_identifier.py

import itertools import logging from enum import Enum from typing import Dict, List, Optional, Union import sympy as sp import sympy.stats as spstats from dowhy.causal_graph import CausalGraph from dowhy.causal_identifier.efficient_backdoor import EfficientBackdoor from dowhy.causal_identifier.identified_estimand import IdentifiedEstimand from dowhy.utils.api import parse_state logger = logging.getLogger(__name__) class EstimandType(Enum): # Average total effect NONPARAMETRIC_ATE = "nonparametric-ate" # Natural direct effect NONPARAMETRIC_NDE = "nonparametric-nde" # Natural indirect effect NONPARAMETRIC_NIE = "nonparametric-nie" # Controlled direct effect NONPARAMETRIC_CDE = "nonparametric-cde" class BackdoorAdjustment(Enum): # Backdoor method names BACKDOOR_DEFAULT = "default" BACKDOOR_EXHAUSTIVE = "exhaustive-search" BACKDOOR_MIN = "minimal-adjustment" BACKDOOR_MAX = "maximal-adjustment" BACKDOOR_EFFICIENT = "efficient-adjustment" BACKDOOR_MIN_EFFICIENT = "efficient-minimal-adjustment" BACKDOOR_MINCOST_EFFICIENT = "efficient-mincost-adjustment" MAX_BACKDOOR_ITERATIONS = 100000 METHOD_NAMES = { BackdoorAdjustment.BACKDOOR_DEFAULT, BackdoorAdjustment.BACKDOOR_EXHAUSTIVE, BackdoorAdjustment.BACKDOOR_MIN, BackdoorAdjustment.BACKDOOR_MAX, BackdoorAdjustment.BACKDOOR_EFFICIENT, BackdoorAdjustment.BACKDOOR_MIN_EFFICIENT, BackdoorAdjustment.BACKDOOR_MINCOST_EFFICIENT, } EFFICIENT_METHODS = { BackdoorAdjustment.BACKDOOR_EFFICIENT, BackdoorAdjustment.BACKDOOR_MIN_EFFICIENT, BackdoorAdjustment.BACKDOOR_MINCOST_EFFICIENT, } DEFAULT_BACKDOOR_METHOD = BackdoorAdjustment.BACKDOOR_DEFAULT class AutoIdentifier: """Class that implements different identification methods. Currently supports backdoor and instrumental variable identification methods. The identification is based on the causal graph provided. This class is for backwards compatibility with CausalModel Will be deprecated in the future in favor of function call auto_identify_effect() """ def __init__( self, estimand_type: EstimandType, backdoor_adjustment: BackdoorAdjustment = BackdoorAdjustment.BACKDOOR_DEFAULT, proceed_when_unidentifiable: bool = False, optimize_backdoor: bool = False, costs: Optional[List] = None, ): self.estimand_type = estimand_type self.backdoor_adjustment = backdoor_adjustment self._proceed_when_unidentifiable = proceed_when_unidentifiable self.optimize_backdoor = optimize_backdoor self.costs = costs self.logger = logging.getLogger(__name__) def identify_effect( self, graph: CausalGraph, treatment_name: Union[str, List[str]], outcome_name: Union[str, List[str]], conditional_node_names: List[str] = None, **kwargs, ): estimand = auto_identify_effect( graph, treatment_name, outcome_name, self.estimand_type, conditional_node_names, self.backdoor_adjustment, self._proceed_when_unidentifiable, self.optimize_backdoor, self.costs, **kwargs, ) estimand.identifier = self return estimand def identify_backdoor( self, graph: CausalGraph, treatment_name: List[str], outcome_name: str, include_unobserved: bool = False, dseparation_algo: str = "default", direct_effect: bool = False, ): return identify_backdoor( graph, treatment_name, outcome_name, self.backdoor_adjustment, include_unobserved, dseparation_algo, direct_effect, ) def auto_identify_effect( graph: CausalGraph, treatment_name: Union[str, List[str]], outcome_name: Union[str, List[str]], estimand_type: EstimandType, conditional_node_names: List[str] = None, backdoor_adjustment: BackdoorAdjustment = BackdoorAdjustment.BACKDOOR_DEFAULT, proceed_when_unidentifiable: bool = False, optimize_backdoor: bool = False, costs: Optional[List] = None, **kwargs, ): """Main method that returns an identified estimand (if one exists). If estimand_type is non-parametric ATE, then uses backdoor, instrumental variable and frontdoor identification methods, to check if an identified estimand exists, based on the causal graph. :param optimize_backdoor: if True, uses an optimised algorithm to compute the backdoor sets :param costs: non-negative costs associated with variables in the graph. Only used for estimand_type='non-parametric-ate' and backdoor_adjustment='efficient-mincost-adjustment'. If no costs are provided by the user, and backdoor_adjustment='efficient-mincost-adjustment', costs are assumed to be equal to one for all variables in the graph. :param conditional_node_names: variables that are used to determine treatment. If none are provided, it is assumed that the intervention is static. :returns: target estimand, an instance of the IdentifiedEstimand class """ treatment_name = parse_state(treatment_name) outcome_name = parse_state(outcome_name) # First, check if there is a directed path from action to outcome if not graph.has_directed_path(treatment_name, outcome_name): logger.warn("No directed path from treatment to outcome. Causal Effect is zero.") return IdentifiedEstimand( None, treatment_variable=treatment_name, outcome_variable=outcome_name, no_directed_path=True, ) if estimand_type == EstimandType.NONPARAMETRIC_ATE: return identify_ate_effect( graph, treatment_name, outcome_name, backdoor_adjustment, optimize_backdoor, estimand_type, costs, conditional_node_names, proceed_when_unidentifiable, ) elif estimand_type == EstimandType.NONPARAMETRIC_NDE: return identify_nde_effect( graph, treatment_name, outcome_name, backdoor_adjustment, estimand_type, proceed_when_unidentifiable ) elif estimand_type == EstimandType.NONPARAMETRIC_NIE: return identify_nie_effect( graph, treatment_name, outcome_name, backdoor_adjustment, estimand_type, proceed_when_unidentifiable ) elif estimand_type == EstimandType.NONPARAMETRIC_CDE: return identify_cde_effect( graph, treatment_name, outcome_name, backdoor_adjustment, estimand_type, proceed_when_unidentifiable ) else: raise ValueError( "Estimand type is not supported. Use either {0}, {1}, or {2}.".format( EstimandType.NONPARAMETRIC_ATE, EstimandType.NONPARAMETRIC_CDE, EstimandType.NONPARAMETRIC_NDE, EstimandType.NONPARAMETRIC_NIE, ) ) def identify_ate_effect( graph: CausalGraph, treatment_name: List[str], outcome_name: str, backdoor_adjustment: BackdoorAdjustment, optimize_backdoor: bool, estimand_type: EstimandType, costs: List, conditional_node_names: List[str] = None, proceed_when_unidentifiable: bool = False, ): estimands_dict = {} mediation_first_stage_confounders = None mediation_second_stage_confounders = None ### 1. BACKDOOR IDENTIFICATION # Pick algorithm to compute backdoor sets according to method chosen if backdoor_adjustment not in EFFICIENT_METHODS: # First, checking if there are any valid backdoor adjustment sets if optimize_backdoor == False: backdoor_sets = identify_backdoor(graph, treatment_name, outcome_name, backdoor_adjustment) else: from dowhy.causal_identifier.backdoor import Backdoor path = Backdoor(graph._graph, treatment_name, outcome_name) backdoor_sets = path.get_backdoor_vars() elif backdoor_adjustment in EFFICIENT_METHODS: backdoor_sets = identify_efficient_backdoor( graph, backdoor_adjustment, costs, conditional_node_names=conditional_node_names ) estimands_dict, backdoor_variables_dict = build_backdoor_estimands_dict( graph, treatment_name, outcome_name, backdoor_sets, estimands_dict ) # Setting default "backdoor" identification adjustment set default_backdoor_id = get_default_backdoor_set_id(graph, treatment_name, outcome_name, backdoor_variables_dict) if len(backdoor_variables_dict) > 0: estimands_dict["backdoor"] = estimands_dict.get(str(default_backdoor_id), None) backdoor_variables_dict["backdoor"] = backdoor_variables_dict.get(str(default_backdoor_id), None) else: estimands_dict["backdoor"] = None ### 2. INSTRUMENTAL VARIABLE IDENTIFICATION # Now checking if there is also a valid iv estimand instrument_names = graph.get_instruments(treatment_name, outcome_name) logger.info("Instrumental variables for treatment and outcome:" + str(instrument_names)) if len(instrument_names) > 0: iv_estimand_expr = construct_iv_estimand( treatment_name, outcome_name, instrument_names, ) logger.debug("Identified expression = " + str(iv_estimand_expr)) estimands_dict["iv"] = iv_estimand_expr else: estimands_dict["iv"] = None ### 3. FRONTDOOR IDENTIFICATION # Now checking if there is a valid frontdoor variable frontdoor_variables_names = identify_frontdoor(graph, treatment_name, outcome_name) logger.info("Frontdoor variables for treatment and outcome:" + str(frontdoor_variables_names)) if len(frontdoor_variables_names) > 0: frontdoor_estimand_expr = construct_frontdoor_estimand( treatment_name, outcome_name, frontdoor_variables_names, ) logger.debug("Identified expression = " + str(frontdoor_estimand_expr)) estimands_dict["frontdoor"] = frontdoor_estimand_expr mediation_first_stage_confounders = identify_mediation_first_stage_confounders( graph, treatment_name, outcome_name, frontdoor_variables_names, backdoor_adjustment ) mediation_second_stage_confounders = identify_mediation_second_stage_confounders( graph, treatment_name, frontdoor_variables_names, outcome_name, backdoor_adjustment ) else: estimands_dict["frontdoor"] = None # Finally returning the estimand object estimand = IdentifiedEstimand( None, treatment_variable=treatment_name, outcome_variable=outcome_name, estimand_type=estimand_type, estimands=estimands_dict, backdoor_variables=backdoor_variables_dict, instrumental_variables=instrument_names, frontdoor_variables=frontdoor_variables_names, mediation_first_stage_confounders=mediation_first_stage_confounders, mediation_second_stage_confounders=mediation_second_stage_confounders, default_backdoor_id=default_backdoor_id, ) return estimand def identify_cde_effect( graph: CausalGraph, treatment_name: List[str], outcome_name: str, backdoor_adjustment: BackdoorAdjustment, estimand_type: EstimandType, proceed_when_unidentifiable: bool = False, ): """Identify controlled direct effect. For a definition, see Vanderwheele (2011). Controlled direct and mediated effects: definition, identification and bounds. https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4193506/ Using do-calculus rules, identification yields a adjustment set. It is based on the principle that under a graph where the direct edge from treatment to outcome is removed, conditioning on the adjustment set should d-separate treatment and outcome. """ estimands_dict = {} # Pick algorithm to compute backdoor sets according to method chosen backdoor_sets = identify_backdoor(graph, treatment_name, outcome_name, backdoor_adjustment, direct_effect=True) estimands_dict, backdoor_variables_dict = build_backdoor_estimands_dict( graph, treatment_name, outcome_name, backdoor_sets, estimands_dict ) # Setting default "backdoor" identification adjustment set default_backdoor_id = get_default_backdoor_set_id(graph, treatment_name, outcome_name, backdoor_variables_dict) if len(backdoor_variables_dict) > 0: estimands_dict["backdoor"] = estimands_dict.get(str(default_backdoor_id), None) backdoor_variables_dict["backdoor"] = backdoor_variables_dict.get(str(default_backdoor_id), None) else: estimands_dict["backdoor"] = None # Finally returning the estimand object estimand = IdentifiedEstimand( None, treatment_variable=treatment_name, outcome_variable=outcome_name, estimand_type=estimand_type, estimands=estimands_dict, backdoor_variables=backdoor_variables_dict, instrumental_variables=None, frontdoor_variables=None, mediation_first_stage_confounders=None, mediation_second_stage_confounders=None, default_backdoor_id=default_backdoor_id, ) return estimand def identify_nie_effect( graph: CausalGraph, treatment_name: List[str], outcome_name: str, backdoor_adjustment: BackdoorAdjustment, estimand_type: EstimandType, proceed_when_unidentifiable: bool = False, ): estimands_dict = {} ### 1. FIRST DOING BACKDOOR IDENTIFICATION # First, checking if there are any valid backdoor adjustment sets backdoor_sets = identify_backdoor(graph, treatment_name, outcome_name, backdoor_adjustment) estimands_dict, backdoor_variables_dict = build_backdoor_estimands_dict( graph, treatment_name, outcome_name, backdoor_sets, estimands_dict ) # Setting default "backdoor" identification adjustment set default_backdoor_id = get_default_backdoor_set_id(graph, treatment_name, outcome_name, backdoor_variables_dict) backdoor_variables_dict["backdoor"] = backdoor_variables_dict.get(str(default_backdoor_id), None) ### 2. SECOND, CHECKING FOR MEDIATORS # Now checking if there are valid mediator variables estimands_dict = {} # Need to reinitialize this dictionary to avoid including the backdoor sets mediation_first_stage_confounders = None mediation_second_stage_confounders = None mediators_names = identify_mediation(graph, treatment_name, outcome_name) logger.info("Mediators for treatment and outcome:" + str(mediators_names)) if len(mediators_names) > 0: mediation_estimand_expr = construct_mediation_estimand( estimand_type, treatment_name, outcome_name, mediators_names, ) logger.debug("Identified expression = " + str(mediation_estimand_expr)) estimands_dict["mediation"] = mediation_estimand_expr mediation_first_stage_confounders = identify_mediation_first_stage_confounders( graph, treatment_name, outcome_name, mediators_names, backdoor_adjustment ) mediation_second_stage_confounders = identify_mediation_second_stage_confounders( graph, treatment_name, mediators_names, outcome_name, backdoor_adjustment ) else: estimands_dict["mediation"] = None # Finally returning the estimand object estimand = IdentifiedEstimand( None, treatment_variable=treatment_name, outcome_variable=outcome_name, estimand_type=estimand_type, estimands=estimands_dict, backdoor_variables=backdoor_variables_dict, instrumental_variables=None, frontdoor_variables=None, mediator_variables=mediators_names, mediation_first_stage_confounders=mediation_first_stage_confounders, mediation_second_stage_confounders=mediation_second_stage_confounders, default_backdoor_id=None, ) return estimand def identify_nde_effect( graph: CausalGraph, treatment_name: List[str], outcome_name: str, backdoor_adjustment: BackdoorAdjustment, estimand_type: EstimandType, proceed_when_unidentifiable: bool = False, ): estimands_dict = {} ### 1. FIRST DOING BACKDOOR IDENTIFICATION # First, checking if there are any valid backdoor adjustment sets backdoor_sets = identify_backdoor(graph, treatment_name, outcome_name, backdoor_adjustment) estimands_dict, backdoor_variables_dict = build_backdoor_estimands_dict( graph, treatment_name, outcome_name, backdoor_sets, estimands_dict ) # Setting default "backdoor" identification adjustment set default_backdoor_id = get_default_backdoor_set_id(graph, treatment_name, outcome_name, backdoor_variables_dict) backdoor_variables_dict["backdoor"] = backdoor_variables_dict.get(str(default_backdoor_id), None) ### 2. SECOND, CHECKING FOR MEDIATORS # Now checking if there are valid mediator variables estimands_dict = {} mediation_first_stage_confounders = None mediation_second_stage_confounders = None mediators_names = identify_mediation(graph, treatment_name, outcome_name) logger.info("Mediators for treatment and outcome:" + str(mediators_names)) if len(mediators_names) > 0: mediation_estimand_expr = construct_mediation_estimand( estimand_type, treatment_name, outcome_name, mediators_names, ) logger.debug("Identified expression = " + str(mediation_estimand_expr)) estimands_dict["mediation"] = mediation_estimand_expr mediation_first_stage_confounders = identify_mediation_first_stage_confounders( graph, treatment_name, outcome_name, mediators_names, backdoor_adjustment ) mediation_second_stage_confounders = identify_mediation_second_stage_confounders( graph, treatment_name, mediators_names, outcome_name, backdoor_adjustment ) else: estimands_dict["mediation"] = None # Finally returning the estimand object estimand = IdentifiedEstimand( None, treatment_variable=treatment_name, outcome_variable=outcome_name, estimand_type=estimand_type, estimands=estimands_dict, backdoor_variables=backdoor_variables_dict, instrumental_variables=None, frontdoor_variables=None, mediator_variables=mediators_names, mediation_first_stage_confounders=mediation_first_stage_confounders, mediation_second_stage_confounders=mediation_second_stage_confounders, default_backdoor_id=None, ) return estimand def identify_backdoor( graph: CausalGraph, treatment_name: List[str], outcome_name: str, backdoor_adjustment: BackdoorAdjustment, include_unobserved: bool = False, dseparation_algo: str = "default", direct_effect: bool = False, ): backdoor_sets = [] backdoor_paths = None bdoor_graph = None if dseparation_algo == "naive": backdoor_paths = graph.get_backdoor_paths(treatment_name, outcome_name) elif dseparation_algo == "default": bdoor_graph = graph.do_surgery( treatment_name, target_node_names=outcome_name, remove_outgoing_edges=True, remove_only_direct_edges_to_target=direct_effect, ) else: raise ValueError(f"d-separation algorithm {dseparation_algo} is not supported") backdoor_adjustment = ( backdoor_adjustment if backdoor_adjustment != BackdoorAdjustment.BACKDOOR_DEFAULT else DEFAULT_BACKDOOR_METHOD ) # First, checking if empty set is a valid backdoor set empty_set = set() check = graph.check_valid_backdoor_set( treatment_name, outcome_name, empty_set, backdoor_paths=backdoor_paths, new_graph=bdoor_graph, dseparation_algo=dseparation_algo, ) if check["is_dseparated"]: backdoor_sets.append({"backdoor_set": empty_set}) # If the method is `minimal-adjustment`, return the empty set right away. if backdoor_adjustment == BackdoorAdjustment.BACKDOOR_MIN: return backdoor_sets # Second, checking for all other sets of variables. If include_unobserved is false, then only observed variables are eligible. eligible_variables = ( graph.get_all_nodes(include_unobserved=include_unobserved) - set(treatment_name) - set(outcome_name) ) if direct_effect: # only remove descendants of Y # also allow any causes of Y that are not caused by T (for lower variance) eligible_variables -= graph.get_descendants(outcome_name) else: # remove descendants of T (mediators) and descendants of Y eligible_variables -= graph.get_descendants(treatment_name) # If var is d-separated from both treatment or outcome, it cannot # be a part of the backdoor set filt_eligible_variables = set() for var in eligible_variables: dsep_treat_var = graph.check_dseparation(treatment_name, parse_state(var), set()) dsep_outcome_var = graph.check_dseparation(outcome_name, parse_state(var), set()) if not dsep_outcome_var or not dsep_treat_var: filt_eligible_variables.add(var) if backdoor_adjustment in METHOD_NAMES: backdoor_sets, found_valid_adjustment_set = find_valid_adjustment_sets( graph, treatment_name, outcome_name, backdoor_paths, bdoor_graph, dseparation_algo, backdoor_sets, filt_eligible_variables, backdoor_adjustment=backdoor_adjustment, max_iterations=MAX_BACKDOOR_ITERATIONS, ) if backdoor_adjustment == BackdoorAdjustment.BACKDOOR_DEFAULT and found_valid_adjustment_set: # repeat the above search with BACKDOOR_MIN backdoor_sets, _ = find_valid_adjustment_sets( graph, treatment_name, outcome_name, backdoor_paths, bdoor_graph, dseparation_algo, backdoor_sets, filt_eligible_variables, backdoor_adjustment=BackdoorAdjustment.BACKDOOR_MIN, max_iterations=MAX_BACKDOOR_ITERATIONS, ) else: raise ValueError( f"Identifier method {backdoor_adjustment} not supported. Try one of the following: {METHOD_NAMES}" ) return backdoor_sets def identify_efficient_backdoor( graph: CausalGraph, backdoor_adjustment: BackdoorAdjustment, costs: List, conditional_node_names: List[str] = None, ): """Method implementing algorithms to compute efficient backdoor sets, as described in Rotnitzky and Smucler (2020), Smucler, Sapienza and Rotnitzky (2021) and Smucler and Rotnitzky (2022). For backdoor_adjustment='efficient-adjustment', computes an optimal backdoor set, that is, a backdoor set comprised of observable variables that yields non-parametric estimators of the interventional mean with the smallest asymptotic variance among those that are based on observable backdoor sets. This optimal backdoor set always exists when no variables are latent, and the algorithm is guaranteed to compute it in this case. Under a non-parametric graphical model with latent variables, such a backdoor set can fail to exist. When certain sufficient conditions under which it is known that such a backdoor set exists are not satisfied, an error is raised. For backdoor_adjustment='efficient-minimal-adjustment', computes an optimal minimal backdoor set, that is, a minimal backdoor set comprised of observable variables that yields non-parametric estimators of the interventional mean with the smallest asymptotic variance among those that are based on observable minimal backdoor sets. For backdoor_adjustment='efficient-mincost-adjustment', computes an optimal minimum cost backdoor set, that is, a minimum cost backdoor set comprised of observable variables that yields non-parametric estimators of the interventional mean with the smallest asymptotic variance among those that are based on observable minimum cost backdoor sets. The cost of a backdoor set is defined as the sum of the costs of the variables that comprise it. The various optimal backdoor sets computed by this method are not only optimal under non-parametric graphical models and non-parametric estimators of interventional mean, but also under linear graphical models and OLS estimators, per results in Henckel, Perkovic and Maathuis (2020). :param costs: a list with non-negative costs associated with variables in the graph. Only used for estimatand_type='non-parametric-ate' and backdoor_adjustment='efficient-mincost-adjustment'. If not costs are provided by the user, and backdoor_adjustment='efficient-mincost-adjustment', costs are assumed to be equal to one for all variables in the graph. The structure of the list should be of the form [(node, {"cost": x}) for node in nodes]. :param conditional_node_names: variables that are used to determine treatment. If none are provided, it is assumed that the intervention sets the treatment to a constant. :returns: backdoor_sets, a list of dictionaries, with each dictionary having as values a backdoor set. """ if costs is None and backdoor_adjustment == "efficient-mincost-adjustment": logger.warning("No costs were passed, so they will be assumed to be constant and equal to 1.") efficient_bd = EfficientBackdoor( graph=graph, conditional_node_names=conditional_node_names, costs=costs, ) if backdoor_adjustment == BackdoorAdjustment.BACKDOOR_EFFICIENT: backdoor_set = efficient_bd.optimal_adj_set() backdoor_sets = [{"backdoor_set": tuple(backdoor_set)}] elif backdoor_adjustment == BackdoorAdjustment.BACKDOOR_MIN_EFFICIENT: backdoor_set = efficient_bd.optimal_minimal_adj_set() backdoor_sets = [{"backdoor_set": tuple(backdoor_set)}] elif backdoor_adjustment == BackdoorAdjustment.BACKDOOR_MINCOST_EFFICIENT: backdoor_set = efficient_bd.optimal_mincost_adj_set() backdoor_sets = [{"backdoor_set": tuple(backdoor_set)}] return backdoor_sets def find_valid_adjustment_sets( graph: CausalGraph, treatment_name: List, outcome_name: List, backdoor_paths: List, bdoor_graph: CausalGraph, dseparation_algo: str, backdoor_sets: List, filt_eligible_variables: List, backdoor_adjustment: BackdoorAdjustment, max_iterations: int, ): num_iterations = 0 found_valid_adjustment_set = False all_nodes_observed = graph.all_observed(graph.get_all_nodes()) # If `minimal-adjustment` method is specified, start the search from the set with minimum size. Otherwise, start from the largest. set_sizes = ( range(1, len(filt_eligible_variables) + 1, 1) if backdoor_adjustment == BackdoorAdjustment.BACKDOOR_MIN else range(len(filt_eligible_variables), 0, -1) ) for size_candidate_set in set_sizes: for candidate_set in itertools.combinations(filt_eligible_variables, size_candidate_set): check = graph.check_valid_backdoor_set( treatment_name, outcome_name, candidate_set, backdoor_paths=backdoor_paths, new_graph=bdoor_graph, dseparation_algo=dseparation_algo, ) logger.debug( "Candidate backdoor set: {0}, is_dseparated: {1}".format(candidate_set, check["is_dseparated"]) ) if check["is_dseparated"]: backdoor_sets.append({"backdoor_set": candidate_set}) found_valid_adjustment_set = True num_iterations += 1 if backdoor_adjustment == BackdoorAdjustment.BACKDOOR_EXHAUSTIVE and num_iterations > max_iterations: logger.warning(f"Max number of iterations {max_iterations} reached.") break # If the backdoor method is `maximal-adjustment` or `minimal-adjustment`, return the first found adjustment set. if ( backdoor_adjustment in { BackdoorAdjustment.BACKDOOR_DEFAULT, BackdoorAdjustment.BACKDOOR_MAX, BackdoorAdjustment.BACKDOOR_MIN, } and found_valid_adjustment_set ): break # If all variables are observed, and the biggest eligible set # does not satisfy backdoor, then none of its subsets will. if ( backdoor_adjustment in {BackdoorAdjustment.BACKDOOR_DEFAULT, BackdoorAdjustment.BACKDOOR_MAX} and all_nodes_observed ): break if num_iterations > max_iterations: logger.warning(f"Max number of iterations {max_iterations} reached. Could not find a valid backdoor set.") break return backdoor_sets, found_valid_adjustment_set def get_default_backdoor_set_id( graph: CausalGraph, treatment_name: List[str], outcome_name: List[str], backdoor_sets_dict: Dict ): # Adding a None estimand if no backdoor set found if len(backdoor_sets_dict) == 0: return None # Default set contains minimum possible number of instrumental variables, to prevent lowering variance in the treatment variable. instrument_names = set(graph.get_instruments(treatment_name, outcome_name)) iv_count_dict = { key: len(set(bdoor_set).intersection(instrument_names)) for key, bdoor_set in backdoor_sets_dict.items() } min_iv_count = min(iv_count_dict.values()) min_iv_keys = {key for key, iv_count in iv_count_dict.items() if iv_count == min_iv_count} min_iv_backdoor_sets_dict = {key: backdoor_sets_dict[key] for key in min_iv_keys} # Default set is the one with the least number of adjustment variables (optimizing for efficiency) min_set_length = 1000000 default_key = None for key, bdoor_set in min_iv_backdoor_sets_dict.items(): if len(bdoor_set) < min_set_length: min_set_length = len(bdoor_set) default_key = key return default_key def build_backdoor_estimands_dict( graph: CausalGraph, treatment_name: List[str], outcome_name: List[str], backdoor_sets: List[str], estimands_dict: Dict, ): """Build the final dict for backdoor sets by filtering unobserved variables if needed.""" backdoor_variables_dict = {} is_identified = [graph.all_observed(bset["backdoor_set"]) for bset in backdoor_sets] if any(is_identified): logger.info("Causal effect can be identified.") backdoor_sets_arr = [ list(bset["backdoor_set"]) for bset in backdoor_sets if graph.all_observed(bset["backdoor_set"]) ] else: # there is unobserved confounding logger.warning("Backdoor identification failed.") backdoor_sets_arr = [] for i in range(len(backdoor_sets_arr)): backdoor_estimand_expr = construct_backdoor_estimand(treatment_name, outcome_name, backdoor_sets_arr[i]) logger.debug("Identified expression = " + str(backdoor_estimand_expr)) estimands_dict["backdoor" + str(i + 1)] = backdoor_estimand_expr backdoor_variables_dict["backdoor" + str(i + 1)] = backdoor_sets_arr[i] return estimands_dict, backdoor_variables_dict def identify_frontdoor( graph: CausalGraph, treatment_name: List[str], outcome_name: List[str], dseparation_algo: str = "default" ): """Find a valid frontdoor variable if it exists. Currently only supports a single variable frontdoor set. """ frontdoor_var = None frontdoor_paths = None fdoor_graph = None if dseparation_algo == "default": cond1_graph = graph.do_surgery(treatment_name, remove_incoming_edges=True) bdoor_graph1 = graph.do_surgery(treatment_name, remove_outgoing_edges=True) elif dseparation_algo == "naive": frontdoor_paths = graph.get_all_directed_paths(treatment_name, outcome_name) else: raise ValueError(f"d-separation algorithm {dseparation_algo} is not supported") eligible_variables = ( graph.get_descendants(treatment_name) - set(outcome_name) - set(graph.get_descendants(outcome_name)) ) # For simplicity, assuming a one-variable frontdoor set for candidate_var in eligible_variables: # Cond 1: All directed paths intercepted by candidate_var cond1 = graph.check_valid_frontdoor_set( treatment_name, outcome_name, parse_state(candidate_var), frontdoor_paths=frontdoor_paths, new_graph=cond1_graph, dseparation_algo=dseparation_algo, ) logger.debug("Candidate frontdoor set: {0}, is_dseparated: {1}".format(candidate_var, cond1)) if not cond1: continue # Cond 2: No confounding between treatment and candidate var cond2 = graph.check_valid_backdoor_set( treatment_name, parse_state(candidate_var), set(), backdoor_paths=None, new_graph=bdoor_graph1, dseparation_algo=dseparation_algo, ) if not cond2: continue # Cond 3: treatment blocks all confounding between candidate_var and outcome bdoor_graph2 = graph.do_surgery(candidate_var, remove_outgoing_edges=True) cond3 = graph.check_valid_backdoor_set( parse_state(candidate_var), outcome_name, treatment_name, backdoor_paths=None, new_graph=bdoor_graph2, dseparation_algo=dseparation_algo, ) is_valid_frontdoor = cond1 and cond2 and cond3 if is_valid_frontdoor: frontdoor_var = candidate_var break return parse_state(frontdoor_var) def identify_mediation(graph: CausalGraph, treatment_name: List[str], outcome_name: List[str]): """Find a valid mediator if it exists. Currently only supports a single variable mediator set. """ mediation_var = None mediation_paths = graph.get_all_directed_paths(treatment_name, outcome_name) eligible_variables = graph.get_descendants(treatment_name) - set(outcome_name) # For simplicity, assuming a one-variable mediation set for candidate_var in eligible_variables: is_valid_mediation = graph.check_valid_mediation_set( treatment_name, outcome_name, parse_state(candidate_var), mediation_paths=mediation_paths, ) logger.debug("Candidate mediation set: {0}, on_mediating_path: {1}".format(candidate_var, is_valid_mediation)) if is_valid_mediation: mediation_var = candidate_var break return parse_state(mediation_var) def identify_mediation_first_stage_confounders( graph: CausalGraph, treatment_name: List[str], outcome_name: List[str], mediators_names: List[str], backdoor_adjustment: BackdoorAdjustment, ): # Create estimands dict as per the API for backdoor, but do not return it estimands_dict = {} backdoor_sets = identify_backdoor(graph, treatment_name, mediators_names, backdoor_adjustment) estimands_dict, backdoor_variables_dict = build_backdoor_estimands_dict( graph, treatment_name, mediators_names, backdoor_sets, estimands_dict, ) # Setting default "backdoor" identification adjustment set default_backdoor_id = get_default_backdoor_set_id(graph, treatment_name, outcome_name, backdoor_variables_dict) estimands_dict["backdoor"] = estimands_dict.get(str(default_backdoor_id), None) backdoor_variables_dict["backdoor"] = backdoor_variables_dict.get(str(default_backdoor_id), None) return backdoor_variables_dict def identify_mediation_second_stage_confounders( graph: CausalGraph, treatment_name: List[str], mediators_names: List[str], outcome_name: List[str], backdoor_adjustment: BackdoorAdjustment, ): # Create estimands dict as per the API for backdoor, but do not return it estimands_dict = {} backdoor_sets = identify_backdoor(graph, mediators_names, outcome_name, backdoor_adjustment) estimands_dict, backdoor_variables_dict = build_backdoor_estimands_dict( graph, mediators_names, outcome_name, backdoor_sets, estimands_dict, ) # Setting default "backdoor" identification adjustment set default_backdoor_id = get_default_backdoor_set_id(graph, treatment_name, outcome_name, backdoor_variables_dict) estimands_dict["backdoor"] = estimands_dict.get(str(default_backdoor_id), None) backdoor_variables_dict["backdoor"] = backdoor_variables_dict.get(str(default_backdoor_id), None) return backdoor_variables_dict def construct_backdoor_estimand(treatment_name: List[str], outcome_name: List[str], common_causes: List[str]): # TODO: outputs string for now, but ideally should do symbolic # expressions Mon 19 Feb 2018 04:54:17 PM DST # TODO Better support for multivariate treatments expr = None outcome_name = outcome_name[0] num_expr_str = outcome_name if len(common_causes) > 0: num_expr_str += "|" + ",".join(common_causes) expr = "d(" + num_expr_str + ")/d" + ",".join(treatment_name) sym_mu = sp.Symbol("mu") sym_sigma = sp.Symbol("sigma", positive=True) sym_outcome = spstats.Normal(num_expr_str, sym_mu, sym_sigma) sym_treatment_symbols = [sp.Symbol(t) for t in treatment_name] sym_treatment = sp.Array(sym_treatment_symbols) sym_conditional_outcome = spstats.Expectation(sym_outcome) sym_effect = sp.Derivative(sym_conditional_outcome, sym_treatment) sym_assumptions = { "Unconfoundedness": ( "If U\N{RIGHTWARDS ARROW}{{{0}}} and U\N{RIGHTWARDS ARROW}{1}" " then P({1}|{0},{2},U) = P({1}|{0},{2})" ).format(",".join(treatment_name), outcome_name, ",".join(common_causes)) } estimand = {"estimand": sym_effect, "assumptions": sym_assumptions} return estimand def construct_iv_estimand(treatment_name: List[str], outcome_name: List[str], instrument_names: List[str]): # TODO: support multivariate treatments better. expr = None outcome_name = outcome_name[0] sym_outcome = spstats.Normal(outcome_name, 0, 1) sym_treatment_symbols = [spstats.Normal(t, 0, 1) for t in treatment_name] sym_treatment = sp.Array(sym_treatment_symbols) sym_instrument_symbols = [sp.Symbol(inst) for inst in instrument_names] sym_instrument = sp.Array(sym_instrument_symbols) # ",".join(instrument_names)) sym_outcome_derivative = sp.Derivative(sym_outcome, sym_instrument) sym_treatment_derivative = sp.Derivative(sym_treatment, sym_instrument) sym_effect = spstats.Expectation(sym_outcome_derivative / sym_treatment_derivative) sym_assumptions = { "As-if-random": ( "If U\N{RIGHTWARDS ARROW}\N{RIGHTWARDS ARROW}{0} then " "\N{NOT SIGN}(U \N{RIGHTWARDS ARROW}\N{RIGHTWARDS ARROW}{{{1}}})" ).format(outcome_name, ",".join(instrument_names)), "Exclusion": ( "If we remove {{{0}}}\N{RIGHTWARDS ARROW}{{{1}}}, then " "\N{NOT SIGN}({{{0}}}\N{RIGHTWARDS ARROW}{2})" ).format(",".join(instrument_names), ",".join(treatment_name), outcome_name), } estimand = {"estimand": sym_effect, "assumptions": sym_assumptions} return estimand def construct_frontdoor_estimand( treatment_name: List[str], outcome_name: List[str], frontdoor_variables_names: List[str] ): # TODO: support multivariate treatments better. expr = None outcome_name = outcome_name[0] sym_outcome = spstats.Normal(outcome_name, 0, 1) sym_treatment_symbols = [spstats.Normal(t, 0, 1) for t in treatment_name] sym_treatment = sp.Array(sym_treatment_symbols) sym_frontdoor_symbols = [sp.Symbol(inst) for inst in frontdoor_variables_names] sym_frontdoor = sp.Array(sym_frontdoor_symbols) # ",".join(instrument_names)) sym_outcome_derivative = sp.Derivative(sym_outcome, sym_frontdoor) sym_treatment_derivative = sp.Derivative(sym_frontdoor, sym_treatment) sym_effect = spstats.Expectation(sym_treatment_derivative * sym_outcome_derivative) sym_assumptions = { "Full-mediation": ("{2} intercepts (blocks) all directed paths from {0} to {1}.").format( ",".join(treatment_name), ",".join(outcome_name), ",".join(frontdoor_variables_names), ), "First-stage-unconfoundedness": ( "If U\N{RIGHTWARDS ARROW}{{{0}}} and U\N{RIGHTWARDS ARROW}{{{1}}}" " then P({1}|{0},U) = P({1}|{0})" ).format(",".join(treatment_name), ",".join(frontdoor_variables_names)), "Second-stage-unconfoundedness": ( "If U\N{RIGHTWARDS ARROW}{{{2}}} and U\N{RIGHTWARDS ARROW}{1}" " then P({1}|{2}, {0}, U) = P({1}|{2}, {0})" ).format( ",".join(treatment_name), outcome_name, ",".join(frontdoor_variables_names), ), } estimand = {"estimand": sym_effect, "assumptions": sym_assumptions} return estimand def construct_mediation_estimand( estimand_type: EstimandType, treatment_name: List[str], outcome_name: List[str], mediators_names: List[str] ): # TODO: support multivariate treatments better. expr = None if estimand_type in ( EstimandType.NONPARAMETRIC_NDE, EstimandType.NONPARAMETRIC_NIE, ): outcome_name = outcome_name[0] sym_outcome = spstats.Normal(outcome_name, 0, 1) sym_treatment_symbols = [spstats.Normal(t, 0, 1) for t in treatment_name] sym_treatment = sp.Array(sym_treatment_symbols) sym_mediators_symbols = [sp.Symbol(inst) for inst in mediators_names] sym_mediators = sp.Array(sym_mediators_symbols) sym_outcome_derivative = sp.Derivative(sym_outcome, sym_mediators) sym_treatment_derivative = sp.Derivative(sym_mediators, sym_treatment) # For direct effect num_expr_str = outcome_name if len(mediators_names) > 0: num_expr_str += "|" + ",".join(mediators_names) sym_mu = sp.Symbol("mu") sym_sigma = sp.Symbol("sigma", positive=True) sym_conditional_outcome = spstats.Normal(num_expr_str, sym_mu, sym_sigma) sym_directeffect_derivative = sp.Derivative(sym_conditional_outcome, sym_treatment) if estimand_type == EstimandType.NONPARAMETRIC_NIE: sym_effect = spstats.Expectation(sym_treatment_derivative * sym_outcome_derivative) elif estimand_type == EstimandType.NONPARAMETRIC_NDE: sym_effect = spstats.Expectation(sym_directeffect_derivative) sym_assumptions = { "Mediation": ( "{2} intercepts (blocks) all directed paths from {0} to {1} except the path {{{0}}}\N{RIGHTWARDS ARROW}{{{1}}}." ).format( ",".join(treatment_name), ",".join(outcome_name), ",".join(mediators_names), ), "First-stage-unconfoundedness": ( "If U\N{RIGHTWARDS ARROW}{{{0}}} and U\N{RIGHTWARDS ARROW}{{{1}}}" " then P({1}|{0},U) = P({1}|{0})" ).format(",".join(treatment_name), ",".join(mediators_names)), "Second-stage-unconfoundedness": ( "If U\N{RIGHTWARDS ARROW}{{{2}}} and U\N{RIGHTWARDS ARROW}{1}" " then P({1}|{2}, {0}, U) = P({1}|{2}, {0})" ).format(",".join(treatment_name), outcome_name, ",".join(mediators_names)), } else: raise ValueError( "Estimand type not supported. Supported estimand types are {0} or {1}'.".format( EstimandType.NONPARAMETRIC_NDE, EstimandType.NONPARAMETRIC_NIE, ) ) estimand = {"estimand": sym_effect, "assumptions": sym_assumptions} return estimand

import itertools import logging from enum import Enum from typing import Dict, List, Optional, Union import sympy as sp import sympy.stats as spstats from dowhy.causal_graph import CausalGraph from dowhy.causal_identifier.efficient_backdoor import EfficientBackdoor from dowhy.causal_identifier.identified_estimand import IdentifiedEstimand from dowhy.utils.api import parse_state logger = logging.getLogger(__name__) class EstimandType(Enum): # Average total effect NONPARAMETRIC_ATE = "nonparametric-ate" # Natural direct effect NONPARAMETRIC_NDE = "nonparametric-nde" # Natural indirect effect NONPARAMETRIC_NIE = "nonparametric-nie" # Controlled direct effect NONPARAMETRIC_CDE = "nonparametric-cde" class BackdoorAdjustment(Enum): # Backdoor method names BACKDOOR_DEFAULT = "default" BACKDOOR_EXHAUSTIVE = "exhaustive-search" BACKDOOR_MIN = "minimal-adjustment" BACKDOOR_MAX = "maximal-adjustment" BACKDOOR_EFFICIENT = "efficient-adjustment" BACKDOOR_MIN_EFFICIENT = "efficient-minimal-adjustment" BACKDOOR_MINCOST_EFFICIENT = "efficient-mincost-adjustment" MAX_BACKDOOR_ITERATIONS = 100000 METHOD_NAMES = { BackdoorAdjustment.BACKDOOR_DEFAULT, BackdoorAdjustment.BACKDOOR_EXHAUSTIVE, BackdoorAdjustment.BACKDOOR_MIN, BackdoorAdjustment.BACKDOOR_MAX, BackdoorAdjustment.BACKDOOR_EFFICIENT, BackdoorAdjustment.BACKDOOR_MIN_EFFICIENT, BackdoorAdjustment.BACKDOOR_MINCOST_EFFICIENT, } EFFICIENT_METHODS = { BackdoorAdjustment.BACKDOOR_EFFICIENT, BackdoorAdjustment.BACKDOOR_MIN_EFFICIENT, BackdoorAdjustment.BACKDOOR_MINCOST_EFFICIENT, } DEFAULT_BACKDOOR_METHOD = BackdoorAdjustment.BACKDOOR_DEFAULT class AutoIdentifier: """Class that implements different identification methods. Currently supports backdoor and instrumental variable identification methods. The identification is based on the causal graph provided. This class is for backwards compatibility with CausalModel Will be deprecated in the future in favor of function call auto_identify_effect() """ def __init__( self, estimand_type: EstimandType, backdoor_adjustment: BackdoorAdjustment = BackdoorAdjustment.BACKDOOR_DEFAULT, proceed_when_unidentifiable: bool = False, optimize_backdoor: bool = False, costs: Optional[List] = None, ): self.estimand_type = estimand_type self.backdoor_adjustment = backdoor_adjustment self._proceed_when_unidentifiable = proceed_when_unidentifiable self.optimize_backdoor = optimize_backdoor self.costs = costs self.logger = logging.getLogger(__name__) def identify_effect( self, graph: CausalGraph, treatment_name: Union[str, List[str]], outcome_name: Union[str, List[str]], conditional_node_names: List[str] = None, **kwargs, ): estimand = identify_effect_auto( graph, treatment_name, outcome_name, self.estimand_type, conditional_node_names, self.backdoor_adjustment, self._proceed_when_unidentifiable, self.optimize_backdoor, self.costs, **kwargs, ) estimand.identifier = self return estimand def identify_backdoor( self, graph: CausalGraph, treatment_name: List[str], outcome_name: str, include_unobserved: bool = False, dseparation_algo: str = "default", direct_effect: bool = False, ): return identify_backdoor( graph, treatment_name, outcome_name, self.backdoor_adjustment, include_unobserved, dseparation_algo, direct_effect, ) def identify_effect_auto( graph: CausalGraph, treatment_name: Union[str, List[str]], outcome_name: Union[str, List[str]], estimand_type: EstimandType, conditional_node_names: List[str] = None, backdoor_adjustment: BackdoorAdjustment = BackdoorAdjustment.BACKDOOR_DEFAULT, proceed_when_unidentifiable: bool = False, optimize_backdoor: bool = False, costs: Optional[List] = None, **kwargs, ) -> IdentifiedEstimand: """Main method that returns an identified estimand (if one exists). If estimand_type is non-parametric ATE, then uses backdoor, instrumental variable and frontdoor identification methods, to check if an identified estimand exists, based on the causal graph. :param optimize_backdoor: if True, uses an optimised algorithm to compute the backdoor sets :param costs: non-negative costs associated with variables in the graph. Only used for estimand_type='non-parametric-ate' and backdoor_adjustment='efficient-mincost-adjustment'. If no costs are provided by the user, and backdoor_adjustment='efficient-mincost-adjustment', costs are assumed to be equal to one for all variables in the graph. :param conditional_node_names: variables that are used to determine treatment. If none are provided, it is assumed that the intervention is static. :returns: target estimand, an instance of the IdentifiedEstimand class """ treatment_name = parse_state(treatment_name) outcome_name = parse_state(outcome_name) # First, check if there is a directed path from action to outcome if not graph.has_directed_path(treatment_name, outcome_name): logger.warn("No directed path from treatment to outcome. Causal Effect is zero.") return IdentifiedEstimand( None, treatment_variable=treatment_name, outcome_variable=outcome_name, no_directed_path=True, ) if estimand_type == EstimandType.NONPARAMETRIC_ATE: return identify_ate_effect( graph, treatment_name, outcome_name, backdoor_adjustment, optimize_backdoor, estimand_type, costs, conditional_node_names, proceed_when_unidentifiable, ) elif estimand_type == EstimandType.NONPARAMETRIC_NDE: return identify_nde_effect( graph, treatment_name, outcome_name, backdoor_adjustment, estimand_type, proceed_when_unidentifiable ) elif estimand_type == EstimandType.NONPARAMETRIC_NIE: return identify_nie_effect( graph, treatment_name, outcome_name, backdoor_adjustment, estimand_type, proceed_when_unidentifiable ) elif estimand_type == EstimandType.NONPARAMETRIC_CDE: return identify_cde_effect( graph, treatment_name, outcome_name, backdoor_adjustment, estimand_type, proceed_when_unidentifiable ) else: raise ValueError( "Estimand type is not supported. Use either {0}, {1}, or {2}.".format( EstimandType.NONPARAMETRIC_ATE, EstimandType.NONPARAMETRIC_CDE, EstimandType.NONPARAMETRIC_NDE, EstimandType.NONPARAMETRIC_NIE, ) ) def identify_ate_effect( graph: CausalGraph, treatment_name: List[str], outcome_name: str, backdoor_adjustment: BackdoorAdjustment, optimize_backdoor: bool, estimand_type: EstimandType, costs: List, conditional_node_names: List[str] = None, proceed_when_unidentifiable: bool = False, ): estimands_dict = {} mediation_first_stage_confounders = None mediation_second_stage_confounders = None ### 1. BACKDOOR IDENTIFICATION # Pick algorithm to compute backdoor sets according to method chosen if backdoor_adjustment not in EFFICIENT_METHODS: # First, checking if there are any valid backdoor adjustment sets if optimize_backdoor == False: backdoor_sets = identify_backdoor(graph, treatment_name, outcome_name, backdoor_adjustment) else: from dowhy.causal_identifier.backdoor import Backdoor path = Backdoor(graph._graph, treatment_name, outcome_name) backdoor_sets = path.get_backdoor_vars() elif backdoor_adjustment in EFFICIENT_METHODS: backdoor_sets = identify_efficient_backdoor( graph, backdoor_adjustment, costs, conditional_node_names=conditional_node_names ) estimands_dict, backdoor_variables_dict = build_backdoor_estimands_dict( graph, treatment_name, outcome_name, backdoor_sets, estimands_dict ) # Setting default "backdoor" identification adjustment set default_backdoor_id = get_default_backdoor_set_id(graph, treatment_name, outcome_name, backdoor_variables_dict) if len(backdoor_variables_dict) > 0: estimands_dict["backdoor"] = estimands_dict.get(str(default_backdoor_id), None) backdoor_variables_dict["backdoor"] = backdoor_variables_dict.get(str(default_backdoor_id), None) else: estimands_dict["backdoor"] = None ### 2. INSTRUMENTAL VARIABLE IDENTIFICATION # Now checking if there is also a valid iv estimand instrument_names = graph.get_instruments(treatment_name, outcome_name) logger.info("Instrumental variables for treatment and outcome:" + str(instrument_names)) if len(instrument_names) > 0: iv_estimand_expr = construct_iv_estimand( treatment_name, outcome_name, instrument_names, ) logger.debug("Identified expression = " + str(iv_estimand_expr)) estimands_dict["iv"] = iv_estimand_expr else: estimands_dict["iv"] = None ### 3. FRONTDOOR IDENTIFICATION # Now checking if there is a valid frontdoor variable frontdoor_variables_names = identify_frontdoor(graph, treatment_name, outcome_name) logger.info("Frontdoor variables for treatment and outcome:" + str(frontdoor_variables_names)) if len(frontdoor_variables_names) > 0: frontdoor_estimand_expr = construct_frontdoor_estimand( treatment_name, outcome_name, frontdoor_variables_names, ) logger.debug("Identified expression = " + str(frontdoor_estimand_expr)) estimands_dict["frontdoor"] = frontdoor_estimand_expr mediation_first_stage_confounders = identify_mediation_first_stage_confounders( graph, treatment_name, outcome_name, frontdoor_variables_names, backdoor_adjustment ) mediation_second_stage_confounders = identify_mediation_second_stage_confounders( graph, treatment_name, frontdoor_variables_names, outcome_name, backdoor_adjustment ) else: estimands_dict["frontdoor"] = None # Finally returning the estimand object estimand = IdentifiedEstimand( None, treatment_variable=treatment_name, outcome_variable=outcome_name, estimand_type=estimand_type, estimands=estimands_dict, backdoor_variables=backdoor_variables_dict, instrumental_variables=instrument_names, frontdoor_variables=frontdoor_variables_names, mediation_first_stage_confounders=mediation_first_stage_confounders, mediation_second_stage_confounders=mediation_second_stage_confounders, default_backdoor_id=default_backdoor_id, ) return estimand def identify_cde_effect( graph: CausalGraph, treatment_name: List[str], outcome_name: str, backdoor_adjustment: BackdoorAdjustment, estimand_type: EstimandType, proceed_when_unidentifiable: bool = False, ): """Identify controlled direct effect. For a definition, see Vanderwheele (2011). Controlled direct and mediated effects: definition, identification and bounds. https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4193506/ Using do-calculus rules, identification yields a adjustment set. It is based on the principle that under a graph where the direct edge from treatment to outcome is removed, conditioning on the adjustment set should d-separate treatment and outcome. """ estimands_dict = {} # Pick algorithm to compute backdoor sets according to method chosen backdoor_sets = identify_backdoor(graph, treatment_name, outcome_name, backdoor_adjustment, direct_effect=True) estimands_dict, backdoor_variables_dict = build_backdoor_estimands_dict( graph, treatment_name, outcome_name, backdoor_sets, estimands_dict ) # Setting default "backdoor" identification adjustment set default_backdoor_id = get_default_backdoor_set_id(graph, treatment_name, outcome_name, backdoor_variables_dict) if len(backdoor_variables_dict) > 0: estimands_dict["backdoor"] = estimands_dict.get(str(default_backdoor_id), None) backdoor_variables_dict["backdoor"] = backdoor_variables_dict.get(str(default_backdoor_id), None) else: estimands_dict["backdoor"] = None # Finally returning the estimand object estimand = IdentifiedEstimand( None, treatment_variable=treatment_name, outcome_variable=outcome_name, estimand_type=estimand_type, estimands=estimands_dict, backdoor_variables=backdoor_variables_dict, instrumental_variables=None, frontdoor_variables=None, mediation_first_stage_confounders=None, mediation_second_stage_confounders=None, default_backdoor_id=default_backdoor_id, ) return estimand def identify_nie_effect( graph: CausalGraph, treatment_name: List[str], outcome_name: str, backdoor_adjustment: BackdoorAdjustment, estimand_type: EstimandType, proceed_when_unidentifiable: bool = False, ): estimands_dict = {} ### 1. FIRST DOING BACKDOOR IDENTIFICATION # First, checking if there are any valid backdoor adjustment sets backdoor_sets = identify_backdoor(graph, treatment_name, outcome_name, backdoor_adjustment) estimands_dict, backdoor_variables_dict = build_backdoor_estimands_dict( graph, treatment_name, outcome_name, backdoor_sets, estimands_dict ) # Setting default "backdoor" identification adjustment set default_backdoor_id = get_default_backdoor_set_id(graph, treatment_name, outcome_name, backdoor_variables_dict) backdoor_variables_dict["backdoor"] = backdoor_variables_dict.get(str(default_backdoor_id), None) ### 2. SECOND, CHECKING FOR MEDIATORS # Now checking if there are valid mediator variables estimands_dict = {} # Need to reinitialize this dictionary to avoid including the backdoor sets mediation_first_stage_confounders = None mediation_second_stage_confounders = None mediators_names = identify_mediation(graph, treatment_name, outcome_name) logger.info("Mediators for treatment and outcome:" + str(mediators_names)) if len(mediators_names) > 0: mediation_estimand_expr = construct_mediation_estimand( estimand_type, treatment_name, outcome_name, mediators_names, ) logger.debug("Identified expression = " + str(mediation_estimand_expr)) estimands_dict["mediation"] = mediation_estimand_expr mediation_first_stage_confounders = identify_mediation_first_stage_confounders( graph, treatment_name, outcome_name, mediators_names, backdoor_adjustment ) mediation_second_stage_confounders = identify_mediation_second_stage_confounders( graph, treatment_name, mediators_names, outcome_name, backdoor_adjustment ) else: estimands_dict["mediation"] = None # Finally returning the estimand object estimand = IdentifiedEstimand( None, treatment_variable=treatment_name, outcome_variable=outcome_name, estimand_type=estimand_type, estimands=estimands_dict, backdoor_variables=backdoor_variables_dict, instrumental_variables=None, frontdoor_variables=None, mediator_variables=mediators_names, mediation_first_stage_confounders=mediation_first_stage_confounders, mediation_second_stage_confounders=mediation_second_stage_confounders, default_backdoor_id=None, ) return estimand def identify_nde_effect( graph: CausalGraph, treatment_name: List[str], outcome_name: str, backdoor_adjustment: BackdoorAdjustment, estimand_type: EstimandType, proceed_when_unidentifiable: bool = False, ): estimands_dict = {} ### 1. FIRST DOING BACKDOOR IDENTIFICATION # First, checking if there are any valid backdoor adjustment sets backdoor_sets = identify_backdoor(graph, treatment_name, outcome_name, backdoor_adjustment) estimands_dict, backdoor_variables_dict = build_backdoor_estimands_dict( graph, treatment_name, outcome_name, backdoor_sets, estimands_dict ) # Setting default "backdoor" identification adjustment set default_backdoor_id = get_default_backdoor_set_id(graph, treatment_name, outcome_name, backdoor_variables_dict) backdoor_variables_dict["backdoor"] = backdoor_variables_dict.get(str(default_backdoor_id), None) ### 2. SECOND, CHECKING FOR MEDIATORS # Now checking if there are valid mediator variables estimands_dict = {} mediation_first_stage_confounders = None mediation_second_stage_confounders = None mediators_names = identify_mediation(graph, treatment_name, outcome_name) logger.info("Mediators for treatment and outcome:" + str(mediators_names)) if len(mediators_names) > 0: mediation_estimand_expr = construct_mediation_estimand( estimand_type, treatment_name, outcome_name, mediators_names, ) logger.debug("Identified expression = " + str(mediation_estimand_expr)) estimands_dict["mediation"] = mediation_estimand_expr mediation_first_stage_confounders = identify_mediation_first_stage_confounders( graph, treatment_name, outcome_name, mediators_names, backdoor_adjustment ) mediation_second_stage_confounders = identify_mediation_second_stage_confounders( graph, treatment_name, mediators_names, outcome_name, backdoor_adjustment ) else: estimands_dict["mediation"] = None # Finally returning the estimand object estimand = IdentifiedEstimand( None, treatment_variable=treatment_name, outcome_variable=outcome_name, estimand_type=estimand_type, estimands=estimands_dict, backdoor_variables=backdoor_variables_dict, instrumental_variables=None, frontdoor_variables=None, mediator_variables=mediators_names, mediation_first_stage_confounders=mediation_first_stage_confounders, mediation_second_stage_confounders=mediation_second_stage_confounders, default_backdoor_id=None, ) return estimand def identify_backdoor( graph: CausalGraph, treatment_name: List[str], outcome_name: str, backdoor_adjustment: BackdoorAdjustment, include_unobserved: bool = False, dseparation_algo: str = "default", direct_effect: bool = False, ): backdoor_sets = [] backdoor_paths = None bdoor_graph = None if dseparation_algo == "naive": backdoor_paths = graph.get_backdoor_paths(treatment_name, outcome_name) elif dseparation_algo == "default": bdoor_graph = graph.do_surgery( treatment_name, target_node_names=outcome_name, remove_outgoing_edges=True, remove_only_direct_edges_to_target=direct_effect, ) else: raise ValueError(f"d-separation algorithm {dseparation_algo} is not supported") backdoor_adjustment = ( backdoor_adjustment if backdoor_adjustment != BackdoorAdjustment.BACKDOOR_DEFAULT else DEFAULT_BACKDOOR_METHOD ) # First, checking if empty set is a valid backdoor set empty_set = set() check = graph.check_valid_backdoor_set( treatment_name, outcome_name, empty_set, backdoor_paths=backdoor_paths, new_graph=bdoor_graph, dseparation_algo=dseparation_algo, ) if check["is_dseparated"]: backdoor_sets.append({"backdoor_set": empty_set}) # If the method is `minimal-adjustment`, return the empty set right away. if backdoor_adjustment == BackdoorAdjustment.BACKDOOR_MIN: return backdoor_sets # Second, checking for all other sets of variables. If include_unobserved is false, then only observed variables are eligible. eligible_variables = ( graph.get_all_nodes(include_unobserved=include_unobserved) - set(treatment_name) - set(outcome_name) ) if direct_effect: # only remove descendants of Y # also allow any causes of Y that are not caused by T (for lower variance) eligible_variables -= graph.get_descendants(outcome_name) else: # remove descendants of T (mediators) and descendants of Y eligible_variables -= graph.get_descendants(treatment_name) # If var is d-separated from both treatment or outcome, it cannot # be a part of the backdoor set filt_eligible_variables = set() for var in eligible_variables: dsep_treat_var = graph.check_dseparation(treatment_name, parse_state(var), set()) dsep_outcome_var = graph.check_dseparation(outcome_name, parse_state(var), set()) if not dsep_outcome_var or not dsep_treat_var: filt_eligible_variables.add(var) if backdoor_adjustment in METHOD_NAMES: backdoor_sets, found_valid_adjustment_set = find_valid_adjustment_sets( graph, treatment_name, outcome_name, backdoor_paths, bdoor_graph, dseparation_algo, backdoor_sets, filt_eligible_variables, backdoor_adjustment=backdoor_adjustment, max_iterations=MAX_BACKDOOR_ITERATIONS, ) if backdoor_adjustment == BackdoorAdjustment.BACKDOOR_DEFAULT and found_valid_adjustment_set: # repeat the above search with BACKDOOR_MIN backdoor_sets, _ = find_valid_adjustment_sets( graph, treatment_name, outcome_name, backdoor_paths, bdoor_graph, dseparation_algo, backdoor_sets, filt_eligible_variables, backdoor_adjustment=BackdoorAdjustment.BACKDOOR_MIN, max_iterations=MAX_BACKDOOR_ITERATIONS, ) else: raise ValueError( f"Identifier method {backdoor_adjustment} not supported. Try one of the following: {METHOD_NAMES}" ) return backdoor_sets def identify_efficient_backdoor( graph: CausalGraph, backdoor_adjustment: BackdoorAdjustment, costs: List, conditional_node_names: List[str] = None, ): """Method implementing algorithms to compute efficient backdoor sets, as described in Rotnitzky and Smucler (2020), Smucler, Sapienza and Rotnitzky (2021) and Smucler and Rotnitzky (2022). For backdoor_adjustment='efficient-adjustment', computes an optimal backdoor set, that is, a backdoor set comprised of observable variables that yields non-parametric estimators of the interventional mean with the smallest asymptotic variance among those that are based on observable backdoor sets. This optimal backdoor set always exists when no variables are latent, and the algorithm is guaranteed to compute it in this case. Under a non-parametric graphical model with latent variables, such a backdoor set can fail to exist. When certain sufficient conditions under which it is known that such a backdoor set exists are not satisfied, an error is raised. For backdoor_adjustment='efficient-minimal-adjustment', computes an optimal minimal backdoor set, that is, a minimal backdoor set comprised of observable variables that yields non-parametric estimators of the interventional mean with the smallest asymptotic variance among those that are based on observable minimal backdoor sets. For backdoor_adjustment='efficient-mincost-adjustment', computes an optimal minimum cost backdoor set, that is, a minimum cost backdoor set comprised of observable variables that yields non-parametric estimators of the interventional mean with the smallest asymptotic variance among those that are based on observable minimum cost backdoor sets. The cost of a backdoor set is defined as the sum of the costs of the variables that comprise it. The various optimal backdoor sets computed by this method are not only optimal under non-parametric graphical models and non-parametric estimators of interventional mean, but also under linear graphical models and OLS estimators, per results in Henckel, Perkovic and Maathuis (2020). :param costs: a list with non-negative costs associated with variables in the graph. Only used for estimatand_type='non-parametric-ate' and backdoor_adjustment='efficient-mincost-adjustment'. If not costs are provided by the user, and backdoor_adjustment='efficient-mincost-adjustment', costs are assumed to be equal to one for all variables in the graph. The structure of the list should be of the form [(node, {"cost": x}) for node in nodes]. :param conditional_node_names: variables that are used to determine treatment. If none are provided, it is assumed that the intervention sets the treatment to a constant. :returns: backdoor_sets, a list of dictionaries, with each dictionary having as values a backdoor set. """ if costs is None and backdoor_adjustment == "efficient-mincost-adjustment": logger.warning("No costs were passed, so they will be assumed to be constant and equal to 1.") efficient_bd = EfficientBackdoor( graph=graph, conditional_node_names=conditional_node_names, costs=costs, ) if backdoor_adjustment == BackdoorAdjustment.BACKDOOR_EFFICIENT: backdoor_set = efficient_bd.optimal_adj_set() backdoor_sets = [{"backdoor_set": tuple(backdoor_set)}] elif backdoor_adjustment == BackdoorAdjustment.BACKDOOR_MIN_EFFICIENT: backdoor_set = efficient_bd.optimal_minimal_adj_set() backdoor_sets = [{"backdoor_set": tuple(backdoor_set)}] elif backdoor_adjustment == BackdoorAdjustment.BACKDOOR_MINCOST_EFFICIENT: backdoor_set = efficient_bd.optimal_mincost_adj_set() backdoor_sets = [{"backdoor_set": tuple(backdoor_set)}] return backdoor_sets def find_valid_adjustment_sets( graph: CausalGraph, treatment_name: List, outcome_name: List, backdoor_paths: List, bdoor_graph: CausalGraph, dseparation_algo: str, backdoor_sets: List, filt_eligible_variables: List, backdoor_adjustment: BackdoorAdjustment, max_iterations: int, ): num_iterations = 0 found_valid_adjustment_set = False all_nodes_observed = graph.all_observed(graph.get_all_nodes()) # If `minimal-adjustment` method is specified, start the search from the set with minimum size. Otherwise, start from the largest. set_sizes = ( range(1, len(filt_eligible_variables) + 1, 1) if backdoor_adjustment == BackdoorAdjustment.BACKDOOR_MIN else range(len(filt_eligible_variables), 0, -1) ) for size_candidate_set in set_sizes: for candidate_set in itertools.combinations(filt_eligible_variables, size_candidate_set): check = graph.check_valid_backdoor_set( treatment_name, outcome_name, candidate_set, backdoor_paths=backdoor_paths, new_graph=bdoor_graph, dseparation_algo=dseparation_algo, ) logger.debug( "Candidate backdoor set: {0}, is_dseparated: {1}".format(candidate_set, check["is_dseparated"]) ) if check["is_dseparated"]: backdoor_sets.append({"backdoor_set": candidate_set}) found_valid_adjustment_set = True num_iterations += 1 if backdoor_adjustment == BackdoorAdjustment.BACKDOOR_EXHAUSTIVE and num_iterations > max_iterations: logger.warning(f"Max number of iterations {max_iterations} reached.") break # If the backdoor method is `maximal-adjustment` or `minimal-adjustment`, return the first found adjustment set. if ( backdoor_adjustment in { BackdoorAdjustment.BACKDOOR_DEFAULT, BackdoorAdjustment.BACKDOOR_MAX, BackdoorAdjustment.BACKDOOR_MIN, } and found_valid_adjustment_set ): break # If all variables are observed, and the biggest eligible set # does not satisfy backdoor, then none of its subsets will. if ( backdoor_adjustment in {BackdoorAdjustment.BACKDOOR_DEFAULT, BackdoorAdjustment.BACKDOOR_MAX} and all_nodes_observed ): break if num_iterations > max_iterations: logger.warning(f"Max number of iterations {max_iterations} reached. Could not find a valid backdoor set.") break return backdoor_sets, found_valid_adjustment_set def get_default_backdoor_set_id( graph: CausalGraph, treatment_name: List[str], outcome_name: List[str], backdoor_sets_dict: Dict ): # Adding a None estimand if no backdoor set found if len(backdoor_sets_dict) == 0: return None # Default set contains minimum possible number of instrumental variables, to prevent lowering variance in the treatment variable. instrument_names = set(graph.get_instruments(treatment_name, outcome_name)) iv_count_dict = { key: len(set(bdoor_set).intersection(instrument_names)) for key, bdoor_set in backdoor_sets_dict.items() } min_iv_count = min(iv_count_dict.values()) min_iv_keys = {key for key, iv_count in iv_count_dict.items() if iv_count == min_iv_count} min_iv_backdoor_sets_dict = {key: backdoor_sets_dict[key] for key in min_iv_keys} # Default set is the one with the least number of adjustment variables (optimizing for efficiency) min_set_length = 1000000 default_key = None for key, bdoor_set in min_iv_backdoor_sets_dict.items(): if len(bdoor_set) < min_set_length: min_set_length = len(bdoor_set) default_key = key return default_key def build_backdoor_estimands_dict( graph: CausalGraph, treatment_name: List[str], outcome_name: List[str], backdoor_sets: List[str], estimands_dict: Dict, ): """Build the final dict for backdoor sets by filtering unobserved variables if needed.""" backdoor_variables_dict = {} is_identified = [graph.all_observed(bset["backdoor_set"]) for bset in backdoor_sets] if any(is_identified): logger.info("Causal effect can be identified.") backdoor_sets_arr = [ list(bset["backdoor_set"]) for bset in backdoor_sets if graph.all_observed(bset["backdoor_set"]) ] else: # there is unobserved confounding logger.warning("Backdoor identification failed.") backdoor_sets_arr = [] for i in range(len(backdoor_sets_arr)): backdoor_estimand_expr = construct_backdoor_estimand(treatment_name, outcome_name, backdoor_sets_arr[i]) logger.debug("Identified expression = " + str(backdoor_estimand_expr)) estimands_dict["backdoor" + str(i + 1)] = backdoor_estimand_expr backdoor_variables_dict["backdoor" + str(i + 1)] = backdoor_sets_arr[i] return estimands_dict, backdoor_variables_dict def identify_frontdoor( graph: CausalGraph, treatment_name: List[str], outcome_name: List[str], dseparation_algo: str = "default" ): """Find a valid frontdoor variable if it exists. Currently only supports a single variable frontdoor set. """ frontdoor_var = None frontdoor_paths = None fdoor_graph = None if dseparation_algo == "default": cond1_graph = graph.do_surgery(treatment_name, remove_incoming_edges=True) bdoor_graph1 = graph.do_surgery(treatment_name, remove_outgoing_edges=True) elif dseparation_algo == "naive": frontdoor_paths = graph.get_all_directed_paths(treatment_name, outcome_name) else: raise ValueError(f"d-separation algorithm {dseparation_algo} is not supported") eligible_variables = ( graph.get_descendants(treatment_name) - set(outcome_name) - set(graph.get_descendants(outcome_name)) ) # For simplicity, assuming a one-variable frontdoor set for candidate_var in eligible_variables: # Cond 1: All directed paths intercepted by candidate_var cond1 = graph.check_valid_frontdoor_set( treatment_name, outcome_name, parse_state(candidate_var), frontdoor_paths=frontdoor_paths, new_graph=cond1_graph, dseparation_algo=dseparation_algo, ) logger.debug("Candidate frontdoor set: {0}, is_dseparated: {1}".format(candidate_var, cond1)) if not cond1: continue # Cond 2: No confounding between treatment and candidate var cond2 = graph.check_valid_backdoor_set( treatment_name, parse_state(candidate_var), set(), backdoor_paths=None, new_graph=bdoor_graph1, dseparation_algo=dseparation_algo, ) if not cond2: continue # Cond 3: treatment blocks all confounding between candidate_var and outcome bdoor_graph2 = graph.do_surgery(candidate_var, remove_outgoing_edges=True) cond3 = graph.check_valid_backdoor_set( parse_state(candidate_var), outcome_name, treatment_name, backdoor_paths=None, new_graph=bdoor_graph2, dseparation_algo=dseparation_algo, ) is_valid_frontdoor = cond1 and cond2 and cond3 if is_valid_frontdoor: frontdoor_var = candidate_var break return parse_state(frontdoor_var) def identify_mediation(graph: CausalGraph, treatment_name: List[str], outcome_name: List[str]): """Find a valid mediator if it exists. Currently only supports a single variable mediator set. """ mediation_var = None mediation_paths = graph.get_all_directed_paths(treatment_name, outcome_name) eligible_variables = graph.get_descendants(treatment_name) - set(outcome_name) # For simplicity, assuming a one-variable mediation set for candidate_var in eligible_variables: is_valid_mediation = graph.check_valid_mediation_set( treatment_name, outcome_name, parse_state(candidate_var), mediation_paths=mediation_paths, ) logger.debug("Candidate mediation set: {0}, on_mediating_path: {1}".format(candidate_var, is_valid_mediation)) if is_valid_mediation: mediation_var = candidate_var break return parse_state(mediation_var) def identify_mediation_first_stage_confounders( graph: CausalGraph, treatment_name: List[str], outcome_name: List[str], mediators_names: List[str], backdoor_adjustment: BackdoorAdjustment, ): # Create estimands dict as per the API for backdoor, but do not return it estimands_dict = {} backdoor_sets = identify_backdoor(graph, treatment_name, mediators_names, backdoor_adjustment) estimands_dict, backdoor_variables_dict = build_backdoor_estimands_dict( graph, treatment_name, mediators_names, backdoor_sets, estimands_dict, ) # Setting default "backdoor" identification adjustment set default_backdoor_id = get_default_backdoor_set_id(graph, treatment_name, outcome_name, backdoor_variables_dict) estimands_dict["backdoor"] = estimands_dict.get(str(default_backdoor_id), None) backdoor_variables_dict["backdoor"] = backdoor_variables_dict.get(str(default_backdoor_id), None) return backdoor_variables_dict def identify_mediation_second_stage_confounders( graph: CausalGraph, treatment_name: List[str], mediators_names: List[str], outcome_name: List[str], backdoor_adjustment: BackdoorAdjustment, ): # Create estimands dict as per the API for backdoor, but do not return it estimands_dict = {} backdoor_sets = identify_backdoor(graph, mediators_names, outcome_name, backdoor_adjustment) estimands_dict, backdoor_variables_dict = build_backdoor_estimands_dict( graph, mediators_names, outcome_name, backdoor_sets, estimands_dict, ) # Setting default "backdoor" identification adjustment set default_backdoor_id = get_default_backdoor_set_id(graph, treatment_name, outcome_name, backdoor_variables_dict) estimands_dict["backdoor"] = estimands_dict.get(str(default_backdoor_id), None) backdoor_variables_dict["backdoor"] = backdoor_variables_dict.get(str(default_backdoor_id), None) return backdoor_variables_dict def construct_backdoor_estimand(treatment_name: List[str], outcome_name: List[str], common_causes: List[str]): # TODO: outputs string for now, but ideally should do symbolic # expressions Mon 19 Feb 2018 04:54:17 PM DST # TODO Better support for multivariate treatments expr = None outcome_name = outcome_name[0] num_expr_str = outcome_name if len(common_causes) > 0: num_expr_str += "|" + ",".join(common_causes) expr = "d(" + num_expr_str + ")/d" + ",".join(treatment_name) sym_mu = sp.Symbol("mu") sym_sigma = sp.Symbol("sigma", positive=True) sym_outcome = spstats.Normal(num_expr_str, sym_mu, sym_sigma) sym_treatment_symbols = [sp.Symbol(t) for t in treatment_name] sym_treatment = sp.Array(sym_treatment_symbols) sym_conditional_outcome = spstats.Expectation(sym_outcome) sym_effect = sp.Derivative(sym_conditional_outcome, sym_treatment) sym_assumptions = { "Unconfoundedness": ( "If U\N{RIGHTWARDS ARROW}{{{0}}} and U\N{RIGHTWARDS ARROW}{1}" " then P({1}|{0},{2},U) = P({1}|{0},{2})" ).format(",".join(treatment_name), outcome_name, ",".join(common_causes)) } estimand = {"estimand": sym_effect, "assumptions": sym_assumptions} return estimand def construct_iv_estimand(treatment_name: List[str], outcome_name: List[str], instrument_names: List[str]): # TODO: support multivariate treatments better. expr = None outcome_name = outcome_name[0] sym_outcome = spstats.Normal(outcome_name, 0, 1) sym_treatment_symbols = [spstats.Normal(t, 0, 1) for t in treatment_name] sym_treatment = sp.Array(sym_treatment_symbols) sym_instrument_symbols = [sp.Symbol(inst) for inst in instrument_names] sym_instrument = sp.Array(sym_instrument_symbols) # ",".join(instrument_names)) sym_outcome_derivative = sp.Derivative(sym_outcome, sym_instrument) sym_treatment_derivative = sp.Derivative(sym_treatment, sym_instrument) sym_effect = spstats.Expectation(sym_outcome_derivative / sym_treatment_derivative) sym_assumptions = { "As-if-random": ( "If U\N{RIGHTWARDS ARROW}\N{RIGHTWARDS ARROW}{0} then " "\N{NOT SIGN}(U \N{RIGHTWARDS ARROW}\N{RIGHTWARDS ARROW}{{{1}}})" ).format(outcome_name, ",".join(instrument_names)), "Exclusion": ( "If we remove {{{0}}}\N{RIGHTWARDS ARROW}{{{1}}}, then " "\N{NOT SIGN}({{{0}}}\N{RIGHTWARDS ARROW}{2})" ).format(",".join(instrument_names), ",".join(treatment_name), outcome_name), } estimand = {"estimand": sym_effect, "assumptions": sym_assumptions} return estimand def construct_frontdoor_estimand( treatment_name: List[str], outcome_name: List[str], frontdoor_variables_names: List[str] ): # TODO: support multivariate treatments better. expr = None outcome_name = outcome_name[0] sym_outcome = spstats.Normal(outcome_name, 0, 1) sym_treatment_symbols = [spstats.Normal(t, 0, 1) for t in treatment_name] sym_treatment = sp.Array(sym_treatment_symbols) sym_frontdoor_symbols = [sp.Symbol(inst) for inst in frontdoor_variables_names] sym_frontdoor = sp.Array(sym_frontdoor_symbols) # ",".join(instrument_names)) sym_outcome_derivative = sp.Derivative(sym_outcome, sym_frontdoor) sym_treatment_derivative = sp.Derivative(sym_frontdoor, sym_treatment) sym_effect = spstats.Expectation(sym_treatment_derivative * sym_outcome_derivative) sym_assumptions = { "Full-mediation": ("{2} intercepts (blocks) all directed paths from {0} to {1}.").format( ",".join(treatment_name), ",".join(outcome_name), ",".join(frontdoor_variables_names), ), "First-stage-unconfoundedness": ( "If U\N{RIGHTWARDS ARROW}{{{0}}} and U\N{RIGHTWARDS ARROW}{{{1}}}" " then P({1}|{0},U) = P({1}|{0})" ).format(",".join(treatment_name), ",".join(frontdoor_variables_names)), "Second-stage-unconfoundedness": ( "If U\N{RIGHTWARDS ARROW}{{{2}}} and U\N{RIGHTWARDS ARROW}{1}" " then P({1}|{2}, {0}, U) = P({1}|{2}, {0})" ).format( ",".join(treatment_name), outcome_name, ",".join(frontdoor_variables_names), ), } estimand = {"estimand": sym_effect, "assumptions": sym_assumptions} return estimand def construct_mediation_estimand( estimand_type: EstimandType, treatment_name: List[str], outcome_name: List[str], mediators_names: List[str] ): # TODO: support multivariate treatments better. expr = None if estimand_type in ( EstimandType.NONPARAMETRIC_NDE, EstimandType.NONPARAMETRIC_NIE, ): outcome_name = outcome_name[0] sym_outcome = spstats.Normal(outcome_name, 0, 1) sym_treatment_symbols = [spstats.Normal(t, 0, 1) for t in treatment_name] sym_treatment = sp.Array(sym_treatment_symbols) sym_mediators_symbols = [sp.Symbol(inst) for inst in mediators_names] sym_mediators = sp.Array(sym_mediators_symbols) sym_outcome_derivative = sp.Derivative(sym_outcome, sym_mediators) sym_treatment_derivative = sp.Derivative(sym_mediators, sym_treatment) # For direct effect num_expr_str = outcome_name if len(mediators_names) > 0: num_expr_str += "|" + ",".join(mediators_names) sym_mu = sp.Symbol("mu") sym_sigma = sp.Symbol("sigma", positive=True) sym_conditional_outcome = spstats.Normal(num_expr_str, sym_mu, sym_sigma) sym_directeffect_derivative = sp.Derivative(sym_conditional_outcome, sym_treatment) if estimand_type == EstimandType.NONPARAMETRIC_NIE: sym_effect = spstats.Expectation(sym_treatment_derivative * sym_outcome_derivative) elif estimand_type == EstimandType.NONPARAMETRIC_NDE: sym_effect = spstats.Expectation(sym_directeffect_derivative) sym_assumptions = { "Mediation": ( "{2} intercepts (blocks) all directed paths from {0} to {1} except the path {{{0}}}\N{RIGHTWARDS ARROW}{{{1}}}." ).format( ",".join(treatment_name), ",".join(outcome_name), ",".join(mediators_names), ), "First-stage-unconfoundedness": ( "If U\N{RIGHTWARDS ARROW}{{{0}}} and U\N{RIGHTWARDS ARROW}{{{1}}}" " then P({1}|{0},U) = P({1}|{0})" ).format(",".join(treatment_name), ",".join(mediators_names)), "Second-stage-unconfoundedness": ( "If U\N{RIGHTWARDS ARROW}{{{2}}} and U\N{RIGHTWARDS ARROW}{1}" " then P({1}|{2}, {0}, U) = P({1}|{2}, {0})" ).format(",".join(treatment_name), outcome_name, ",".join(mediators_names)), } else: raise ValueError( "Estimand type not supported. Supported estimand types are {0} or {1}'.".format( EstimandType.NONPARAMETRIC_NDE, EstimandType.NONPARAMETRIC_NIE, ) ) estimand = {"estimand": sym_effect, "assumptions": sym_assumptions} return estimand

andresmor-ms

133e7b9a4ed32aae8ab5f39a01eb02b3a4d1c0ba

e1652ec3c6606b1bb2dfe91ef830e4b4b566712d

does it return None otherwise? If yes, good to add to the docstring on line 141

amit-sharma

py-why/dowhy

Functional api/refute estimate

* Refactor refuters into functions * Rename functional_api notebook for clarity * Add return types to identify_estimate * Update `__init__.py` for imports * Add joblib for bootstrap refuter * Create `refute_estimate` function * Add types for refuter parameters & return types

2022-10-04 16:18:49+00:00

2022-10-07 04:30:22+00:00

dowhy/causal_identifier/auto_identifier.py

import itertools import logging from enum import Enum from typing import Dict, List, Optional, Union import sympy as sp import sympy.stats as spstats from dowhy.causal_graph import CausalGraph from dowhy.causal_identifier.efficient_backdoor import EfficientBackdoor from dowhy.causal_identifier.identified_estimand import IdentifiedEstimand from dowhy.utils.api import parse_state logger = logging.getLogger(__name__) class EstimandType(Enum): # Average total effect NONPARAMETRIC_ATE = "nonparametric-ate" # Natural direct effect NONPARAMETRIC_NDE = "nonparametric-nde" # Natural indirect effect NONPARAMETRIC_NIE = "nonparametric-nie" # Controlled direct effect NONPARAMETRIC_CDE = "nonparametric-cde" class BackdoorAdjustment(Enum): # Backdoor method names BACKDOOR_DEFAULT = "default" BACKDOOR_EXHAUSTIVE = "exhaustive-search" BACKDOOR_MIN = "minimal-adjustment" BACKDOOR_MAX = "maximal-adjustment" BACKDOOR_EFFICIENT = "efficient-adjustment" BACKDOOR_MIN_EFFICIENT = "efficient-minimal-adjustment" BACKDOOR_MINCOST_EFFICIENT = "efficient-mincost-adjustment" MAX_BACKDOOR_ITERATIONS = 100000 METHOD_NAMES = { BackdoorAdjustment.BACKDOOR_DEFAULT, BackdoorAdjustment.BACKDOOR_EXHAUSTIVE, BackdoorAdjustment.BACKDOOR_MIN, BackdoorAdjustment.BACKDOOR_MAX, BackdoorAdjustment.BACKDOOR_EFFICIENT, BackdoorAdjustment.BACKDOOR_MIN_EFFICIENT, BackdoorAdjustment.BACKDOOR_MINCOST_EFFICIENT, } EFFICIENT_METHODS = { BackdoorAdjustment.BACKDOOR_EFFICIENT, BackdoorAdjustment.BACKDOOR_MIN_EFFICIENT, BackdoorAdjustment.BACKDOOR_MINCOST_EFFICIENT, } DEFAULT_BACKDOOR_METHOD = BackdoorAdjustment.BACKDOOR_DEFAULT class AutoIdentifier: """Class that implements different identification methods. Currently supports backdoor and instrumental variable identification methods. The identification is based on the causal graph provided. This class is for backwards compatibility with CausalModel Will be deprecated in the future in favor of function call auto_identify_effect() """ def __init__( self, estimand_type: EstimandType, backdoor_adjustment: BackdoorAdjustment = BackdoorAdjustment.BACKDOOR_DEFAULT, proceed_when_unidentifiable: bool = False, optimize_backdoor: bool = False, costs: Optional[List] = None, ): self.estimand_type = estimand_type self.backdoor_adjustment = backdoor_adjustment self._proceed_when_unidentifiable = proceed_when_unidentifiable self.optimize_backdoor = optimize_backdoor self.costs = costs self.logger = logging.getLogger(__name__) def identify_effect( self, graph: CausalGraph, treatment_name: Union[str, List[str]], outcome_name: Union[str, List[str]], conditional_node_names: List[str] = None, **kwargs, ): estimand = auto_identify_effect( graph, treatment_name, outcome_name, self.estimand_type, conditional_node_names, self.backdoor_adjustment, self._proceed_when_unidentifiable, self.optimize_backdoor, self.costs, **kwargs, ) estimand.identifier = self return estimand def identify_backdoor( self, graph: CausalGraph, treatment_name: List[str], outcome_name: str, include_unobserved: bool = False, dseparation_algo: str = "default", direct_effect: bool = False, ): return identify_backdoor( graph, treatment_name, outcome_name, self.backdoor_adjustment, include_unobserved, dseparation_algo, direct_effect, ) def auto_identify_effect( graph: CausalGraph, treatment_name: Union[str, List[str]], outcome_name: Union[str, List[str]], estimand_type: EstimandType, conditional_node_names: List[str] = None, backdoor_adjustment: BackdoorAdjustment = BackdoorAdjustment.BACKDOOR_DEFAULT, proceed_when_unidentifiable: bool = False, optimize_backdoor: bool = False, costs: Optional[List] = None, **kwargs, ): """Main method that returns an identified estimand (if one exists). If estimand_type is non-parametric ATE, then uses backdoor, instrumental variable and frontdoor identification methods, to check if an identified estimand exists, based on the causal graph. :param optimize_backdoor: if True, uses an optimised algorithm to compute the backdoor sets :param costs: non-negative costs associated with variables in the graph. Only used for estimand_type='non-parametric-ate' and backdoor_adjustment='efficient-mincost-adjustment'. If no costs are provided by the user, and backdoor_adjustment='efficient-mincost-adjustment', costs are assumed to be equal to one for all variables in the graph. :param conditional_node_names: variables that are used to determine treatment. If none are provided, it is assumed that the intervention is static. :returns: target estimand, an instance of the IdentifiedEstimand class """ treatment_name = parse_state(treatment_name) outcome_name = parse_state(outcome_name) # First, check if there is a directed path from action to outcome if not graph.has_directed_path(treatment_name, outcome_name): logger.warn("No directed path from treatment to outcome. Causal Effect is zero.") return IdentifiedEstimand( None, treatment_variable=treatment_name, outcome_variable=outcome_name, no_directed_path=True, ) if estimand_type == EstimandType.NONPARAMETRIC_ATE: return identify_ate_effect( graph, treatment_name, outcome_name, backdoor_adjustment, optimize_backdoor, estimand_type, costs, conditional_node_names, proceed_when_unidentifiable, ) elif estimand_type == EstimandType.NONPARAMETRIC_NDE: return identify_nde_effect( graph, treatment_name, outcome_name, backdoor_adjustment, estimand_type, proceed_when_unidentifiable ) elif estimand_type == EstimandType.NONPARAMETRIC_NIE: return identify_nie_effect( graph, treatment_name, outcome_name, backdoor_adjustment, estimand_type, proceed_when_unidentifiable ) elif estimand_type == EstimandType.NONPARAMETRIC_CDE: return identify_cde_effect( graph, treatment_name, outcome_name, backdoor_adjustment, estimand_type, proceed_when_unidentifiable ) else: raise ValueError( "Estimand type is not supported. Use either {0}, {1}, or {2}.".format( EstimandType.NONPARAMETRIC_ATE, EstimandType.NONPARAMETRIC_CDE, EstimandType.NONPARAMETRIC_NDE, EstimandType.NONPARAMETRIC_NIE, ) ) def identify_ate_effect( graph: CausalGraph, treatment_name: List[str], outcome_name: str, backdoor_adjustment: BackdoorAdjustment, optimize_backdoor: bool, estimand_type: EstimandType, costs: List, conditional_node_names: List[str] = None, proceed_when_unidentifiable: bool = False, ): estimands_dict = {} mediation_first_stage_confounders = None mediation_second_stage_confounders = None ### 1. BACKDOOR IDENTIFICATION # Pick algorithm to compute backdoor sets according to method chosen if backdoor_adjustment not in EFFICIENT_METHODS: # First, checking if there are any valid backdoor adjustment sets if optimize_backdoor == False: backdoor_sets = identify_backdoor(graph, treatment_name, outcome_name, backdoor_adjustment) else: from dowhy.causal_identifier.backdoor import Backdoor path = Backdoor(graph._graph, treatment_name, outcome_name) backdoor_sets = path.get_backdoor_vars() elif backdoor_adjustment in EFFICIENT_METHODS: backdoor_sets = identify_efficient_backdoor( graph, backdoor_adjustment, costs, conditional_node_names=conditional_node_names ) estimands_dict, backdoor_variables_dict = build_backdoor_estimands_dict( graph, treatment_name, outcome_name, backdoor_sets, estimands_dict ) # Setting default "backdoor" identification adjustment set default_backdoor_id = get_default_backdoor_set_id(graph, treatment_name, outcome_name, backdoor_variables_dict) if len(backdoor_variables_dict) > 0: estimands_dict["backdoor"] = estimands_dict.get(str(default_backdoor_id), None) backdoor_variables_dict["backdoor"] = backdoor_variables_dict.get(str(default_backdoor_id), None) else: estimands_dict["backdoor"] = None ### 2. INSTRUMENTAL VARIABLE IDENTIFICATION # Now checking if there is also a valid iv estimand instrument_names = graph.get_instruments(treatment_name, outcome_name) logger.info("Instrumental variables for treatment and outcome:" + str(instrument_names)) if len(instrument_names) > 0: iv_estimand_expr = construct_iv_estimand( treatment_name, outcome_name, instrument_names, ) logger.debug("Identified expression = " + str(iv_estimand_expr)) estimands_dict["iv"] = iv_estimand_expr else: estimands_dict["iv"] = None ### 3. FRONTDOOR IDENTIFICATION # Now checking if there is a valid frontdoor variable frontdoor_variables_names = identify_frontdoor(graph, treatment_name, outcome_name) logger.info("Frontdoor variables for treatment and outcome:" + str(frontdoor_variables_names)) if len(frontdoor_variables_names) > 0: frontdoor_estimand_expr = construct_frontdoor_estimand( treatment_name, outcome_name, frontdoor_variables_names, ) logger.debug("Identified expression = " + str(frontdoor_estimand_expr)) estimands_dict["frontdoor"] = frontdoor_estimand_expr mediation_first_stage_confounders = identify_mediation_first_stage_confounders( graph, treatment_name, outcome_name, frontdoor_variables_names, backdoor_adjustment ) mediation_second_stage_confounders = identify_mediation_second_stage_confounders( graph, treatment_name, frontdoor_variables_names, outcome_name, backdoor_adjustment ) else: estimands_dict["frontdoor"] = None # Finally returning the estimand object estimand = IdentifiedEstimand( None, treatment_variable=treatment_name, outcome_variable=outcome_name, estimand_type=estimand_type, estimands=estimands_dict, backdoor_variables=backdoor_variables_dict, instrumental_variables=instrument_names, frontdoor_variables=frontdoor_variables_names, mediation_first_stage_confounders=mediation_first_stage_confounders, mediation_second_stage_confounders=mediation_second_stage_confounders, default_backdoor_id=default_backdoor_id, ) return estimand def identify_cde_effect( graph: CausalGraph, treatment_name: List[str], outcome_name: str, backdoor_adjustment: BackdoorAdjustment, estimand_type: EstimandType, proceed_when_unidentifiable: bool = False, ): """Identify controlled direct effect. For a definition, see Vanderwheele (2011). Controlled direct and mediated effects: definition, identification and bounds. https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4193506/ Using do-calculus rules, identification yields a adjustment set. It is based on the principle that under a graph where the direct edge from treatment to outcome is removed, conditioning on the adjustment set should d-separate treatment and outcome. """ estimands_dict = {} # Pick algorithm to compute backdoor sets according to method chosen backdoor_sets = identify_backdoor(graph, treatment_name, outcome_name, backdoor_adjustment, direct_effect=True) estimands_dict, backdoor_variables_dict = build_backdoor_estimands_dict( graph, treatment_name, outcome_name, backdoor_sets, estimands_dict ) # Setting default "backdoor" identification adjustment set default_backdoor_id = get_default_backdoor_set_id(graph, treatment_name, outcome_name, backdoor_variables_dict) if len(backdoor_variables_dict) > 0: estimands_dict["backdoor"] = estimands_dict.get(str(default_backdoor_id), None) backdoor_variables_dict["backdoor"] = backdoor_variables_dict.get(str(default_backdoor_id), None) else: estimands_dict["backdoor"] = None # Finally returning the estimand object estimand = IdentifiedEstimand( None, treatment_variable=treatment_name, outcome_variable=outcome_name, estimand_type=estimand_type, estimands=estimands_dict, backdoor_variables=backdoor_variables_dict, instrumental_variables=None, frontdoor_variables=None, mediation_first_stage_confounders=None, mediation_second_stage_confounders=None, default_backdoor_id=default_backdoor_id, ) return estimand def identify_nie_effect( graph: CausalGraph, treatment_name: List[str], outcome_name: str, backdoor_adjustment: BackdoorAdjustment, estimand_type: EstimandType, proceed_when_unidentifiable: bool = False, ): estimands_dict = {} ### 1. FIRST DOING BACKDOOR IDENTIFICATION # First, checking if there are any valid backdoor adjustment sets backdoor_sets = identify_backdoor(graph, treatment_name, outcome_name, backdoor_adjustment) estimands_dict, backdoor_variables_dict = build_backdoor_estimands_dict( graph, treatment_name, outcome_name, backdoor_sets, estimands_dict ) # Setting default "backdoor" identification adjustment set default_backdoor_id = get_default_backdoor_set_id(graph, treatment_name, outcome_name, backdoor_variables_dict) backdoor_variables_dict["backdoor"] = backdoor_variables_dict.get(str(default_backdoor_id), None) ### 2. SECOND, CHECKING FOR MEDIATORS # Now checking if there are valid mediator variables estimands_dict = {} # Need to reinitialize this dictionary to avoid including the backdoor sets mediation_first_stage_confounders = None mediation_second_stage_confounders = None mediators_names = identify_mediation(graph, treatment_name, outcome_name) logger.info("Mediators for treatment and outcome:" + str(mediators_names)) if len(mediators_names) > 0: mediation_estimand_expr = construct_mediation_estimand( estimand_type, treatment_name, outcome_name, mediators_names, ) logger.debug("Identified expression = " + str(mediation_estimand_expr)) estimands_dict["mediation"] = mediation_estimand_expr mediation_first_stage_confounders = identify_mediation_first_stage_confounders( graph, treatment_name, outcome_name, mediators_names, backdoor_adjustment ) mediation_second_stage_confounders = identify_mediation_second_stage_confounders( graph, treatment_name, mediators_names, outcome_name, backdoor_adjustment ) else: estimands_dict["mediation"] = None # Finally returning the estimand object estimand = IdentifiedEstimand( None, treatment_variable=treatment_name, outcome_variable=outcome_name, estimand_type=estimand_type, estimands=estimands_dict, backdoor_variables=backdoor_variables_dict, instrumental_variables=None, frontdoor_variables=None, mediator_variables=mediators_names, mediation_first_stage_confounders=mediation_first_stage_confounders, mediation_second_stage_confounders=mediation_second_stage_confounders, default_backdoor_id=None, ) return estimand def identify_nde_effect( graph: CausalGraph, treatment_name: List[str], outcome_name: str, backdoor_adjustment: BackdoorAdjustment, estimand_type: EstimandType, proceed_when_unidentifiable: bool = False, ): estimands_dict = {} ### 1. FIRST DOING BACKDOOR IDENTIFICATION # First, checking if there are any valid backdoor adjustment sets backdoor_sets = identify_backdoor(graph, treatment_name, outcome_name, backdoor_adjustment) estimands_dict, backdoor_variables_dict = build_backdoor_estimands_dict( graph, treatment_name, outcome_name, backdoor_sets, estimands_dict ) # Setting default "backdoor" identification adjustment set default_backdoor_id = get_default_backdoor_set_id(graph, treatment_name, outcome_name, backdoor_variables_dict) backdoor_variables_dict["backdoor"] = backdoor_variables_dict.get(str(default_backdoor_id), None) ### 2. SECOND, CHECKING FOR MEDIATORS # Now checking if there are valid mediator variables estimands_dict = {} mediation_first_stage_confounders = None mediation_second_stage_confounders = None mediators_names = identify_mediation(graph, treatment_name, outcome_name) logger.info("Mediators for treatment and outcome:" + str(mediators_names)) if len(mediators_names) > 0: mediation_estimand_expr = construct_mediation_estimand( estimand_type, treatment_name, outcome_name, mediators_names, ) logger.debug("Identified expression = " + str(mediation_estimand_expr)) estimands_dict["mediation"] = mediation_estimand_expr mediation_first_stage_confounders = identify_mediation_first_stage_confounders( graph, treatment_name, outcome_name, mediators_names, backdoor_adjustment ) mediation_second_stage_confounders = identify_mediation_second_stage_confounders( graph, treatment_name, mediators_names, outcome_name, backdoor_adjustment ) else: estimands_dict["mediation"] = None # Finally returning the estimand object estimand = IdentifiedEstimand( None, treatment_variable=treatment_name, outcome_variable=outcome_name, estimand_type=estimand_type, estimands=estimands_dict, backdoor_variables=backdoor_variables_dict, instrumental_variables=None, frontdoor_variables=None, mediator_variables=mediators_names, mediation_first_stage_confounders=mediation_first_stage_confounders, mediation_second_stage_confounders=mediation_second_stage_confounders, default_backdoor_id=None, ) return estimand def identify_backdoor( graph: CausalGraph, treatment_name: List[str], outcome_name: str, backdoor_adjustment: BackdoorAdjustment, include_unobserved: bool = False, dseparation_algo: str = "default", direct_effect: bool = False, ): backdoor_sets = [] backdoor_paths = None bdoor_graph = None if dseparation_algo == "naive": backdoor_paths = graph.get_backdoor_paths(treatment_name, outcome_name) elif dseparation_algo == "default": bdoor_graph = graph.do_surgery( treatment_name, target_node_names=outcome_name, remove_outgoing_edges=True, remove_only_direct_edges_to_target=direct_effect, ) else: raise ValueError(f"d-separation algorithm {dseparation_algo} is not supported") backdoor_adjustment = ( backdoor_adjustment if backdoor_adjustment != BackdoorAdjustment.BACKDOOR_DEFAULT else DEFAULT_BACKDOOR_METHOD ) # First, checking if empty set is a valid backdoor set empty_set = set() check = graph.check_valid_backdoor_set( treatment_name, outcome_name, empty_set, backdoor_paths=backdoor_paths, new_graph=bdoor_graph, dseparation_algo=dseparation_algo, ) if check["is_dseparated"]: backdoor_sets.append({"backdoor_set": empty_set}) # If the method is `minimal-adjustment`, return the empty set right away. if backdoor_adjustment == BackdoorAdjustment.BACKDOOR_MIN: return backdoor_sets # Second, checking for all other sets of variables. If include_unobserved is false, then only observed variables are eligible. eligible_variables = ( graph.get_all_nodes(include_unobserved=include_unobserved) - set(treatment_name) - set(outcome_name) ) if direct_effect: # only remove descendants of Y # also allow any causes of Y that are not caused by T (for lower variance) eligible_variables -= graph.get_descendants(outcome_name) else: # remove descendants of T (mediators) and descendants of Y eligible_variables -= graph.get_descendants(treatment_name) # If var is d-separated from both treatment or outcome, it cannot # be a part of the backdoor set filt_eligible_variables = set() for var in eligible_variables: dsep_treat_var = graph.check_dseparation(treatment_name, parse_state(var), set()) dsep_outcome_var = graph.check_dseparation(outcome_name, parse_state(var), set()) if not dsep_outcome_var or not dsep_treat_var: filt_eligible_variables.add(var) if backdoor_adjustment in METHOD_NAMES: backdoor_sets, found_valid_adjustment_set = find_valid_adjustment_sets( graph, treatment_name, outcome_name, backdoor_paths, bdoor_graph, dseparation_algo, backdoor_sets, filt_eligible_variables, backdoor_adjustment=backdoor_adjustment, max_iterations=MAX_BACKDOOR_ITERATIONS, ) if backdoor_adjustment == BackdoorAdjustment.BACKDOOR_DEFAULT and found_valid_adjustment_set: # repeat the above search with BACKDOOR_MIN backdoor_sets, _ = find_valid_adjustment_sets( graph, treatment_name, outcome_name, backdoor_paths, bdoor_graph, dseparation_algo, backdoor_sets, filt_eligible_variables, backdoor_adjustment=BackdoorAdjustment.BACKDOOR_MIN, max_iterations=MAX_BACKDOOR_ITERATIONS, ) else: raise ValueError( f"Identifier method {backdoor_adjustment} not supported. Try one of the following: {METHOD_NAMES}" ) return backdoor_sets def identify_efficient_backdoor( graph: CausalGraph, backdoor_adjustment: BackdoorAdjustment, costs: List, conditional_node_names: List[str] = None, ): """Method implementing algorithms to compute efficient backdoor sets, as described in Rotnitzky and Smucler (2020), Smucler, Sapienza and Rotnitzky (2021) and Smucler and Rotnitzky (2022). For backdoor_adjustment='efficient-adjustment', computes an optimal backdoor set, that is, a backdoor set comprised of observable variables that yields non-parametric estimators of the interventional mean with the smallest asymptotic variance among those that are based on observable backdoor sets. This optimal backdoor set always exists when no variables are latent, and the algorithm is guaranteed to compute it in this case. Under a non-parametric graphical model with latent variables, such a backdoor set can fail to exist. When certain sufficient conditions under which it is known that such a backdoor set exists are not satisfied, an error is raised. For backdoor_adjustment='efficient-minimal-adjustment', computes an optimal minimal backdoor set, that is, a minimal backdoor set comprised of observable variables that yields non-parametric estimators of the interventional mean with the smallest asymptotic variance among those that are based on observable minimal backdoor sets. For backdoor_adjustment='efficient-mincost-adjustment', computes an optimal minimum cost backdoor set, that is, a minimum cost backdoor set comprised of observable variables that yields non-parametric estimators of the interventional mean with the smallest asymptotic variance among those that are based on observable minimum cost backdoor sets. The cost of a backdoor set is defined as the sum of the costs of the variables that comprise it. The various optimal backdoor sets computed by this method are not only optimal under non-parametric graphical models and non-parametric estimators of interventional mean, but also under linear graphical models and OLS estimators, per results in Henckel, Perkovic and Maathuis (2020). :param costs: a list with non-negative costs associated with variables in the graph. Only used for estimatand_type='non-parametric-ate' and backdoor_adjustment='efficient-mincost-adjustment'. If not costs are provided by the user, and backdoor_adjustment='efficient-mincost-adjustment', costs are assumed to be equal to one for all variables in the graph. The structure of the list should be of the form [(node, {"cost": x}) for node in nodes]. :param conditional_node_names: variables that are used to determine treatment. If none are provided, it is assumed that the intervention sets the treatment to a constant. :returns: backdoor_sets, a list of dictionaries, with each dictionary having as values a backdoor set. """ if costs is None and backdoor_adjustment == "efficient-mincost-adjustment": logger.warning("No costs were passed, so they will be assumed to be constant and equal to 1.") efficient_bd = EfficientBackdoor( graph=graph, conditional_node_names=conditional_node_names, costs=costs, ) if backdoor_adjustment == BackdoorAdjustment.BACKDOOR_EFFICIENT: backdoor_set = efficient_bd.optimal_adj_set() backdoor_sets = [{"backdoor_set": tuple(backdoor_set)}] elif backdoor_adjustment == BackdoorAdjustment.BACKDOOR_MIN_EFFICIENT: backdoor_set = efficient_bd.optimal_minimal_adj_set() backdoor_sets = [{"backdoor_set": tuple(backdoor_set)}] elif backdoor_adjustment == BackdoorAdjustment.BACKDOOR_MINCOST_EFFICIENT: backdoor_set = efficient_bd.optimal_mincost_adj_set() backdoor_sets = [{"backdoor_set": tuple(backdoor_set)}] return backdoor_sets def find_valid_adjustment_sets( graph: CausalGraph, treatment_name: List, outcome_name: List, backdoor_paths: List, bdoor_graph: CausalGraph, dseparation_algo: str, backdoor_sets: List, filt_eligible_variables: List, backdoor_adjustment: BackdoorAdjustment, max_iterations: int, ): num_iterations = 0 found_valid_adjustment_set = False all_nodes_observed = graph.all_observed(graph.get_all_nodes()) # If `minimal-adjustment` method is specified, start the search from the set with minimum size. Otherwise, start from the largest. set_sizes = ( range(1, len(filt_eligible_variables) + 1, 1) if backdoor_adjustment == BackdoorAdjustment.BACKDOOR_MIN else range(len(filt_eligible_variables), 0, -1) ) for size_candidate_set in set_sizes: for candidate_set in itertools.combinations(filt_eligible_variables, size_candidate_set): check = graph.check_valid_backdoor_set( treatment_name, outcome_name, candidate_set, backdoor_paths=backdoor_paths, new_graph=bdoor_graph, dseparation_algo=dseparation_algo, ) logger.debug( "Candidate backdoor set: {0}, is_dseparated: {1}".format(candidate_set, check["is_dseparated"]) ) if check["is_dseparated"]: backdoor_sets.append({"backdoor_set": candidate_set}) found_valid_adjustment_set = True num_iterations += 1 if backdoor_adjustment == BackdoorAdjustment.BACKDOOR_EXHAUSTIVE and num_iterations > max_iterations: logger.warning(f"Max number of iterations {max_iterations} reached.") break # If the backdoor method is `maximal-adjustment` or `minimal-adjustment`, return the first found adjustment set. if ( backdoor_adjustment in { BackdoorAdjustment.BACKDOOR_DEFAULT, BackdoorAdjustment.BACKDOOR_MAX, BackdoorAdjustment.BACKDOOR_MIN, } and found_valid_adjustment_set ): break # If all variables are observed, and the biggest eligible set # does not satisfy backdoor, then none of its subsets will. if ( backdoor_adjustment in {BackdoorAdjustment.BACKDOOR_DEFAULT, BackdoorAdjustment.BACKDOOR_MAX} and all_nodes_observed ): break if num_iterations > max_iterations: logger.warning(f"Max number of iterations {max_iterations} reached. Could not find a valid backdoor set.") break return backdoor_sets, found_valid_adjustment_set def get_default_backdoor_set_id( graph: CausalGraph, treatment_name: List[str], outcome_name: List[str], backdoor_sets_dict: Dict ): # Adding a None estimand if no backdoor set found if len(backdoor_sets_dict) == 0: return None # Default set contains minimum possible number of instrumental variables, to prevent lowering variance in the treatment variable. instrument_names = set(graph.get_instruments(treatment_name, outcome_name)) iv_count_dict = { key: len(set(bdoor_set).intersection(instrument_names)) for key, bdoor_set in backdoor_sets_dict.items() } min_iv_count = min(iv_count_dict.values()) min_iv_keys = {key for key, iv_count in iv_count_dict.items() if iv_count == min_iv_count} min_iv_backdoor_sets_dict = {key: backdoor_sets_dict[key] for key in min_iv_keys} # Default set is the one with the least number of adjustment variables (optimizing for efficiency) min_set_length = 1000000 default_key = None for key, bdoor_set in min_iv_backdoor_sets_dict.items(): if len(bdoor_set) < min_set_length: min_set_length = len(bdoor_set) default_key = key return default_key def build_backdoor_estimands_dict( graph: CausalGraph, treatment_name: List[str], outcome_name: List[str], backdoor_sets: List[str], estimands_dict: Dict, ): """Build the final dict for backdoor sets by filtering unobserved variables if needed.""" backdoor_variables_dict = {} is_identified = [graph.all_observed(bset["backdoor_set"]) for bset in backdoor_sets] if any(is_identified): logger.info("Causal effect can be identified.") backdoor_sets_arr = [ list(bset["backdoor_set"]) for bset in backdoor_sets if graph.all_observed(bset["backdoor_set"]) ] else: # there is unobserved confounding logger.warning("Backdoor identification failed.") backdoor_sets_arr = [] for i in range(len(backdoor_sets_arr)): backdoor_estimand_expr = construct_backdoor_estimand(treatment_name, outcome_name, backdoor_sets_arr[i]) logger.debug("Identified expression = " + str(backdoor_estimand_expr)) estimands_dict["backdoor" + str(i + 1)] = backdoor_estimand_expr backdoor_variables_dict["backdoor" + str(i + 1)] = backdoor_sets_arr[i] return estimands_dict, backdoor_variables_dict def identify_frontdoor( graph: CausalGraph, treatment_name: List[str], outcome_name: List[str], dseparation_algo: str = "default" ): """Find a valid frontdoor variable if it exists. Currently only supports a single variable frontdoor set. """ frontdoor_var = None frontdoor_paths = None fdoor_graph = None if dseparation_algo == "default": cond1_graph = graph.do_surgery(treatment_name, remove_incoming_edges=True) bdoor_graph1 = graph.do_surgery(treatment_name, remove_outgoing_edges=True) elif dseparation_algo == "naive": frontdoor_paths = graph.get_all_directed_paths(treatment_name, outcome_name) else: raise ValueError(f"d-separation algorithm {dseparation_algo} is not supported") eligible_variables = ( graph.get_descendants(treatment_name) - set(outcome_name) - set(graph.get_descendants(outcome_name)) ) # For simplicity, assuming a one-variable frontdoor set for candidate_var in eligible_variables: # Cond 1: All directed paths intercepted by candidate_var cond1 = graph.check_valid_frontdoor_set( treatment_name, outcome_name, parse_state(candidate_var), frontdoor_paths=frontdoor_paths, new_graph=cond1_graph, dseparation_algo=dseparation_algo, ) logger.debug("Candidate frontdoor set: {0}, is_dseparated: {1}".format(candidate_var, cond1)) if not cond1: continue # Cond 2: No confounding between treatment and candidate var cond2 = graph.check_valid_backdoor_set( treatment_name, parse_state(candidate_var), set(), backdoor_paths=None, new_graph=bdoor_graph1, dseparation_algo=dseparation_algo, ) if not cond2: continue # Cond 3: treatment blocks all confounding between candidate_var and outcome bdoor_graph2 = graph.do_surgery(candidate_var, remove_outgoing_edges=True) cond3 = graph.check_valid_backdoor_set( parse_state(candidate_var), outcome_name, treatment_name, backdoor_paths=None, new_graph=bdoor_graph2, dseparation_algo=dseparation_algo, ) is_valid_frontdoor = cond1 and cond2 and cond3 if is_valid_frontdoor: frontdoor_var = candidate_var break return parse_state(frontdoor_var) def identify_mediation(graph: CausalGraph, treatment_name: List[str], outcome_name: List[str]): """Find a valid mediator if it exists. Currently only supports a single variable mediator set. """ mediation_var = None mediation_paths = graph.get_all_directed_paths(treatment_name, outcome_name) eligible_variables = graph.get_descendants(treatment_name) - set(outcome_name) # For simplicity, assuming a one-variable mediation set for candidate_var in eligible_variables: is_valid_mediation = graph.check_valid_mediation_set( treatment_name, outcome_name, parse_state(candidate_var), mediation_paths=mediation_paths, ) logger.debug("Candidate mediation set: {0}, on_mediating_path: {1}".format(candidate_var, is_valid_mediation)) if is_valid_mediation: mediation_var = candidate_var break return parse_state(mediation_var) def identify_mediation_first_stage_confounders( graph: CausalGraph, treatment_name: List[str], outcome_name: List[str], mediators_names: List[str], backdoor_adjustment: BackdoorAdjustment, ): # Create estimands dict as per the API for backdoor, but do not return it estimands_dict = {} backdoor_sets = identify_backdoor(graph, treatment_name, mediators_names, backdoor_adjustment) estimands_dict, backdoor_variables_dict = build_backdoor_estimands_dict( graph, treatment_name, mediators_names, backdoor_sets, estimands_dict, ) # Setting default "backdoor" identification adjustment set default_backdoor_id = get_default_backdoor_set_id(graph, treatment_name, outcome_name, backdoor_variables_dict) estimands_dict["backdoor"] = estimands_dict.get(str(default_backdoor_id), None) backdoor_variables_dict["backdoor"] = backdoor_variables_dict.get(str(default_backdoor_id), None) return backdoor_variables_dict def identify_mediation_second_stage_confounders( graph: CausalGraph, treatment_name: List[str], mediators_names: List[str], outcome_name: List[str], backdoor_adjustment: BackdoorAdjustment, ): # Create estimands dict as per the API for backdoor, but do not return it estimands_dict = {} backdoor_sets = identify_backdoor(graph, mediators_names, outcome_name, backdoor_adjustment) estimands_dict, backdoor_variables_dict = build_backdoor_estimands_dict( graph, mediators_names, outcome_name, backdoor_sets, estimands_dict, ) # Setting default "backdoor" identification adjustment set default_backdoor_id = get_default_backdoor_set_id(graph, treatment_name, outcome_name, backdoor_variables_dict) estimands_dict["backdoor"] = estimands_dict.get(str(default_backdoor_id), None) backdoor_variables_dict["backdoor"] = backdoor_variables_dict.get(str(default_backdoor_id), None) return backdoor_variables_dict def construct_backdoor_estimand(treatment_name: List[str], outcome_name: List[str], common_causes: List[str]): # TODO: outputs string for now, but ideally should do symbolic # expressions Mon 19 Feb 2018 04:54:17 PM DST # TODO Better support for multivariate treatments expr = None outcome_name = outcome_name[0] num_expr_str = outcome_name if len(common_causes) > 0: num_expr_str += "|" + ",".join(common_causes) expr = "d(" + num_expr_str + ")/d" + ",".join(treatment_name) sym_mu = sp.Symbol("mu") sym_sigma = sp.Symbol("sigma", positive=True) sym_outcome = spstats.Normal(num_expr_str, sym_mu, sym_sigma) sym_treatment_symbols = [sp.Symbol(t) for t in treatment_name] sym_treatment = sp.Array(sym_treatment_symbols) sym_conditional_outcome = spstats.Expectation(sym_outcome) sym_effect = sp.Derivative(sym_conditional_outcome, sym_treatment) sym_assumptions = { "Unconfoundedness": ( "If U\N{RIGHTWARDS ARROW}{{{0}}} and U\N{RIGHTWARDS ARROW}{1}" " then P({1}|{0},{2},U) = P({1}|{0},{2})" ).format(",".join(treatment_name), outcome_name, ",".join(common_causes)) } estimand = {"estimand": sym_effect, "assumptions": sym_assumptions} return estimand def construct_iv_estimand(treatment_name: List[str], outcome_name: List[str], instrument_names: List[str]): # TODO: support multivariate treatments better. expr = None outcome_name = outcome_name[0] sym_outcome = spstats.Normal(outcome_name, 0, 1) sym_treatment_symbols = [spstats.Normal(t, 0, 1) for t in treatment_name] sym_treatment = sp.Array(sym_treatment_symbols) sym_instrument_symbols = [sp.Symbol(inst) for inst in instrument_names] sym_instrument = sp.Array(sym_instrument_symbols) # ",".join(instrument_names)) sym_outcome_derivative = sp.Derivative(sym_outcome, sym_instrument) sym_treatment_derivative = sp.Derivative(sym_treatment, sym_instrument) sym_effect = spstats.Expectation(sym_outcome_derivative / sym_treatment_derivative) sym_assumptions = { "As-if-random": ( "If U\N{RIGHTWARDS ARROW}\N{RIGHTWARDS ARROW}{0} then " "\N{NOT SIGN}(U \N{RIGHTWARDS ARROW}\N{RIGHTWARDS ARROW}{{{1}}})" ).format(outcome_name, ",".join(instrument_names)), "Exclusion": ( "If we remove {{{0}}}\N{RIGHTWARDS ARROW}{{{1}}}, then " "\N{NOT SIGN}({{{0}}}\N{RIGHTWARDS ARROW}{2})" ).format(",".join(instrument_names), ",".join(treatment_name), outcome_name), } estimand = {"estimand": sym_effect, "assumptions": sym_assumptions} return estimand def construct_frontdoor_estimand( treatment_name: List[str], outcome_name: List[str], frontdoor_variables_names: List[str] ): # TODO: support multivariate treatments better. expr = None outcome_name = outcome_name[0] sym_outcome = spstats.Normal(outcome_name, 0, 1) sym_treatment_symbols = [spstats.Normal(t, 0, 1) for t in treatment_name] sym_treatment = sp.Array(sym_treatment_symbols) sym_frontdoor_symbols = [sp.Symbol(inst) for inst in frontdoor_variables_names] sym_frontdoor = sp.Array(sym_frontdoor_symbols) # ",".join(instrument_names)) sym_outcome_derivative = sp.Derivative(sym_outcome, sym_frontdoor) sym_treatment_derivative = sp.Derivative(sym_frontdoor, sym_treatment) sym_effect = spstats.Expectation(sym_treatment_derivative * sym_outcome_derivative) sym_assumptions = { "Full-mediation": ("{2} intercepts (blocks) all directed paths from {0} to {1}.").format( ",".join(treatment_name), ",".join(outcome_name), ",".join(frontdoor_variables_names), ), "First-stage-unconfoundedness": ( "If U\N{RIGHTWARDS ARROW}{{{0}}} and U\N{RIGHTWARDS ARROW}{{{1}}}" " then P({1}|{0},U) = P({1}|{0})" ).format(",".join(treatment_name), ",".join(frontdoor_variables_names)), "Second-stage-unconfoundedness": ( "If U\N{RIGHTWARDS ARROW}{{{2}}} and U\N{RIGHTWARDS ARROW}{1}" " then P({1}|{2}, {0}, U) = P({1}|{2}, {0})" ).format( ",".join(treatment_name), outcome_name, ",".join(frontdoor_variables_names), ), } estimand = {"estimand": sym_effect, "assumptions": sym_assumptions} return estimand def construct_mediation_estimand( estimand_type: EstimandType, treatment_name: List[str], outcome_name: List[str], mediators_names: List[str] ): # TODO: support multivariate treatments better. expr = None if estimand_type in ( EstimandType.NONPARAMETRIC_NDE, EstimandType.NONPARAMETRIC_NIE, ): outcome_name = outcome_name[0] sym_outcome = spstats.Normal(outcome_name, 0, 1) sym_treatment_symbols = [spstats.Normal(t, 0, 1) for t in treatment_name] sym_treatment = sp.Array(sym_treatment_symbols) sym_mediators_symbols = [sp.Symbol(inst) for inst in mediators_names] sym_mediators = sp.Array(sym_mediators_symbols) sym_outcome_derivative = sp.Derivative(sym_outcome, sym_mediators) sym_treatment_derivative = sp.Derivative(sym_mediators, sym_treatment) # For direct effect num_expr_str = outcome_name if len(mediators_names) > 0: num_expr_str += "|" + ",".join(mediators_names) sym_mu = sp.Symbol("mu") sym_sigma = sp.Symbol("sigma", positive=True) sym_conditional_outcome = spstats.Normal(num_expr_str, sym_mu, sym_sigma) sym_directeffect_derivative = sp.Derivative(sym_conditional_outcome, sym_treatment) if estimand_type == EstimandType.NONPARAMETRIC_NIE: sym_effect = spstats.Expectation(sym_treatment_derivative * sym_outcome_derivative) elif estimand_type == EstimandType.NONPARAMETRIC_NDE: sym_effect = spstats.Expectation(sym_directeffect_derivative) sym_assumptions = { "Mediation": ( "{2} intercepts (blocks) all directed paths from {0} to {1} except the path {{{0}}}\N{RIGHTWARDS ARROW}{{{1}}}." ).format( ",".join(treatment_name), ",".join(outcome_name), ",".join(mediators_names), ), "First-stage-unconfoundedness": ( "If U\N{RIGHTWARDS ARROW}{{{0}}} and U\N{RIGHTWARDS ARROW}{{{1}}}" " then P({1}|{0},U) = P({1}|{0})" ).format(",".join(treatment_name), ",".join(mediators_names)), "Second-stage-unconfoundedness": ( "If U\N{RIGHTWARDS ARROW}{{{2}}} and U\N{RIGHTWARDS ARROW}{1}" " then P({1}|{2}, {0}, U) = P({1}|{2}, {0})" ).format(",".join(treatment_name), outcome_name, ",".join(mediators_names)), } else: raise ValueError( "Estimand type not supported. Supported estimand types are {0} or {1}'.".format( EstimandType.NONPARAMETRIC_NDE, EstimandType.NONPARAMETRIC_NIE, ) ) estimand = {"estimand": sym_effect, "assumptions": sym_assumptions} return estimand

import itertools import logging from enum import Enum from typing import Dict, List, Optional, Union import sympy as sp import sympy.stats as spstats from dowhy.causal_graph import CausalGraph from dowhy.causal_identifier.efficient_backdoor import EfficientBackdoor from dowhy.causal_identifier.identified_estimand import IdentifiedEstimand from dowhy.utils.api import parse_state logger = logging.getLogger(__name__) class EstimandType(Enum): # Average total effect NONPARAMETRIC_ATE = "nonparametric-ate" # Natural direct effect NONPARAMETRIC_NDE = "nonparametric-nde" # Natural indirect effect NONPARAMETRIC_NIE = "nonparametric-nie" # Controlled direct effect NONPARAMETRIC_CDE = "nonparametric-cde" class BackdoorAdjustment(Enum): # Backdoor method names BACKDOOR_DEFAULT = "default" BACKDOOR_EXHAUSTIVE = "exhaustive-search" BACKDOOR_MIN = "minimal-adjustment" BACKDOOR_MAX = "maximal-adjustment" BACKDOOR_EFFICIENT = "efficient-adjustment" BACKDOOR_MIN_EFFICIENT = "efficient-minimal-adjustment" BACKDOOR_MINCOST_EFFICIENT = "efficient-mincost-adjustment" MAX_BACKDOOR_ITERATIONS = 100000 METHOD_NAMES = { BackdoorAdjustment.BACKDOOR_DEFAULT, BackdoorAdjustment.BACKDOOR_EXHAUSTIVE, BackdoorAdjustment.BACKDOOR_MIN, BackdoorAdjustment.BACKDOOR_MAX, BackdoorAdjustment.BACKDOOR_EFFICIENT, BackdoorAdjustment.BACKDOOR_MIN_EFFICIENT, BackdoorAdjustment.BACKDOOR_MINCOST_EFFICIENT, } EFFICIENT_METHODS = { BackdoorAdjustment.BACKDOOR_EFFICIENT, BackdoorAdjustment.BACKDOOR_MIN_EFFICIENT, BackdoorAdjustment.BACKDOOR_MINCOST_EFFICIENT, } DEFAULT_BACKDOOR_METHOD = BackdoorAdjustment.BACKDOOR_DEFAULT class AutoIdentifier: """Class that implements different identification methods. Currently supports backdoor and instrumental variable identification methods. The identification is based on the causal graph provided. This class is for backwards compatibility with CausalModel Will be deprecated in the future in favor of function call auto_identify_effect() """ def __init__( self, estimand_type: EstimandType, backdoor_adjustment: BackdoorAdjustment = BackdoorAdjustment.BACKDOOR_DEFAULT, proceed_when_unidentifiable: bool = False, optimize_backdoor: bool = False, costs: Optional[List] = None, ): self.estimand_type = estimand_type self.backdoor_adjustment = backdoor_adjustment self._proceed_when_unidentifiable = proceed_when_unidentifiable self.optimize_backdoor = optimize_backdoor self.costs = costs self.logger = logging.getLogger(__name__) def identify_effect( self, graph: CausalGraph, treatment_name: Union[str, List[str]], outcome_name: Union[str, List[str]], conditional_node_names: List[str] = None, **kwargs, ): estimand = identify_effect_auto( graph, treatment_name, outcome_name, self.estimand_type, conditional_node_names, self.backdoor_adjustment, self._proceed_when_unidentifiable, self.optimize_backdoor, self.costs, **kwargs, ) estimand.identifier = self return estimand def identify_backdoor( self, graph: CausalGraph, treatment_name: List[str], outcome_name: str, include_unobserved: bool = False, dseparation_algo: str = "default", direct_effect: bool = False, ): return identify_backdoor( graph, treatment_name, outcome_name, self.backdoor_adjustment, include_unobserved, dseparation_algo, direct_effect, ) def identify_effect_auto( graph: CausalGraph, treatment_name: Union[str, List[str]], outcome_name: Union[str, List[str]], estimand_type: EstimandType, conditional_node_names: List[str] = None, backdoor_adjustment: BackdoorAdjustment = BackdoorAdjustment.BACKDOOR_DEFAULT, proceed_when_unidentifiable: bool = False, optimize_backdoor: bool = False, costs: Optional[List] = None, **kwargs, ) -> IdentifiedEstimand: """Main method that returns an identified estimand (if one exists). If estimand_type is non-parametric ATE, then uses backdoor, instrumental variable and frontdoor identification methods, to check if an identified estimand exists, based on the causal graph. :param optimize_backdoor: if True, uses an optimised algorithm to compute the backdoor sets :param costs: non-negative costs associated with variables in the graph. Only used for estimand_type='non-parametric-ate' and backdoor_adjustment='efficient-mincost-adjustment'. If no costs are provided by the user, and backdoor_adjustment='efficient-mincost-adjustment', costs are assumed to be equal to one for all variables in the graph. :param conditional_node_names: variables that are used to determine treatment. If none are provided, it is assumed that the intervention is static. :returns: target estimand, an instance of the IdentifiedEstimand class """ treatment_name = parse_state(treatment_name) outcome_name = parse_state(outcome_name) # First, check if there is a directed path from action to outcome if not graph.has_directed_path(treatment_name, outcome_name): logger.warn("No directed path from treatment to outcome. Causal Effect is zero.") return IdentifiedEstimand( None, treatment_variable=treatment_name, outcome_variable=outcome_name, no_directed_path=True, ) if estimand_type == EstimandType.NONPARAMETRIC_ATE: return identify_ate_effect( graph, treatment_name, outcome_name, backdoor_adjustment, optimize_backdoor, estimand_type, costs, conditional_node_names, proceed_when_unidentifiable, ) elif estimand_type == EstimandType.NONPARAMETRIC_NDE: return identify_nde_effect( graph, treatment_name, outcome_name, backdoor_adjustment, estimand_type, proceed_when_unidentifiable ) elif estimand_type == EstimandType.NONPARAMETRIC_NIE: return identify_nie_effect( graph, treatment_name, outcome_name, backdoor_adjustment, estimand_type, proceed_when_unidentifiable ) elif estimand_type == EstimandType.NONPARAMETRIC_CDE: return identify_cde_effect( graph, treatment_name, outcome_name, backdoor_adjustment, estimand_type, proceed_when_unidentifiable ) else: raise ValueError( "Estimand type is not supported. Use either {0}, {1}, or {2}.".format( EstimandType.NONPARAMETRIC_ATE, EstimandType.NONPARAMETRIC_CDE, EstimandType.NONPARAMETRIC_NDE, EstimandType.NONPARAMETRIC_NIE, ) ) def identify_ate_effect( graph: CausalGraph, treatment_name: List[str], outcome_name: str, backdoor_adjustment: BackdoorAdjustment, optimize_backdoor: bool, estimand_type: EstimandType, costs: List, conditional_node_names: List[str] = None, proceed_when_unidentifiable: bool = False, ): estimands_dict = {} mediation_first_stage_confounders = None mediation_second_stage_confounders = None ### 1. BACKDOOR IDENTIFICATION # Pick algorithm to compute backdoor sets according to method chosen if backdoor_adjustment not in EFFICIENT_METHODS: # First, checking if there are any valid backdoor adjustment sets if optimize_backdoor == False: backdoor_sets = identify_backdoor(graph, treatment_name, outcome_name, backdoor_adjustment) else: from dowhy.causal_identifier.backdoor import Backdoor path = Backdoor(graph._graph, treatment_name, outcome_name) backdoor_sets = path.get_backdoor_vars() elif backdoor_adjustment in EFFICIENT_METHODS: backdoor_sets = identify_efficient_backdoor( graph, backdoor_adjustment, costs, conditional_node_names=conditional_node_names ) estimands_dict, backdoor_variables_dict = build_backdoor_estimands_dict( graph, treatment_name, outcome_name, backdoor_sets, estimands_dict ) # Setting default "backdoor" identification adjustment set default_backdoor_id = get_default_backdoor_set_id(graph, treatment_name, outcome_name, backdoor_variables_dict) if len(backdoor_variables_dict) > 0: estimands_dict["backdoor"] = estimands_dict.get(str(default_backdoor_id), None) backdoor_variables_dict["backdoor"] = backdoor_variables_dict.get(str(default_backdoor_id), None) else: estimands_dict["backdoor"] = None ### 2. INSTRUMENTAL VARIABLE IDENTIFICATION # Now checking if there is also a valid iv estimand instrument_names = graph.get_instruments(treatment_name, outcome_name) logger.info("Instrumental variables for treatment and outcome:" + str(instrument_names)) if len(instrument_names) > 0: iv_estimand_expr = construct_iv_estimand( treatment_name, outcome_name, instrument_names, ) logger.debug("Identified expression = " + str(iv_estimand_expr)) estimands_dict["iv"] = iv_estimand_expr else: estimands_dict["iv"] = None ### 3. FRONTDOOR IDENTIFICATION # Now checking if there is a valid frontdoor variable frontdoor_variables_names = identify_frontdoor(graph, treatment_name, outcome_name) logger.info("Frontdoor variables for treatment and outcome:" + str(frontdoor_variables_names)) if len(frontdoor_variables_names) > 0: frontdoor_estimand_expr = construct_frontdoor_estimand( treatment_name, outcome_name, frontdoor_variables_names, ) logger.debug("Identified expression = " + str(frontdoor_estimand_expr)) estimands_dict["frontdoor"] = frontdoor_estimand_expr mediation_first_stage_confounders = identify_mediation_first_stage_confounders( graph, treatment_name, outcome_name, frontdoor_variables_names, backdoor_adjustment ) mediation_second_stage_confounders = identify_mediation_second_stage_confounders( graph, treatment_name, frontdoor_variables_names, outcome_name, backdoor_adjustment ) else: estimands_dict["frontdoor"] = None # Finally returning the estimand object estimand = IdentifiedEstimand( None, treatment_variable=treatment_name, outcome_variable=outcome_name, estimand_type=estimand_type, estimands=estimands_dict, backdoor_variables=backdoor_variables_dict, instrumental_variables=instrument_names, frontdoor_variables=frontdoor_variables_names, mediation_first_stage_confounders=mediation_first_stage_confounders, mediation_second_stage_confounders=mediation_second_stage_confounders, default_backdoor_id=default_backdoor_id, ) return estimand def identify_cde_effect( graph: CausalGraph, treatment_name: List[str], outcome_name: str, backdoor_adjustment: BackdoorAdjustment, estimand_type: EstimandType, proceed_when_unidentifiable: bool = False, ): """Identify controlled direct effect. For a definition, see Vanderwheele (2011). Controlled direct and mediated effects: definition, identification and bounds. https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4193506/ Using do-calculus rules, identification yields a adjustment set. It is based on the principle that under a graph where the direct edge from treatment to outcome is removed, conditioning on the adjustment set should d-separate treatment and outcome. """ estimands_dict = {} # Pick algorithm to compute backdoor sets according to method chosen backdoor_sets = identify_backdoor(graph, treatment_name, outcome_name, backdoor_adjustment, direct_effect=True) estimands_dict, backdoor_variables_dict = build_backdoor_estimands_dict( graph, treatment_name, outcome_name, backdoor_sets, estimands_dict ) # Setting default "backdoor" identification adjustment set default_backdoor_id = get_default_backdoor_set_id(graph, treatment_name, outcome_name, backdoor_variables_dict) if len(backdoor_variables_dict) > 0: estimands_dict["backdoor"] = estimands_dict.get(str(default_backdoor_id), None) backdoor_variables_dict["backdoor"] = backdoor_variables_dict.get(str(default_backdoor_id), None) else: estimands_dict["backdoor"] = None # Finally returning the estimand object estimand = IdentifiedEstimand( None, treatment_variable=treatment_name, outcome_variable=outcome_name, estimand_type=estimand_type, estimands=estimands_dict, backdoor_variables=backdoor_variables_dict, instrumental_variables=None, frontdoor_variables=None, mediation_first_stage_confounders=None, mediation_second_stage_confounders=None, default_backdoor_id=default_backdoor_id, ) return estimand def identify_nie_effect( graph: CausalGraph, treatment_name: List[str], outcome_name: str, backdoor_adjustment: BackdoorAdjustment, estimand_type: EstimandType, proceed_when_unidentifiable: bool = False, ): estimands_dict = {} ### 1. FIRST DOING BACKDOOR IDENTIFICATION # First, checking if there are any valid backdoor adjustment sets backdoor_sets = identify_backdoor(graph, treatment_name, outcome_name, backdoor_adjustment) estimands_dict, backdoor_variables_dict = build_backdoor_estimands_dict( graph, treatment_name, outcome_name, backdoor_sets, estimands_dict ) # Setting default "backdoor" identification adjustment set default_backdoor_id = get_default_backdoor_set_id(graph, treatment_name, outcome_name, backdoor_variables_dict) backdoor_variables_dict["backdoor"] = backdoor_variables_dict.get(str(default_backdoor_id), None) ### 2. SECOND, CHECKING FOR MEDIATORS # Now checking if there are valid mediator variables estimands_dict = {} # Need to reinitialize this dictionary to avoid including the backdoor sets mediation_first_stage_confounders = None mediation_second_stage_confounders = None mediators_names = identify_mediation(graph, treatment_name, outcome_name) logger.info("Mediators for treatment and outcome:" + str(mediators_names)) if len(mediators_names) > 0: mediation_estimand_expr = construct_mediation_estimand( estimand_type, treatment_name, outcome_name, mediators_names, ) logger.debug("Identified expression = " + str(mediation_estimand_expr)) estimands_dict["mediation"] = mediation_estimand_expr mediation_first_stage_confounders = identify_mediation_first_stage_confounders( graph, treatment_name, outcome_name, mediators_names, backdoor_adjustment ) mediation_second_stage_confounders = identify_mediation_second_stage_confounders( graph, treatment_name, mediators_names, outcome_name, backdoor_adjustment ) else: estimands_dict["mediation"] = None # Finally returning the estimand object estimand = IdentifiedEstimand( None, treatment_variable=treatment_name, outcome_variable=outcome_name, estimand_type=estimand_type, estimands=estimands_dict, backdoor_variables=backdoor_variables_dict, instrumental_variables=None, frontdoor_variables=None, mediator_variables=mediators_names, mediation_first_stage_confounders=mediation_first_stage_confounders, mediation_second_stage_confounders=mediation_second_stage_confounders, default_backdoor_id=None, ) return estimand def identify_nde_effect( graph: CausalGraph, treatment_name: List[str], outcome_name: str, backdoor_adjustment: BackdoorAdjustment, estimand_type: EstimandType, proceed_when_unidentifiable: bool = False, ): estimands_dict = {} ### 1. FIRST DOING BACKDOOR IDENTIFICATION # First, checking if there are any valid backdoor adjustment sets backdoor_sets = identify_backdoor(graph, treatment_name, outcome_name, backdoor_adjustment) estimands_dict, backdoor_variables_dict = build_backdoor_estimands_dict( graph, treatment_name, outcome_name, backdoor_sets, estimands_dict ) # Setting default "backdoor" identification adjustment set default_backdoor_id = get_default_backdoor_set_id(graph, treatment_name, outcome_name, backdoor_variables_dict) backdoor_variables_dict["backdoor"] = backdoor_variables_dict.get(str(default_backdoor_id), None) ### 2. SECOND, CHECKING FOR MEDIATORS # Now checking if there are valid mediator variables estimands_dict = {} mediation_first_stage_confounders = None mediation_second_stage_confounders = None mediators_names = identify_mediation(graph, treatment_name, outcome_name) logger.info("Mediators for treatment and outcome:" + str(mediators_names)) if len(mediators_names) > 0: mediation_estimand_expr = construct_mediation_estimand( estimand_type, treatment_name, outcome_name, mediators_names, ) logger.debug("Identified expression = " + str(mediation_estimand_expr)) estimands_dict["mediation"] = mediation_estimand_expr mediation_first_stage_confounders = identify_mediation_first_stage_confounders( graph, treatment_name, outcome_name, mediators_names, backdoor_adjustment ) mediation_second_stage_confounders = identify_mediation_second_stage_confounders( graph, treatment_name, mediators_names, outcome_name, backdoor_adjustment ) else: estimands_dict["mediation"] = None # Finally returning the estimand object estimand = IdentifiedEstimand( None, treatment_variable=treatment_name, outcome_variable=outcome_name, estimand_type=estimand_type, estimands=estimands_dict, backdoor_variables=backdoor_variables_dict, instrumental_variables=None, frontdoor_variables=None, mediator_variables=mediators_names, mediation_first_stage_confounders=mediation_first_stage_confounders, mediation_second_stage_confounders=mediation_second_stage_confounders, default_backdoor_id=None, ) return estimand def identify_backdoor( graph: CausalGraph, treatment_name: List[str], outcome_name: str, backdoor_adjustment: BackdoorAdjustment, include_unobserved: bool = False, dseparation_algo: str = "default", direct_effect: bool = False, ): backdoor_sets = [] backdoor_paths = None bdoor_graph = None if dseparation_algo == "naive": backdoor_paths = graph.get_backdoor_paths(treatment_name, outcome_name) elif dseparation_algo == "default": bdoor_graph = graph.do_surgery( treatment_name, target_node_names=outcome_name, remove_outgoing_edges=True, remove_only_direct_edges_to_target=direct_effect, ) else: raise ValueError(f"d-separation algorithm {dseparation_algo} is not supported") backdoor_adjustment = ( backdoor_adjustment if backdoor_adjustment != BackdoorAdjustment.BACKDOOR_DEFAULT else DEFAULT_BACKDOOR_METHOD ) # First, checking if empty set is a valid backdoor set empty_set = set() check = graph.check_valid_backdoor_set( treatment_name, outcome_name, empty_set, backdoor_paths=backdoor_paths, new_graph=bdoor_graph, dseparation_algo=dseparation_algo, ) if check["is_dseparated"]: backdoor_sets.append({"backdoor_set": empty_set}) # If the method is `minimal-adjustment`, return the empty set right away. if backdoor_adjustment == BackdoorAdjustment.BACKDOOR_MIN: return backdoor_sets # Second, checking for all other sets of variables. If include_unobserved is false, then only observed variables are eligible. eligible_variables = ( graph.get_all_nodes(include_unobserved=include_unobserved) - set(treatment_name) - set(outcome_name) ) if direct_effect: # only remove descendants of Y # also allow any causes of Y that are not caused by T (for lower variance) eligible_variables -= graph.get_descendants(outcome_name) else: # remove descendants of T (mediators) and descendants of Y eligible_variables -= graph.get_descendants(treatment_name) # If var is d-separated from both treatment or outcome, it cannot # be a part of the backdoor set filt_eligible_variables = set() for var in eligible_variables: dsep_treat_var = graph.check_dseparation(treatment_name, parse_state(var), set()) dsep_outcome_var = graph.check_dseparation(outcome_name, parse_state(var), set()) if not dsep_outcome_var or not dsep_treat_var: filt_eligible_variables.add(var) if backdoor_adjustment in METHOD_NAMES: backdoor_sets, found_valid_adjustment_set = find_valid_adjustment_sets( graph, treatment_name, outcome_name, backdoor_paths, bdoor_graph, dseparation_algo, backdoor_sets, filt_eligible_variables, backdoor_adjustment=backdoor_adjustment, max_iterations=MAX_BACKDOOR_ITERATIONS, ) if backdoor_adjustment == BackdoorAdjustment.BACKDOOR_DEFAULT and found_valid_adjustment_set: # repeat the above search with BACKDOOR_MIN backdoor_sets, _ = find_valid_adjustment_sets( graph, treatment_name, outcome_name, backdoor_paths, bdoor_graph, dseparation_algo, backdoor_sets, filt_eligible_variables, backdoor_adjustment=BackdoorAdjustment.BACKDOOR_MIN, max_iterations=MAX_BACKDOOR_ITERATIONS, ) else: raise ValueError( f"Identifier method {backdoor_adjustment} not supported. Try one of the following: {METHOD_NAMES}" ) return backdoor_sets def identify_efficient_backdoor( graph: CausalGraph, backdoor_adjustment: BackdoorAdjustment, costs: List, conditional_node_names: List[str] = None, ): """Method implementing algorithms to compute efficient backdoor sets, as described in Rotnitzky and Smucler (2020), Smucler, Sapienza and Rotnitzky (2021) and Smucler and Rotnitzky (2022). For backdoor_adjustment='efficient-adjustment', computes an optimal backdoor set, that is, a backdoor set comprised of observable variables that yields non-parametric estimators of the interventional mean with the smallest asymptotic variance among those that are based on observable backdoor sets. This optimal backdoor set always exists when no variables are latent, and the algorithm is guaranteed to compute it in this case. Under a non-parametric graphical model with latent variables, such a backdoor set can fail to exist. When certain sufficient conditions under which it is known that such a backdoor set exists are not satisfied, an error is raised. For backdoor_adjustment='efficient-minimal-adjustment', computes an optimal minimal backdoor set, that is, a minimal backdoor set comprised of observable variables that yields non-parametric estimators of the interventional mean with the smallest asymptotic variance among those that are based on observable minimal backdoor sets. For backdoor_adjustment='efficient-mincost-adjustment', computes an optimal minimum cost backdoor set, that is, a minimum cost backdoor set comprised of observable variables that yields non-parametric estimators of the interventional mean with the smallest asymptotic variance among those that are based on observable minimum cost backdoor sets. The cost of a backdoor set is defined as the sum of the costs of the variables that comprise it. The various optimal backdoor sets computed by this method are not only optimal under non-parametric graphical models and non-parametric estimators of interventional mean, but also under linear graphical models and OLS estimators, per results in Henckel, Perkovic and Maathuis (2020). :param costs: a list with non-negative costs associated with variables in the graph. Only used for estimatand_type='non-parametric-ate' and backdoor_adjustment='efficient-mincost-adjustment'. If not costs are provided by the user, and backdoor_adjustment='efficient-mincost-adjustment', costs are assumed to be equal to one for all variables in the graph. The structure of the list should be of the form [(node, {"cost": x}) for node in nodes]. :param conditional_node_names: variables that are used to determine treatment. If none are provided, it is assumed that the intervention sets the treatment to a constant. :returns: backdoor_sets, a list of dictionaries, with each dictionary having as values a backdoor set. """ if costs is None and backdoor_adjustment == "efficient-mincost-adjustment": logger.warning("No costs were passed, so they will be assumed to be constant and equal to 1.") efficient_bd = EfficientBackdoor( graph=graph, conditional_node_names=conditional_node_names, costs=costs, ) if backdoor_adjustment == BackdoorAdjustment.BACKDOOR_EFFICIENT: backdoor_set = efficient_bd.optimal_adj_set() backdoor_sets = [{"backdoor_set": tuple(backdoor_set)}] elif backdoor_adjustment == BackdoorAdjustment.BACKDOOR_MIN_EFFICIENT: backdoor_set = efficient_bd.optimal_minimal_adj_set() backdoor_sets = [{"backdoor_set": tuple(backdoor_set)}] elif backdoor_adjustment == BackdoorAdjustment.BACKDOOR_MINCOST_EFFICIENT: backdoor_set = efficient_bd.optimal_mincost_adj_set() backdoor_sets = [{"backdoor_set": tuple(backdoor_set)}] return backdoor_sets def find_valid_adjustment_sets( graph: CausalGraph, treatment_name: List, outcome_name: List, backdoor_paths: List, bdoor_graph: CausalGraph, dseparation_algo: str, backdoor_sets: List, filt_eligible_variables: List, backdoor_adjustment: BackdoorAdjustment, max_iterations: int, ): num_iterations = 0 found_valid_adjustment_set = False all_nodes_observed = graph.all_observed(graph.get_all_nodes()) # If `minimal-adjustment` method is specified, start the search from the set with minimum size. Otherwise, start from the largest. set_sizes = ( range(1, len(filt_eligible_variables) + 1, 1) if backdoor_adjustment == BackdoorAdjustment.BACKDOOR_MIN else range(len(filt_eligible_variables), 0, -1) ) for size_candidate_set in set_sizes: for candidate_set in itertools.combinations(filt_eligible_variables, size_candidate_set): check = graph.check_valid_backdoor_set( treatment_name, outcome_name, candidate_set, backdoor_paths=backdoor_paths, new_graph=bdoor_graph, dseparation_algo=dseparation_algo, ) logger.debug( "Candidate backdoor set: {0}, is_dseparated: {1}".format(candidate_set, check["is_dseparated"]) ) if check["is_dseparated"]: backdoor_sets.append({"backdoor_set": candidate_set}) found_valid_adjustment_set = True num_iterations += 1 if backdoor_adjustment == BackdoorAdjustment.BACKDOOR_EXHAUSTIVE and num_iterations > max_iterations: logger.warning(f"Max number of iterations {max_iterations} reached.") break # If the backdoor method is `maximal-adjustment` or `minimal-adjustment`, return the first found adjustment set. if ( backdoor_adjustment in { BackdoorAdjustment.BACKDOOR_DEFAULT, BackdoorAdjustment.BACKDOOR_MAX, BackdoorAdjustment.BACKDOOR_MIN, } and found_valid_adjustment_set ): break # If all variables are observed, and the biggest eligible set # does not satisfy backdoor, then none of its subsets will. if ( backdoor_adjustment in {BackdoorAdjustment.BACKDOOR_DEFAULT, BackdoorAdjustment.BACKDOOR_MAX} and all_nodes_observed ): break if num_iterations > max_iterations: logger.warning(f"Max number of iterations {max_iterations} reached. Could not find a valid backdoor set.") break return backdoor_sets, found_valid_adjustment_set def get_default_backdoor_set_id( graph: CausalGraph, treatment_name: List[str], outcome_name: List[str], backdoor_sets_dict: Dict ): # Adding a None estimand if no backdoor set found if len(backdoor_sets_dict) == 0: return None # Default set contains minimum possible number of instrumental variables, to prevent lowering variance in the treatment variable. instrument_names = set(graph.get_instruments(treatment_name, outcome_name)) iv_count_dict = { key: len(set(bdoor_set).intersection(instrument_names)) for key, bdoor_set in backdoor_sets_dict.items() } min_iv_count = min(iv_count_dict.values()) min_iv_keys = {key for key, iv_count in iv_count_dict.items() if iv_count == min_iv_count} min_iv_backdoor_sets_dict = {key: backdoor_sets_dict[key] for key in min_iv_keys} # Default set is the one with the least number of adjustment variables (optimizing for efficiency) min_set_length = 1000000 default_key = None for key, bdoor_set in min_iv_backdoor_sets_dict.items(): if len(bdoor_set) < min_set_length: min_set_length = len(bdoor_set) default_key = key return default_key def build_backdoor_estimands_dict( graph: CausalGraph, treatment_name: List[str], outcome_name: List[str], backdoor_sets: List[str], estimands_dict: Dict, ): """Build the final dict for backdoor sets by filtering unobserved variables if needed.""" backdoor_variables_dict = {} is_identified = [graph.all_observed(bset["backdoor_set"]) for bset in backdoor_sets] if any(is_identified): logger.info("Causal effect can be identified.") backdoor_sets_arr = [ list(bset["backdoor_set"]) for bset in backdoor_sets if graph.all_observed(bset["backdoor_set"]) ] else: # there is unobserved confounding logger.warning("Backdoor identification failed.") backdoor_sets_arr = [] for i in range(len(backdoor_sets_arr)): backdoor_estimand_expr = construct_backdoor_estimand(treatment_name, outcome_name, backdoor_sets_arr[i]) logger.debug("Identified expression = " + str(backdoor_estimand_expr)) estimands_dict["backdoor" + str(i + 1)] = backdoor_estimand_expr backdoor_variables_dict["backdoor" + str(i + 1)] = backdoor_sets_arr[i] return estimands_dict, backdoor_variables_dict def identify_frontdoor( graph: CausalGraph, treatment_name: List[str], outcome_name: List[str], dseparation_algo: str = "default" ): """Find a valid frontdoor variable if it exists. Currently only supports a single variable frontdoor set. """ frontdoor_var = None frontdoor_paths = None fdoor_graph = None if dseparation_algo == "default": cond1_graph = graph.do_surgery(treatment_name, remove_incoming_edges=True) bdoor_graph1 = graph.do_surgery(treatment_name, remove_outgoing_edges=True) elif dseparation_algo == "naive": frontdoor_paths = graph.get_all_directed_paths(treatment_name, outcome_name) else: raise ValueError(f"d-separation algorithm {dseparation_algo} is not supported") eligible_variables = ( graph.get_descendants(treatment_name) - set(outcome_name) - set(graph.get_descendants(outcome_name)) ) # For simplicity, assuming a one-variable frontdoor set for candidate_var in eligible_variables: # Cond 1: All directed paths intercepted by candidate_var cond1 = graph.check_valid_frontdoor_set( treatment_name, outcome_name, parse_state(candidate_var), frontdoor_paths=frontdoor_paths, new_graph=cond1_graph, dseparation_algo=dseparation_algo, ) logger.debug("Candidate frontdoor set: {0}, is_dseparated: {1}".format(candidate_var, cond1)) if not cond1: continue # Cond 2: No confounding between treatment and candidate var cond2 = graph.check_valid_backdoor_set( treatment_name, parse_state(candidate_var), set(), backdoor_paths=None, new_graph=bdoor_graph1, dseparation_algo=dseparation_algo, ) if not cond2: continue # Cond 3: treatment blocks all confounding between candidate_var and outcome bdoor_graph2 = graph.do_surgery(candidate_var, remove_outgoing_edges=True) cond3 = graph.check_valid_backdoor_set( parse_state(candidate_var), outcome_name, treatment_name, backdoor_paths=None, new_graph=bdoor_graph2, dseparation_algo=dseparation_algo, ) is_valid_frontdoor = cond1 and cond2 and cond3 if is_valid_frontdoor: frontdoor_var = candidate_var break return parse_state(frontdoor_var) def identify_mediation(graph: CausalGraph, treatment_name: List[str], outcome_name: List[str]): """Find a valid mediator if it exists. Currently only supports a single variable mediator set. """ mediation_var = None mediation_paths = graph.get_all_directed_paths(treatment_name, outcome_name) eligible_variables = graph.get_descendants(treatment_name) - set(outcome_name) # For simplicity, assuming a one-variable mediation set for candidate_var in eligible_variables: is_valid_mediation = graph.check_valid_mediation_set( treatment_name, outcome_name, parse_state(candidate_var), mediation_paths=mediation_paths, ) logger.debug("Candidate mediation set: {0}, on_mediating_path: {1}".format(candidate_var, is_valid_mediation)) if is_valid_mediation: mediation_var = candidate_var break return parse_state(mediation_var) def identify_mediation_first_stage_confounders( graph: CausalGraph, treatment_name: List[str], outcome_name: List[str], mediators_names: List[str], backdoor_adjustment: BackdoorAdjustment, ): # Create estimands dict as per the API for backdoor, but do not return it estimands_dict = {} backdoor_sets = identify_backdoor(graph, treatment_name, mediators_names, backdoor_adjustment) estimands_dict, backdoor_variables_dict = build_backdoor_estimands_dict( graph, treatment_name, mediators_names, backdoor_sets, estimands_dict, ) # Setting default "backdoor" identification adjustment set default_backdoor_id = get_default_backdoor_set_id(graph, treatment_name, outcome_name, backdoor_variables_dict) estimands_dict["backdoor"] = estimands_dict.get(str(default_backdoor_id), None) backdoor_variables_dict["backdoor"] = backdoor_variables_dict.get(str(default_backdoor_id), None) return backdoor_variables_dict def identify_mediation_second_stage_confounders( graph: CausalGraph, treatment_name: List[str], mediators_names: List[str], outcome_name: List[str], backdoor_adjustment: BackdoorAdjustment, ): # Create estimands dict as per the API for backdoor, but do not return it estimands_dict = {} backdoor_sets = identify_backdoor(graph, mediators_names, outcome_name, backdoor_adjustment) estimands_dict, backdoor_variables_dict = build_backdoor_estimands_dict( graph, mediators_names, outcome_name, backdoor_sets, estimands_dict, ) # Setting default "backdoor" identification adjustment set default_backdoor_id = get_default_backdoor_set_id(graph, treatment_name, outcome_name, backdoor_variables_dict) estimands_dict["backdoor"] = estimands_dict.get(str(default_backdoor_id), None) backdoor_variables_dict["backdoor"] = backdoor_variables_dict.get(str(default_backdoor_id), None) return backdoor_variables_dict def construct_backdoor_estimand(treatment_name: List[str], outcome_name: List[str], common_causes: List[str]): # TODO: outputs string for now, but ideally should do symbolic # expressions Mon 19 Feb 2018 04:54:17 PM DST # TODO Better support for multivariate treatments expr = None outcome_name = outcome_name[0] num_expr_str = outcome_name if len(common_causes) > 0: num_expr_str += "|" + ",".join(common_causes) expr = "d(" + num_expr_str + ")/d" + ",".join(treatment_name) sym_mu = sp.Symbol("mu") sym_sigma = sp.Symbol("sigma", positive=True) sym_outcome = spstats.Normal(num_expr_str, sym_mu, sym_sigma) sym_treatment_symbols = [sp.Symbol(t) for t in treatment_name] sym_treatment = sp.Array(sym_treatment_symbols) sym_conditional_outcome = spstats.Expectation(sym_outcome) sym_effect = sp.Derivative(sym_conditional_outcome, sym_treatment) sym_assumptions = { "Unconfoundedness": ( "If U\N{RIGHTWARDS ARROW}{{{0}}} and U\N{RIGHTWARDS ARROW}{1}" " then P({1}|{0},{2},U) = P({1}|{0},{2})" ).format(",".join(treatment_name), outcome_name, ",".join(common_causes)) } estimand = {"estimand": sym_effect, "assumptions": sym_assumptions} return estimand def construct_iv_estimand(treatment_name: List[str], outcome_name: List[str], instrument_names: List[str]): # TODO: support multivariate treatments better. expr = None outcome_name = outcome_name[0] sym_outcome = spstats.Normal(outcome_name, 0, 1) sym_treatment_symbols = [spstats.Normal(t, 0, 1) for t in treatment_name] sym_treatment = sp.Array(sym_treatment_symbols) sym_instrument_symbols = [sp.Symbol(inst) for inst in instrument_names] sym_instrument = sp.Array(sym_instrument_symbols) # ",".join(instrument_names)) sym_outcome_derivative = sp.Derivative(sym_outcome, sym_instrument) sym_treatment_derivative = sp.Derivative(sym_treatment, sym_instrument) sym_effect = spstats.Expectation(sym_outcome_derivative / sym_treatment_derivative) sym_assumptions = { "As-if-random": ( "If U\N{RIGHTWARDS ARROW}\N{RIGHTWARDS ARROW}{0} then " "\N{NOT SIGN}(U \N{RIGHTWARDS ARROW}\N{RIGHTWARDS ARROW}{{{1}}})" ).format(outcome_name, ",".join(instrument_names)), "Exclusion": ( "If we remove {{{0}}}\N{RIGHTWARDS ARROW}{{{1}}}, then " "\N{NOT SIGN}({{{0}}}\N{RIGHTWARDS ARROW}{2})" ).format(",".join(instrument_names), ",".join(treatment_name), outcome_name), } estimand = {"estimand": sym_effect, "assumptions": sym_assumptions} return estimand def construct_frontdoor_estimand( treatment_name: List[str], outcome_name: List[str], frontdoor_variables_names: List[str] ): # TODO: support multivariate treatments better. expr = None outcome_name = outcome_name[0] sym_outcome = spstats.Normal(outcome_name, 0, 1) sym_treatment_symbols = [spstats.Normal(t, 0, 1) for t in treatment_name] sym_treatment = sp.Array(sym_treatment_symbols) sym_frontdoor_symbols = [sp.Symbol(inst) for inst in frontdoor_variables_names] sym_frontdoor = sp.Array(sym_frontdoor_symbols) # ",".join(instrument_names)) sym_outcome_derivative = sp.Derivative(sym_outcome, sym_frontdoor) sym_treatment_derivative = sp.Derivative(sym_frontdoor, sym_treatment) sym_effect = spstats.Expectation(sym_treatment_derivative * sym_outcome_derivative) sym_assumptions = { "Full-mediation": ("{2} intercepts (blocks) all directed paths from {0} to {1}.").format( ",".join(treatment_name), ",".join(outcome_name), ",".join(frontdoor_variables_names), ), "First-stage-unconfoundedness": ( "If U\N{RIGHTWARDS ARROW}{{{0}}} and U\N{RIGHTWARDS ARROW}{{{1}}}" " then P({1}|{0},U) = P({1}|{0})" ).format(",".join(treatment_name), ",".join(frontdoor_variables_names)), "Second-stage-unconfoundedness": ( "If U\N{RIGHTWARDS ARROW}{{{2}}} and U\N{RIGHTWARDS ARROW}{1}" " then P({1}|{2}, {0}, U) = P({1}|{2}, {0})" ).format( ",".join(treatment_name), outcome_name, ",".join(frontdoor_variables_names), ), } estimand = {"estimand": sym_effect, "assumptions": sym_assumptions} return estimand def construct_mediation_estimand( estimand_type: EstimandType, treatment_name: List[str], outcome_name: List[str], mediators_names: List[str] ): # TODO: support multivariate treatments better. expr = None if estimand_type in ( EstimandType.NONPARAMETRIC_NDE, EstimandType.NONPARAMETRIC_NIE, ): outcome_name = outcome_name[0] sym_outcome = spstats.Normal(outcome_name, 0, 1) sym_treatment_symbols = [spstats.Normal(t, 0, 1) for t in treatment_name] sym_treatment = sp.Array(sym_treatment_symbols) sym_mediators_symbols = [sp.Symbol(inst) for inst in mediators_names] sym_mediators = sp.Array(sym_mediators_symbols) sym_outcome_derivative = sp.Derivative(sym_outcome, sym_mediators) sym_treatment_derivative = sp.Derivative(sym_mediators, sym_treatment) # For direct effect num_expr_str = outcome_name if len(mediators_names) > 0: num_expr_str += "|" + ",".join(mediators_names) sym_mu = sp.Symbol("mu") sym_sigma = sp.Symbol("sigma", positive=True) sym_conditional_outcome = spstats.Normal(num_expr_str, sym_mu, sym_sigma) sym_directeffect_derivative = sp.Derivative(sym_conditional_outcome, sym_treatment) if estimand_type == EstimandType.NONPARAMETRIC_NIE: sym_effect = spstats.Expectation(sym_treatment_derivative * sym_outcome_derivative) elif estimand_type == EstimandType.NONPARAMETRIC_NDE: sym_effect = spstats.Expectation(sym_directeffect_derivative) sym_assumptions = { "Mediation": ( "{2} intercepts (blocks) all directed paths from {0} to {1} except the path {{{0}}}\N{RIGHTWARDS ARROW}{{{1}}}." ).format( ",".join(treatment_name), ",".join(outcome_name), ",".join(mediators_names), ), "First-stage-unconfoundedness": ( "If U\N{RIGHTWARDS ARROW}{{{0}}} and U\N{RIGHTWARDS ARROW}{{{1}}}" " then P({1}|{0},U) = P({1}|{0})" ).format(",".join(treatment_name), ",".join(mediators_names)), "Second-stage-unconfoundedness": ( "If U\N{RIGHTWARDS ARROW}{{{2}}} and U\N{RIGHTWARDS ARROW}{1}" " then P({1}|{2}, {0}, U) = P({1}|{2}, {0})" ).format(",".join(treatment_name), outcome_name, ",".join(mediators_names)), } else: raise ValueError( "Estimand type not supported. Supported estimand types are {0} or {1}'.".format( EstimandType.NONPARAMETRIC_NDE, EstimandType.NONPARAMETRIC_NIE, ) ) estimand = {"estimand": sym_effect, "assumptions": sym_assumptions} return estimand

andresmor-ms

133e7b9a4ed32aae8ab5f39a01eb02b3a4d1c0ba

e1652ec3c6606b1bb2dfe91ef830e4b4b566712d

I was reading the code and I believe it always returns an `IdentifiedEstimand` object, I'm not 100% sure if there's a case in which it returns `None`. It does raise errors in many places, but does not return None

andresmor-ms

py-why/dowhy

Functional api/refute estimate

* Refactor refuters into functions * Rename functional_api notebook for clarity * Add return types to identify_estimate * Update `__init__.py` for imports * Add joblib for bootstrap refuter * Create `refute_estimate` function * Add types for refuter parameters & return types

2022-10-04 16:18:49+00:00

2022-10-07 04:30:22+00:00

dowhy/causal_refuter.py

import logging import random import numpy as np import scipy.stats as st from dowhy.utils.api import parse_state class CausalRefuter: """Base class for different refutation methods. Subclasses implement specific refutations methods. # todo: add docstring for common parameters here and remove from child refuter classes """ # Default value for the number of simulations to be conducted DEFAULT_NUM_SIMULATIONS = 100 PROGRESS_BAR_COLOR = "green" def __init__(self, data, identified_estimand, estimate, **kwargs): self._data = data self._target_estimand = identified_estimand self._estimate = estimate self._treatment_name = self._target_estimand.treatment_variable self._outcome_name = self._target_estimand.outcome_variable self._random_seed = None # joblib params for parallel processing self._n_jobs = kwargs.pop("n_jobs", None) self._verbose = kwargs.pop("verbose", 0) if "random_seed" in kwargs: self._random_seed = kwargs["random_seed"] np.random.seed(self._random_seed) self.logger = logging.getLogger(__name__) # Concatenate the confounders, instruments and effect modifiers try: self._variables_of_interest = ( self._target_estimand.get_backdoor_variables() + self._target_estimand.instrumental_variables + self._estimate.params["effect_modifiers"] ) except AttributeError as attr_error: self.logger.error(attr_error) def choose_variables(self, required_variables): """ This method provides a way to choose the confounders whose values we wish to modify for finding its effect on the ability of the treatment to affect the outcome. """ invert = None if required_variables is False: self.logger.info( "All variables required: Running bootstrap adding noise to confounders, instrumental variables and effect modifiers." ) return None elif required_variables is True: self.logger.info( "All variables required: Running bootstrap adding noise to confounders, instrumental variables and effect modifiers." ) return self._variables_of_interest elif type(required_variables) is int: if len(self._variables_of_interest) < required_variables: self.logger.error( "Too many variables passed.\n The number of variables is: {}.\n The number of variables passed: {}".format( len(self._variables_of_interest), required_variables ) ) raise ValueError( "The number of variables in the required_variables is greater than the number of confounders, instrumental variables and effect modifiers" ) else: # Shuffle the confounders random.shuffle(self._variables_of_interest) return self._variables_of_interest[:required_variables] elif type(required_variables) is list: # Check if all are select or deselect variables if all(variable[0] == "-" for variable in required_variables): invert = True required_variables = [variable[1:] for variable in required_variables] elif all(variable[0] != "-" for variable in required_variables): invert = False else: self.logger.error("{} has both select and delect variables".format(required_variables)) raise ValueError( "It appears that there are some select and deselect variables. Note you can either select or delect variables at a time, but not both" ) # Check if all the required_variables belong to confounders, instrumental variables or effect if set(required_variables) - set(self._variables_of_interest) != set([]): self.logger.error( "{} are not confounder, instrumental variable or effect modifier".format( list(set(required_variables) - set(self._variables_of_interest)) ) ) raise ValueError( "At least one of required_variables is not a valid variable name, or it is not a confounder, instrumental variable or effect modifier" ) if invert is False: return required_variables elif invert is True: return list(set(self._variables_of_interest) - set(required_variables)) else: self.logger.error("Incorrect type: {}. Expected an int,list or bool".format(type(required_variables))) raise TypeError("Expected int, list or bool. Got an unexpected datatype") def test_significance(self, estimate, simulations, test_type="auto", significance_level=0.05): """Tests the statistical significance of the estimate obtained to the simulations produced by a refuter. The basis behind using the sample statistics of the refuter when we are in fact testing the estimate, is due to the fact that, we would ideally expect them to follow the same distribition. For refutation tests (e.g., placebo refuters), consider the null distribution as a distribution of effect estimates over multiple simulations with placebo treatment, and compute how likely the true estimate (e.g., zero for placebo test) is under the null. If the probability of true effect estimate is lower than the p-value, then estimator method fails the test. For sensitivity analysis tests (e.g., bootstrap, subset or common cause refuters), the null distribution captures the distribution of effect estimates under the "true" dataset (e.g., with an additional confounder or different sampling), and we compute the probability of the obtained estimate under this distribution. If the probability is lower than the p-value, then the estimator method fails the test. Null Hypothesis- The estimate is a part of the distribution Alternative Hypothesis- The estimate does not fall in the distribution. :param 'estimate': CausalEstimate The estimate obtained from the estimator for the original data. :param 'simulations': np.array An array containing the result of the refuter for the simulations :param 'test_type': string, default 'auto' The type of test the user wishes to perform. :param 'significance_level': float, default 0.05 The significance level for the statistical test :returns: significance_dict: Dict A Dict containing the p_value and a boolean that indicates if the result is statistically significant """ # Initializing the p_value p_value = 0 if test_type == "auto": num_simulations = len(simulations) if num_simulations >= 100: # Bootstrapping self.logger.info( "Making use of Bootstrap as we have more than 100 examples.\n \ Note: The greater the number of examples, the more accurate are the confidence estimates" ) # Perform Bootstrap Significance Test with the original estimate and the set of refutations p_value = self.perform_bootstrap_test(estimate, simulations) else: self.logger.warning( "We assume a Normal Distribution as the sample has less than 100 examples.\n \ Note: The underlying distribution may not be Normal. We assume that it approaches normal with the increase in sample size." ) # Perform Normal Tests of Significance with the original estimate and the set of refutations p_value = self.perform_normal_distribution_test(estimate, simulations) elif test_type == "bootstrap": self.logger.info( "Performing Bootstrap Test with {} samples\n \ Note: The greater the number of examples, the more accurate are the confidence estimates".format( len(simulations) ) ) # Perform Bootstrap Significance Test with the original estimate and the set of refutations p_value = self.perform_bootstrap_test(estimate, simulations) elif test_type == "normal_test": self.logger.info( "Performing Normal Test with {} samples\n \ Note: We assume that the underlying distribution is Normal.".format( len(simulations) ) ) # Perform Normal Tests of Significance with the original estimate and the set of refutations p_value = self.perform_normal_distribution_test(estimate, simulations) else: raise NotImplementedError significance_dict = {"p_value": p_value, "is_statistically_significant": p_value <= significance_level} return significance_dict def perform_bootstrap_test(self, estimate, simulations): # Get the number of simulations num_simulations = len(simulations) # Sort the simulations simulations.sort() # Obtain the median value median_refute_values = simulations[int(num_simulations / 2)] # Performing a two sided test if estimate.value > median_refute_values: # np.searchsorted tells us the index if it were a part of the array # We select side to be left as we want to find the first value that matches estimate_index = np.searchsorted(simulations, estimate.value, side="left") # We subtact 1 as we are finding the value from the right tail p_value = 1 - (estimate_index / num_simulations) else: # We take the side to be right as we want to find the last index that matches estimate_index = np.searchsorted(simulations, estimate.value, side="right") # We get the probability with respect to the left tail. p_value = estimate_index / num_simulations # return twice the determined quantile as this is a two sided test return 2 * p_value def perform_normal_distribution_test(self, estimate, simulations): # Get the mean for the simulations mean_refute_values = np.mean(simulations) # Get the standard deviation for the simulations std_dev_refute_values = np.std(simulations) # Get the Z Score [(val - mean)/ std_dev ] z_score = (estimate.value - mean_refute_values) / std_dev_refute_values if z_score > 0: # Right Tail p_value = 1 - st.norm.cdf(z_score) else: # Left Tail p_value = st.norm.cdf(z_score) return p_value def refute_estimate(self, show_progress_bar=False): raise NotImplementedError class CausalRefutation: """Class for storing the result of a refutation method.""" def __init__(self, estimated_effect, new_effect, refutation_type): self.estimated_effect = estimated_effect self.new_effect = new_effect self.refutation_type = refutation_type self.refutation_result = None def add_significance_test_results(self, refutation_result): self.refutation_result = refutation_result def add_refuter(self, refuter_instance): self.refuter = refuter_instance def interpret(self, method_name=None, **kwargs): """Interpret the refutation results. :param method_name: Method used (string) or a list of methods. If None, then the default for the specific refuter is used. :returns: None """ if method_name is None: method_name = self.refuter.interpret_method method_name_arr = parse_state(method_name) import dowhy.interpreters as interpreters for method in method_name_arr: interpreter = interpreters.get_class_object(method) interpreter(self, **kwargs).interpret() def __str__(self): if self.refutation_result is None: return "{0}\nEstimated effect:{1}\nNew effect:{2}\n".format( self.refutation_type, self.estimated_effect, self.new_effect ) else: return "{0}\nEstimated effect:{1}\nNew effect:{2}\np value:{3}\n".format( self.refutation_type, self.estimated_effect, self.new_effect, self.refutation_result["p_value"] )

import logging import random from enum import Enum from typing import List, Union import numpy as np import scipy.stats as st from dowhy.utils.api import parse_state class SignificanceTestType(Enum): AUTO = "auto" BOOTSTRAP = "bootstrap" NORMAL = "normal_test" logger = logging.getLogger(__name__) class CausalRefuter: """Base class for different refutation methods. Subclasses implement specific refutations methods. # todo: add docstring for common parameters here and remove from child refuter classes This class is for backwards compatibility with CausalModel Will be deprecated in the future in favor of function call refute_method_name() functions """ # Default value for the number of simulations to be conducted DEFAULT_NUM_SIMULATIONS = 100 PROGRESS_BAR_COLOR = "green" def __init__(self, data, identified_estimand, estimate, **kwargs): self._data = data self._target_estimand = identified_estimand self._estimate = estimate self._treatment_name = self._target_estimand.treatment_variable self._outcome_name = self._target_estimand.outcome_variable self._random_seed = None # joblib params for parallel processing self._n_jobs = kwargs.pop("n_jobs", None) self._verbose = kwargs.pop("verbose", 0) if "random_seed" in kwargs: self._random_seed = kwargs["random_seed"] np.random.seed(self._random_seed) # Concatenate the confounders, instruments and effect modifiers try: self._variables_of_interest = ( self._target_estimand.get_backdoor_variables() + self._target_estimand.instrumental_variables + self._estimate.params["effect_modifiers"] ) except AttributeError as attr_error: logger.error(attr_error) def choose_variables(self, required_variables): return choose_variables(required_variables, self._variables_of_interest) def test_significance(self, estimate, simulations, test_type="auto", significance_level=0.05): return test_significance(estimate, simulations, SignificanceTestType(test_type), significance_level) def perform_bootstrap_test(self, estimate, simulations): return perform_bootstrap_test(estimate, simulations) def perform_normal_distribution_test(self, estimate, simulations): return perform_normal_distribution_test(estimate, simulations) def refute_estimate(self, show_progress_bar=False): raise NotImplementedError def choose_variables(required_variables: Union[bool, int, list], variables_of_interest: List): """ This method provides a way to choose the confounders whose values we wish to modify for finding its effect on the ability of the treatment to affect the outcome. """ invert = None if required_variables is False: logger.info( "All variables required: Running bootstrap adding noise to confounders, instrumental variables and effect modifiers." ) return None elif required_variables is True: logger.info( "All variables required: Running bootstrap adding noise to confounders, instrumental variables and effect modifiers." ) return variables_of_interest elif type(required_variables) is int: if len(variables_of_interest) < required_variables: logger.error( "Too many variables passed.\n The number of variables is: {}.\n The number of variables passed: {}".format( len(variables_of_interest), required_variables ) ) raise ValueError( "The number of variables in the required_variables is greater than the number of confounders, instrumental variables and effect modifiers" ) else: # Shuffle the confounders return random.sample(variables_of_interest, required_variables) elif type(required_variables) is list: # Check if all are select or deselect variables if all(variable[0] == "-" for variable in required_variables): invert = True required_variables = [variable[1:] for variable in required_variables] elif all(variable[0] != "-" for variable in required_variables): invert = False else: logger.error("{} has both select and delect variables".format(required_variables)) raise ValueError( "It appears that there are some select and deselect variables. Note you can either select or delect variables at a time, but not both" ) # Check if all the required_variables belong to confounders, instrumental variables or effect if set(required_variables) - set(variables_of_interest) != set([]): logger.error( "{} are not confounder, instrumental variable or effect modifier".format( list(set(required_variables) - set(variables_of_interest)) ) ) raise ValueError( "At least one of required_variables is not a valid variable name, or it is not a confounder, instrumental variable or effect modifier" ) if invert is False: return required_variables elif invert is True: return list(set(variables_of_interest) - set(required_variables)) def perform_bootstrap_test(estimate, simulations: List): # Get the number of simulations num_simulations = len(simulations) # Sort the simulations simulations.sort() # Obtain the median value median_refute_values = simulations[int(num_simulations / 2)] # Performing a two sided test if estimate.value > median_refute_values: # np.searchsorted tells us the index if it were a part of the array # We select side to be left as we want to find the first value that matches estimate_index = np.searchsorted(simulations, estimate.value, side="left") # We subtact 1 as we are finding the value from the right tail p_value = 1 - (estimate_index / num_simulations) else: # We take the side to be right as we want to find the last index that matches estimate_index = np.searchsorted(simulations, estimate.value, side="right") # We get the probability with respect to the left tail. p_value = estimate_index / num_simulations # return twice the determined quantile as this is a two sided test return 2 * p_value def perform_normal_distribution_test(estimate, simulations: List): # Get the mean for the simulations mean_refute_values = np.mean(simulations) # Get the standard deviation for the simulations std_dev_refute_values = np.std(simulations) # Get the Z Score [(val - mean)/ std_dev ] z_score = (estimate.value - mean_refute_values) / std_dev_refute_values if z_score > 0: # Right Tail p_value = 1 - st.norm.cdf(z_score) else: # Left Tail p_value = st.norm.cdf(z_score) return p_value def test_significance( estimate, simulations: List, test_type: SignificanceTestType = SignificanceTestType.AUTO, significance_level: float = 0.85, ): """Tests the statistical significance of the estimate obtained to the simulations produced by a refuter. The basis behind using the sample statistics of the refuter when we are in fact testing the estimate, is due to the fact that, we would ideally expect them to follow the same distribition. For refutation tests (e.g., placebo refuters), consider the null distribution as a distribution of effect estimates over multiple simulations with placebo treatment, and compute how likely the true estimate (e.g., zero for placebo test) is under the null. If the probability of true effect estimate is lower than the p-value, then estimator method fails the test. For sensitivity analysis tests (e.g., bootstrap, subset or common cause refuters), the null distribution captures the distribution of effect estimates under the "true" dataset (e.g., with an additional confounder or different sampling), and we compute the probability of the obtained estimate under this distribution. If the probability is lower than the p-value, then the estimator method fails the test. Null Hypothesis- The estimate is a part of the distribution Alternative Hypothesis- The estimate does not fall in the distribution. :param 'estimate': CausalEstimate The estimate obtained from the estimator for the original data. :param 'simulations': np.array An array containing the result of the refuter for the simulations :param 'test_type': string, default 'auto' The type of test the user wishes to perform. :param 'significance_level': float, default 0.05 The significance level for the statistical test :returns: significance_dict: Dict A Dict containing the p_value and a boolean that indicates if the result is statistically significant """ # Initializing the p_value p_value = 0 if test_type == SignificanceTestType.AUTO: num_simulations = len(simulations) if num_simulations >= 100: # Bootstrapping logger.info( "Making use of Bootstrap as we have more than 100 examples.\n \ Note: The greater the number of examples, the more accurate are the confidence estimates" ) # Perform Bootstrap Significance Test with the original estimate and the set of refutations p_value = perform_bootstrap_test(estimate, simulations) else: logger.warning( "We assume a Normal Distribution as the sample has less than 100 examples.\n \ Note: The underlying distribution may not be Normal. We assume that it approaches normal with the increase in sample size." ) # Perform Normal Tests of Significance with the original estimate and the set of refutations p_value = perform_normal_distribution_test(estimate, simulations) elif test_type == SignificanceTestType.BOOTSTRAP: logger.info( "Performing Bootstrap Test with {} samples\n \ Note: The greater the number of examples, the more accurate are the confidence estimates".format( len(simulations) ) ) # Perform Bootstrap Significance Test with the original estimate and the set of refutations p_value = perform_bootstrap_test(estimate, simulations) elif test_type == SignificanceTestType.NORMAL: logger.info( "Performing Normal Test with {} samples\n \ Note: We assume that the underlying distribution is Normal.".format( len(simulations) ) ) # Perform Normal Tests of Significance with the original estimate and the set of refutations p_value = perform_normal_distribution_test(estimate, simulations) significance_dict = {"p_value": p_value, "is_statistically_significant": p_value <= significance_level} return significance_dict class CausalRefutation: """Class for storing the result of a refutation method.""" def __init__(self, estimated_effect, new_effect, refutation_type): self.estimated_effect = estimated_effect self.new_effect = new_effect self.refutation_type = refutation_type self.refutation_result = None def add_significance_test_results(self, refutation_result): self.refutation_result = refutation_result def add_refuter(self, refuter_instance): self.refuter = refuter_instance def interpret(self, method_name=None, **kwargs): """Interpret the refutation results. :param method_name: Method used (string) or a list of methods. If None, then the default for the specific refuter is used. :returns: None """ if method_name is None: method_name = self.refuter.interpret_method method_name_arr = parse_state(method_name) import dowhy.interpreters as interpreters for method in method_name_arr: interpreter = interpreters.get_class_object(method) interpreter(self, **kwargs).interpret() def __str__(self): if self.refutation_result is None: return "{0}\nEstimated effect:{1}\nNew effect:{2}\n".format( self.refutation_type, self.estimated_effect, self.new_effect ) else: return "{0}\nEstimated effect:{1}\nNew effect:{2}\np value:{3}\n".format( self.refutation_type, self.estimated_effect, self.new_effect, self.refutation_result["p_value"] )

andresmor-ms

133e7b9a4ed32aae8ab5f39a01eb02b3a4d1c0ba

e1652ec3c6606b1bb2dfe91ef830e4b4b566712d

typo in boostrap

amit-sharma

py-why/dowhy

Functional api/refute estimate

* Refactor refuters into functions * Rename functional_api notebook for clarity * Add return types to identify_estimate * Update `__init__.py` for imports * Add joblib for bootstrap refuter * Create `refute_estimate` function * Add types for refuter parameters & return types

2022-10-04 16:18:49+00:00

2022-10-07 04:30:22+00:00

dowhy/causal_refuter.py

import logging import random import numpy as np import scipy.stats as st from dowhy.utils.api import parse_state class CausalRefuter: """Base class for different refutation methods. Subclasses implement specific refutations methods. # todo: add docstring for common parameters here and remove from child refuter classes """ # Default value for the number of simulations to be conducted DEFAULT_NUM_SIMULATIONS = 100 PROGRESS_BAR_COLOR = "green" def __init__(self, data, identified_estimand, estimate, **kwargs): self._data = data self._target_estimand = identified_estimand self._estimate = estimate self._treatment_name = self._target_estimand.treatment_variable self._outcome_name = self._target_estimand.outcome_variable self._random_seed = None # joblib params for parallel processing self._n_jobs = kwargs.pop("n_jobs", None) self._verbose = kwargs.pop("verbose", 0) if "random_seed" in kwargs: self._random_seed = kwargs["random_seed"] np.random.seed(self._random_seed) self.logger = logging.getLogger(__name__) # Concatenate the confounders, instruments and effect modifiers try: self._variables_of_interest = ( self._target_estimand.get_backdoor_variables() + self._target_estimand.instrumental_variables + self._estimate.params["effect_modifiers"] ) except AttributeError as attr_error: self.logger.error(attr_error) def choose_variables(self, required_variables): """ This method provides a way to choose the confounders whose values we wish to modify for finding its effect on the ability of the treatment to affect the outcome. """ invert = None if required_variables is False: self.logger.info( "All variables required: Running bootstrap adding noise to confounders, instrumental variables and effect modifiers." ) return None elif required_variables is True: self.logger.info( "All variables required: Running bootstrap adding noise to confounders, instrumental variables and effect modifiers." ) return self._variables_of_interest elif type(required_variables) is int: if len(self._variables_of_interest) < required_variables: self.logger.error( "Too many variables passed.\n The number of variables is: {}.\n The number of variables passed: {}".format( len(self._variables_of_interest), required_variables ) ) raise ValueError( "The number of variables in the required_variables is greater than the number of confounders, instrumental variables and effect modifiers" ) else: # Shuffle the confounders random.shuffle(self._variables_of_interest) return self._variables_of_interest[:required_variables] elif type(required_variables) is list: # Check if all are select or deselect variables if all(variable[0] == "-" for variable in required_variables): invert = True required_variables = [variable[1:] for variable in required_variables] elif all(variable[0] != "-" for variable in required_variables): invert = False else: self.logger.error("{} has both select and delect variables".format(required_variables)) raise ValueError( "It appears that there are some select and deselect variables. Note you can either select or delect variables at a time, but not both" ) # Check if all the required_variables belong to confounders, instrumental variables or effect if set(required_variables) - set(self._variables_of_interest) != set([]): self.logger.error( "{} are not confounder, instrumental variable or effect modifier".format( list(set(required_variables) - set(self._variables_of_interest)) ) ) raise ValueError( "At least one of required_variables is not a valid variable name, or it is not a confounder, instrumental variable or effect modifier" ) if invert is False: return required_variables elif invert is True: return list(set(self._variables_of_interest) - set(required_variables)) else: self.logger.error("Incorrect type: {}. Expected an int,list or bool".format(type(required_variables))) raise TypeError("Expected int, list or bool. Got an unexpected datatype") def test_significance(self, estimate, simulations, test_type="auto", significance_level=0.05): """Tests the statistical significance of the estimate obtained to the simulations produced by a refuter. The basis behind using the sample statistics of the refuter when we are in fact testing the estimate, is due to the fact that, we would ideally expect them to follow the same distribition. For refutation tests (e.g., placebo refuters), consider the null distribution as a distribution of effect estimates over multiple simulations with placebo treatment, and compute how likely the true estimate (e.g., zero for placebo test) is under the null. If the probability of true effect estimate is lower than the p-value, then estimator method fails the test. For sensitivity analysis tests (e.g., bootstrap, subset or common cause refuters), the null distribution captures the distribution of effect estimates under the "true" dataset (e.g., with an additional confounder or different sampling), and we compute the probability of the obtained estimate under this distribution. If the probability is lower than the p-value, then the estimator method fails the test. Null Hypothesis- The estimate is a part of the distribution Alternative Hypothesis- The estimate does not fall in the distribution. :param 'estimate': CausalEstimate The estimate obtained from the estimator for the original data. :param 'simulations': np.array An array containing the result of the refuter for the simulations :param 'test_type': string, default 'auto' The type of test the user wishes to perform. :param 'significance_level': float, default 0.05 The significance level for the statistical test :returns: significance_dict: Dict A Dict containing the p_value and a boolean that indicates if the result is statistically significant """ # Initializing the p_value p_value = 0 if test_type == "auto": num_simulations = len(simulations) if num_simulations >= 100: # Bootstrapping self.logger.info( "Making use of Bootstrap as we have more than 100 examples.\n \ Note: The greater the number of examples, the more accurate are the confidence estimates" ) # Perform Bootstrap Significance Test with the original estimate and the set of refutations p_value = self.perform_bootstrap_test(estimate, simulations) else: self.logger.warning( "We assume a Normal Distribution as the sample has less than 100 examples.\n \ Note: The underlying distribution may not be Normal. We assume that it approaches normal with the increase in sample size." ) # Perform Normal Tests of Significance with the original estimate and the set of refutations p_value = self.perform_normal_distribution_test(estimate, simulations) elif test_type == "bootstrap": self.logger.info( "Performing Bootstrap Test with {} samples\n \ Note: The greater the number of examples, the more accurate are the confidence estimates".format( len(simulations) ) ) # Perform Bootstrap Significance Test with the original estimate and the set of refutations p_value = self.perform_bootstrap_test(estimate, simulations) elif test_type == "normal_test": self.logger.info( "Performing Normal Test with {} samples\n \ Note: We assume that the underlying distribution is Normal.".format( len(simulations) ) ) # Perform Normal Tests of Significance with the original estimate and the set of refutations p_value = self.perform_normal_distribution_test(estimate, simulations) else: raise NotImplementedError significance_dict = {"p_value": p_value, "is_statistically_significant": p_value <= significance_level} return significance_dict def perform_bootstrap_test(self, estimate, simulations): # Get the number of simulations num_simulations = len(simulations) # Sort the simulations simulations.sort() # Obtain the median value median_refute_values = simulations[int(num_simulations / 2)] # Performing a two sided test if estimate.value > median_refute_values: # np.searchsorted tells us the index if it were a part of the array # We select side to be left as we want to find the first value that matches estimate_index = np.searchsorted(simulations, estimate.value, side="left") # We subtact 1 as we are finding the value from the right tail p_value = 1 - (estimate_index / num_simulations) else: # We take the side to be right as we want to find the last index that matches estimate_index = np.searchsorted(simulations, estimate.value, side="right") # We get the probability with respect to the left tail. p_value = estimate_index / num_simulations # return twice the determined quantile as this is a two sided test return 2 * p_value def perform_normal_distribution_test(self, estimate, simulations): # Get the mean for the simulations mean_refute_values = np.mean(simulations) # Get the standard deviation for the simulations std_dev_refute_values = np.std(simulations) # Get the Z Score [(val - mean)/ std_dev ] z_score = (estimate.value - mean_refute_values) / std_dev_refute_values if z_score > 0: # Right Tail p_value = 1 - st.norm.cdf(z_score) else: # Left Tail p_value = st.norm.cdf(z_score) return p_value def refute_estimate(self, show_progress_bar=False): raise NotImplementedError class CausalRefutation: """Class for storing the result of a refutation method.""" def __init__(self, estimated_effect, new_effect, refutation_type): self.estimated_effect = estimated_effect self.new_effect = new_effect self.refutation_type = refutation_type self.refutation_result = None def add_significance_test_results(self, refutation_result): self.refutation_result = refutation_result def add_refuter(self, refuter_instance): self.refuter = refuter_instance def interpret(self, method_name=None, **kwargs): """Interpret the refutation results. :param method_name: Method used (string) or a list of methods. If None, then the default for the specific refuter is used. :returns: None """ if method_name is None: method_name = self.refuter.interpret_method method_name_arr = parse_state(method_name) import dowhy.interpreters as interpreters for method in method_name_arr: interpreter = interpreters.get_class_object(method) interpreter(self, **kwargs).interpret() def __str__(self): if self.refutation_result is None: return "{0}\nEstimated effect:{1}\nNew effect:{2}\n".format( self.refutation_type, self.estimated_effect, self.new_effect ) else: return "{0}\nEstimated effect:{1}\nNew effect:{2}\np value:{3}\n".format( self.refutation_type, self.estimated_effect, self.new_effect, self.refutation_result["p_value"] )

import logging import random from enum import Enum from typing import List, Union import numpy as np import scipy.stats as st from dowhy.utils.api import parse_state class SignificanceTestType(Enum): AUTO = "auto" BOOTSTRAP = "bootstrap" NORMAL = "normal_test" logger = logging.getLogger(__name__) class CausalRefuter: """Base class for different refutation methods. Subclasses implement specific refutations methods. # todo: add docstring for common parameters here and remove from child refuter classes This class is for backwards compatibility with CausalModel Will be deprecated in the future in favor of function call refute_method_name() functions """ # Default value for the number of simulations to be conducted DEFAULT_NUM_SIMULATIONS = 100 PROGRESS_BAR_COLOR = "green" def __init__(self, data, identified_estimand, estimate, **kwargs): self._data = data self._target_estimand = identified_estimand self._estimate = estimate self._treatment_name = self._target_estimand.treatment_variable self._outcome_name = self._target_estimand.outcome_variable self._random_seed = None # joblib params for parallel processing self._n_jobs = kwargs.pop("n_jobs", None) self._verbose = kwargs.pop("verbose", 0) if "random_seed" in kwargs: self._random_seed = kwargs["random_seed"] np.random.seed(self._random_seed) # Concatenate the confounders, instruments and effect modifiers try: self._variables_of_interest = ( self._target_estimand.get_backdoor_variables() + self._target_estimand.instrumental_variables + self._estimate.params["effect_modifiers"] ) except AttributeError as attr_error: logger.error(attr_error) def choose_variables(self, required_variables): return choose_variables(required_variables, self._variables_of_interest) def test_significance(self, estimate, simulations, test_type="auto", significance_level=0.05): return test_significance(estimate, simulations, SignificanceTestType(test_type), significance_level) def perform_bootstrap_test(self, estimate, simulations): return perform_bootstrap_test(estimate, simulations) def perform_normal_distribution_test(self, estimate, simulations): return perform_normal_distribution_test(estimate, simulations) def refute_estimate(self, show_progress_bar=False): raise NotImplementedError def choose_variables(required_variables: Union[bool, int, list], variables_of_interest: List): """ This method provides a way to choose the confounders whose values we wish to modify for finding its effect on the ability of the treatment to affect the outcome. """ invert = None if required_variables is False: logger.info( "All variables required: Running bootstrap adding noise to confounders, instrumental variables and effect modifiers." ) return None elif required_variables is True: logger.info( "All variables required: Running bootstrap adding noise to confounders, instrumental variables and effect modifiers." ) return variables_of_interest elif type(required_variables) is int: if len(variables_of_interest) < required_variables: logger.error( "Too many variables passed.\n The number of variables is: {}.\n The number of variables passed: {}".format( len(variables_of_interest), required_variables ) ) raise ValueError( "The number of variables in the required_variables is greater than the number of confounders, instrumental variables and effect modifiers" ) else: # Shuffle the confounders return random.sample(variables_of_interest, required_variables) elif type(required_variables) is list: # Check if all are select or deselect variables if all(variable[0] == "-" for variable in required_variables): invert = True required_variables = [variable[1:] for variable in required_variables] elif all(variable[0] != "-" for variable in required_variables): invert = False else: logger.error("{} has both select and delect variables".format(required_variables)) raise ValueError( "It appears that there are some select and deselect variables. Note you can either select or delect variables at a time, but not both" ) # Check if all the required_variables belong to confounders, instrumental variables or effect if set(required_variables) - set(variables_of_interest) != set([]): logger.error( "{} are not confounder, instrumental variable or effect modifier".format( list(set(required_variables) - set(variables_of_interest)) ) ) raise ValueError( "At least one of required_variables is not a valid variable name, or it is not a confounder, instrumental variable or effect modifier" ) if invert is False: return required_variables elif invert is True: return list(set(variables_of_interest) - set(required_variables)) def perform_bootstrap_test(estimate, simulations: List): # Get the number of simulations num_simulations = len(simulations) # Sort the simulations simulations.sort() # Obtain the median value median_refute_values = simulations[int(num_simulations / 2)] # Performing a two sided test if estimate.value > median_refute_values: # np.searchsorted tells us the index if it were a part of the array # We select side to be left as we want to find the first value that matches estimate_index = np.searchsorted(simulations, estimate.value, side="left") # We subtact 1 as we are finding the value from the right tail p_value = 1 - (estimate_index / num_simulations) else: # We take the side to be right as we want to find the last index that matches estimate_index = np.searchsorted(simulations, estimate.value, side="right") # We get the probability with respect to the left tail. p_value = estimate_index / num_simulations # return twice the determined quantile as this is a two sided test return 2 * p_value def perform_normal_distribution_test(estimate, simulations: List): # Get the mean for the simulations mean_refute_values = np.mean(simulations) # Get the standard deviation for the simulations std_dev_refute_values = np.std(simulations) # Get the Z Score [(val - mean)/ std_dev ] z_score = (estimate.value - mean_refute_values) / std_dev_refute_values if z_score > 0: # Right Tail p_value = 1 - st.norm.cdf(z_score) else: # Left Tail p_value = st.norm.cdf(z_score) return p_value def test_significance( estimate, simulations: List, test_type: SignificanceTestType = SignificanceTestType.AUTO, significance_level: float = 0.85, ): """Tests the statistical significance of the estimate obtained to the simulations produced by a refuter. The basis behind using the sample statistics of the refuter when we are in fact testing the estimate, is due to the fact that, we would ideally expect them to follow the same distribition. For refutation tests (e.g., placebo refuters), consider the null distribution as a distribution of effect estimates over multiple simulations with placebo treatment, and compute how likely the true estimate (e.g., zero for placebo test) is under the null. If the probability of true effect estimate is lower than the p-value, then estimator method fails the test. For sensitivity analysis tests (e.g., bootstrap, subset or common cause refuters), the null distribution captures the distribution of effect estimates under the "true" dataset (e.g., with an additional confounder or different sampling), and we compute the probability of the obtained estimate under this distribution. If the probability is lower than the p-value, then the estimator method fails the test. Null Hypothesis- The estimate is a part of the distribution Alternative Hypothesis- The estimate does not fall in the distribution. :param 'estimate': CausalEstimate The estimate obtained from the estimator for the original data. :param 'simulations': np.array An array containing the result of the refuter for the simulations :param 'test_type': string, default 'auto' The type of test the user wishes to perform. :param 'significance_level': float, default 0.05 The significance level for the statistical test :returns: significance_dict: Dict A Dict containing the p_value and a boolean that indicates if the result is statistically significant """ # Initializing the p_value p_value = 0 if test_type == SignificanceTestType.AUTO: num_simulations = len(simulations) if num_simulations >= 100: # Bootstrapping logger.info( "Making use of Bootstrap as we have more than 100 examples.\n \ Note: The greater the number of examples, the more accurate are the confidence estimates" ) # Perform Bootstrap Significance Test with the original estimate and the set of refutations p_value = perform_bootstrap_test(estimate, simulations) else: logger.warning( "We assume a Normal Distribution as the sample has less than 100 examples.\n \ Note: The underlying distribution may not be Normal. We assume that it approaches normal with the increase in sample size." ) # Perform Normal Tests of Significance with the original estimate and the set of refutations p_value = perform_normal_distribution_test(estimate, simulations) elif test_type == SignificanceTestType.BOOTSTRAP: logger.info( "Performing Bootstrap Test with {} samples\n \ Note: The greater the number of examples, the more accurate are the confidence estimates".format( len(simulations) ) ) # Perform Bootstrap Significance Test with the original estimate and the set of refutations p_value = perform_bootstrap_test(estimate, simulations) elif test_type == SignificanceTestType.NORMAL: logger.info( "Performing Normal Test with {} samples\n \ Note: We assume that the underlying distribution is Normal.".format( len(simulations) ) ) # Perform Normal Tests of Significance with the original estimate and the set of refutations p_value = perform_normal_distribution_test(estimate, simulations) significance_dict = {"p_value": p_value, "is_statistically_significant": p_value <= significance_level} return significance_dict class CausalRefutation: """Class for storing the result of a refutation method.""" def __init__(self, estimated_effect, new_effect, refutation_type): self.estimated_effect = estimated_effect self.new_effect = new_effect self.refutation_type = refutation_type self.refutation_result = None def add_significance_test_results(self, refutation_result): self.refutation_result = refutation_result def add_refuter(self, refuter_instance): self.refuter = refuter_instance def interpret(self, method_name=None, **kwargs): """Interpret the refutation results. :param method_name: Method used (string) or a list of methods. If None, then the default for the specific refuter is used. :returns: None """ if method_name is None: method_name = self.refuter.interpret_method method_name_arr = parse_state(method_name) import dowhy.interpreters as interpreters for method in method_name_arr: interpreter = interpreters.get_class_object(method) interpreter(self, **kwargs).interpret() def __str__(self): if self.refutation_result is None: return "{0}\nEstimated effect:{1}\nNew effect:{2}\n".format( self.refutation_type, self.estimated_effect, self.new_effect ) else: return "{0}\nEstimated effect:{1}\nNew effect:{2}\np value:{3}\n".format( self.refutation_type, self.estimated_effect, self.new_effect, self.refutation_result["p_value"] )

andresmor-ms

133e7b9a4ed32aae8ab5f39a01eb02b3a4d1c0ba

e1652ec3c6606b1bb2dfe91ef830e4b4b566712d

I assume that CausalRefuter class is kept only for backwards compatibility? In that case, it will be good to add that to the docstring.

amit-sharma

py-why/dowhy

Functional api/refute estimate

* Refactor refuters into functions * Rename functional_api notebook for clarity * Add return types to identify_estimate * Update `__init__.py` for imports * Add joblib for bootstrap refuter * Create `refute_estimate` function * Add types for refuter parameters & return types

2022-10-04 16:18:49+00:00

2022-10-07 04:30:22+00:00

dowhy/causal_refuter.py

import logging import random import numpy as np import scipy.stats as st from dowhy.utils.api import parse_state class CausalRefuter: """Base class for different refutation methods. Subclasses implement specific refutations methods. # todo: add docstring for common parameters here and remove from child refuter classes """ # Default value for the number of simulations to be conducted DEFAULT_NUM_SIMULATIONS = 100 PROGRESS_BAR_COLOR = "green" def __init__(self, data, identified_estimand, estimate, **kwargs): self._data = data self._target_estimand = identified_estimand self._estimate = estimate self._treatment_name = self._target_estimand.treatment_variable self._outcome_name = self._target_estimand.outcome_variable self._random_seed = None # joblib params for parallel processing self._n_jobs = kwargs.pop("n_jobs", None) self._verbose = kwargs.pop("verbose", 0) if "random_seed" in kwargs: self._random_seed = kwargs["random_seed"] np.random.seed(self._random_seed) self.logger = logging.getLogger(__name__) # Concatenate the confounders, instruments and effect modifiers try: self._variables_of_interest = ( self._target_estimand.get_backdoor_variables() + self._target_estimand.instrumental_variables + self._estimate.params["effect_modifiers"] ) except AttributeError as attr_error: self.logger.error(attr_error) def choose_variables(self, required_variables): """ This method provides a way to choose the confounders whose values we wish to modify for finding its effect on the ability of the treatment to affect the outcome. """ invert = None if required_variables is False: self.logger.info( "All variables required: Running bootstrap adding noise to confounders, instrumental variables and effect modifiers." ) return None elif required_variables is True: self.logger.info( "All variables required: Running bootstrap adding noise to confounders, instrumental variables and effect modifiers." ) return self._variables_of_interest elif type(required_variables) is int: if len(self._variables_of_interest) < required_variables: self.logger.error( "Too many variables passed.\n The number of variables is: {}.\n The number of variables passed: {}".format( len(self._variables_of_interest), required_variables ) ) raise ValueError( "The number of variables in the required_variables is greater than the number of confounders, instrumental variables and effect modifiers" ) else: # Shuffle the confounders random.shuffle(self._variables_of_interest) return self._variables_of_interest[:required_variables] elif type(required_variables) is list: # Check if all are select or deselect variables if all(variable[0] == "-" for variable in required_variables): invert = True required_variables = [variable[1:] for variable in required_variables] elif all(variable[0] != "-" for variable in required_variables): invert = False else: self.logger.error("{} has both select and delect variables".format(required_variables)) raise ValueError( "It appears that there are some select and deselect variables. Note you can either select or delect variables at a time, but not both" ) # Check if all the required_variables belong to confounders, instrumental variables or effect if set(required_variables) - set(self._variables_of_interest) != set([]): self.logger.error( "{} are not confounder, instrumental variable or effect modifier".format( list(set(required_variables) - set(self._variables_of_interest)) ) ) raise ValueError( "At least one of required_variables is not a valid variable name, or it is not a confounder, instrumental variable or effect modifier" ) if invert is False: return required_variables elif invert is True: return list(set(self._variables_of_interest) - set(required_variables)) else: self.logger.error("Incorrect type: {}. Expected an int,list or bool".format(type(required_variables))) raise TypeError("Expected int, list or bool. Got an unexpected datatype") def test_significance(self, estimate, simulations, test_type="auto", significance_level=0.05): """Tests the statistical significance of the estimate obtained to the simulations produced by a refuter. The basis behind using the sample statistics of the refuter when we are in fact testing the estimate, is due to the fact that, we would ideally expect them to follow the same distribition. For refutation tests (e.g., placebo refuters), consider the null distribution as a distribution of effect estimates over multiple simulations with placebo treatment, and compute how likely the true estimate (e.g., zero for placebo test) is under the null. If the probability of true effect estimate is lower than the p-value, then estimator method fails the test. For sensitivity analysis tests (e.g., bootstrap, subset or common cause refuters), the null distribution captures the distribution of effect estimates under the "true" dataset (e.g., with an additional confounder or different sampling), and we compute the probability of the obtained estimate under this distribution. If the probability is lower than the p-value, then the estimator method fails the test. Null Hypothesis- The estimate is a part of the distribution Alternative Hypothesis- The estimate does not fall in the distribution. :param 'estimate': CausalEstimate The estimate obtained from the estimator for the original data. :param 'simulations': np.array An array containing the result of the refuter for the simulations :param 'test_type': string, default 'auto' The type of test the user wishes to perform. :param 'significance_level': float, default 0.05 The significance level for the statistical test :returns: significance_dict: Dict A Dict containing the p_value and a boolean that indicates if the result is statistically significant """ # Initializing the p_value p_value = 0 if test_type == "auto": num_simulations = len(simulations) if num_simulations >= 100: # Bootstrapping self.logger.info( "Making use of Bootstrap as we have more than 100 examples.\n \ Note: The greater the number of examples, the more accurate are the confidence estimates" ) # Perform Bootstrap Significance Test with the original estimate and the set of refutations p_value = self.perform_bootstrap_test(estimate, simulations) else: self.logger.warning( "We assume a Normal Distribution as the sample has less than 100 examples.\n \ Note: The underlying distribution may not be Normal. We assume that it approaches normal with the increase in sample size." ) # Perform Normal Tests of Significance with the original estimate and the set of refutations p_value = self.perform_normal_distribution_test(estimate, simulations) elif test_type == "bootstrap": self.logger.info( "Performing Bootstrap Test with {} samples\n \ Note: The greater the number of examples, the more accurate are the confidence estimates".format( len(simulations) ) ) # Perform Bootstrap Significance Test with the original estimate and the set of refutations p_value = self.perform_bootstrap_test(estimate, simulations) elif test_type == "normal_test": self.logger.info( "Performing Normal Test with {} samples\n \ Note: We assume that the underlying distribution is Normal.".format( len(simulations) ) ) # Perform Normal Tests of Significance with the original estimate and the set of refutations p_value = self.perform_normal_distribution_test(estimate, simulations) else: raise NotImplementedError significance_dict = {"p_value": p_value, "is_statistically_significant": p_value <= significance_level} return significance_dict def perform_bootstrap_test(self, estimate, simulations): # Get the number of simulations num_simulations = len(simulations) # Sort the simulations simulations.sort() # Obtain the median value median_refute_values = simulations[int(num_simulations / 2)] # Performing a two sided test if estimate.value > median_refute_values: # np.searchsorted tells us the index if it were a part of the array # We select side to be left as we want to find the first value that matches estimate_index = np.searchsorted(simulations, estimate.value, side="left") # We subtact 1 as we are finding the value from the right tail p_value = 1 - (estimate_index / num_simulations) else: # We take the side to be right as we want to find the last index that matches estimate_index = np.searchsorted(simulations, estimate.value, side="right") # We get the probability with respect to the left tail. p_value = estimate_index / num_simulations # return twice the determined quantile as this is a two sided test return 2 * p_value def perform_normal_distribution_test(self, estimate, simulations): # Get the mean for the simulations mean_refute_values = np.mean(simulations) # Get the standard deviation for the simulations std_dev_refute_values = np.std(simulations) # Get the Z Score [(val - mean)/ std_dev ] z_score = (estimate.value - mean_refute_values) / std_dev_refute_values if z_score > 0: # Right Tail p_value = 1 - st.norm.cdf(z_score) else: # Left Tail p_value = st.norm.cdf(z_score) return p_value def refute_estimate(self, show_progress_bar=False): raise NotImplementedError class CausalRefutation: """Class for storing the result of a refutation method.""" def __init__(self, estimated_effect, new_effect, refutation_type): self.estimated_effect = estimated_effect self.new_effect = new_effect self.refutation_type = refutation_type self.refutation_result = None def add_significance_test_results(self, refutation_result): self.refutation_result = refutation_result def add_refuter(self, refuter_instance): self.refuter = refuter_instance def interpret(self, method_name=None, **kwargs): """Interpret the refutation results. :param method_name: Method used (string) or a list of methods. If None, then the default for the specific refuter is used. :returns: None """ if method_name is None: method_name = self.refuter.interpret_method method_name_arr = parse_state(method_name) import dowhy.interpreters as interpreters for method in method_name_arr: interpreter = interpreters.get_class_object(method) interpreter(self, **kwargs).interpret() def __str__(self): if self.refutation_result is None: return "{0}\nEstimated effect:{1}\nNew effect:{2}\n".format( self.refutation_type, self.estimated_effect, self.new_effect ) else: return "{0}\nEstimated effect:{1}\nNew effect:{2}\np value:{3}\n".format( self.refutation_type, self.estimated_effect, self.new_effect, self.refutation_result["p_value"] )

import logging import random from enum import Enum from typing import List, Union import numpy as np import scipy.stats as st from dowhy.utils.api import parse_state class SignificanceTestType(Enum): AUTO = "auto" BOOTSTRAP = "bootstrap" NORMAL = "normal_test" logger = logging.getLogger(__name__) class CausalRefuter: """Base class for different refutation methods. Subclasses implement specific refutations methods. # todo: add docstring for common parameters here and remove from child refuter classes This class is for backwards compatibility with CausalModel Will be deprecated in the future in favor of function call refute_method_name() functions """ # Default value for the number of simulations to be conducted DEFAULT_NUM_SIMULATIONS = 100 PROGRESS_BAR_COLOR = "green" def __init__(self, data, identified_estimand, estimate, **kwargs): self._data = data self._target_estimand = identified_estimand self._estimate = estimate self._treatment_name = self._target_estimand.treatment_variable self._outcome_name = self._target_estimand.outcome_variable self._random_seed = None # joblib params for parallel processing self._n_jobs = kwargs.pop("n_jobs", None) self._verbose = kwargs.pop("verbose", 0) if "random_seed" in kwargs: self._random_seed = kwargs["random_seed"] np.random.seed(self._random_seed) # Concatenate the confounders, instruments and effect modifiers try: self._variables_of_interest = ( self._target_estimand.get_backdoor_variables() + self._target_estimand.instrumental_variables + self._estimate.params["effect_modifiers"] ) except AttributeError as attr_error: logger.error(attr_error) def choose_variables(self, required_variables): return choose_variables(required_variables, self._variables_of_interest) def test_significance(self, estimate, simulations, test_type="auto", significance_level=0.05): return test_significance(estimate, simulations, SignificanceTestType(test_type), significance_level) def perform_bootstrap_test(self, estimate, simulations): return perform_bootstrap_test(estimate, simulations) def perform_normal_distribution_test(self, estimate, simulations): return perform_normal_distribution_test(estimate, simulations) def refute_estimate(self, show_progress_bar=False): raise NotImplementedError def choose_variables(required_variables: Union[bool, int, list], variables_of_interest: List): """ This method provides a way to choose the confounders whose values we wish to modify for finding its effect on the ability of the treatment to affect the outcome. """ invert = None if required_variables is False: logger.info( "All variables required: Running bootstrap adding noise to confounders, instrumental variables and effect modifiers." ) return None elif required_variables is True: logger.info( "All variables required: Running bootstrap adding noise to confounders, instrumental variables and effect modifiers." ) return variables_of_interest elif type(required_variables) is int: if len(variables_of_interest) < required_variables: logger.error( "Too many variables passed.\n The number of variables is: {}.\n The number of variables passed: {}".format( len(variables_of_interest), required_variables ) ) raise ValueError( "The number of variables in the required_variables is greater than the number of confounders, instrumental variables and effect modifiers" ) else: # Shuffle the confounders return random.sample(variables_of_interest, required_variables) elif type(required_variables) is list: # Check if all are select or deselect variables if all(variable[0] == "-" for variable in required_variables): invert = True required_variables = [variable[1:] for variable in required_variables] elif all(variable[0] != "-" for variable in required_variables): invert = False else: logger.error("{} has both select and delect variables".format(required_variables)) raise ValueError( "It appears that there are some select and deselect variables. Note you can either select or delect variables at a time, but not both" ) # Check if all the required_variables belong to confounders, instrumental variables or effect if set(required_variables) - set(variables_of_interest) != set([]): logger.error( "{} are not confounder, instrumental variable or effect modifier".format( list(set(required_variables) - set(variables_of_interest)) ) ) raise ValueError( "At least one of required_variables is not a valid variable name, or it is not a confounder, instrumental variable or effect modifier" ) if invert is False: return required_variables elif invert is True: return list(set(variables_of_interest) - set(required_variables)) def perform_bootstrap_test(estimate, simulations: List): # Get the number of simulations num_simulations = len(simulations) # Sort the simulations simulations.sort() # Obtain the median value median_refute_values = simulations[int(num_simulations / 2)] # Performing a two sided test if estimate.value > median_refute_values: # np.searchsorted tells us the index if it were a part of the array # We select side to be left as we want to find the first value that matches estimate_index = np.searchsorted(simulations, estimate.value, side="left") # We subtact 1 as we are finding the value from the right tail p_value = 1 - (estimate_index / num_simulations) else: # We take the side to be right as we want to find the last index that matches estimate_index = np.searchsorted(simulations, estimate.value, side="right") # We get the probability with respect to the left tail. p_value = estimate_index / num_simulations # return twice the determined quantile as this is a two sided test return 2 * p_value def perform_normal_distribution_test(estimate, simulations: List): # Get the mean for the simulations mean_refute_values = np.mean(simulations) # Get the standard deviation for the simulations std_dev_refute_values = np.std(simulations) # Get the Z Score [(val - mean)/ std_dev ] z_score = (estimate.value - mean_refute_values) / std_dev_refute_values if z_score > 0: # Right Tail p_value = 1 - st.norm.cdf(z_score) else: # Left Tail p_value = st.norm.cdf(z_score) return p_value def test_significance( estimate, simulations: List, test_type: SignificanceTestType = SignificanceTestType.AUTO, significance_level: float = 0.85, ): """Tests the statistical significance of the estimate obtained to the simulations produced by a refuter. The basis behind using the sample statistics of the refuter when we are in fact testing the estimate, is due to the fact that, we would ideally expect them to follow the same distribition. For refutation tests (e.g., placebo refuters), consider the null distribution as a distribution of effect estimates over multiple simulations with placebo treatment, and compute how likely the true estimate (e.g., zero for placebo test) is under the null. If the probability of true effect estimate is lower than the p-value, then estimator method fails the test. For sensitivity analysis tests (e.g., bootstrap, subset or common cause refuters), the null distribution captures the distribution of effect estimates under the "true" dataset (e.g., with an additional confounder or different sampling), and we compute the probability of the obtained estimate under this distribution. If the probability is lower than the p-value, then the estimator method fails the test. Null Hypothesis- The estimate is a part of the distribution Alternative Hypothesis- The estimate does not fall in the distribution. :param 'estimate': CausalEstimate The estimate obtained from the estimator for the original data. :param 'simulations': np.array An array containing the result of the refuter for the simulations :param 'test_type': string, default 'auto' The type of test the user wishes to perform. :param 'significance_level': float, default 0.05 The significance level for the statistical test :returns: significance_dict: Dict A Dict containing the p_value and a boolean that indicates if the result is statistically significant """ # Initializing the p_value p_value = 0 if test_type == SignificanceTestType.AUTO: num_simulations = len(simulations) if num_simulations >= 100: # Bootstrapping logger.info( "Making use of Bootstrap as we have more than 100 examples.\n \ Note: The greater the number of examples, the more accurate are the confidence estimates" ) # Perform Bootstrap Significance Test with the original estimate and the set of refutations p_value = perform_bootstrap_test(estimate, simulations) else: logger.warning( "We assume a Normal Distribution as the sample has less than 100 examples.\n \ Note: The underlying distribution may not be Normal. We assume that it approaches normal with the increase in sample size." ) # Perform Normal Tests of Significance with the original estimate and the set of refutations p_value = perform_normal_distribution_test(estimate, simulations) elif test_type == SignificanceTestType.BOOTSTRAP: logger.info( "Performing Bootstrap Test with {} samples\n \ Note: The greater the number of examples, the more accurate are the confidence estimates".format( len(simulations) ) ) # Perform Bootstrap Significance Test with the original estimate and the set of refutations p_value = perform_bootstrap_test(estimate, simulations) elif test_type == SignificanceTestType.NORMAL: logger.info( "Performing Normal Test with {} samples\n \ Note: We assume that the underlying distribution is Normal.".format( len(simulations) ) ) # Perform Normal Tests of Significance with the original estimate and the set of refutations p_value = perform_normal_distribution_test(estimate, simulations) significance_dict = {"p_value": p_value, "is_statistically_significant": p_value <= significance_level} return significance_dict class CausalRefutation: """Class for storing the result of a refutation method.""" def __init__(self, estimated_effect, new_effect, refutation_type): self.estimated_effect = estimated_effect self.new_effect = new_effect self.refutation_type = refutation_type self.refutation_result = None def add_significance_test_results(self, refutation_result): self.refutation_result = refutation_result def add_refuter(self, refuter_instance): self.refuter = refuter_instance def interpret(self, method_name=None, **kwargs): """Interpret the refutation results. :param method_name: Method used (string) or a list of methods. If None, then the default for the specific refuter is used. :returns: None """ if method_name is None: method_name = self.refuter.interpret_method method_name_arr = parse_state(method_name) import dowhy.interpreters as interpreters for method in method_name_arr: interpreter = interpreters.get_class_object(method) interpreter(self, **kwargs).interpret() def __str__(self): if self.refutation_result is None: return "{0}\nEstimated effect:{1}\nNew effect:{2}\n".format( self.refutation_type, self.estimated_effect, self.new_effect ) else: return "{0}\nEstimated effect:{1}\nNew effect:{2}\np value:{3}\n".format( self.refutation_type, self.estimated_effect, self.new_effect, self.refutation_result["p_value"] )

andresmor-ms

133e7b9a4ed32aae8ab5f39a01eb02b3a4d1c0ba

e1652ec3c6606b1bb2dfe91ef830e4b4b566712d

Yep, that's correct, I'll add it in the next commit

andresmor-ms

py-why/dowhy

Functional api/refute estimate

* Refactor refuters into functions * Rename functional_api notebook for clarity * Add return types to identify_estimate * Update `__init__.py` for imports * Add joblib for bootstrap refuter * Create `refute_estimate` function * Add types for refuter parameters & return types

2022-10-04 16:18:49+00:00

2022-10-07 04:30:22+00:00

dowhy/causal_refuter.py

import logging import random import numpy as np import scipy.stats as st from dowhy.utils.api import parse_state class CausalRefuter: """Base class for different refutation methods. Subclasses implement specific refutations methods. # todo: add docstring for common parameters here and remove from child refuter classes """ # Default value for the number of simulations to be conducted DEFAULT_NUM_SIMULATIONS = 100 PROGRESS_BAR_COLOR = "green" def __init__(self, data, identified_estimand, estimate, **kwargs): self._data = data self._target_estimand = identified_estimand self._estimate = estimate self._treatment_name = self._target_estimand.treatment_variable self._outcome_name = self._target_estimand.outcome_variable self._random_seed = None # joblib params for parallel processing self._n_jobs = kwargs.pop("n_jobs", None) self._verbose = kwargs.pop("verbose", 0) if "random_seed" in kwargs: self._random_seed = kwargs["random_seed"] np.random.seed(self._random_seed) self.logger = logging.getLogger(__name__) # Concatenate the confounders, instruments and effect modifiers try: self._variables_of_interest = ( self._target_estimand.get_backdoor_variables() + self._target_estimand.instrumental_variables + self._estimate.params["effect_modifiers"] ) except AttributeError as attr_error: self.logger.error(attr_error) def choose_variables(self, required_variables): """ This method provides a way to choose the confounders whose values we wish to modify for finding its effect on the ability of the treatment to affect the outcome. """ invert = None if required_variables is False: self.logger.info( "All variables required: Running bootstrap adding noise to confounders, instrumental variables and effect modifiers." ) return None elif required_variables is True: self.logger.info( "All variables required: Running bootstrap adding noise to confounders, instrumental variables and effect modifiers." ) return self._variables_of_interest elif type(required_variables) is int: if len(self._variables_of_interest) < required_variables: self.logger.error( "Too many variables passed.\n The number of variables is: {}.\n The number of variables passed: {}".format( len(self._variables_of_interest), required_variables ) ) raise ValueError( "The number of variables in the required_variables is greater than the number of confounders, instrumental variables and effect modifiers" ) else: # Shuffle the confounders random.shuffle(self._variables_of_interest) return self._variables_of_interest[:required_variables] elif type(required_variables) is list: # Check if all are select or deselect variables if all(variable[0] == "-" for variable in required_variables): invert = True required_variables = [variable[1:] for variable in required_variables] elif all(variable[0] != "-" for variable in required_variables): invert = False else: self.logger.error("{} has both select and delect variables".format(required_variables)) raise ValueError( "It appears that there are some select and deselect variables. Note you can either select or delect variables at a time, but not both" ) # Check if all the required_variables belong to confounders, instrumental variables or effect if set(required_variables) - set(self._variables_of_interest) != set([]): self.logger.error( "{} are not confounder, instrumental variable or effect modifier".format( list(set(required_variables) - set(self._variables_of_interest)) ) ) raise ValueError( "At least one of required_variables is not a valid variable name, or it is not a confounder, instrumental variable or effect modifier" ) if invert is False: return required_variables elif invert is True: return list(set(self._variables_of_interest) - set(required_variables)) else: self.logger.error("Incorrect type: {}. Expected an int,list or bool".format(type(required_variables))) raise TypeError("Expected int, list or bool. Got an unexpected datatype") def test_significance(self, estimate, simulations, test_type="auto", significance_level=0.05): """Tests the statistical significance of the estimate obtained to the simulations produced by a refuter. The basis behind using the sample statistics of the refuter when we are in fact testing the estimate, is due to the fact that, we would ideally expect them to follow the same distribition. For refutation tests (e.g., placebo refuters), consider the null distribution as a distribution of effect estimates over multiple simulations with placebo treatment, and compute how likely the true estimate (e.g., zero for placebo test) is under the null. If the probability of true effect estimate is lower than the p-value, then estimator method fails the test. For sensitivity analysis tests (e.g., bootstrap, subset or common cause refuters), the null distribution captures the distribution of effect estimates under the "true" dataset (e.g., with an additional confounder or different sampling), and we compute the probability of the obtained estimate under this distribution. If the probability is lower than the p-value, then the estimator method fails the test. Null Hypothesis- The estimate is a part of the distribution Alternative Hypothesis- The estimate does not fall in the distribution. :param 'estimate': CausalEstimate The estimate obtained from the estimator for the original data. :param 'simulations': np.array An array containing the result of the refuter for the simulations :param 'test_type': string, default 'auto' The type of test the user wishes to perform. :param 'significance_level': float, default 0.05 The significance level for the statistical test :returns: significance_dict: Dict A Dict containing the p_value and a boolean that indicates if the result is statistically significant """ # Initializing the p_value p_value = 0 if test_type == "auto": num_simulations = len(simulations) if num_simulations >= 100: # Bootstrapping self.logger.info( "Making use of Bootstrap as we have more than 100 examples.\n \ Note: The greater the number of examples, the more accurate are the confidence estimates" ) # Perform Bootstrap Significance Test with the original estimate and the set of refutations p_value = self.perform_bootstrap_test(estimate, simulations) else: self.logger.warning( "We assume a Normal Distribution as the sample has less than 100 examples.\n \ Note: The underlying distribution may not be Normal. We assume that it approaches normal with the increase in sample size." ) # Perform Normal Tests of Significance with the original estimate and the set of refutations p_value = self.perform_normal_distribution_test(estimate, simulations) elif test_type == "bootstrap": self.logger.info( "Performing Bootstrap Test with {} samples\n \ Note: The greater the number of examples, the more accurate are the confidence estimates".format( len(simulations) ) ) # Perform Bootstrap Significance Test with the original estimate and the set of refutations p_value = self.perform_bootstrap_test(estimate, simulations) elif test_type == "normal_test": self.logger.info( "Performing Normal Test with {} samples\n \ Note: We assume that the underlying distribution is Normal.".format( len(simulations) ) ) # Perform Normal Tests of Significance with the original estimate and the set of refutations p_value = self.perform_normal_distribution_test(estimate, simulations) else: raise NotImplementedError significance_dict = {"p_value": p_value, "is_statistically_significant": p_value <= significance_level} return significance_dict def perform_bootstrap_test(self, estimate, simulations): # Get the number of simulations num_simulations = len(simulations) # Sort the simulations simulations.sort() # Obtain the median value median_refute_values = simulations[int(num_simulations / 2)] # Performing a two sided test if estimate.value > median_refute_values: # np.searchsorted tells us the index if it were a part of the array # We select side to be left as we want to find the first value that matches estimate_index = np.searchsorted(simulations, estimate.value, side="left") # We subtact 1 as we are finding the value from the right tail p_value = 1 - (estimate_index / num_simulations) else: # We take the side to be right as we want to find the last index that matches estimate_index = np.searchsorted(simulations, estimate.value, side="right") # We get the probability with respect to the left tail. p_value = estimate_index / num_simulations # return twice the determined quantile as this is a two sided test return 2 * p_value def perform_normal_distribution_test(self, estimate, simulations): # Get the mean for the simulations mean_refute_values = np.mean(simulations) # Get the standard deviation for the simulations std_dev_refute_values = np.std(simulations) # Get the Z Score [(val - mean)/ std_dev ] z_score = (estimate.value - mean_refute_values) / std_dev_refute_values if z_score > 0: # Right Tail p_value = 1 - st.norm.cdf(z_score) else: # Left Tail p_value = st.norm.cdf(z_score) return p_value def refute_estimate(self, show_progress_bar=False): raise NotImplementedError class CausalRefutation: """Class for storing the result of a refutation method.""" def __init__(self, estimated_effect, new_effect, refutation_type): self.estimated_effect = estimated_effect self.new_effect = new_effect self.refutation_type = refutation_type self.refutation_result = None def add_significance_test_results(self, refutation_result): self.refutation_result = refutation_result def add_refuter(self, refuter_instance): self.refuter = refuter_instance def interpret(self, method_name=None, **kwargs): """Interpret the refutation results. :param method_name: Method used (string) or a list of methods. If None, then the default for the specific refuter is used. :returns: None """ if method_name is None: method_name = self.refuter.interpret_method method_name_arr = parse_state(method_name) import dowhy.interpreters as interpreters for method in method_name_arr: interpreter = interpreters.get_class_object(method) interpreter(self, **kwargs).interpret() def __str__(self): if self.refutation_result is None: return "{0}\nEstimated effect:{1}\nNew effect:{2}\n".format( self.refutation_type, self.estimated_effect, self.new_effect ) else: return "{0}\nEstimated effect:{1}\nNew effect:{2}\np value:{3}\n".format( self.refutation_type, self.estimated_effect, self.new_effect, self.refutation_result["p_value"] )

import logging import random from enum import Enum from typing import List, Union import numpy as np import scipy.stats as st from dowhy.utils.api import parse_state class SignificanceTestType(Enum): AUTO = "auto" BOOTSTRAP = "bootstrap" NORMAL = "normal_test" logger = logging.getLogger(__name__) class CausalRefuter: """Base class for different refutation methods. Subclasses implement specific refutations methods. # todo: add docstring for common parameters here and remove from child refuter classes This class is for backwards compatibility with CausalModel Will be deprecated in the future in favor of function call refute_method_name() functions """ # Default value for the number of simulations to be conducted DEFAULT_NUM_SIMULATIONS = 100 PROGRESS_BAR_COLOR = "green" def __init__(self, data, identified_estimand, estimate, **kwargs): self._data = data self._target_estimand = identified_estimand self._estimate = estimate self._treatment_name = self._target_estimand.treatment_variable self._outcome_name = self._target_estimand.outcome_variable self._random_seed = None # joblib params for parallel processing self._n_jobs = kwargs.pop("n_jobs", None) self._verbose = kwargs.pop("verbose", 0) if "random_seed" in kwargs: self._random_seed = kwargs["random_seed"] np.random.seed(self._random_seed) # Concatenate the confounders, instruments and effect modifiers try: self._variables_of_interest = ( self._target_estimand.get_backdoor_variables() + self._target_estimand.instrumental_variables + self._estimate.params["effect_modifiers"] ) except AttributeError as attr_error: logger.error(attr_error) def choose_variables(self, required_variables): return choose_variables(required_variables, self._variables_of_interest) def test_significance(self, estimate, simulations, test_type="auto", significance_level=0.05): return test_significance(estimate, simulations, SignificanceTestType(test_type), significance_level) def perform_bootstrap_test(self, estimate, simulations): return perform_bootstrap_test(estimate, simulations) def perform_normal_distribution_test(self, estimate, simulations): return perform_normal_distribution_test(estimate, simulations) def refute_estimate(self, show_progress_bar=False): raise NotImplementedError def choose_variables(required_variables: Union[bool, int, list], variables_of_interest: List): """ This method provides a way to choose the confounders whose values we wish to modify for finding its effect on the ability of the treatment to affect the outcome. """ invert = None if required_variables is False: logger.info( "All variables required: Running bootstrap adding noise to confounders, instrumental variables and effect modifiers." ) return None elif required_variables is True: logger.info( "All variables required: Running bootstrap adding noise to confounders, instrumental variables and effect modifiers." ) return variables_of_interest elif type(required_variables) is int: if len(variables_of_interest) < required_variables: logger.error( "Too many variables passed.\n The number of variables is: {}.\n The number of variables passed: {}".format( len(variables_of_interest), required_variables ) ) raise ValueError( "The number of variables in the required_variables is greater than the number of confounders, instrumental variables and effect modifiers" ) else: # Shuffle the confounders return random.sample(variables_of_interest, required_variables) elif type(required_variables) is list: # Check if all are select or deselect variables if all(variable[0] == "-" for variable in required_variables): invert = True required_variables = [variable[1:] for variable in required_variables] elif all(variable[0] != "-" for variable in required_variables): invert = False else: logger.error("{} has both select and delect variables".format(required_variables)) raise ValueError( "It appears that there are some select and deselect variables. Note you can either select or delect variables at a time, but not both" ) # Check if all the required_variables belong to confounders, instrumental variables or effect if set(required_variables) - set(variables_of_interest) != set([]): logger.error( "{} are not confounder, instrumental variable or effect modifier".format( list(set(required_variables) - set(variables_of_interest)) ) ) raise ValueError( "At least one of required_variables is not a valid variable name, or it is not a confounder, instrumental variable or effect modifier" ) if invert is False: return required_variables elif invert is True: return list(set(variables_of_interest) - set(required_variables)) def perform_bootstrap_test(estimate, simulations: List): # Get the number of simulations num_simulations = len(simulations) # Sort the simulations simulations.sort() # Obtain the median value median_refute_values = simulations[int(num_simulations / 2)] # Performing a two sided test if estimate.value > median_refute_values: # np.searchsorted tells us the index if it were a part of the array # We select side to be left as we want to find the first value that matches estimate_index = np.searchsorted(simulations, estimate.value, side="left") # We subtact 1 as we are finding the value from the right tail p_value = 1 - (estimate_index / num_simulations) else: # We take the side to be right as we want to find the last index that matches estimate_index = np.searchsorted(simulations, estimate.value, side="right") # We get the probability with respect to the left tail. p_value = estimate_index / num_simulations # return twice the determined quantile as this is a two sided test return 2 * p_value def perform_normal_distribution_test(estimate, simulations: List): # Get the mean for the simulations mean_refute_values = np.mean(simulations) # Get the standard deviation for the simulations std_dev_refute_values = np.std(simulations) # Get the Z Score [(val - mean)/ std_dev ] z_score = (estimate.value - mean_refute_values) / std_dev_refute_values if z_score > 0: # Right Tail p_value = 1 - st.norm.cdf(z_score) else: # Left Tail p_value = st.norm.cdf(z_score) return p_value def test_significance( estimate, simulations: List, test_type: SignificanceTestType = SignificanceTestType.AUTO, significance_level: float = 0.85, ): """Tests the statistical significance of the estimate obtained to the simulations produced by a refuter. The basis behind using the sample statistics of the refuter when we are in fact testing the estimate, is due to the fact that, we would ideally expect them to follow the same distribition. For refutation tests (e.g., placebo refuters), consider the null distribution as a distribution of effect estimates over multiple simulations with placebo treatment, and compute how likely the true estimate (e.g., zero for placebo test) is under the null. If the probability of true effect estimate is lower than the p-value, then estimator method fails the test. For sensitivity analysis tests (e.g., bootstrap, subset or common cause refuters), the null distribution captures the distribution of effect estimates under the "true" dataset (e.g., with an additional confounder or different sampling), and we compute the probability of the obtained estimate under this distribution. If the probability is lower than the p-value, then the estimator method fails the test. Null Hypothesis- The estimate is a part of the distribution Alternative Hypothesis- The estimate does not fall in the distribution. :param 'estimate': CausalEstimate The estimate obtained from the estimator for the original data. :param 'simulations': np.array An array containing the result of the refuter for the simulations :param 'test_type': string, default 'auto' The type of test the user wishes to perform. :param 'significance_level': float, default 0.05 The significance level for the statistical test :returns: significance_dict: Dict A Dict containing the p_value and a boolean that indicates if the result is statistically significant """ # Initializing the p_value p_value = 0 if test_type == SignificanceTestType.AUTO: num_simulations = len(simulations) if num_simulations >= 100: # Bootstrapping logger.info( "Making use of Bootstrap as we have more than 100 examples.\n \ Note: The greater the number of examples, the more accurate are the confidence estimates" ) # Perform Bootstrap Significance Test with the original estimate and the set of refutations p_value = perform_bootstrap_test(estimate, simulations) else: logger.warning( "We assume a Normal Distribution as the sample has less than 100 examples.\n \ Note: The underlying distribution may not be Normal. We assume that it approaches normal with the increase in sample size." ) # Perform Normal Tests of Significance with the original estimate and the set of refutations p_value = perform_normal_distribution_test(estimate, simulations) elif test_type == SignificanceTestType.BOOTSTRAP: logger.info( "Performing Bootstrap Test with {} samples\n \ Note: The greater the number of examples, the more accurate are the confidence estimates".format( len(simulations) ) ) # Perform Bootstrap Significance Test with the original estimate and the set of refutations p_value = perform_bootstrap_test(estimate, simulations) elif test_type == SignificanceTestType.NORMAL: logger.info( "Performing Normal Test with {} samples\n \ Note: We assume that the underlying distribution is Normal.".format( len(simulations) ) ) # Perform Normal Tests of Significance with the original estimate and the set of refutations p_value = perform_normal_distribution_test(estimate, simulations) significance_dict = {"p_value": p_value, "is_statistically_significant": p_value <= significance_level} return significance_dict class CausalRefutation: """Class for storing the result of a refutation method.""" def __init__(self, estimated_effect, new_effect, refutation_type): self.estimated_effect = estimated_effect self.new_effect = new_effect self.refutation_type = refutation_type self.refutation_result = None def add_significance_test_results(self, refutation_result): self.refutation_result = refutation_result def add_refuter(self, refuter_instance): self.refuter = refuter_instance def interpret(self, method_name=None, **kwargs): """Interpret the refutation results. :param method_name: Method used (string) or a list of methods. If None, then the default for the specific refuter is used. :returns: None """ if method_name is None: method_name = self.refuter.interpret_method method_name_arr = parse_state(method_name) import dowhy.interpreters as interpreters for method in method_name_arr: interpreter = interpreters.get_class_object(method) interpreter(self, **kwargs).interpret() def __str__(self): if self.refutation_result is None: return "{0}\nEstimated effect:{1}\nNew effect:{2}\n".format( self.refutation_type, self.estimated_effect, self.new_effect ) else: return "{0}\nEstimated effect:{1}\nNew effect:{2}\np value:{3}\n".format( self.refutation_type, self.estimated_effect, self.new_effect, self.refutation_result["p_value"] )

andresmor-ms

133e7b9a4ed32aae8ab5f39a01eb02b3a4d1c0ba

e1652ec3c6606b1bb2dfe91ef830e4b4b566712d

found more instances of this typo, fixed them all

andresmor-ms

py-why/dowhy

Functional api/refute estimate

* Refactor refuters into functions * Rename functional_api notebook for clarity * Add return types to identify_estimate * Update `__init__.py` for imports * Add joblib for bootstrap refuter * Create `refute_estimate` function * Add types for refuter parameters & return types

2022-10-04 16:18:49+00:00

2022-10-07 04:30:22+00:00

dowhy/causal_refuters/add_unobserved_common_cause.py

import copy import logging import math import numpy as np import pandas as pd import scipy.stats import statsmodels.api as sm from sklearn.linear_model import LogisticRegression from sklearn.preprocessing import StandardScaler from tqdm.auto import tqdm import dowhy.causal_estimators.econml from dowhy.causal_estimator import CausalEstimator from dowhy.causal_estimators.linear_regression_estimator import LinearRegressionEstimator from dowhy.causal_estimators.regression_estimator import RegressionEstimator from dowhy.causal_refuter import CausalRefutation, CausalRefuter from dowhy.causal_refuters.evalue_sensitivity_analyzer import EValueSensitivityAnalyzer from dowhy.causal_refuters.linear_sensitivity_analyzer import LinearSensitivityAnalyzer from dowhy.causal_refuters.non_parametric_sensitivity_analyzer import NonParametricSensitivityAnalyzer from dowhy.causal_refuters.partial_linear_sensitivity_analyzer import PartialLinearSensitivityAnalyzer class AddUnobservedCommonCause(CausalRefuter): """Add an unobserved confounder for refutation. AddUnobservedCommonCause class supports three methods: 1) Simulation of an unobserved confounder 2) Linear partial R2 : Sensitivity Analysis for linear models. 3) Non-Parametric partial R2 based : Sensitivity Analyis for non-parametric models. Supports additional parameters that can be specified in the refute_estimate() method. """ def __init__(self, *args, **kwargs): """ Initialize the parameters required for the refuter. For direct_simulation, if effect_strength_on_treatment or effect_strength_on_outcome is not given, it is calculated automatically as a range between the minimum and maximum effect strength of observed confounders on treatment and outcome respectively. :param simulation_method: The method to use for simulating effect of unobserved confounder. Possible values are ["direct-simulation", "linear-partial-R2", "non-parametric-partial-R2", "e-value"]. :param confounders_effect_on_treatment: str : The type of effect on the treatment due to the unobserved confounder. Possible values are ['binary_flip', 'linear'] :param confounders_effect_on_outcome: str : The type of effect on the outcome due to the unobserved confounder. Possible values are ['binary_flip', 'linear'] :param effect_strength_on_treatment: float, numpy.ndarray: [Used when simulation_method="direct-simulation"] Strength of the confounder's effect on treatment. When confounders_effect_on_treatment is linear, it is the regression coefficient. When the confounders_effect_on_treatment is binary flip, it is the probability with which effect of unobserved confounder can invert the value of the treatment. :param effect_strength_on_outcome: float, numpy.ndarray: Strength of the confounder's effect on outcome. Its interpretation depends on confounders_effect_on_outcome and the simulation_method. When simulation_method is direct-simulation, for a linear effect it behaves like the regression coefficient and for a binary flip, it is the probability with which it can invert the value of the outcome. :param partial_r2_confounder_treatment: float, numpy.ndarray: [Used when simulation_method is linear-partial-R2 or non-parametric-partial-R2] Partial R2 of the unobserved confounder wrt the treatment conditioned on the observed confounders. Only in the case of general non-parametric-partial-R2, it is the fraction of variance in the reisz representer that is explained by the unobserved confounder; specifically (1-r), where r is the ratio of variance of reisz representer, alpha^2, based on observed confounders and that based on all confounders. :param partial_r2_confounder_outcome: float, numpy.ndarray: [Used when simulation_method is linear-partial-R2 or non-parametric-partial-R2] Partial R2 of the unobserved confounder wrt the outcome conditioned on the treatment and observed confounders. :param frac_strength_treatment: float: This parameter decides the effect strength of the simulated confounder as a fraction of the effect strength of observed confounders on treatment. Defaults to 1. :param frac_strength_outcome: float: This parameter decides the effect strength of the simulated confounder as a fraction of the effect strength of observed confounders on outcome. Defaults to 1. :param plotmethod: string: Type of plot to be shown. If None, no plot is generated. This parameter is used only only when more than one treatment confounder effect values or outcome confounder effect values are provided. Default is "colormesh". Supported values are "contour", "colormesh" when more than one value is provided for both confounder effect value parameters; "line" when provided for only one of them. :param percent_change_estimate: It is the percentage of reduction of treatment estimate that could alter the results (default = 1). if percent_change_estimate = 1, the robustness value describes the strength of association of confounders with treatment and outcome in order to reduce the estimate by 100% i.e bring it down to 0. (relevant only for Linear Sensitivity Analysis, ignore for rest) :param confounder_increases_estimate: True implies that confounder increases the absolute value of estimate and vice versa. (Default = False). (relevant only for Linear Sensitivity Analysis, ignore for rest) :param benchmark_common_causes: names of variables for bounding strength of confounders. (relevant only for partial-r2 based simulation methods) :param significance_level: confidence interval for statistical inference(default = 0.05). (relevant only for partial-r2 based simulation methods) :param null_hypothesis_effect: assumed effect under the null hypothesis. (relevant only for linear-partial-R2, ignore for rest) :param plot_estimate: Generate contour plot for estimate while performing sensitivity analysis. (default = True). (relevant only for partial-r2 based simulation methods) :param num_splits: number of splits for cross validation. (default = 5). (relevant only for non-parametric-partial-R2 simulation method) :param shuffle_data : shuffle data or not before splitting into folds (default = False). (relevant only for non-parametric-partial-R2 simulation method) :param shuffle_random_seed: seed for randomly shuffling data. (relevant only for non-parametric-partial-R2 simulation method) :param alpha_s_estimator_param_list: list of dictionaries with parameters for finding alpha_s. (relevant only for non-parametric-partial-R2 simulation method) :param g_s_estimator_list: list of estimator objects for finding g_s. These objects should have fit() and predict() functions implemented. (relevant only for non-parametric-partial-R2 simulation method) :param g_s_estimator_param_list: list of dictionaries with parameters for tuning respective estimators in "g_s_estimator_list". The order of the dictionaries in the list should be consistent with the estimator objects order in "g_s_estimator_list". (relevant only for non-parametric-partial-R2 simulation method) """ super().__init__(*args, **kwargs) self.simulation_method = kwargs["simulation_method"] if "simulation_method" in kwargs else "direct-simulation" self.effect_on_t = ( kwargs["confounders_effect_on_treatment"] if "confounders_effect_on_treatment" in kwargs else "binary_flip" ) self.effect_on_y = ( kwargs["confounders_effect_on_outcome"] if "confounders_effect_on_outcome" in kwargs else "linear" ) if self.simulation_method == "direct-simulation": self.kappa_t = kwargs["effect_strength_on_treatment"] if "effect_strength_on_treatment" in kwargs else None self.kappa_y = kwargs["effect_strength_on_outcome"] if "effect_strength_on_outcome" in kwargs else None elif self.simulation_method in ["linear-partial-R2", "non-parametric-partial-R2"]: self.kappa_t = ( kwargs["partial_r2_confounder_treatment"] if "partial_r2_confounder_treatment" in kwargs else None ) self.kappa_y = ( kwargs["partial_r2_confounder_outcome"] if "partial_r2_confounder_outcome" in kwargs else None ) elif self.simulation_method == "e-value": pass else: raise ValueError( "simulation method is not supported. Try direct-simulation, linear-partial-R2, non-parametric-partial-R2, or e-value" ) self.frac_strength_treatment = ( kwargs["effect_fraction_on_treatment"] if "effect_fraction_on_treatment" in kwargs else 1 ) self.frac_strength_outcome = ( kwargs["effect_fraction_on_outcome"] if "effect_fraction_on_outcome" in kwargs else 1 ) self.plotmethod = kwargs["plotmethod"] if "plotmethod" in kwargs else "colormesh" self.percent_change_estimate = kwargs["percent_change_estimate"] if "percent_change_estimate" in kwargs else 1.0 self.significance_level = kwargs["significance_level"] if "significance_level" in kwargs else 0.05 self.confounder_increases_estimate = ( kwargs["confounder_increases_estimate"] if "confounder_increases_estimate" in kwargs else False ) self.benchmark_common_causes = ( kwargs["benchmark_common_causes"] if "benchmark_common_causes" in kwargs else None ) self.null_hypothesis_effect = kwargs["null_hypothesis_effect"] if "null_hypothesis_effect" in kwargs else 0 self.plot_estimate = kwargs["plot_estimate"] if "plot_estimate" in kwargs else True self.num_splits = kwargs["num_splits"] if "num_splits" in kwargs else 5 self.shuffle_data = kwargs["shuffle_data"] if "shuffle_data" in kwargs else False self.shuffle_random_seed = kwargs["shuffle_random_seed"] if "shuffle_random_seed" in kwargs else None self.alpha_s_estimator_param_list = ( kwargs["alpha_s_estimator_param_list"] if "alpha_s_estimator_param_list" in kwargs else None ) self.alpha_s_estimator_list = kwargs["alpha_s_estimator_list"] if "alpha_s_estimator_list" in kwargs else None self.g_s_estimator_list = kwargs["g_s_estimator_list"] if "g_s_estimator_list" in kwargs else None self.g_s_estimator_param_list = ( kwargs["g_s_estimator_param_list"] if "g_s_estimator_param_list" in kwargs else None ) self.plugin_reisz = kwargs["plugin_reisz"] if "plugin_reisz" in kwargs else False self.logger = logging.getLogger(__name__) def infer_default_kappa_t(self, len_kappa_t=10): """Infer default effect strength of simulated confounder on treatment.""" observed_common_causes_names = self._target_estimand.get_backdoor_variables() if len(observed_common_causes_names) > 0: observed_common_causes = self._data[observed_common_causes_names] observed_common_causes = pd.get_dummies(observed_common_causes, drop_first=True) else: raise ValueError( "There needs to be at least one common cause to" + "automatically compute the default value of kappa_t." + " Provide a value for kappa_t" ) t = self._data[self._treatment_name] # Standardizing the data observed_common_causes = StandardScaler().fit_transform(observed_common_causes) if self.effect_on_t == "binary_flip": # Fit a model containing all confounders and compare predictions # using all features compared to all features except a given # confounder. tmodel = LogisticRegression().fit(observed_common_causes, t) tpred = tmodel.predict(observed_common_causes).astype(int) flips = [] for i in range(observed_common_causes.shape[1]): oldval = np.copy(observed_common_causes[:, i]) observed_common_causes[:, i] = 0 tcap = tmodel.predict(observed_common_causes).astype(int) observed_common_causes[:, i] = oldval flips.append(np.sum(abs(tcap - tpred)) / tpred.shape[0]) min_coeff, max_coeff = min(flips), max(flips) elif self.effect_on_t == "linear": # Estimating the regression coefficient from standardized features to t corrcoef_var_t = np.corrcoef(observed_common_causes, t, rowvar=False)[-1, :-1] std_dev_t = np.std(t)[0] max_coeff = max(corrcoef_var_t) * std_dev_t min_coeff = min(corrcoef_var_t) * std_dev_t else: raise NotImplementedError( "'" + self.effect_on_t + "' method not supported for confounders' effect on treatment" ) min_coeff, max_coeff = self._compute_min_max_coeff(min_coeff, max_coeff, self.frac_strength_treatment) # By default, return a plot with 10 points # consider 10 values of the effect of the unobserved confounder step = (max_coeff - min_coeff) / len_kappa_t self.logger.info("(Min, Max) kappa_t for observed common causes, ({0}, {1})".format(min_coeff, max_coeff)) if np.equal(max_coeff, min_coeff): return max_coeff else: return np.arange(min_coeff, max_coeff, step) def _compute_min_max_coeff(self, min_coeff, max_coeff, effect_strength_fraction): max_coeff = effect_strength_fraction * max_coeff min_coeff = effect_strength_fraction * min_coeff return min_coeff, max_coeff def infer_default_kappa_y(self, len_kappa_y=10): """Infer default effect strength of simulated confounder on treatment.""" observed_common_causes_names = self._target_estimand.get_backdoor_variables() if len(observed_common_causes_names) > 0: observed_common_causes = self._data[observed_common_causes_names] observed_common_causes = pd.get_dummies(observed_common_causes, drop_first=True) else: raise ValueError( "There needs to be at least one common cause to" + "automatically compute the default value of kappa_y." + " Provide a value for kappa_y" ) y = self._data[self._outcome_name] # Standardizing the data observed_common_causes = StandardScaler().fit_transform(observed_common_causes) if self.effect_on_y == "binary_flip": # Fit a model containing all confounders and compare predictions # using all features compared to all features except a given # confounder. ymodel = LogisticRegression().fit(observed_common_causes, y) ypred = ymodel.predict(observed_common_causes).astype(int) flips = [] for i in range(observed_common_causes.shape[1]): oldval = np.copy(observed_common_causes[:, i]) observed_common_causes[:, i] = 0 ycap = ymodel.predict(observed_common_causes).astype(int) observed_common_causes[:, i] = oldval flips.append(np.sum(abs(ycap - ypred)) / ypred.shape[0]) min_coeff, max_coeff = min(flips), max(flips) elif self.effect_on_y == "linear": corrcoef_var_y = np.corrcoef(observed_common_causes, y, rowvar=False)[-1, :-1] std_dev_y = np.std(y)[0] max_coeff = max(corrcoef_var_y) * std_dev_y min_coeff = min(corrcoef_var_y) * std_dev_y else: raise NotImplementedError( "'" + self.effect_on_y + "' method not supported for confounders' effect on outcome" ) min_coeff, max_coeff = self._compute_min_max_coeff(min_coeff, max_coeff, self.frac_strength_outcome) # By default, return a plot with 10 points # consider 10 values of the effect of the unobserved confounder step = (max_coeff - min_coeff) / len_kappa_y self.logger.info("(Min, Max) kappa_y for observed common causes, ({0}, {1})".format(min_coeff, max_coeff)) if np.equal(max_coeff, min_coeff): return max_coeff else: return np.arange(min_coeff, max_coeff, step) def refute_estimate(self, show_progress_bar=False): """ This function attempts to add an unobserved common cause to the outcome and the treatment. At present, we have implemented the behavior for one dimensional behaviors for continuous and binary variables. This function can either take single valued inputs or a range of inputs. The function then looks at the data type of the input and then decides on the course of action. :return: CausalRefuter: An object that contains the estimated effect and a new effect and the name of the refutation used. """ if self.simulation_method == "linear-partial-R2": if not (isinstance(self._estimate.estimator, LinearRegressionEstimator)): raise NotImplementedError( "Currently only LinearRegressionEstimator is supported for Sensitivity Analysis" ) if len(self._estimate.estimator._effect_modifier_names) > 0: raise NotImplementedError("The current implementation does not support effect modifiers") if self.frac_strength_outcome == 1: self.frac_strength_outcome = self.frac_strength_treatment analyzer = LinearSensitivityAnalyzer( estimator=self._estimate.estimator, data=self._data, treatment_name=self._treatment_name, percent_change_estimate=self.percent_change_estimate, significance_level=self.significance_level, benchmark_common_causes=self.benchmark_common_causes, null_hypothesis_effect=self.null_hypothesis_effect, frac_strength_treatment=self.frac_strength_treatment, frac_strength_outcome=self.frac_strength_outcome, common_causes_order=self._estimate.estimator._observed_common_causes.columns, ) analyzer.check_sensitivity(plot=self.plot_estimate) return analyzer if self.simulation_method == "non-parametric-partial-R2": # If the estimator used is LinearDML, partially linear sensitivity analysis will be automatically chosen if isinstance(self._estimate.estimator, dowhy.causal_estimators.econml.Econml): if self._estimate.estimator._econml_methodname == "econml.dml.LinearDML": analyzer = PartialLinearSensitivityAnalyzer( estimator=self._estimate._estimator_object, observed_common_causes=self._estimate.estimator._observed_common_causes, treatment=self._estimate.estimator._treatment, outcome=self._estimate.estimator._outcome, alpha_s_estimator_param_list=self.alpha_s_estimator_param_list, g_s_estimator_list=self.g_s_estimator_list, g_s_estimator_param_list=self.g_s_estimator_param_list, effect_strength_treatment=self.kappa_t, effect_strength_outcome=self.kappa_y, benchmark_common_causes=self.benchmark_common_causes, frac_strength_treatment=self.frac_strength_treatment, frac_strength_outcome=self.frac_strength_outcome, ) analyzer.check_sensitivity(plot=self.plot_estimate) return analyzer analyzer = NonParametricSensitivityAnalyzer( estimator=self._estimate.estimator, observed_common_causes=self._estimate.estimator._observed_common_causes, treatment=self._estimate.estimator._treatment, outcome=self._estimate.estimator._outcome, alpha_s_estimator_list=self.alpha_s_estimator_list, alpha_s_estimator_param_list=self.alpha_s_estimator_param_list, g_s_estimator_list=self.g_s_estimator_list, g_s_estimator_param_list=self.g_s_estimator_param_list, effect_strength_treatment=self.kappa_t, effect_strength_outcome=self.kappa_y, benchmark_common_causes=self.benchmark_common_causes, frac_strength_treatment=self.frac_strength_treatment, frac_strength_outcome=self.frac_strength_outcome, theta_s=self._estimate.value, plugin_reisz=self.plugin_reisz, ) analyzer.check_sensitivity(plot=self.plot_estimate) return analyzer if self.simulation_method == "e-value": if not isinstance(self._estimate.estimator, RegressionEstimator): raise NotImplementedError( "E-Value sensitivity analysis is currently only implemented RegressionEstimator." ) if len(self._estimate.estimator._effect_modifier_names) > 0: raise NotImplementedError("The current implementation does not support effect modifiers") analyzer = EValueSensitivityAnalyzer( estimate=self._estimate, estimand=self._target_estimand, data=self._data, treatment_name=self._treatment_name[0], outcome_name=self._outcome_name[0], ) analyzer.check_sensitivity(plot=self.plot_estimate) return analyzer if self.kappa_t is None: self.kappa_t = self.infer_default_kappa_t() if self.kappa_y is None: self.kappa_y = self.infer_default_kappa_y() if not isinstance(self.kappa_t, (list, np.ndarray)) and not isinstance( self.kappa_y, (list, np.ndarray) ): # Deal with single value inputs new_data = copy.deepcopy(self._data) new_data = self.include_confounders_effect(new_data, self.kappa_t, self.kappa_y) new_estimator = CausalEstimator.get_estimator_object(new_data, self._target_estimand, self._estimate) new_effect = new_estimator.estimate_effect() refute = CausalRefutation( self._estimate.value, new_effect.value, refutation_type="Refute: Add an Unobserved Common Cause" ) refute.new_effect_array = np.array(new_effect.value) refute.new_effect = new_effect.value refute.add_refuter(self) return refute else: # Deal with multiple value inputs if isinstance(self.kappa_t, (list, np.ndarray)) and isinstance( self.kappa_y, (list, np.ndarray) ): # Deal with range inputs # Get a 2D matrix of values # x,y = np.meshgrid(self.kappa_t, self.kappa_y) # x,y are both MxN results_matrix = np.random.rand( len(self.kappa_t), len(self.kappa_y) ) # Matrix to hold all the results of NxM orig_data = copy.deepcopy(self._data) for i in tqdm( range(len(self.kappa_t)), colour=CausalRefuter.PROGRESS_BAR_COLOR, disable=not show_progress_bar, desc="Refuting Estimates: ", ): for j in range(len(self.kappa_y)): new_data = self.include_confounders_effect(orig_data, self.kappa_t[i], self.kappa_y[j]) new_estimator = CausalEstimator.get_estimator_object( new_data, self._target_estimand, self._estimate ) new_effect = new_estimator.estimate_effect() refute = CausalRefutation( self._estimate.value, new_effect.value, refutation_type="Refute: Add an Unobserved Common Cause", ) results_matrix[i][j] = refute.new_effect # Populate the results refute.new_effect_array = results_matrix refute.new_effect = (np.min(results_matrix), np.max(results_matrix)) # Store the values into the refute object refute.add_refuter(self) if self.plotmethod is None: return refute import matplotlib import matplotlib.pyplot as plt fig = plt.figure(figsize=(6, 5)) left, bottom, width, height = 0.1, 0.1, 0.8, 0.8 ax = fig.add_axes([left, bottom, width, height]) oe = self._estimate.value contour_levels = [oe / 4.0, oe / 2.0, (3.0 / 4) * oe, oe] contour_levels.extend([0, np.min(results_matrix), np.max(results_matrix)]) if self.plotmethod == "contour": cp = plt.contourf(self.kappa_y, self.kappa_t, results_matrix, levels=sorted(contour_levels)) # Adding a label on the contour line for the original estimate fmt = {} trueeffect_index = np.where(cp.levels == oe)[0][0] fmt[cp.levels[trueeffect_index]] = "Estimated Effect" # Label every other level using strings plt.clabel(cp, [cp.levels[trueeffect_index]], inline=True, fmt=fmt) plt.colorbar(cp) elif self.plotmethod == "colormesh": cp = plt.pcolormesh(self.kappa_y, self.kappa_t, results_matrix, shading="nearest") plt.colorbar(cp, ticks=contour_levels) ax.yaxis.set_ticks(self.kappa_t) ax.xaxis.set_ticks(self.kappa_y) plt.xticks(rotation=45) ax.set_title("Effect of Unobserved Common Cause") ax.set_ylabel("Value of Linear Constant on Treatment") ax.set_xlabel("Value of Linear Constant on Outcome") plt.show() return refute elif isinstance(self.kappa_t, (list, np.ndarray)): outcomes = np.random.rand(len(self.kappa_t)) orig_data = copy.deepcopy(self._data) for i in tqdm( range(0, len(self.kappa_t)), colour=CausalRefuter.PROGRESS_BAR_COLOR, disable=not show_progress_bar, desc="Refuting Estimates: ", ): new_data = self.include_confounders_effect(orig_data, self.kappa_t[i], self.kappa_y) new_estimator = CausalEstimator.get_estimator_object( new_data, self._target_estimand, self._estimate ) new_effect = new_estimator.estimate_effect() refute = CausalRefutation( self._estimate.value, new_effect.value, refutation_type="Refute: Add an Unobserved Common Cause" ) self.logger.debug(refute) outcomes[i] = refute.new_effect # Populate the results refute.new_effect_array = outcomes refute.new_effect = (np.min(outcomes), np.max(outcomes)) refute.add_refuter(self) if self.plotmethod is None: return refute import matplotlib import matplotlib.pyplot as plt fig = plt.figure(figsize=(6, 5)) left, bottom, width, height = 0.1, 0.1, 0.8, 0.8 ax = fig.add_axes([left, bottom, width, height]) plt.plot(self.kappa_t, outcomes) plt.axhline(self._estimate.value, linestyle="--", color="gray") ax.set_title("Effect of Unobserved Common Cause") ax.set_xlabel("Value of Linear Constant on Treatment") ax.set_ylabel("Estimated Effect after adding the common cause") plt.show() return refute elif isinstance(self.kappa_y, (list, np.ndarray)): outcomes = np.random.rand(len(self.kappa_y)) orig_data = copy.deepcopy(self._data) for i in tqdm( range(0, len(self.kappa_y)), colour=CausalRefuter.PROGRESS_BAR_COLOR, disable=not show_progress_bar, desc="Refuting Estimates: ", ): new_data = self.include_confounders_effect(orig_data, self.kappa_t, self.kappa_y[i]) new_estimator = CausalEstimator.get_estimator_object( new_data, self._target_estimand, self._estimate ) new_effect = new_estimator.estimate_effect() refute = CausalRefutation( self._estimate.value, new_effect.value, refutation_type="Refute: Add an Unobserved Common Cause" ) self.logger.debug(refute) outcomes[i] = refute.new_effect # Populate the results refute.new_effect_array = outcomes refute.new_effect = (np.min(outcomes), np.max(outcomes)) refute.add_refuter(self) if self.plotmethod is None: return refute import matplotlib import matplotlib.pyplot as plt fig = plt.figure(figsize=(6, 5)) left, bottom, width, height = 0.1, 0.1, 0.8, 0.8 ax = fig.add_axes([left, bottom, width, height]) plt.plot(self.kappa_y, outcomes) plt.axhline(self._estimate.value, linestyle="--", color="gray") ax.set_title("Effect of Unobserved Common Cause") ax.set_xlabel("Value of Linear Constant on Outcome") ax.set_ylabel("Estimated Effect after adding the common cause") plt.show() return refute def include_confounders_effect(self, new_data, kappa_t, kappa_y): """ This function deals with the change in the value of the data due to the effect of the unobserved confounder. In the case of a binary flip, we flip only if the random number is greater than the threshold set. In the case of a linear effect, we use the variable as the linear regression constant. :param new_data: pandas.DataFrame: The data to be changed due to the effects of the unobserved confounder. :param kappa_t: numpy.float64: The value of the threshold for binary_flip or the value of the regression coefficient for linear effect. :param kappa_y: numpy.float64: The value of the threshold for binary_flip or the value of the regression coefficient for linear effect. :return: pandas.DataFrame: The DataFrame that includes the effects of the unobserved confounder. """ num_rows = self._data.shape[0] stdnorm = scipy.stats.norm() w_random = stdnorm.rvs(num_rows) if self.effect_on_t == "binary_flip": alpha = 2 * kappa_t - 1 if kappa_t >= 0.5 else 1 - 2 * kappa_t interval = stdnorm.interval(alpha) rel_interval = interval[0] if kappa_t >= 0.5 else interval[1] new_data.loc[rel_interval <= w_random, self._treatment_name] = ( 1 - new_data.loc[rel_interval <= w_random, self._treatment_name] ) for tname in self._treatment_name: if pd.api.types.is_bool_dtype(self._data[tname]): new_data = new_data.astype({tname: "bool"}, copy=False) elif self.effect_on_t == "linear": confounder_t_effect = kappa_t * w_random # By default, we add the effect of simulated confounder for treatment. # But subtract it from outcome to create a negative correlation # assuming that the original confounder's effect was positive on both. # This is to remove the effect of the original confounder. new_data[self._treatment_name] = new_data[self._treatment_name].values + np.ndarray( shape=(num_rows, 1), buffer=confounder_t_effect ) else: raise NotImplementedError( "'" + self.effect_on_t + "' method not supported for confounders' effect on treatment" ) if self.effect_on_y == "binary_flip": alpha = 2 * kappa_y - 1 if kappa_y >= 0.5 else 1 - 2 * kappa_y interval = stdnorm.interval(alpha) rel_interval = interval[0] if kappa_y >= 0.5 else interval[1] new_data.loc[rel_interval <= w_random, self._outcome_name] = ( 1 - new_data.loc[rel_interval <= w_random, self._outcome_name] ) for yname in self._outcome_name: if pd.api.types.is_bool_dtype(self._data[yname]): new_data = new_data.astype({yname: "bool"}, copy=False) elif self.effect_on_y == "linear": confounder_y_effect = (-1) * kappa_y * w_random # By default, we add the effect of simulated confounder for treatment. # But subtract it from outcome to create a negative correlation # assuming that the original confounder's effect was positive on both. # This is to remove the effect of the original confounder. new_data[self._outcome_name] = new_data[self._outcome_name].values + np.ndarray( shape=(num_rows, 1), buffer=confounder_y_effect ) else: raise NotImplementedError( "'" + self.effect_on_y + "' method not supported for confounders' effect on outcome" ) return new_data def include_simulated_confounder(self, convergence_threshold=0.1, c_star_max=1000): """ This function simulates an unobserved confounder based on the data using the following steps: 1. It calculates the "residuals" from the treatment and outcome model i.) The outcome model has outcome as the dependent variable and all the observed variables including treatment as independent variables ii.) The treatment model has treatment as the dependent variable and all the observed variables as independent variables. 2. U is an intermediate random variable drawn from the normal distribution with the weighted average of residuals as mean and a unit variance U ~ N(c1*d_y + c2*d_t, 1) where *d_y and d_t are residuals from the treatment and outcome model *c1 and c2 are coefficients to the residuals 3. The final U, which is the simulated unobserved confounder is obtained by debiasing the intermediate variable U by residualising it with X Choosing the coefficients c1 and c2: The coefficients are chosen based on these basic assumptions: 1. There is a hyperbolic relationship satisfying c1*c2 = c_star 2. c_star is chosen from a range of possible values based on the correlation of the obtained simulated variable with outcome and treatment. 3. The product of correlations with treatment and outcome should be at a minimum distance to the maximum correlations with treatment and outcome in any of the observed confounders 4. The ratio of the weights should be such that they maintain the ratio of the maximum possible observed coefficients within some confidence interval :param c_star_max: The maximum possible value for the hyperbolic curve on which the coefficients to the residuals lie. It defaults to 1000 in the code if not specified by the user. :type int :param convergence_threshold: The threshold to check the plateauing of the correlation while selecting a c_star. It defaults to 0.1 in the code if not specified by the user :type float :returns: The simulated values of the unobserved confounder based on the data :type pandas.core.series.Series """ # Obtaining the list of observed variables required_variables = True observed_variables = self.choose_variables(required_variables) observed_variables_with_treatment_and_outcome = observed_variables + self._treatment_name + self._outcome_name # Taking a subset of the dataframe that has only observed variables self._data = self._data[observed_variables_with_treatment_and_outcome] # Residuals from the outcome model obtained by fitting a linear model y = self._data[self._outcome_name[0]] observed_variables_with_treatment = observed_variables + self._treatment_name X = self._data[observed_variables_with_treatment] model = sm.OLS(y, X.astype("float")) results = model.fit() residuals_y = y - results.fittedvalues d_y = list(pd.Series(residuals_y)) # Residuals from the treatment model obtained by fitting a linear model t = self._data[self._treatment_name[0]].astype("int64") X = self._data[observed_variables] model = sm.OLS(t, X) results = model.fit() residuals_t = t - results.fittedvalues d_t = list(pd.Series(residuals_t)) # Initialising product_cor_metric_observed with a really low value as finding maximum product_cor_metric_observed = -10000000000 for i in observed_variables: current_obs_confounder = self._data[i] outcome_values = self._data[self._outcome_name[0]] correlation_y = current_obs_confounder.corr(outcome_values) treatment_values = t correlation_t = current_obs_confounder.corr(treatment_values) product_cor_metric_current = correlation_y * correlation_t if product_cor_metric_current >= product_cor_metric_observed: product_cor_metric_observed = product_cor_metric_current correlation_t_observed = correlation_t correlation_y_observed = correlation_y # The user has an option to give the the effect_strength_on_y and effect_strength_on_t which can be then used instead of maximum correlation with treatment and outcome in the observed variables as it specifies the desired effect. if self.kappa_t is not None: correlation_t_observed = self.kappa_t if self.kappa_y is not None: correlation_y_observed = self.kappa_y # Choosing a c_star based on the data. # The correlations stop increasing upon increasing c_star after a certain value, that is it plateaus and we choose the value of c_star to be the value it plateaus. correlation_y_list = [] correlation_t_list = [] product_cor_metric_simulated_list = [] x_list = [] step = int(c_star_max / 10) for i in range(0, int(c_star_max), step): c1 = math.sqrt(i) c2 = c1 final_U = self.generate_confounder_from_residuals(c1, c2, d_y, d_t, X) current_simulated_confounder = final_U outcome_values = self._data[self._outcome_name[0]] correlation_y = current_simulated_confounder.corr(outcome_values) correlation_y_list.append(correlation_y) treatment_values = t correlation_t = current_simulated_confounder.corr(treatment_values) correlation_t_list.append(correlation_t) product_cor_metric_simulated = correlation_y * correlation_t product_cor_metric_simulated_list.append(product_cor_metric_simulated) x_list.append(i) index = 1 while index < len(correlation_y_list): if (correlation_y_list[index] - correlation_y_list[index - 1]) <= convergence_threshold: c_star = x_list[index] break index = index + 1 # Choosing c1 and c2 based on the hyperbolic relationship once c_star is chosen by going over various combinations of c1 and c2 values and choosing the combination which # which maintains the minimum distance between the product of correlations of the simulated variable and the product of maximum correlations of one of the observed variables # and additionally checks if the ratio of the weights are such that they maintain the ratio of the maximum possible observed coefficients within some confidence interval # c1_final and c2_final are initialised to the values on the hyperbolic curve such that c1_final = c2_final and c1_final*c2_final = c_star c1_final = math.sqrt(c_star) c2_final = math.sqrt(c_star) # initialising min_distance_between_product_cor_metrics to be a value greater than 1 min_distance_between_product_cor_metrics = 1.5 i = 0.05 threshold = c_star / 0.05 while i <= threshold: c2 = i c1 = c_star / c2 final_U = self.generate_confounder_from_residuals(c1, c2, d_y, d_t, X) current_simulated_confounder = final_U outcome_values = self._data[self._outcome_name[0]] correlation_y = current_simulated_confounder.corr(outcome_values) treatment_values = t correlation_t = current_simulated_confounder.corr(treatment_values) product_cor_metric_simulated = correlation_y * correlation_t if min_distance_between_product_cor_metrics >= abs( product_cor_metric_simulated - product_cor_metric_observed ): min_distance_between_product_cor_metrics = abs( product_cor_metric_simulated - product_cor_metric_observed ) additional_condition = correlation_y_observed / correlation_t_observed if ((c1 / c2) <= (additional_condition + 0.3 * additional_condition)) and ( (c1 / c2) >= (additional_condition - 0.3 * additional_condition) ): # choose minimum positive value c1_final = c1 c2_final = c2 i = i * 1.5 """#closed form solution print("c_star_max before closed form", c_star_max) if max_correlation_with_t == -1000: c2 = 0 c1 = c_star_max else: additional_condition = abs(max_correlation_with_y/max_correlation_with_t) print("additional_condition", additional_condition) c2 = math.sqrt(c_star_max/additional_condition) c1 = c_star_max/c2""" final_U = self.generate_confounder_from_residuals(c1_final, c2_final, d_y, d_t, X) return final_U def generate_confounder_from_residuals(self, c1, c2, d_y, d_t, X): """ This function takes the residuals from the treatment and outcome model and their coefficients and simulates the intermediate random variable U by taking the row wise normal distribution corresponding to each residual value and then debiasing the intermediate variable to get the final variable. :param c1: coefficient to the residual from the outcome model :type float :param c2: coefficient to the residual from the treatment model :type float :param d_y: residuals from the outcome model :type list :param d_t: residuals from the treatment model :type list :returns: The simulated values of the unobserved confounder based on the data :type pandas.core.series.Series """ U = [] for j in range(len(d_t)): simulated_variable_mean = c1 * d_y[j] + c2 * d_t[j] simulated_variable_stddev = 1 U.append(np.random.normal(simulated_variable_mean, simulated_variable_stddev, 1)) U = np.array(U) model = sm.OLS(U, X) results = model.fit() U = U.reshape( -1, ) final_U = U - results.fittedvalues.values final_U = pd.Series(U) return final_U

import copy import logging import math from typing import Dict, List, Optional, Union import numpy as np import pandas as pd import scipy.stats import statsmodels.api as sm from sklearn.linear_model import LogisticRegression from sklearn.preprocessing import StandardScaler from tqdm.auto import tqdm import dowhy.causal_estimators.econml from dowhy.causal_estimator import CausalEstimate, CausalEstimator from dowhy.causal_estimators.linear_regression_estimator import LinearRegressionEstimator from dowhy.causal_estimators.regression_estimator import RegressionEstimator from dowhy.causal_identifier.identified_estimand import IdentifiedEstimand from dowhy.causal_refuter import CausalRefutation, CausalRefuter, choose_variables from dowhy.causal_refuters.evalue_sensitivity_analyzer import EValueSensitivityAnalyzer from dowhy.causal_refuters.linear_sensitivity_analyzer import LinearSensitivityAnalyzer from dowhy.causal_refuters.non_parametric_sensitivity_analyzer import NonParametricSensitivityAnalyzer from dowhy.causal_refuters.partial_linear_sensitivity_analyzer import PartialLinearSensitivityAnalyzer logger = logging.getLogger(__name__) class AddUnobservedCommonCause(CausalRefuter): """Add an unobserved confounder for refutation. AddUnobservedCommonCause class supports three methods: 1) Simulation of an unobserved confounder 2) Linear partial R2 : Sensitivity Analysis for linear models. 3) Non-Parametric partial R2 based : Sensitivity Analyis for non-parametric models. Supports additional parameters that can be specified in the refute_estimate() method. """ def __init__(self, *args, **kwargs): """ Initialize the parameters required for the refuter. For direct_simulation, if effect_strength_on_treatment or effect_strength_on_outcome is not given, it is calculated automatically as a range between the minimum and maximum effect strength of observed confounders on treatment and outcome respectively. :param simulation_method: The method to use for simulating effect of unobserved confounder. Possible values are ["direct-simulation", "linear-partial-R2", "non-parametric-partial-R2", "e-value"]. :param confounders_effect_on_treatment: str : The type of effect on the treatment due to the unobserved confounder. Possible values are ['binary_flip', 'linear'] :param confounders_effect_on_outcome: str : The type of effect on the outcome due to the unobserved confounder. Possible values are ['binary_flip', 'linear'] :param effect_strength_on_treatment: float, numpy.ndarray: [Used when simulation_method="direct-simulation"] Strength of the confounder's effect on treatment. When confounders_effect_on_treatment is linear, it is the regression coefficient. When the confounders_effect_on_treatment is binary flip, it is the probability with which effect of unobserved confounder can invert the value of the treatment. :param effect_strength_on_outcome: float, numpy.ndarray: Strength of the confounder's effect on outcome. Its interpretation depends on confounders_effect_on_outcome and the simulation_method. When simulation_method is direct-simulation, for a linear effect it behaves like the regression coefficient and for a binary flip, it is the probability with which it can invert the value of the outcome. :param partial_r2_confounder_treatment: float, numpy.ndarray: [Used when simulation_method is linear-partial-R2 or non-parametric-partial-R2] Partial R2 of the unobserved confounder wrt the treatment conditioned on the observed confounders. Only in the case of general non-parametric-partial-R2, it is the fraction of variance in the reisz representer that is explained by the unobserved confounder; specifically (1-r), where r is the ratio of variance of reisz representer, alpha^2, based on observed confounders and that based on all confounders. :param partial_r2_confounder_outcome: float, numpy.ndarray: [Used when simulation_method is linear-partial-R2 or non-parametric-partial-R2] Partial R2 of the unobserved confounder wrt the outcome conditioned on the treatment and observed confounders. :param frac_strength_treatment: float: This parameter decides the effect strength of the simulated confounder as a fraction of the effect strength of observed confounders on treatment. Defaults to 1. :param frac_strength_outcome: float: This parameter decides the effect strength of the simulated confounder as a fraction of the effect strength of observed confounders on outcome. Defaults to 1. :param plotmethod: string: Type of plot to be shown. If None, no plot is generated. This parameter is used only only when more than one treatment confounder effect values or outcome confounder effect values are provided. Default is "colormesh". Supported values are "contour", "colormesh" when more than one value is provided for both confounder effect value parameters; "line" when provided for only one of them. :param percent_change_estimate: It is the percentage of reduction of treatment estimate that could alter the results (default = 1). if percent_change_estimate = 1, the robustness value describes the strength of association of confounders with treatment and outcome in order to reduce the estimate by 100% i.e bring it down to 0. (relevant only for Linear Sensitivity Analysis, ignore for rest) :param confounder_increases_estimate: True implies that confounder increases the absolute value of estimate and vice versa. (Default = False). (relevant only for Linear Sensitivity Analysis, ignore for rest) :param benchmark_common_causes: names of variables for bounding strength of confounders. (relevant only for partial-r2 based simulation methods) :param significance_level: confidence interval for statistical inference(default = 0.05). (relevant only for partial-r2 based simulation methods) :param null_hypothesis_effect: assumed effect under the null hypothesis. (relevant only for linear-partial-R2, ignore for rest) :param plot_estimate: Generate contour plot for estimate while performing sensitivity analysis. (default = True). (relevant only for partial-r2 based simulation methods) :param num_splits: number of splits for cross validation. (default = 5). (relevant only for non-parametric-partial-R2 simulation method) :param shuffle_data : shuffle data or not before splitting into folds (default = False). (relevant only for non-parametric-partial-R2 simulation method) :param shuffle_random_seed: seed for randomly shuffling data. (relevant only for non-parametric-partial-R2 simulation method) :param alpha_s_estimator_param_list: list of dictionaries with parameters for finding alpha_s. (relevant only for non-parametric-partial-R2 simulation method) :param g_s_estimator_list: list of estimator objects for finding g_s. These objects should have fit() and predict() functions implemented. (relevant only for non-parametric-partial-R2 simulation method) :param g_s_estimator_param_list: list of dictionaries with parameters for tuning respective estimators in "g_s_estimator_list". The order of the dictionaries in the list should be consistent with the estimator objects order in "g_s_estimator_list". (relevant only for non-parametric-partial-R2 simulation method) """ super().__init__(*args, **kwargs) self.simulation_method = kwargs["simulation_method"] if "simulation_method" in kwargs else "direct-simulation" self.effect_on_t = ( kwargs["confounders_effect_on_treatment"] if "confounders_effect_on_treatment" in kwargs else "binary_flip" ) self.effect_on_y = ( kwargs["confounders_effect_on_outcome"] if "confounders_effect_on_outcome" in kwargs else "linear" ) if self.simulation_method == "direct-simulation": self.kappa_t = kwargs["effect_strength_on_treatment"] if "effect_strength_on_treatment" in kwargs else None self.kappa_y = kwargs["effect_strength_on_outcome"] if "effect_strength_on_outcome" in kwargs else None elif self.simulation_method in ["linear-partial-R2", "non-parametric-partial-R2"]: self.kappa_t = ( kwargs["partial_r2_confounder_treatment"] if "partial_r2_confounder_treatment" in kwargs else None ) self.kappa_y = ( kwargs["partial_r2_confounder_outcome"] if "partial_r2_confounder_outcome" in kwargs else None ) elif self.simulation_method == "e-value": pass else: raise ValueError( "simulation method is not supported. Try direct-simulation, linear-partial-R2, non-parametric-partial-R2, or e-value" ) self.frac_strength_treatment = ( kwargs["effect_fraction_on_treatment"] if "effect_fraction_on_treatment" in kwargs else 1 ) self.frac_strength_outcome = ( kwargs["effect_fraction_on_outcome"] if "effect_fraction_on_outcome" in kwargs else 1 ) self.plotmethod = kwargs["plotmethod"] if "plotmethod" in kwargs else "colormesh" self.percent_change_estimate = kwargs["percent_change_estimate"] if "percent_change_estimate" in kwargs else 1.0 self.significance_level = kwargs["significance_level"] if "significance_level" in kwargs else 0.05 self.confounder_increases_estimate = ( kwargs["confounder_increases_estimate"] if "confounder_increases_estimate" in kwargs else False ) self.benchmark_common_causes = ( kwargs["benchmark_common_causes"] if "benchmark_common_causes" in kwargs else None ) self.null_hypothesis_effect = kwargs["null_hypothesis_effect"] if "null_hypothesis_effect" in kwargs else 0 self.plot_estimate = kwargs["plot_estimate"] if "plot_estimate" in kwargs else True self.num_splits = kwargs["num_splits"] if "num_splits" in kwargs else 5 self.shuffle_data = kwargs["shuffle_data"] if "shuffle_data" in kwargs else False self.shuffle_random_seed = kwargs["shuffle_random_seed"] if "shuffle_random_seed" in kwargs else None self.alpha_s_estimator_param_list = ( kwargs["alpha_s_estimator_param_list"] if "alpha_s_estimator_param_list" in kwargs else None ) self.alpha_s_estimator_list = kwargs["alpha_s_estimator_list"] if "alpha_s_estimator_list" in kwargs else None self.g_s_estimator_list = kwargs["g_s_estimator_list"] if "g_s_estimator_list" in kwargs else None self.g_s_estimator_param_list = ( kwargs["g_s_estimator_param_list"] if "g_s_estimator_param_list" in kwargs else None ) self.plugin_reisz = kwargs["plugin_reisz"] if "plugin_reisz" in kwargs else False self.logger = logging.getLogger(__name__) def refute_estimate(self, show_progress_bar=False): if self.simulation_method == "linear-partial-R2": return sensitivity_linear_partial_r2( self._data, self._estimate, self._treatment_name, self.frac_strength_treatment, self.frac_strength_outcome, self.percent_change_estimate, self.benchmark_common_causes, self.significance_level, self.null_hypothesis_effect, self.plot_estimate, ) elif self.simulation_method == "non-parametric-partial-R2": return sensitivity_non_parametric_partial_r2( self._estimate, self.kappa_t, self.kappa_y, self.frac_strength_treatment, self.frac_strength_outcome, self.benchmark_common_causes, self.plot_estimate, self.alpha_s_estimator_list, self.alpha_s_estimator_param_list, self.g_s_estimator_list, self.g_s_estimator_param_list, self.plugin_reisz, ) elif self.simulation_method == "e-value": return sensitivity_e_value( self._data, self._target_estimand, self._estimate, self._treatment_name, self._outcome_name, self.plot_estimate, ) elif self.simulation_method == "direct-simulation": refute = sensitivity_simulation( self._data, self._target_estimand, self._estimate, self._treatment_name, self._outcome_name, self.kappa_t, self.kappa_y, self.effect_on_t, self.effect_on_y, self.frac_strength_treatment, self.frac_strength_outcome, self.plotmethod, show_progress_bar, ) refute.add_refuter(self) return refute def _infer_default_kappa_t( data: pd.DataFrame, target_estimand: IdentifiedEstimand, treatment_name: List[str], effect_on_t: str, frac_strength_treatment: float, len_kappa_t: int = 10, ): """Infer default effect strength of simulated confounder on treatment.""" observed_common_causes_names = target_estimand.get_backdoor_variables() if len(observed_common_causes_names) > 0: observed_common_causes = data[observed_common_causes_names] observed_common_causes = pd.get_dummies(observed_common_causes, drop_first=True) else: raise ValueError( "There needs to be at least one common cause to" + "automatically compute the default value of kappa_t." + " Provide a value for kappa_t" ) t = data[treatment_name] # Standardizing the data observed_common_causes = StandardScaler().fit_transform(observed_common_causes) if effect_on_t == "binary_flip": # Fit a model containing all confounders and compare predictions # using all features compared to all features except a given # confounder. tmodel = LogisticRegression().fit(observed_common_causes, t) tpred = tmodel.predict(observed_common_causes).astype(int) flips = [] for i in range(observed_common_causes.shape[1]): oldval = np.copy(observed_common_causes[:, i]) observed_common_causes[:, i] = 0 tcap = tmodel.predict(observed_common_causes).astype(int) observed_common_causes[:, i] = oldval flips.append(np.sum(abs(tcap - tpred)) / tpred.shape[0]) min_coeff, max_coeff = min(flips), max(flips) elif effect_on_t == "linear": # Estimating the regression coefficient from standardized features to t corrcoef_var_t = np.corrcoef(observed_common_causes, t, rowvar=False)[-1, :-1] std_dev_t = np.std(t)[0] max_coeff = max(corrcoef_var_t) * std_dev_t min_coeff = min(corrcoef_var_t) * std_dev_t else: raise NotImplementedError("'" + effect_on_t + "' method not supported for confounders' effect on treatment") min_coeff, max_coeff = _compute_min_max_coeff(min_coeff, max_coeff, frac_strength_treatment) # By default, return a plot with 10 points # consider 10 values of the effect of the unobserved confounder step = (max_coeff - min_coeff) / len_kappa_t logger.info("(Min, Max) kappa_t for observed common causes, ({0}, {1})".format(min_coeff, max_coeff)) if np.equal(max_coeff, min_coeff): return max_coeff else: return np.arange(min_coeff, max_coeff, step) def _compute_min_max_coeff(min_coeff: float, max_coeff: float, effect_strength_fraction: np.ndarray): max_coeff = effect_strength_fraction * max_coeff min_coeff = effect_strength_fraction * min_coeff return min_coeff, max_coeff def _infer_default_kappa_y( data: pd.DataFrame, target_estimand: IdentifiedEstimand, outcome_name: List[str], effect_on_y: str, frac_strength_outcome: float, len_kappa_y: int = 10, ): """Infer default effect strength of simulated confounder on treatment.""" observed_common_causes_names = target_estimand.get_backdoor_variables() if len(observed_common_causes_names) > 0: observed_common_causes = data[observed_common_causes_names] observed_common_causes = pd.get_dummies(observed_common_causes, drop_first=True) else: raise ValueError( "There needs to be at least one common cause to" + "automatically compute the default value of kappa_y." + " Provide a value for kappa_y" ) y = data[outcome_name] # Standardizing the data observed_common_causes = StandardScaler().fit_transform(observed_common_causes) if effect_on_y == "binary_flip": # Fit a model containing all confounders and compare predictions # using all features compared to all features except a given # confounder. ymodel = LogisticRegression().fit(observed_common_causes, y) ypred = ymodel.predict(observed_common_causes).astype(int) flips = [] for i in range(observed_common_causes.shape[1]): oldval = np.copy(observed_common_causes[:, i]) observed_common_causes[:, i] = 0 ycap = ymodel.predict(observed_common_causes).astype(int) observed_common_causes[:, i] = oldval flips.append(np.sum(abs(ycap - ypred)) / ypred.shape[0]) min_coeff, max_coeff = min(flips), max(flips) elif effect_on_y == "linear": corrcoef_var_y = np.corrcoef(observed_common_causes, y, rowvar=False)[-1, :-1] std_dev_y = np.std(y)[0] max_coeff = max(corrcoef_var_y) * std_dev_y min_coeff = min(corrcoef_var_y) * std_dev_y else: raise NotImplementedError("'" + effect_on_y + "' method not supported for confounders' effect on outcome") min_coeff, max_coeff = _compute_min_max_coeff(min_coeff, max_coeff, frac_strength_outcome) # By default, return a plot with 10 points # consider 10 values of the effect of the unobserved confounder step = (max_coeff - min_coeff) / len_kappa_y logger.info("(Min, Max) kappa_y for observed common causes, ({0}, {1})".format(min_coeff, max_coeff)) if np.equal(max_coeff, min_coeff): return max_coeff else: return np.arange(min_coeff, max_coeff, step) def _include_confounders_effect( data: pd.DataFrame, new_data: pd.DataFrame, effect_on_t: str, treatment_name: str, kappa_t: float, effect_on_y: str, outcome_name: str, kappa_y: float, ): """ This function deals with the change in the value of the data due to the effect of the unobserved confounder. In the case of a binary flip, we flip only if the random number is greater than the threshold set. In the case of a linear effect, we use the variable as the linear regression constant. :param new_data: pandas.DataFrame: The data to be changed due to the effects of the unobserved confounder. :param kappa_t: numpy.float64: The value of the threshold for binary_flip or the value of the regression coefficient for linear effect. :param kappa_y: numpy.float64: The value of the threshold for binary_flip or the value of the regression coefficient for linear effect. :return: pandas.DataFrame: The DataFrame that includes the effects of the unobserved confounder. """ num_rows = data.shape[0] stdnorm = scipy.stats.norm() w_random = stdnorm.rvs(num_rows) if effect_on_t == "binary_flip": alpha = 2 * kappa_t - 1 if kappa_t >= 0.5 else 1 - 2 * kappa_t interval = stdnorm.interval(alpha) rel_interval = interval[0] if kappa_t >= 0.5 else interval[1] new_data.loc[rel_interval <= w_random, treatment_name] = ( 1 - new_data.loc[rel_interval <= w_random, treatment_name] ) for tname in treatment_name: if pd.api.types.is_bool_dtype(data[tname]): new_data = new_data.astype({tname: "bool"}, copy=False) elif effect_on_t == "linear": confounder_t_effect = kappa_t * w_random # By default, we add the effect of simulated confounder for treatment. # But subtract it from outcome to create a negative correlation # assuming that the original confounder's effect was positive on both. # This is to remove the effect of the original confounder. new_data[treatment_name] = new_data[treatment_name].values + np.ndarray( shape=(num_rows, 1), buffer=confounder_t_effect ) else: raise NotImplementedError("'" + effect_on_t + "' method not supported for confounders' effect on treatment") if effect_on_y == "binary_flip": alpha = 2 * kappa_y - 1 if kappa_y >= 0.5 else 1 - 2 * kappa_y interval = stdnorm.interval(alpha) rel_interval = interval[0] if kappa_y >= 0.5 else interval[1] new_data.loc[rel_interval <= w_random, outcome_name] = 1 - new_data.loc[rel_interval <= w_random, outcome_name] for yname in outcome_name: if pd.api.types.is_bool_dtype(data[yname]): new_data = new_data.astype({yname: "bool"}, copy=False) elif effect_on_y == "linear": confounder_y_effect = (-1) * kappa_y * w_random # By default, we add the effect of simulated confounder for treatment. # But subtract it from outcome to create a negative correlation # assuming that the original confounder's effect was positive on both. # This is to remove the effect of the original confounder. new_data[outcome_name] = new_data[outcome_name].values + np.ndarray( shape=(num_rows, 1), buffer=confounder_y_effect ) else: raise NotImplementedError("'" + effect_on_y + "' method not supported for confounders' effect on outcome") return new_data def include_simulated_confounder( data: pd.DataFrame, treatment_name: str, outcome_name: str, kappa_t: float, kappa_y: float, convergence_threshold: float = 0.1, c_star_max: int = 1000, ): """ This function simulates an unobserved confounder based on the data using the following steps: 1. It calculates the "residuals" from the treatment and outcome model i.) The outcome model has outcome as the dependent variable and all the observed variables including treatment as independent variables ii.) The treatment model has treatment as the dependent variable and all the observed variables as independent variables. 2. U is an intermediate random variable drawn from the normal distribution with the weighted average of residuals as mean and a unit variance U ~ N(c1*d_y + c2*d_t, 1) where *d_y and d_t are residuals from the treatment and outcome model *c1 and c2 are coefficients to the residuals 3. The final U, which is the simulated unobserved confounder is obtained by debiasing the intermediate variable U by residualising it with X Choosing the coefficients c1 and c2: The coefficients are chosen based on these basic assumptions: 1. There is a hyperbolic relationship satisfying c1*c2 = c_star 2. c_star is chosen from a range of possible values based on the correlation of the obtained simulated variable with outcome and treatment. 3. The product of correlations with treatment and outcome should be at a minimum distance to the maximum correlations with treatment and outcome in any of the observed confounders 4. The ratio of the weights should be such that they maintain the ratio of the maximum possible observed coefficients within some confidence interval :param c_star_max: The maximum possible value for the hyperbolic curve on which the coefficients to the residuals lie. It defaults to 1000 in the code if not specified by the user. :type int :param convergence_threshold: The threshold to check the plateauing of the correlation while selecting a c_star. It defaults to 0.1 in the code if not specified by the user :type float :returns: The simulated values of the unobserved confounder based on the data :type pandas.core.series.Series """ # Obtaining the list of observed variables required_variables = True observed_variables = choose_variables(required_variables) observed_variables_with_treatment_and_outcome = observed_variables + treatment_name + outcome_name # Taking a subset of the dataframe that has only observed variables data = data[observed_variables_with_treatment_and_outcome] # Residuals from the outcome model obtained by fitting a linear model y = data[outcome_name[0]] observed_variables_with_treatment = observed_variables + treatment_name X = data[observed_variables_with_treatment] model = sm.OLS(y, X.astype("float")) results = model.fit() residuals_y = y - results.fittedvalues d_y = list(pd.Series(residuals_y)) # Residuals from the treatment model obtained by fitting a linear model t = data[treatment_name[0]].astype("int64") X = data[observed_variables] model = sm.OLS(t, X) results = model.fit() residuals_t = t - results.fittedvalues d_t = list(pd.Series(residuals_t)) # Initialising product_cor_metric_observed with a really low value as finding maximum product_cor_metric_observed = -10000000000 for i in observed_variables: current_obs_confounder = data[i] outcome_values = data[outcome_name[0]] correlation_y = current_obs_confounder.corr(outcome_values) treatment_values = t correlation_t = current_obs_confounder.corr(treatment_values) product_cor_metric_current = correlation_y * correlation_t if product_cor_metric_current >= product_cor_metric_observed: product_cor_metric_observed = product_cor_metric_current correlation_t_observed = correlation_t correlation_y_observed = correlation_y # The user has an option to give the the effect_strength_on_y and effect_strength_on_t which can be then used instead of maximum correlation with treatment and outcome in the observed variables as it specifies the desired effect. if kappa_t is not None: correlation_t_observed = kappa_t if kappa_y is not None: correlation_y_observed = kappa_y # Choosing a c_star based on the data. # The correlations stop increasing upon increasing c_star after a certain value, that is it plateaus and we choose the value of c_star to be the value it plateaus. correlation_y_list = [] correlation_t_list = [] product_cor_metric_simulated_list = [] x_list = [] step = int(c_star_max / 10) for i in range(0, int(c_star_max), step): c1 = math.sqrt(i) c2 = c1 final_U = _generate_confounder_from_residuals(c1, c2, d_y, d_t, X) current_simulated_confounder = final_U outcome_values = data[outcome_name[0]] correlation_y = current_simulated_confounder.corr(outcome_values) correlation_y_list.append(correlation_y) treatment_values = t correlation_t = current_simulated_confounder.corr(treatment_values) correlation_t_list.append(correlation_t) product_cor_metric_simulated = correlation_y * correlation_t product_cor_metric_simulated_list.append(product_cor_metric_simulated) x_list.append(i) index = 1 while index < len(correlation_y_list): if (correlation_y_list[index] - correlation_y_list[index - 1]) <= convergence_threshold: c_star = x_list[index] break index = index + 1 # Choosing c1 and c2 based on the hyperbolic relationship once c_star is chosen by going over various combinations of c1 and c2 values and choosing the combination which # which maintains the minimum distance between the product of correlations of the simulated variable and the product of maximum correlations of one of the observed variables # and additionally checks if the ratio of the weights are such that they maintain the ratio of the maximum possible observed coefficients within some confidence interval # c1_final and c2_final are initialised to the values on the hyperbolic curve such that c1_final = c2_final and c1_final*c2_final = c_star c1_final = math.sqrt(c_star) c2_final = math.sqrt(c_star) # initialising min_distance_between_product_cor_metrics to be a value greater than 1 min_distance_between_product_cor_metrics = 1.5 i = 0.05 threshold = c_star / 0.05 while i <= threshold: c2 = i c1 = c_star / c2 final_U = _generate_confounder_from_residuals(c1, c2, d_y, d_t, X) current_simulated_confounder = final_U outcome_values = data[outcome_name[0]] correlation_y = current_simulated_confounder.corr(outcome_values) treatment_values = t correlation_t = current_simulated_confounder.corr(treatment_values) product_cor_metric_simulated = correlation_y * correlation_t if min_distance_between_product_cor_metrics >= abs(product_cor_metric_simulated - product_cor_metric_observed): min_distance_between_product_cor_metrics = abs(product_cor_metric_simulated - product_cor_metric_observed) additional_condition = correlation_y_observed / correlation_t_observed if ((c1 / c2) <= (additional_condition + 0.3 * additional_condition)) and ( (c1 / c2) >= (additional_condition - 0.3 * additional_condition) ): # choose minimum positive value c1_final = c1 c2_final = c2 i = i * 1.5 """#closed form solution print("c_star_max before closed form", c_star_max) if max_correlation_with_t == -1000: c2 = 0 c1 = c_star_max else: additional_condition = abs(max_correlation_with_y/max_correlation_with_t) print("additional_condition", additional_condition) c2 = math.sqrt(c_star_max/additional_condition) c1 = c_star_max/c2""" final_U = _generate_confounder_from_residuals(c1_final, c2_final, d_y, d_t, X) return final_U def _generate_confounder_from_residuals(c1, c2, d_y, d_t, X): """ This function takes the residuals from the treatment and outcome model and their coefficients and simulates the intermediate random variable U by taking the row wise normal distribution corresponding to each residual value and then debiasing the intermediate variable to get the final variable. :param c1: coefficient to the residual from the outcome model :type float :param c2: coefficient to the residual from the treatment model :type float :param d_y: residuals from the outcome model :type list :param d_t: residuals from the treatment model :type list :returns: The simulated values of the unobserved confounder based on the data :type pandas.core.series.Series """ U = [] for j in range(len(d_t)): simulated_variable_mean = c1 * d_y[j] + c2 * d_t[j] simulated_variable_stddev = 1 U.append(np.random.normal(simulated_variable_mean, simulated_variable_stddev, 1)) U = np.array(U) model = sm.OLS(U, X) results = model.fit() U = U.reshape( -1, ) final_U = U - results.fittedvalues.values final_U = pd.Series(U) return final_U def sensitivity_linear_partial_r2( data: pd.DataFrame, estimate: CausalEstimate, treatment_name: str, frac_strength_treatment: float = 1.0, frac_strength_outcome: float = 1.0, percent_change_estimate: float = 1.0, benchmark_common_causes: Optional[List[str]] = None, significance_level: Optional[float] = None, null_hypothesis_effect: Optional[float] = None, plot_estimate: bool = True, ) -> LinearSensitivityAnalyzer: """Add an unobserved confounder for refutation using Linear partial R2 methond (Sensitivity Analysis for linear models). :param data: pd.DataFrame: Data to run the refutation :param estimate: CausalEstimate: Estimate to run the refutation :param treatment_name: str: Name of the treatment :param frac_strength_treatment: float: This parameter decides the effect strength of the simulated confounder as a fraction of the effect strength of observed confounders on treatment. Defaults to 1. :param frac_strength_outcome: float: This parameter decides the effect strength of the simulated confounder as a fraction of the effect strength of observed confounders on outcome. Defaults to 1. :param percent_change_estimate: It is the percentage of reduction of treatment estimate that could alter the results (default = 1). if percent_change_estimate = 1, the robustness value describes the strength of association of confounders with treatment and outcome in order to reduce the estimate by 100% i.e bring it down to 0. (relevant only for Linear Sensitivity Analysis, ignore for rest) :param benchmark_common_causes: names of variables for bounding strength of confounders. (relevant only for partial-r2 based simulation methods) :param significance_level: confidence interval for statistical inference(default = 0.05). (relevant only for partial-r2 based simulation methods) :param null_hypothesis_effect: assumed effect under the null hypothesis. (relevant only for linear-partial-R2, ignore for rest) :param plot_estimate: Generate contour plot for estimate while performing sensitivity analysis. (default = True). (relevant only for partial-r2 based simulation methods) """ if not (isinstance(estimate.estimator, LinearRegressionEstimator)): raise NotImplementedError("Currently only LinearRegressionEstimator is supported for Sensitivity Analysis") if len(estimate.estimator._effect_modifier_names) > 0: raise NotImplementedError("The current implementation does not support effect modifiers") if frac_strength_outcome == 1: frac_strength_outcome = frac_strength_treatment analyzer = LinearSensitivityAnalyzer( estimator=estimate.estimator, data=data, treatment_name=treatment_name, percent_change_estimate=percent_change_estimate, significance_level=significance_level, benchmark_common_causes=benchmark_common_causes, null_hypothesis_effect=null_hypothesis_effect, frac_strength_treatment=frac_strength_treatment, frac_strength_outcome=frac_strength_outcome, common_causes_order=estimate.estimator._observed_common_causes.columns, ) analyzer.check_sensitivity(plot=plot_estimate) return analyzer def sensitivity_non_parametric_partial_r2( estimate: CausalEstimate, kappa_t: Optional[Union[float, np.ndarray]] = None, kappa_y: Optional[Union[float, np.ndarray]] = None, frac_strength_treatment: float = 1.0, frac_strength_outcome: float = 1.0, benchmark_common_causes: Optional[List[str]] = None, plot_estimate: bool = True, alpha_s_estimator_list: Optional[List] = None, alpha_s_estimator_param_list: Optional[List[Dict]] = None, g_s_estimator_list: Optional[List] = None, g_s_estimator_param_list: Optional[List[Dict]] = None, plugin_reisz: bool = False, ) -> Union[PartialLinearSensitivityAnalyzer, NonParametricSensitivityAnalyzer]: """Add an unobserved confounder for refutation using Non-parametric partial R2 methond (Sensitivity Analysis for non-parametric models). :param estimate: CausalEstimate: Estimate to run the refutation :param kappa_t: float, numpy.ndarray: Partial R2 of the unobserved confounder wrt the treatment conditioned on the observed confounders. Only in the case of general non-parametric-partial-R2, it is the fraction of variance in the reisz representer that is explained by the unobserved confounder; specifically (1-r), where r is the ratio of variance of reisz representer, alpha^2, based on observed confounders and that based on all confounders. :param kappa_y: float, numpy.ndarray: Partial R2 of the unobserved confounder wrt the outcome conditioned on the treatment and observed confounders. :param frac_strength_treatment: float: This parameter decides the effect strength of the simulated confounder as a fraction of the effect strength of observed confounders on treatment. Defaults to 1. :param frac_strength_outcome: float: This parameter decides the effect strength of the simulated confounder as a fraction of the effect strength of observed confounders on outcome. Defaults to 1. :param benchmark_common_causes: names of variables for bounding strength of confounders. (relevant only for partial-r2 based simulation methods) :param plot_estimate: Generate contour plot for estimate while performing sensitivity analysis. (default = True). (relevant only for partial-r2 based simulation methods) :param alpha_s_estimator_list: list of estimator objects for estimating alpha_s. These objects should have fit() and predict() methods (relevant only for non-parametric-partial-R2 method) :param alpha_s_estimator_param_list: list of dictionaries with parameters for finding alpha_s. (relevant only for non-parametric-partial-R2 simulation method) :param g_s_estimator_list: list of estimator objects for finding g_s. These objects should have fit() and predict() functions implemented. (relevant only for non-parametric-partial-R2 simulation method) :param g_s_estimator_param_list: list of dictionaries with parameters for tuning respective estimators in "g_s_estimator_list". The order of the dictionaries in the list should be consistent with the estimator objects order in "g_s_estimator_list". (relevant only for non-parametric-partial-R2 simulation method) :plugin_reisz: bool: Flag on whether to use the plugin estimator or the nonparametric estimator for reisz representer function (alpha_s). """ # If the estimator used is LinearDML, partially linear sensitivity analysis will be automatically chosen if isinstance(estimate.estimator, dowhy.causal_estimators.econml.Econml): if estimate.estimator._econml_methodname == "econml.dml.LinearDML": analyzer = PartialLinearSensitivityAnalyzer( estimator=estimate._estimator_object, observed_common_causes=estimate.estimator._observed_common_causes, treatment=estimate.estimator._treatment, outcome=estimate.estimator._outcome, alpha_s_estimator_param_list=alpha_s_estimator_param_list, g_s_estimator_list=g_s_estimator_list, g_s_estimator_param_list=g_s_estimator_param_list, effect_strength_treatment=kappa_t, effect_strength_outcome=kappa_y, benchmark_common_causes=benchmark_common_causes, frac_strength_treatment=frac_strength_treatment, frac_strength_outcome=frac_strength_outcome, ) analyzer.check_sensitivity(plot=plot_estimate) return analyzer analyzer = NonParametricSensitivityAnalyzer( estimator=estimate.estimator, observed_common_causes=estimate.estimator._observed_common_causes, treatment=estimate.estimator._treatment, outcome=estimate.estimator._outcome, alpha_s_estimator_list=alpha_s_estimator_list, alpha_s_estimator_param_list=alpha_s_estimator_param_list, g_s_estimator_list=g_s_estimator_list, g_s_estimator_param_list=g_s_estimator_param_list, effect_strength_treatment=kappa_t, effect_strength_outcome=kappa_y, benchmark_common_causes=benchmark_common_causes, frac_strength_treatment=frac_strength_treatment, frac_strength_outcome=frac_strength_outcome, theta_s=estimate.value, plugin_reisz=plugin_reisz, ) analyzer.check_sensitivity(plot=plot_estimate) return analyzer def sensitivity_e_value( data: pd.DataFrame, target_estimand: IdentifiedEstimand, estimate: CausalEstimate, treatment_name: List[str], outcome_name: List[str], plot_estimate: bool = True, ) -> EValueSensitivityAnalyzer: if not isinstance(estimate.estimator, RegressionEstimator): raise NotImplementedError("E-Value sensitivity analysis is currently only implemented RegressionEstimator.") if len(estimate.estimator._effect_modifier_names) > 0: raise NotImplementedError("The current implementation does not support effect modifiers") analyzer = EValueSensitivityAnalyzer( estimate=estimate, estimand=target_estimand, data=data, treatment_name=treatment_name[0], outcome_name=outcome_name[0], ) analyzer.check_sensitivity(plot=plot_estimate) return analyzer def sensitivity_simulation( data: pd.DataFrame, target_estimand: IdentifiedEstimand, estimate: CausalEstimate, treatment_name: str, outcome_name: str, kappa_t: Optional[Union[float, np.ndarray]] = None, kappa_y: Optional[Union[float, np.ndarray]] = None, confounders_effect_on_treatment: str = "binary_flip", confounders_effect_on_outcome: str = "linear", frac_strength_treatment: float = 1.0, frac_strength_outcome: float = 1.0, plotmethod: Optional[str] = None, show_progress_bar=False, **_, ) -> CausalRefutation: """ This function attempts to add an unobserved common cause to the outcome and the treatment. At present, we have implemented the behavior for one dimensional behaviors for continuous and binary variables. This function can either take single valued inputs or a range of inputs. The function then looks at the data type of the input and then decides on the course of action. :param data: pd.DataFrame: Data to run the refutation :param target_estimand: IdentifiedEstimand: Identified estimand to run the refutation :param estimate: CausalEstimate: Estimate to run the refutation :param treatment_name: str: Name of the treatment :param outcome_name: str: Name of the outcome :param kappa_t: float, numpy.ndarray: Strength of the confounder's effect on treatment. When confounders_effect_on_treatment is linear, it is the regression coefficient. When the confounders_effect_on_treatment is binary flip, it is the probability with which effect of unobserved confounder can invert the value of the treatment. :param kappa_y: float, numpy.ndarray: Strength of the confounder's effect on outcome. Its interpretation depends on confounders_effect_on_outcome and the simulation_method. When simulation_method is direct-simulation, for a linear effect it behaves like the regression coefficient and for a binary flip, it is the probability with which it can invert the value of the outcome. :param confounders_effect_on_treatment: str : The type of effect on the treatment due to the unobserved confounder. Possible values are ['binary_flip', 'linear'] :param confounders_effect_on_outcome: str : The type of effect on the outcome due to the unobserved confounder. Possible values are ['binary_flip', 'linear'] :param frac_strength_treatment: float: This parameter decides the effect strength of the simulated confounder as a fraction of the effect strength of observed confounders on treatment. Defaults to 1. :param frac_strength_outcome: float: This parameter decides the effect strength of the simulated confounder as a fraction of the effect strength of observed confounders on outcome. Defaults to 1. :param plotmethod: string: Type of plot to be shown. If None, no plot is generated. This parameter is used only only when more than one treatment confounder effect values or outcome confounder effect values are provided. Default is "colormesh". Supported values are "contour", "colormesh" when more than one value is provided for both confounder effect value parameters; "line" when provided for only one of them. :return: CausalRefuter: An object that contains the estimated effect and a new effect and the name of the refutation used. """ if kappa_t is None: kappa_t = _infer_default_kappa_t( data, target_estimand, treatment_name, confounders_effect_on_treatment, frac_strength_treatment ) if kappa_y is None: kappa_y = _infer_default_kappa_y( data, target_estimand, outcome_name, confounders_effect_on_outcome, frac_strength_outcome ) if not isinstance(kappa_t, (list, np.ndarray)) and not isinstance( kappa_y, (list, np.ndarray) ): # Deal with single value inputs new_data = copy.deepcopy(data) new_data = _include_confounders_effect( data, new_data, confounders_effect_on_treatment, treatment_name, kappa_t, confounders_effect_on_outcome, outcome_name, kappa_y, ) new_estimator = CausalEstimator.get_estimator_object(new_data, target_estimand, estimate) new_effect = new_estimator.estimate_effect() refute = CausalRefutation( estimate.value, new_effect.value, refutation_type="Refute: Add an Unobserved Common Cause" ) refute.new_effect_array = np.array(new_effect.value) refute.new_effect = new_effect.value return refute else: # Deal with multiple value inputs if isinstance(kappa_t, (list, np.ndarray)) and isinstance( kappa_y, (list, np.ndarray) ): # Deal with range inputs # Get a 2D matrix of values # x,y = np.meshgrid(self.kappa_t, self.kappa_y) # x,y are both MxN results_matrix = np.random.rand(len(kappa_t), len(kappa_y)) # Matrix to hold all the results of NxM orig_data = copy.deepcopy(data) for i in tqdm( range(len(kappa_t)), colour=CausalRefuter.PROGRESS_BAR_COLOR, disable=not show_progress_bar, desc="Refuting Estimates: ", ): for j in range(len(kappa_y)): new_data = _include_confounders_effect( data, orig_data, confounders_effect_on_treatment, treatment_name, kappa_t[i], confounders_effect_on_outcome, outcome_name, kappa_y[j], ) new_estimator = CausalEstimator.get_estimator_object(new_data, target_estimand, estimate) new_effect = new_estimator.estimate_effect() refute = CausalRefutation( estimate.value, new_effect.value, refutation_type="Refute: Add an Unobserved Common Cause", ) results_matrix[i][j] = refute.new_effect # Populate the results refute.new_effect_array = results_matrix refute.new_effect = (np.min(results_matrix), np.max(results_matrix)) # Store the values into the refute object if plotmethod is None: return refute import matplotlib import matplotlib.pyplot as plt fig = plt.figure(figsize=(6, 5)) left, bottom, width, height = 0.1, 0.1, 0.8, 0.8 ax = fig.add_axes([left, bottom, width, height]) oe = estimate.value contour_levels = [oe / 4.0, oe / 2.0, (3.0 / 4) * oe, oe] contour_levels.extend([0, np.min(results_matrix), np.max(results_matrix)]) if plotmethod == "contour": cp = plt.contourf(kappa_y, kappa_t, results_matrix, levels=sorted(contour_levels)) # Adding a label on the contour line for the original estimate fmt = {} trueeffect_index = np.where(cp.levels == oe)[0][0] fmt[cp.levels[trueeffect_index]] = "Estimated Effect" # Label every other level using strings plt.clabel(cp, [cp.levels[trueeffect_index]], inline=True, fmt=fmt) plt.colorbar(cp) elif plotmethod == "colormesh": cp = plt.pcolormesh(kappa_y, kappa_t, results_matrix, shading="nearest") plt.colorbar(cp, ticks=contour_levels) ax.yaxis.set_ticks(kappa_t) ax.xaxis.set_ticks(kappa_y) plt.xticks(rotation=45) ax.set_title("Effect of Unobserved Common Cause") ax.set_ylabel("Value of Linear Constant on Treatment") ax.set_xlabel("Value of Linear Constant on Outcome") plt.show() return refute elif isinstance(kappa_t, (list, np.ndarray)): outcomes = np.random.rand(len(kappa_t)) orig_data = copy.deepcopy(data) for i in tqdm( range(0, len(kappa_t)), colour=CausalRefuter.PROGRESS_BAR_COLOR, disable=not show_progress_bar, desc="Refuting Estimates: ", ): new_data = _include_confounders_effect( data, orig_data, confounders_effect_on_treatment, treatment_name, kappa_t[i], confounders_effect_on_outcome, outcome_name, kappa_y, ) new_estimator = CausalEstimator.get_estimator_object(new_data, target_estimand, estimate) new_effect = new_estimator.estimate_effect() refute = CausalRefutation( estimate.value, new_effect.value, refutation_type="Refute: Add an Unobserved Common Cause" ) logger.debug(refute) outcomes[i] = refute.new_effect # Populate the results refute.new_effect_array = outcomes refute.new_effect = (np.min(outcomes), np.max(outcomes)) if plotmethod is None: return refute import matplotlib import matplotlib.pyplot as plt fig = plt.figure(figsize=(6, 5)) left, bottom, width, height = 0.1, 0.1, 0.8, 0.8 ax = fig.add_axes([left, bottom, width, height]) plt.plot(kappa_t, outcomes) plt.axhline(estimate.value, linestyle="--", color="gray") ax.set_title("Effect of Unobserved Common Cause") ax.set_xlabel("Value of Linear Constant on Treatment") ax.set_ylabel("Estimated Effect after adding the common cause") plt.show() return refute elif isinstance(kappa_y, (list, np.ndarray)): outcomes = np.random.rand(len(kappa_y)) orig_data = copy.deepcopy(data) for i in tqdm( range(0, len(kappa_y)), colour=CausalRefuter.PROGRESS_BAR_COLOR, disable=not show_progress_bar, desc="Refuting Estimates: ", ): new_data = _include_confounders_effect( data, orig_data, confounders_effect_on_treatment, treatment_name, kappa_t, confounders_effect_on_outcome, outcome_name, kappa_y[i], ) new_estimator = CausalEstimator.get_estimator_object(new_data, target_estimand, estimate) new_effect = new_estimator.estimate_effect() refute = CausalRefutation( estimate.value, new_effect.value, refutation_type="Refute: Add an Unobserved Common Cause" ) logger.debug(refute) outcomes[i] = refute.new_effect # Populate the results refute.new_effect_array = outcomes refute.new_effect = (np.min(outcomes), np.max(outcomes)) if plotmethod is None: return refute import matplotlib import matplotlib.pyplot as plt fig = plt.figure(figsize=(6, 5)) left, bottom, width, height = 0.1, 0.1, 0.8, 0.8 ax = fig.add_axes([left, bottom, width, height]) plt.plot(kappa_y, outcomes) plt.axhline(estimate.value, linestyle="--", color="gray") ax.set_title("Effect of Unobserved Common Cause") ax.set_xlabel("Value of Linear Constant on Outcome") ax.set_ylabel("Estimated Effect after adding the common cause") plt.show() return refute

andresmor-ms

133e7b9a4ed32aae8ab5f39a01eb02b3a4d1c0ba

e1652ec3c6606b1bb2dfe91ef830e4b4b566712d

what would be a good naming convention? shall we keep the "_" prefix for non-user facing functions? Or is there a more pythonic way of doing this?

amit-sharma

py-why/dowhy

Functional api/refute estimate

* Refactor refuters into functions * Rename functional_api notebook for clarity * Add return types to identify_estimate * Update `__init__.py` for imports * Add joblib for bootstrap refuter * Create `refute_estimate` function * Add types for refuter parameters & return types

2022-10-04 16:18:49+00:00

2022-10-07 04:30:22+00:00

dowhy/causal_refuters/add_unobserved_common_cause.py

import copy import logging import math import numpy as np import pandas as pd import scipy.stats import statsmodels.api as sm from sklearn.linear_model import LogisticRegression from sklearn.preprocessing import StandardScaler from tqdm.auto import tqdm import dowhy.causal_estimators.econml from dowhy.causal_estimator import CausalEstimator from dowhy.causal_estimators.linear_regression_estimator import LinearRegressionEstimator from dowhy.causal_estimators.regression_estimator import RegressionEstimator from dowhy.causal_refuter import CausalRefutation, CausalRefuter from dowhy.causal_refuters.evalue_sensitivity_analyzer import EValueSensitivityAnalyzer from dowhy.causal_refuters.linear_sensitivity_analyzer import LinearSensitivityAnalyzer from dowhy.causal_refuters.non_parametric_sensitivity_analyzer import NonParametricSensitivityAnalyzer from dowhy.causal_refuters.partial_linear_sensitivity_analyzer import PartialLinearSensitivityAnalyzer class AddUnobservedCommonCause(CausalRefuter): """Add an unobserved confounder for refutation. AddUnobservedCommonCause class supports three methods: 1) Simulation of an unobserved confounder 2) Linear partial R2 : Sensitivity Analysis for linear models. 3) Non-Parametric partial R2 based : Sensitivity Analyis for non-parametric models. Supports additional parameters that can be specified in the refute_estimate() method. """ def __init__(self, *args, **kwargs): """ Initialize the parameters required for the refuter. For direct_simulation, if effect_strength_on_treatment or effect_strength_on_outcome is not given, it is calculated automatically as a range between the minimum and maximum effect strength of observed confounders on treatment and outcome respectively. :param simulation_method: The method to use for simulating effect of unobserved confounder. Possible values are ["direct-simulation", "linear-partial-R2", "non-parametric-partial-R2", "e-value"]. :param confounders_effect_on_treatment: str : The type of effect on the treatment due to the unobserved confounder. Possible values are ['binary_flip', 'linear'] :param confounders_effect_on_outcome: str : The type of effect on the outcome due to the unobserved confounder. Possible values are ['binary_flip', 'linear'] :param effect_strength_on_treatment: float, numpy.ndarray: [Used when simulation_method="direct-simulation"] Strength of the confounder's effect on treatment. When confounders_effect_on_treatment is linear, it is the regression coefficient. When the confounders_effect_on_treatment is binary flip, it is the probability with which effect of unobserved confounder can invert the value of the treatment. :param effect_strength_on_outcome: float, numpy.ndarray: Strength of the confounder's effect on outcome. Its interpretation depends on confounders_effect_on_outcome and the simulation_method. When simulation_method is direct-simulation, for a linear effect it behaves like the regression coefficient and for a binary flip, it is the probability with which it can invert the value of the outcome. :param partial_r2_confounder_treatment: float, numpy.ndarray: [Used when simulation_method is linear-partial-R2 or non-parametric-partial-R2] Partial R2 of the unobserved confounder wrt the treatment conditioned on the observed confounders. Only in the case of general non-parametric-partial-R2, it is the fraction of variance in the reisz representer that is explained by the unobserved confounder; specifically (1-r), where r is the ratio of variance of reisz representer, alpha^2, based on observed confounders and that based on all confounders. :param partial_r2_confounder_outcome: float, numpy.ndarray: [Used when simulation_method is linear-partial-R2 or non-parametric-partial-R2] Partial R2 of the unobserved confounder wrt the outcome conditioned on the treatment and observed confounders. :param frac_strength_treatment: float: This parameter decides the effect strength of the simulated confounder as a fraction of the effect strength of observed confounders on treatment. Defaults to 1. :param frac_strength_outcome: float: This parameter decides the effect strength of the simulated confounder as a fraction of the effect strength of observed confounders on outcome. Defaults to 1. :param plotmethod: string: Type of plot to be shown. If None, no plot is generated. This parameter is used only only when more than one treatment confounder effect values or outcome confounder effect values are provided. Default is "colormesh". Supported values are "contour", "colormesh" when more than one value is provided for both confounder effect value parameters; "line" when provided for only one of them. :param percent_change_estimate: It is the percentage of reduction of treatment estimate that could alter the results (default = 1). if percent_change_estimate = 1, the robustness value describes the strength of association of confounders with treatment and outcome in order to reduce the estimate by 100% i.e bring it down to 0. (relevant only for Linear Sensitivity Analysis, ignore for rest) :param confounder_increases_estimate: True implies that confounder increases the absolute value of estimate and vice versa. (Default = False). (relevant only for Linear Sensitivity Analysis, ignore for rest) :param benchmark_common_causes: names of variables for bounding strength of confounders. (relevant only for partial-r2 based simulation methods) :param significance_level: confidence interval for statistical inference(default = 0.05). (relevant only for partial-r2 based simulation methods) :param null_hypothesis_effect: assumed effect under the null hypothesis. (relevant only for linear-partial-R2, ignore for rest) :param plot_estimate: Generate contour plot for estimate while performing sensitivity analysis. (default = True). (relevant only for partial-r2 based simulation methods) :param num_splits: number of splits for cross validation. (default = 5). (relevant only for non-parametric-partial-R2 simulation method) :param shuffle_data : shuffle data or not before splitting into folds (default = False). (relevant only for non-parametric-partial-R2 simulation method) :param shuffle_random_seed: seed for randomly shuffling data. (relevant only for non-parametric-partial-R2 simulation method) :param alpha_s_estimator_param_list: list of dictionaries with parameters for finding alpha_s. (relevant only for non-parametric-partial-R2 simulation method) :param g_s_estimator_list: list of estimator objects for finding g_s. These objects should have fit() and predict() functions implemented. (relevant only for non-parametric-partial-R2 simulation method) :param g_s_estimator_param_list: list of dictionaries with parameters for tuning respective estimators in "g_s_estimator_list". The order of the dictionaries in the list should be consistent with the estimator objects order in "g_s_estimator_list". (relevant only for non-parametric-partial-R2 simulation method) """ super().__init__(*args, **kwargs) self.simulation_method = kwargs["simulation_method"] if "simulation_method" in kwargs else "direct-simulation" self.effect_on_t = ( kwargs["confounders_effect_on_treatment"] if "confounders_effect_on_treatment" in kwargs else "binary_flip" ) self.effect_on_y = ( kwargs["confounders_effect_on_outcome"] if "confounders_effect_on_outcome" in kwargs else "linear" ) if self.simulation_method == "direct-simulation": self.kappa_t = kwargs["effect_strength_on_treatment"] if "effect_strength_on_treatment" in kwargs else None self.kappa_y = kwargs["effect_strength_on_outcome"] if "effect_strength_on_outcome" in kwargs else None elif self.simulation_method in ["linear-partial-R2", "non-parametric-partial-R2"]: self.kappa_t = ( kwargs["partial_r2_confounder_treatment"] if "partial_r2_confounder_treatment" in kwargs else None ) self.kappa_y = ( kwargs["partial_r2_confounder_outcome"] if "partial_r2_confounder_outcome" in kwargs else None ) elif self.simulation_method == "e-value": pass else: raise ValueError( "simulation method is not supported. Try direct-simulation, linear-partial-R2, non-parametric-partial-R2, or e-value" ) self.frac_strength_treatment = ( kwargs["effect_fraction_on_treatment"] if "effect_fraction_on_treatment" in kwargs else 1 ) self.frac_strength_outcome = ( kwargs["effect_fraction_on_outcome"] if "effect_fraction_on_outcome" in kwargs else 1 ) self.plotmethod = kwargs["plotmethod"] if "plotmethod" in kwargs else "colormesh" self.percent_change_estimate = kwargs["percent_change_estimate"] if "percent_change_estimate" in kwargs else 1.0 self.significance_level = kwargs["significance_level"] if "significance_level" in kwargs else 0.05 self.confounder_increases_estimate = ( kwargs["confounder_increases_estimate"] if "confounder_increases_estimate" in kwargs else False ) self.benchmark_common_causes = ( kwargs["benchmark_common_causes"] if "benchmark_common_causes" in kwargs else None ) self.null_hypothesis_effect = kwargs["null_hypothesis_effect"] if "null_hypothesis_effect" in kwargs else 0 self.plot_estimate = kwargs["plot_estimate"] if "plot_estimate" in kwargs else True self.num_splits = kwargs["num_splits"] if "num_splits" in kwargs else 5 self.shuffle_data = kwargs["shuffle_data"] if "shuffle_data" in kwargs else False self.shuffle_random_seed = kwargs["shuffle_random_seed"] if "shuffle_random_seed" in kwargs else None self.alpha_s_estimator_param_list = ( kwargs["alpha_s_estimator_param_list"] if "alpha_s_estimator_param_list" in kwargs else None ) self.alpha_s_estimator_list = kwargs["alpha_s_estimator_list"] if "alpha_s_estimator_list" in kwargs else None self.g_s_estimator_list = kwargs["g_s_estimator_list"] if "g_s_estimator_list" in kwargs else None self.g_s_estimator_param_list = ( kwargs["g_s_estimator_param_list"] if "g_s_estimator_param_list" in kwargs else None ) self.plugin_reisz = kwargs["plugin_reisz"] if "plugin_reisz" in kwargs else False self.logger = logging.getLogger(__name__) def infer_default_kappa_t(self, len_kappa_t=10): """Infer default effect strength of simulated confounder on treatment.""" observed_common_causes_names = self._target_estimand.get_backdoor_variables() if len(observed_common_causes_names) > 0: observed_common_causes = self._data[observed_common_causes_names] observed_common_causes = pd.get_dummies(observed_common_causes, drop_first=True) else: raise ValueError( "There needs to be at least one common cause to" + "automatically compute the default value of kappa_t." + " Provide a value for kappa_t" ) t = self._data[self._treatment_name] # Standardizing the data observed_common_causes = StandardScaler().fit_transform(observed_common_causes) if self.effect_on_t == "binary_flip": # Fit a model containing all confounders and compare predictions # using all features compared to all features except a given # confounder. tmodel = LogisticRegression().fit(observed_common_causes, t) tpred = tmodel.predict(observed_common_causes).astype(int) flips = [] for i in range(observed_common_causes.shape[1]): oldval = np.copy(observed_common_causes[:, i]) observed_common_causes[:, i] = 0 tcap = tmodel.predict(observed_common_causes).astype(int) observed_common_causes[:, i] = oldval flips.append(np.sum(abs(tcap - tpred)) / tpred.shape[0]) min_coeff, max_coeff = min(flips), max(flips) elif self.effect_on_t == "linear": # Estimating the regression coefficient from standardized features to t corrcoef_var_t = np.corrcoef(observed_common_causes, t, rowvar=False)[-1, :-1] std_dev_t = np.std(t)[0] max_coeff = max(corrcoef_var_t) * std_dev_t min_coeff = min(corrcoef_var_t) * std_dev_t else: raise NotImplementedError( "'" + self.effect_on_t + "' method not supported for confounders' effect on treatment" ) min_coeff, max_coeff = self._compute_min_max_coeff(min_coeff, max_coeff, self.frac_strength_treatment) # By default, return a plot with 10 points # consider 10 values of the effect of the unobserved confounder step = (max_coeff - min_coeff) / len_kappa_t self.logger.info("(Min, Max) kappa_t for observed common causes, ({0}, {1})".format(min_coeff, max_coeff)) if np.equal(max_coeff, min_coeff): return max_coeff else: return np.arange(min_coeff, max_coeff, step) def _compute_min_max_coeff(self, min_coeff, max_coeff, effect_strength_fraction): max_coeff = effect_strength_fraction * max_coeff min_coeff = effect_strength_fraction * min_coeff return min_coeff, max_coeff def infer_default_kappa_y(self, len_kappa_y=10): """Infer default effect strength of simulated confounder on treatment.""" observed_common_causes_names = self._target_estimand.get_backdoor_variables() if len(observed_common_causes_names) > 0: observed_common_causes = self._data[observed_common_causes_names] observed_common_causes = pd.get_dummies(observed_common_causes, drop_first=True) else: raise ValueError( "There needs to be at least one common cause to" + "automatically compute the default value of kappa_y." + " Provide a value for kappa_y" ) y = self._data[self._outcome_name] # Standardizing the data observed_common_causes = StandardScaler().fit_transform(observed_common_causes) if self.effect_on_y == "binary_flip": # Fit a model containing all confounders and compare predictions # using all features compared to all features except a given # confounder. ymodel = LogisticRegression().fit(observed_common_causes, y) ypred = ymodel.predict(observed_common_causes).astype(int) flips = [] for i in range(observed_common_causes.shape[1]): oldval = np.copy(observed_common_causes[:, i]) observed_common_causes[:, i] = 0 ycap = ymodel.predict(observed_common_causes).astype(int) observed_common_causes[:, i] = oldval flips.append(np.sum(abs(ycap - ypred)) / ypred.shape[0]) min_coeff, max_coeff = min(flips), max(flips) elif self.effect_on_y == "linear": corrcoef_var_y = np.corrcoef(observed_common_causes, y, rowvar=False)[-1, :-1] std_dev_y = np.std(y)[0] max_coeff = max(corrcoef_var_y) * std_dev_y min_coeff = min(corrcoef_var_y) * std_dev_y else: raise NotImplementedError( "'" + self.effect_on_y + "' method not supported for confounders' effect on outcome" ) min_coeff, max_coeff = self._compute_min_max_coeff(min_coeff, max_coeff, self.frac_strength_outcome) # By default, return a plot with 10 points # consider 10 values of the effect of the unobserved confounder step = (max_coeff - min_coeff) / len_kappa_y self.logger.info("(Min, Max) kappa_y for observed common causes, ({0}, {1})".format(min_coeff, max_coeff)) if np.equal(max_coeff, min_coeff): return max_coeff else: return np.arange(min_coeff, max_coeff, step) def refute_estimate(self, show_progress_bar=False): """ This function attempts to add an unobserved common cause to the outcome and the treatment. At present, we have implemented the behavior for one dimensional behaviors for continuous and binary variables. This function can either take single valued inputs or a range of inputs. The function then looks at the data type of the input and then decides on the course of action. :return: CausalRefuter: An object that contains the estimated effect and a new effect and the name of the refutation used. """ if self.simulation_method == "linear-partial-R2": if not (isinstance(self._estimate.estimator, LinearRegressionEstimator)): raise NotImplementedError( "Currently only LinearRegressionEstimator is supported for Sensitivity Analysis" ) if len(self._estimate.estimator._effect_modifier_names) > 0: raise NotImplementedError("The current implementation does not support effect modifiers") if self.frac_strength_outcome == 1: self.frac_strength_outcome = self.frac_strength_treatment analyzer = LinearSensitivityAnalyzer( estimator=self._estimate.estimator, data=self._data, treatment_name=self._treatment_name, percent_change_estimate=self.percent_change_estimate, significance_level=self.significance_level, benchmark_common_causes=self.benchmark_common_causes, null_hypothesis_effect=self.null_hypothesis_effect, frac_strength_treatment=self.frac_strength_treatment, frac_strength_outcome=self.frac_strength_outcome, common_causes_order=self._estimate.estimator._observed_common_causes.columns, ) analyzer.check_sensitivity(plot=self.plot_estimate) return analyzer if self.simulation_method == "non-parametric-partial-R2": # If the estimator used is LinearDML, partially linear sensitivity analysis will be automatically chosen if isinstance(self._estimate.estimator, dowhy.causal_estimators.econml.Econml): if self._estimate.estimator._econml_methodname == "econml.dml.LinearDML": analyzer = PartialLinearSensitivityAnalyzer( estimator=self._estimate._estimator_object, observed_common_causes=self._estimate.estimator._observed_common_causes, treatment=self._estimate.estimator._treatment, outcome=self._estimate.estimator._outcome, alpha_s_estimator_param_list=self.alpha_s_estimator_param_list, g_s_estimator_list=self.g_s_estimator_list, g_s_estimator_param_list=self.g_s_estimator_param_list, effect_strength_treatment=self.kappa_t, effect_strength_outcome=self.kappa_y, benchmark_common_causes=self.benchmark_common_causes, frac_strength_treatment=self.frac_strength_treatment, frac_strength_outcome=self.frac_strength_outcome, ) analyzer.check_sensitivity(plot=self.plot_estimate) return analyzer analyzer = NonParametricSensitivityAnalyzer( estimator=self._estimate.estimator, observed_common_causes=self._estimate.estimator._observed_common_causes, treatment=self._estimate.estimator._treatment, outcome=self._estimate.estimator._outcome, alpha_s_estimator_list=self.alpha_s_estimator_list, alpha_s_estimator_param_list=self.alpha_s_estimator_param_list, g_s_estimator_list=self.g_s_estimator_list, g_s_estimator_param_list=self.g_s_estimator_param_list, effect_strength_treatment=self.kappa_t, effect_strength_outcome=self.kappa_y, benchmark_common_causes=self.benchmark_common_causes, frac_strength_treatment=self.frac_strength_treatment, frac_strength_outcome=self.frac_strength_outcome, theta_s=self._estimate.value, plugin_reisz=self.plugin_reisz, ) analyzer.check_sensitivity(plot=self.plot_estimate) return analyzer if self.simulation_method == "e-value": if not isinstance(self._estimate.estimator, RegressionEstimator): raise NotImplementedError( "E-Value sensitivity analysis is currently only implemented RegressionEstimator." ) if len(self._estimate.estimator._effect_modifier_names) > 0: raise NotImplementedError("The current implementation does not support effect modifiers") analyzer = EValueSensitivityAnalyzer( estimate=self._estimate, estimand=self._target_estimand, data=self._data, treatment_name=self._treatment_name[0], outcome_name=self._outcome_name[0], ) analyzer.check_sensitivity(plot=self.plot_estimate) return analyzer if self.kappa_t is None: self.kappa_t = self.infer_default_kappa_t() if self.kappa_y is None: self.kappa_y = self.infer_default_kappa_y() if not isinstance(self.kappa_t, (list, np.ndarray)) and not isinstance( self.kappa_y, (list, np.ndarray) ): # Deal with single value inputs new_data = copy.deepcopy(self._data) new_data = self.include_confounders_effect(new_data, self.kappa_t, self.kappa_y) new_estimator = CausalEstimator.get_estimator_object(new_data, self._target_estimand, self._estimate) new_effect = new_estimator.estimate_effect() refute = CausalRefutation( self._estimate.value, new_effect.value, refutation_type="Refute: Add an Unobserved Common Cause" ) refute.new_effect_array = np.array(new_effect.value) refute.new_effect = new_effect.value refute.add_refuter(self) return refute else: # Deal with multiple value inputs if isinstance(self.kappa_t, (list, np.ndarray)) and isinstance( self.kappa_y, (list, np.ndarray) ): # Deal with range inputs # Get a 2D matrix of values # x,y = np.meshgrid(self.kappa_t, self.kappa_y) # x,y are both MxN results_matrix = np.random.rand( len(self.kappa_t), len(self.kappa_y) ) # Matrix to hold all the results of NxM orig_data = copy.deepcopy(self._data) for i in tqdm( range(len(self.kappa_t)), colour=CausalRefuter.PROGRESS_BAR_COLOR, disable=not show_progress_bar, desc="Refuting Estimates: ", ): for j in range(len(self.kappa_y)): new_data = self.include_confounders_effect(orig_data, self.kappa_t[i], self.kappa_y[j]) new_estimator = CausalEstimator.get_estimator_object( new_data, self._target_estimand, self._estimate ) new_effect = new_estimator.estimate_effect() refute = CausalRefutation( self._estimate.value, new_effect.value, refutation_type="Refute: Add an Unobserved Common Cause", ) results_matrix[i][j] = refute.new_effect # Populate the results refute.new_effect_array = results_matrix refute.new_effect = (np.min(results_matrix), np.max(results_matrix)) # Store the values into the refute object refute.add_refuter(self) if self.plotmethod is None: return refute import matplotlib import matplotlib.pyplot as plt fig = plt.figure(figsize=(6, 5)) left, bottom, width, height = 0.1, 0.1, 0.8, 0.8 ax = fig.add_axes([left, bottom, width, height]) oe = self._estimate.value contour_levels = [oe / 4.0, oe / 2.0, (3.0 / 4) * oe, oe] contour_levels.extend([0, np.min(results_matrix), np.max(results_matrix)]) if self.plotmethod == "contour": cp = plt.contourf(self.kappa_y, self.kappa_t, results_matrix, levels=sorted(contour_levels)) # Adding a label on the contour line for the original estimate fmt = {} trueeffect_index = np.where(cp.levels == oe)[0][0] fmt[cp.levels[trueeffect_index]] = "Estimated Effect" # Label every other level using strings plt.clabel(cp, [cp.levels[trueeffect_index]], inline=True, fmt=fmt) plt.colorbar(cp) elif self.plotmethod == "colormesh": cp = plt.pcolormesh(self.kappa_y, self.kappa_t, results_matrix, shading="nearest") plt.colorbar(cp, ticks=contour_levels) ax.yaxis.set_ticks(self.kappa_t) ax.xaxis.set_ticks(self.kappa_y) plt.xticks(rotation=45) ax.set_title("Effect of Unobserved Common Cause") ax.set_ylabel("Value of Linear Constant on Treatment") ax.set_xlabel("Value of Linear Constant on Outcome") plt.show() return refute elif isinstance(self.kappa_t, (list, np.ndarray)): outcomes = np.random.rand(len(self.kappa_t)) orig_data = copy.deepcopy(self._data) for i in tqdm( range(0, len(self.kappa_t)), colour=CausalRefuter.PROGRESS_BAR_COLOR, disable=not show_progress_bar, desc="Refuting Estimates: ", ): new_data = self.include_confounders_effect(orig_data, self.kappa_t[i], self.kappa_y) new_estimator = CausalEstimator.get_estimator_object( new_data, self._target_estimand, self._estimate ) new_effect = new_estimator.estimate_effect() refute = CausalRefutation( self._estimate.value, new_effect.value, refutation_type="Refute: Add an Unobserved Common Cause" ) self.logger.debug(refute) outcomes[i] = refute.new_effect # Populate the results refute.new_effect_array = outcomes refute.new_effect = (np.min(outcomes), np.max(outcomes)) refute.add_refuter(self) if self.plotmethod is None: return refute import matplotlib import matplotlib.pyplot as plt fig = plt.figure(figsize=(6, 5)) left, bottom, width, height = 0.1, 0.1, 0.8, 0.8 ax = fig.add_axes([left, bottom, width, height]) plt.plot(self.kappa_t, outcomes) plt.axhline(self._estimate.value, linestyle="--", color="gray") ax.set_title("Effect of Unobserved Common Cause") ax.set_xlabel("Value of Linear Constant on Treatment") ax.set_ylabel("Estimated Effect after adding the common cause") plt.show() return refute elif isinstance(self.kappa_y, (list, np.ndarray)): outcomes = np.random.rand(len(self.kappa_y)) orig_data = copy.deepcopy(self._data) for i in tqdm( range(0, len(self.kappa_y)), colour=CausalRefuter.PROGRESS_BAR_COLOR, disable=not show_progress_bar, desc="Refuting Estimates: ", ): new_data = self.include_confounders_effect(orig_data, self.kappa_t, self.kappa_y[i]) new_estimator = CausalEstimator.get_estimator_object( new_data, self._target_estimand, self._estimate ) new_effect = new_estimator.estimate_effect() refute = CausalRefutation( self._estimate.value, new_effect.value, refutation_type="Refute: Add an Unobserved Common Cause" ) self.logger.debug(refute) outcomes[i] = refute.new_effect # Populate the results refute.new_effect_array = outcomes refute.new_effect = (np.min(outcomes), np.max(outcomes)) refute.add_refuter(self) if self.plotmethod is None: return refute import matplotlib import matplotlib.pyplot as plt fig = plt.figure(figsize=(6, 5)) left, bottom, width, height = 0.1, 0.1, 0.8, 0.8 ax = fig.add_axes([left, bottom, width, height]) plt.plot(self.kappa_y, outcomes) plt.axhline(self._estimate.value, linestyle="--", color="gray") ax.set_title("Effect of Unobserved Common Cause") ax.set_xlabel("Value of Linear Constant on Outcome") ax.set_ylabel("Estimated Effect after adding the common cause") plt.show() return refute def include_confounders_effect(self, new_data, kappa_t, kappa_y): """ This function deals with the change in the value of the data due to the effect of the unobserved confounder. In the case of a binary flip, we flip only if the random number is greater than the threshold set. In the case of a linear effect, we use the variable as the linear regression constant. :param new_data: pandas.DataFrame: The data to be changed due to the effects of the unobserved confounder. :param kappa_t: numpy.float64: The value of the threshold for binary_flip or the value of the regression coefficient for linear effect. :param kappa_y: numpy.float64: The value of the threshold for binary_flip or the value of the regression coefficient for linear effect. :return: pandas.DataFrame: The DataFrame that includes the effects of the unobserved confounder. """ num_rows = self._data.shape[0] stdnorm = scipy.stats.norm() w_random = stdnorm.rvs(num_rows) if self.effect_on_t == "binary_flip": alpha = 2 * kappa_t - 1 if kappa_t >= 0.5 else 1 - 2 * kappa_t interval = stdnorm.interval(alpha) rel_interval = interval[0] if kappa_t >= 0.5 else interval[1] new_data.loc[rel_interval <= w_random, self._treatment_name] = ( 1 - new_data.loc[rel_interval <= w_random, self._treatment_name] ) for tname in self._treatment_name: if pd.api.types.is_bool_dtype(self._data[tname]): new_data = new_data.astype({tname: "bool"}, copy=False) elif self.effect_on_t == "linear": confounder_t_effect = kappa_t * w_random # By default, we add the effect of simulated confounder for treatment. # But subtract it from outcome to create a negative correlation # assuming that the original confounder's effect was positive on both. # This is to remove the effect of the original confounder. new_data[self._treatment_name] = new_data[self._treatment_name].values + np.ndarray( shape=(num_rows, 1), buffer=confounder_t_effect ) else: raise NotImplementedError( "'" + self.effect_on_t + "' method not supported for confounders' effect on treatment" ) if self.effect_on_y == "binary_flip": alpha = 2 * kappa_y - 1 if kappa_y >= 0.5 else 1 - 2 * kappa_y interval = stdnorm.interval(alpha) rel_interval = interval[0] if kappa_y >= 0.5 else interval[1] new_data.loc[rel_interval <= w_random, self._outcome_name] = ( 1 - new_data.loc[rel_interval <= w_random, self._outcome_name] ) for yname in self._outcome_name: if pd.api.types.is_bool_dtype(self._data[yname]): new_data = new_data.astype({yname: "bool"}, copy=False) elif self.effect_on_y == "linear": confounder_y_effect = (-1) * kappa_y * w_random # By default, we add the effect of simulated confounder for treatment. # But subtract it from outcome to create a negative correlation # assuming that the original confounder's effect was positive on both. # This is to remove the effect of the original confounder. new_data[self._outcome_name] = new_data[self._outcome_name].values + np.ndarray( shape=(num_rows, 1), buffer=confounder_y_effect ) else: raise NotImplementedError( "'" + self.effect_on_y + "' method not supported for confounders' effect on outcome" ) return new_data def include_simulated_confounder(self, convergence_threshold=0.1, c_star_max=1000): """ This function simulates an unobserved confounder based on the data using the following steps: 1. It calculates the "residuals" from the treatment and outcome model i.) The outcome model has outcome as the dependent variable and all the observed variables including treatment as independent variables ii.) The treatment model has treatment as the dependent variable and all the observed variables as independent variables. 2. U is an intermediate random variable drawn from the normal distribution with the weighted average of residuals as mean and a unit variance U ~ N(c1*d_y + c2*d_t, 1) where *d_y and d_t are residuals from the treatment and outcome model *c1 and c2 are coefficients to the residuals 3. The final U, which is the simulated unobserved confounder is obtained by debiasing the intermediate variable U by residualising it with X Choosing the coefficients c1 and c2: The coefficients are chosen based on these basic assumptions: 1. There is a hyperbolic relationship satisfying c1*c2 = c_star 2. c_star is chosen from a range of possible values based on the correlation of the obtained simulated variable with outcome and treatment. 3. The product of correlations with treatment and outcome should be at a minimum distance to the maximum correlations with treatment and outcome in any of the observed confounders 4. The ratio of the weights should be such that they maintain the ratio of the maximum possible observed coefficients within some confidence interval :param c_star_max: The maximum possible value for the hyperbolic curve on which the coefficients to the residuals lie. It defaults to 1000 in the code if not specified by the user. :type int :param convergence_threshold: The threshold to check the plateauing of the correlation while selecting a c_star. It defaults to 0.1 in the code if not specified by the user :type float :returns: The simulated values of the unobserved confounder based on the data :type pandas.core.series.Series """ # Obtaining the list of observed variables required_variables = True observed_variables = self.choose_variables(required_variables) observed_variables_with_treatment_and_outcome = observed_variables + self._treatment_name + self._outcome_name # Taking a subset of the dataframe that has only observed variables self._data = self._data[observed_variables_with_treatment_and_outcome] # Residuals from the outcome model obtained by fitting a linear model y = self._data[self._outcome_name[0]] observed_variables_with_treatment = observed_variables + self._treatment_name X = self._data[observed_variables_with_treatment] model = sm.OLS(y, X.astype("float")) results = model.fit() residuals_y = y - results.fittedvalues d_y = list(pd.Series(residuals_y)) # Residuals from the treatment model obtained by fitting a linear model t = self._data[self._treatment_name[0]].astype("int64") X = self._data[observed_variables] model = sm.OLS(t, X) results = model.fit() residuals_t = t - results.fittedvalues d_t = list(pd.Series(residuals_t)) # Initialising product_cor_metric_observed with a really low value as finding maximum product_cor_metric_observed = -10000000000 for i in observed_variables: current_obs_confounder = self._data[i] outcome_values = self._data[self._outcome_name[0]] correlation_y = current_obs_confounder.corr(outcome_values) treatment_values = t correlation_t = current_obs_confounder.corr(treatment_values) product_cor_metric_current = correlation_y * correlation_t if product_cor_metric_current >= product_cor_metric_observed: product_cor_metric_observed = product_cor_metric_current correlation_t_observed = correlation_t correlation_y_observed = correlation_y # The user has an option to give the the effect_strength_on_y and effect_strength_on_t which can be then used instead of maximum correlation with treatment and outcome in the observed variables as it specifies the desired effect. if self.kappa_t is not None: correlation_t_observed = self.kappa_t if self.kappa_y is not None: correlation_y_observed = self.kappa_y # Choosing a c_star based on the data. # The correlations stop increasing upon increasing c_star after a certain value, that is it plateaus and we choose the value of c_star to be the value it plateaus. correlation_y_list = [] correlation_t_list = [] product_cor_metric_simulated_list = [] x_list = [] step = int(c_star_max / 10) for i in range(0, int(c_star_max), step): c1 = math.sqrt(i) c2 = c1 final_U = self.generate_confounder_from_residuals(c1, c2, d_y, d_t, X) current_simulated_confounder = final_U outcome_values = self._data[self._outcome_name[0]] correlation_y = current_simulated_confounder.corr(outcome_values) correlation_y_list.append(correlation_y) treatment_values = t correlation_t = current_simulated_confounder.corr(treatment_values) correlation_t_list.append(correlation_t) product_cor_metric_simulated = correlation_y * correlation_t product_cor_metric_simulated_list.append(product_cor_metric_simulated) x_list.append(i) index = 1 while index < len(correlation_y_list): if (correlation_y_list[index] - correlation_y_list[index - 1]) <= convergence_threshold: c_star = x_list[index] break index = index + 1 # Choosing c1 and c2 based on the hyperbolic relationship once c_star is chosen by going over various combinations of c1 and c2 values and choosing the combination which # which maintains the minimum distance between the product of correlations of the simulated variable and the product of maximum correlations of one of the observed variables # and additionally checks if the ratio of the weights are such that they maintain the ratio of the maximum possible observed coefficients within some confidence interval # c1_final and c2_final are initialised to the values on the hyperbolic curve such that c1_final = c2_final and c1_final*c2_final = c_star c1_final = math.sqrt(c_star) c2_final = math.sqrt(c_star) # initialising min_distance_between_product_cor_metrics to be a value greater than 1 min_distance_between_product_cor_metrics = 1.5 i = 0.05 threshold = c_star / 0.05 while i <= threshold: c2 = i c1 = c_star / c2 final_U = self.generate_confounder_from_residuals(c1, c2, d_y, d_t, X) current_simulated_confounder = final_U outcome_values = self._data[self._outcome_name[0]] correlation_y = current_simulated_confounder.corr(outcome_values) treatment_values = t correlation_t = current_simulated_confounder.corr(treatment_values) product_cor_metric_simulated = correlation_y * correlation_t if min_distance_between_product_cor_metrics >= abs( product_cor_metric_simulated - product_cor_metric_observed ): min_distance_between_product_cor_metrics = abs( product_cor_metric_simulated - product_cor_metric_observed ) additional_condition = correlation_y_observed / correlation_t_observed if ((c1 / c2) <= (additional_condition + 0.3 * additional_condition)) and ( (c1 / c2) >= (additional_condition - 0.3 * additional_condition) ): # choose minimum positive value c1_final = c1 c2_final = c2 i = i * 1.5 """#closed form solution print("c_star_max before closed form", c_star_max) if max_correlation_with_t == -1000: c2 = 0 c1 = c_star_max else: additional_condition = abs(max_correlation_with_y/max_correlation_with_t) print("additional_condition", additional_condition) c2 = math.sqrt(c_star_max/additional_condition) c1 = c_star_max/c2""" final_U = self.generate_confounder_from_residuals(c1_final, c2_final, d_y, d_t, X) return final_U def generate_confounder_from_residuals(self, c1, c2, d_y, d_t, X): """ This function takes the residuals from the treatment and outcome model and their coefficients and simulates the intermediate random variable U by taking the row wise normal distribution corresponding to each residual value and then debiasing the intermediate variable to get the final variable. :param c1: coefficient to the residual from the outcome model :type float :param c2: coefficient to the residual from the treatment model :type float :param d_y: residuals from the outcome model :type list :param d_t: residuals from the treatment model :type list :returns: The simulated values of the unobserved confounder based on the data :type pandas.core.series.Series """ U = [] for j in range(len(d_t)): simulated_variable_mean = c1 * d_y[j] + c2 * d_t[j] simulated_variable_stddev = 1 U.append(np.random.normal(simulated_variable_mean, simulated_variable_stddev, 1)) U = np.array(U) model = sm.OLS(U, X) results = model.fit() U = U.reshape( -1, ) final_U = U - results.fittedvalues.values final_U = pd.Series(U) return final_U

import copy import logging import math from typing import Dict, List, Optional, Union import numpy as np import pandas as pd import scipy.stats import statsmodels.api as sm from sklearn.linear_model import LogisticRegression from sklearn.preprocessing import StandardScaler from tqdm.auto import tqdm import dowhy.causal_estimators.econml from dowhy.causal_estimator import CausalEstimate, CausalEstimator from dowhy.causal_estimators.linear_regression_estimator import LinearRegressionEstimator from dowhy.causal_estimators.regression_estimator import RegressionEstimator from dowhy.causal_identifier.identified_estimand import IdentifiedEstimand from dowhy.causal_refuter import CausalRefutation, CausalRefuter, choose_variables from dowhy.causal_refuters.evalue_sensitivity_analyzer import EValueSensitivityAnalyzer from dowhy.causal_refuters.linear_sensitivity_analyzer import LinearSensitivityAnalyzer from dowhy.causal_refuters.non_parametric_sensitivity_analyzer import NonParametricSensitivityAnalyzer from dowhy.causal_refuters.partial_linear_sensitivity_analyzer import PartialLinearSensitivityAnalyzer logger = logging.getLogger(__name__) class AddUnobservedCommonCause(CausalRefuter): """Add an unobserved confounder for refutation. AddUnobservedCommonCause class supports three methods: 1) Simulation of an unobserved confounder 2) Linear partial R2 : Sensitivity Analysis for linear models. 3) Non-Parametric partial R2 based : Sensitivity Analyis for non-parametric models. Supports additional parameters that can be specified in the refute_estimate() method. """ def __init__(self, *args, **kwargs): """ Initialize the parameters required for the refuter. For direct_simulation, if effect_strength_on_treatment or effect_strength_on_outcome is not given, it is calculated automatically as a range between the minimum and maximum effect strength of observed confounders on treatment and outcome respectively. :param simulation_method: The method to use for simulating effect of unobserved confounder. Possible values are ["direct-simulation", "linear-partial-R2", "non-parametric-partial-R2", "e-value"]. :param confounders_effect_on_treatment: str : The type of effect on the treatment due to the unobserved confounder. Possible values are ['binary_flip', 'linear'] :param confounders_effect_on_outcome: str : The type of effect on the outcome due to the unobserved confounder. Possible values are ['binary_flip', 'linear'] :param effect_strength_on_treatment: float, numpy.ndarray: [Used when simulation_method="direct-simulation"] Strength of the confounder's effect on treatment. When confounders_effect_on_treatment is linear, it is the regression coefficient. When the confounders_effect_on_treatment is binary flip, it is the probability with which effect of unobserved confounder can invert the value of the treatment. :param effect_strength_on_outcome: float, numpy.ndarray: Strength of the confounder's effect on outcome. Its interpretation depends on confounders_effect_on_outcome and the simulation_method. When simulation_method is direct-simulation, for a linear effect it behaves like the regression coefficient and for a binary flip, it is the probability with which it can invert the value of the outcome. :param partial_r2_confounder_treatment: float, numpy.ndarray: [Used when simulation_method is linear-partial-R2 or non-parametric-partial-R2] Partial R2 of the unobserved confounder wrt the treatment conditioned on the observed confounders. Only in the case of general non-parametric-partial-R2, it is the fraction of variance in the reisz representer that is explained by the unobserved confounder; specifically (1-r), where r is the ratio of variance of reisz representer, alpha^2, based on observed confounders and that based on all confounders. :param partial_r2_confounder_outcome: float, numpy.ndarray: [Used when simulation_method is linear-partial-R2 or non-parametric-partial-R2] Partial R2 of the unobserved confounder wrt the outcome conditioned on the treatment and observed confounders. :param frac_strength_treatment: float: This parameter decides the effect strength of the simulated confounder as a fraction of the effect strength of observed confounders on treatment. Defaults to 1. :param frac_strength_outcome: float: This parameter decides the effect strength of the simulated confounder as a fraction of the effect strength of observed confounders on outcome. Defaults to 1. :param plotmethod: string: Type of plot to be shown. If None, no plot is generated. This parameter is used only only when more than one treatment confounder effect values or outcome confounder effect values are provided. Default is "colormesh". Supported values are "contour", "colormesh" when more than one value is provided for both confounder effect value parameters; "line" when provided for only one of them. :param percent_change_estimate: It is the percentage of reduction of treatment estimate that could alter the results (default = 1). if percent_change_estimate = 1, the robustness value describes the strength of association of confounders with treatment and outcome in order to reduce the estimate by 100% i.e bring it down to 0. (relevant only for Linear Sensitivity Analysis, ignore for rest) :param confounder_increases_estimate: True implies that confounder increases the absolute value of estimate and vice versa. (Default = False). (relevant only for Linear Sensitivity Analysis, ignore for rest) :param benchmark_common_causes: names of variables for bounding strength of confounders. (relevant only for partial-r2 based simulation methods) :param significance_level: confidence interval for statistical inference(default = 0.05). (relevant only for partial-r2 based simulation methods) :param null_hypothesis_effect: assumed effect under the null hypothesis. (relevant only for linear-partial-R2, ignore for rest) :param plot_estimate: Generate contour plot for estimate while performing sensitivity analysis. (default = True). (relevant only for partial-r2 based simulation methods) :param num_splits: number of splits for cross validation. (default = 5). (relevant only for non-parametric-partial-R2 simulation method) :param shuffle_data : shuffle data or not before splitting into folds (default = False). (relevant only for non-parametric-partial-R2 simulation method) :param shuffle_random_seed: seed for randomly shuffling data. (relevant only for non-parametric-partial-R2 simulation method) :param alpha_s_estimator_param_list: list of dictionaries with parameters for finding alpha_s. (relevant only for non-parametric-partial-R2 simulation method) :param g_s_estimator_list: list of estimator objects for finding g_s. These objects should have fit() and predict() functions implemented. (relevant only for non-parametric-partial-R2 simulation method) :param g_s_estimator_param_list: list of dictionaries with parameters for tuning respective estimators in "g_s_estimator_list". The order of the dictionaries in the list should be consistent with the estimator objects order in "g_s_estimator_list". (relevant only for non-parametric-partial-R2 simulation method) """ super().__init__(*args, **kwargs) self.simulation_method = kwargs["simulation_method"] if "simulation_method" in kwargs else "direct-simulation" self.effect_on_t = ( kwargs["confounders_effect_on_treatment"] if "confounders_effect_on_treatment" in kwargs else "binary_flip" ) self.effect_on_y = ( kwargs["confounders_effect_on_outcome"] if "confounders_effect_on_outcome" in kwargs else "linear" ) if self.simulation_method == "direct-simulation": self.kappa_t = kwargs["effect_strength_on_treatment"] if "effect_strength_on_treatment" in kwargs else None self.kappa_y = kwargs["effect_strength_on_outcome"] if "effect_strength_on_outcome" in kwargs else None elif self.simulation_method in ["linear-partial-R2", "non-parametric-partial-R2"]: self.kappa_t = ( kwargs["partial_r2_confounder_treatment"] if "partial_r2_confounder_treatment" in kwargs else None ) self.kappa_y = ( kwargs["partial_r2_confounder_outcome"] if "partial_r2_confounder_outcome" in kwargs else None ) elif self.simulation_method == "e-value": pass else: raise ValueError( "simulation method is not supported. Try direct-simulation, linear-partial-R2, non-parametric-partial-R2, or e-value" ) self.frac_strength_treatment = ( kwargs["effect_fraction_on_treatment"] if "effect_fraction_on_treatment" in kwargs else 1 ) self.frac_strength_outcome = ( kwargs["effect_fraction_on_outcome"] if "effect_fraction_on_outcome" in kwargs else 1 ) self.plotmethod = kwargs["plotmethod"] if "plotmethod" in kwargs else "colormesh" self.percent_change_estimate = kwargs["percent_change_estimate"] if "percent_change_estimate" in kwargs else 1.0 self.significance_level = kwargs["significance_level"] if "significance_level" in kwargs else 0.05 self.confounder_increases_estimate = ( kwargs["confounder_increases_estimate"] if "confounder_increases_estimate" in kwargs else False ) self.benchmark_common_causes = ( kwargs["benchmark_common_causes"] if "benchmark_common_causes" in kwargs else None ) self.null_hypothesis_effect = kwargs["null_hypothesis_effect"] if "null_hypothesis_effect" in kwargs else 0 self.plot_estimate = kwargs["plot_estimate"] if "plot_estimate" in kwargs else True self.num_splits = kwargs["num_splits"] if "num_splits" in kwargs else 5 self.shuffle_data = kwargs["shuffle_data"] if "shuffle_data" in kwargs else False self.shuffle_random_seed = kwargs["shuffle_random_seed"] if "shuffle_random_seed" in kwargs else None self.alpha_s_estimator_param_list = ( kwargs["alpha_s_estimator_param_list"] if "alpha_s_estimator_param_list" in kwargs else None ) self.alpha_s_estimator_list = kwargs["alpha_s_estimator_list"] if "alpha_s_estimator_list" in kwargs else None self.g_s_estimator_list = kwargs["g_s_estimator_list"] if "g_s_estimator_list" in kwargs else None self.g_s_estimator_param_list = ( kwargs["g_s_estimator_param_list"] if "g_s_estimator_param_list" in kwargs else None ) self.plugin_reisz = kwargs["plugin_reisz"] if "plugin_reisz" in kwargs else False self.logger = logging.getLogger(__name__) def refute_estimate(self, show_progress_bar=False): if self.simulation_method == "linear-partial-R2": return sensitivity_linear_partial_r2( self._data, self._estimate, self._treatment_name, self.frac_strength_treatment, self.frac_strength_outcome, self.percent_change_estimate, self.benchmark_common_causes, self.significance_level, self.null_hypothesis_effect, self.plot_estimate, ) elif self.simulation_method == "non-parametric-partial-R2": return sensitivity_non_parametric_partial_r2( self._estimate, self.kappa_t, self.kappa_y, self.frac_strength_treatment, self.frac_strength_outcome, self.benchmark_common_causes, self.plot_estimate, self.alpha_s_estimator_list, self.alpha_s_estimator_param_list, self.g_s_estimator_list, self.g_s_estimator_param_list, self.plugin_reisz, ) elif self.simulation_method == "e-value": return sensitivity_e_value( self._data, self._target_estimand, self._estimate, self._treatment_name, self._outcome_name, self.plot_estimate, ) elif self.simulation_method == "direct-simulation": refute = sensitivity_simulation( self._data, self._target_estimand, self._estimate, self._treatment_name, self._outcome_name, self.kappa_t, self.kappa_y, self.effect_on_t, self.effect_on_y, self.frac_strength_treatment, self.frac_strength_outcome, self.plotmethod, show_progress_bar, ) refute.add_refuter(self) return refute def _infer_default_kappa_t( data: pd.DataFrame, target_estimand: IdentifiedEstimand, treatment_name: List[str], effect_on_t: str, frac_strength_treatment: float, len_kappa_t: int = 10, ): """Infer default effect strength of simulated confounder on treatment.""" observed_common_causes_names = target_estimand.get_backdoor_variables() if len(observed_common_causes_names) > 0: observed_common_causes = data[observed_common_causes_names] observed_common_causes = pd.get_dummies(observed_common_causes, drop_first=True) else: raise ValueError( "There needs to be at least one common cause to" + "automatically compute the default value of kappa_t." + " Provide a value for kappa_t" ) t = data[treatment_name] # Standardizing the data observed_common_causes = StandardScaler().fit_transform(observed_common_causes) if effect_on_t == "binary_flip": # Fit a model containing all confounders and compare predictions # using all features compared to all features except a given # confounder. tmodel = LogisticRegression().fit(observed_common_causes, t) tpred = tmodel.predict(observed_common_causes).astype(int) flips = [] for i in range(observed_common_causes.shape[1]): oldval = np.copy(observed_common_causes[:, i]) observed_common_causes[:, i] = 0 tcap = tmodel.predict(observed_common_causes).astype(int) observed_common_causes[:, i] = oldval flips.append(np.sum(abs(tcap - tpred)) / tpred.shape[0]) min_coeff, max_coeff = min(flips), max(flips) elif effect_on_t == "linear": # Estimating the regression coefficient from standardized features to t corrcoef_var_t = np.corrcoef(observed_common_causes, t, rowvar=False)[-1, :-1] std_dev_t = np.std(t)[0] max_coeff = max(corrcoef_var_t) * std_dev_t min_coeff = min(corrcoef_var_t) * std_dev_t else: raise NotImplementedError("'" + effect_on_t + "' method not supported for confounders' effect on treatment") min_coeff, max_coeff = _compute_min_max_coeff(min_coeff, max_coeff, frac_strength_treatment) # By default, return a plot with 10 points # consider 10 values of the effect of the unobserved confounder step = (max_coeff - min_coeff) / len_kappa_t logger.info("(Min, Max) kappa_t for observed common causes, ({0}, {1})".format(min_coeff, max_coeff)) if np.equal(max_coeff, min_coeff): return max_coeff else: return np.arange(min_coeff, max_coeff, step) def _compute_min_max_coeff(min_coeff: float, max_coeff: float, effect_strength_fraction: np.ndarray): max_coeff = effect_strength_fraction * max_coeff min_coeff = effect_strength_fraction * min_coeff return min_coeff, max_coeff def _infer_default_kappa_y( data: pd.DataFrame, target_estimand: IdentifiedEstimand, outcome_name: List[str], effect_on_y: str, frac_strength_outcome: float, len_kappa_y: int = 10, ): """Infer default effect strength of simulated confounder on treatment.""" observed_common_causes_names = target_estimand.get_backdoor_variables() if len(observed_common_causes_names) > 0: observed_common_causes = data[observed_common_causes_names] observed_common_causes = pd.get_dummies(observed_common_causes, drop_first=True) else: raise ValueError( "There needs to be at least one common cause to" + "automatically compute the default value of kappa_y." + " Provide a value for kappa_y" ) y = data[outcome_name] # Standardizing the data observed_common_causes = StandardScaler().fit_transform(observed_common_causes) if effect_on_y == "binary_flip": # Fit a model containing all confounders and compare predictions # using all features compared to all features except a given # confounder. ymodel = LogisticRegression().fit(observed_common_causes, y) ypred = ymodel.predict(observed_common_causes).astype(int) flips = [] for i in range(observed_common_causes.shape[1]): oldval = np.copy(observed_common_causes[:, i]) observed_common_causes[:, i] = 0 ycap = ymodel.predict(observed_common_causes).astype(int) observed_common_causes[:, i] = oldval flips.append(np.sum(abs(ycap - ypred)) / ypred.shape[0]) min_coeff, max_coeff = min(flips), max(flips) elif effect_on_y == "linear": corrcoef_var_y = np.corrcoef(observed_common_causes, y, rowvar=False)[-1, :-1] std_dev_y = np.std(y)[0] max_coeff = max(corrcoef_var_y) * std_dev_y min_coeff = min(corrcoef_var_y) * std_dev_y else: raise NotImplementedError("'" + effect_on_y + "' method not supported for confounders' effect on outcome") min_coeff, max_coeff = _compute_min_max_coeff(min_coeff, max_coeff, frac_strength_outcome) # By default, return a plot with 10 points # consider 10 values of the effect of the unobserved confounder step = (max_coeff - min_coeff) / len_kappa_y logger.info("(Min, Max) kappa_y for observed common causes, ({0}, {1})".format(min_coeff, max_coeff)) if np.equal(max_coeff, min_coeff): return max_coeff else: return np.arange(min_coeff, max_coeff, step) def _include_confounders_effect( data: pd.DataFrame, new_data: pd.DataFrame, effect_on_t: str, treatment_name: str, kappa_t: float, effect_on_y: str, outcome_name: str, kappa_y: float, ): """ This function deals with the change in the value of the data due to the effect of the unobserved confounder. In the case of a binary flip, we flip only if the random number is greater than the threshold set. In the case of a linear effect, we use the variable as the linear regression constant. :param new_data: pandas.DataFrame: The data to be changed due to the effects of the unobserved confounder. :param kappa_t: numpy.float64: The value of the threshold for binary_flip or the value of the regression coefficient for linear effect. :param kappa_y: numpy.float64: The value of the threshold for binary_flip or the value of the regression coefficient for linear effect. :return: pandas.DataFrame: The DataFrame that includes the effects of the unobserved confounder. """ num_rows = data.shape[0] stdnorm = scipy.stats.norm() w_random = stdnorm.rvs(num_rows) if effect_on_t == "binary_flip": alpha = 2 * kappa_t - 1 if kappa_t >= 0.5 else 1 - 2 * kappa_t interval = stdnorm.interval(alpha) rel_interval = interval[0] if kappa_t >= 0.5 else interval[1] new_data.loc[rel_interval <= w_random, treatment_name] = ( 1 - new_data.loc[rel_interval <= w_random, treatment_name] ) for tname in treatment_name: if pd.api.types.is_bool_dtype(data[tname]): new_data = new_data.astype({tname: "bool"}, copy=False) elif effect_on_t == "linear": confounder_t_effect = kappa_t * w_random # By default, we add the effect of simulated confounder for treatment. # But subtract it from outcome to create a negative correlation # assuming that the original confounder's effect was positive on both. # This is to remove the effect of the original confounder. new_data[treatment_name] = new_data[treatment_name].values + np.ndarray( shape=(num_rows, 1), buffer=confounder_t_effect ) else: raise NotImplementedError("'" + effect_on_t + "' method not supported for confounders' effect on treatment") if effect_on_y == "binary_flip": alpha = 2 * kappa_y - 1 if kappa_y >= 0.5 else 1 - 2 * kappa_y interval = stdnorm.interval(alpha) rel_interval = interval[0] if kappa_y >= 0.5 else interval[1] new_data.loc[rel_interval <= w_random, outcome_name] = 1 - new_data.loc[rel_interval <= w_random, outcome_name] for yname in outcome_name: if pd.api.types.is_bool_dtype(data[yname]): new_data = new_data.astype({yname: "bool"}, copy=False) elif effect_on_y == "linear": confounder_y_effect = (-1) * kappa_y * w_random # By default, we add the effect of simulated confounder for treatment. # But subtract it from outcome to create a negative correlation # assuming that the original confounder's effect was positive on both. # This is to remove the effect of the original confounder. new_data[outcome_name] = new_data[outcome_name].values + np.ndarray( shape=(num_rows, 1), buffer=confounder_y_effect ) else: raise NotImplementedError("'" + effect_on_y + "' method not supported for confounders' effect on outcome") return new_data def include_simulated_confounder( data: pd.DataFrame, treatment_name: str, outcome_name: str, kappa_t: float, kappa_y: float, convergence_threshold: float = 0.1, c_star_max: int = 1000, ): """ This function simulates an unobserved confounder based on the data using the following steps: 1. It calculates the "residuals" from the treatment and outcome model i.) The outcome model has outcome as the dependent variable and all the observed variables including treatment as independent variables ii.) The treatment model has treatment as the dependent variable and all the observed variables as independent variables. 2. U is an intermediate random variable drawn from the normal distribution with the weighted average of residuals as mean and a unit variance U ~ N(c1*d_y + c2*d_t, 1) where *d_y and d_t are residuals from the treatment and outcome model *c1 and c2 are coefficients to the residuals 3. The final U, which is the simulated unobserved confounder is obtained by debiasing the intermediate variable U by residualising it with X Choosing the coefficients c1 and c2: The coefficients are chosen based on these basic assumptions: 1. There is a hyperbolic relationship satisfying c1*c2 = c_star 2. c_star is chosen from a range of possible values based on the correlation of the obtained simulated variable with outcome and treatment. 3. The product of correlations with treatment and outcome should be at a minimum distance to the maximum correlations with treatment and outcome in any of the observed confounders 4. The ratio of the weights should be such that they maintain the ratio of the maximum possible observed coefficients within some confidence interval :param c_star_max: The maximum possible value for the hyperbolic curve on which the coefficients to the residuals lie. It defaults to 1000 in the code if not specified by the user. :type int :param convergence_threshold: The threshold to check the plateauing of the correlation while selecting a c_star. It defaults to 0.1 in the code if not specified by the user :type float :returns: The simulated values of the unobserved confounder based on the data :type pandas.core.series.Series """ # Obtaining the list of observed variables required_variables = True observed_variables = choose_variables(required_variables) observed_variables_with_treatment_and_outcome = observed_variables + treatment_name + outcome_name # Taking a subset of the dataframe that has only observed variables data = data[observed_variables_with_treatment_and_outcome] # Residuals from the outcome model obtained by fitting a linear model y = data[outcome_name[0]] observed_variables_with_treatment = observed_variables + treatment_name X = data[observed_variables_with_treatment] model = sm.OLS(y, X.astype("float")) results = model.fit() residuals_y = y - results.fittedvalues d_y = list(pd.Series(residuals_y)) # Residuals from the treatment model obtained by fitting a linear model t = data[treatment_name[0]].astype("int64") X = data[observed_variables] model = sm.OLS(t, X) results = model.fit() residuals_t = t - results.fittedvalues d_t = list(pd.Series(residuals_t)) # Initialising product_cor_metric_observed with a really low value as finding maximum product_cor_metric_observed = -10000000000 for i in observed_variables: current_obs_confounder = data[i] outcome_values = data[outcome_name[0]] correlation_y = current_obs_confounder.corr(outcome_values) treatment_values = t correlation_t = current_obs_confounder.corr(treatment_values) product_cor_metric_current = correlation_y * correlation_t if product_cor_metric_current >= product_cor_metric_observed: product_cor_metric_observed = product_cor_metric_current correlation_t_observed = correlation_t correlation_y_observed = correlation_y # The user has an option to give the the effect_strength_on_y and effect_strength_on_t which can be then used instead of maximum correlation with treatment and outcome in the observed variables as it specifies the desired effect. if kappa_t is not None: correlation_t_observed = kappa_t if kappa_y is not None: correlation_y_observed = kappa_y # Choosing a c_star based on the data. # The correlations stop increasing upon increasing c_star after a certain value, that is it plateaus and we choose the value of c_star to be the value it plateaus. correlation_y_list = [] correlation_t_list = [] product_cor_metric_simulated_list = [] x_list = [] step = int(c_star_max / 10) for i in range(0, int(c_star_max), step): c1 = math.sqrt(i) c2 = c1 final_U = _generate_confounder_from_residuals(c1, c2, d_y, d_t, X) current_simulated_confounder = final_U outcome_values = data[outcome_name[0]] correlation_y = current_simulated_confounder.corr(outcome_values) correlation_y_list.append(correlation_y) treatment_values = t correlation_t = current_simulated_confounder.corr(treatment_values) correlation_t_list.append(correlation_t) product_cor_metric_simulated = correlation_y * correlation_t product_cor_metric_simulated_list.append(product_cor_metric_simulated) x_list.append(i) index = 1 while index < len(correlation_y_list): if (correlation_y_list[index] - correlation_y_list[index - 1]) <= convergence_threshold: c_star = x_list[index] break index = index + 1 # Choosing c1 and c2 based on the hyperbolic relationship once c_star is chosen by going over various combinations of c1 and c2 values and choosing the combination which # which maintains the minimum distance between the product of correlations of the simulated variable and the product of maximum correlations of one of the observed variables # and additionally checks if the ratio of the weights are such that they maintain the ratio of the maximum possible observed coefficients within some confidence interval # c1_final and c2_final are initialised to the values on the hyperbolic curve such that c1_final = c2_final and c1_final*c2_final = c_star c1_final = math.sqrt(c_star) c2_final = math.sqrt(c_star) # initialising min_distance_between_product_cor_metrics to be a value greater than 1 min_distance_between_product_cor_metrics = 1.5 i = 0.05 threshold = c_star / 0.05 while i <= threshold: c2 = i c1 = c_star / c2 final_U = _generate_confounder_from_residuals(c1, c2, d_y, d_t, X) current_simulated_confounder = final_U outcome_values = data[outcome_name[0]] correlation_y = current_simulated_confounder.corr(outcome_values) treatment_values = t correlation_t = current_simulated_confounder.corr(treatment_values) product_cor_metric_simulated = correlation_y * correlation_t if min_distance_between_product_cor_metrics >= abs(product_cor_metric_simulated - product_cor_metric_observed): min_distance_between_product_cor_metrics = abs(product_cor_metric_simulated - product_cor_metric_observed) additional_condition = correlation_y_observed / correlation_t_observed if ((c1 / c2) <= (additional_condition + 0.3 * additional_condition)) and ( (c1 / c2) >= (additional_condition - 0.3 * additional_condition) ): # choose minimum positive value c1_final = c1 c2_final = c2 i = i * 1.5 """#closed form solution print("c_star_max before closed form", c_star_max) if max_correlation_with_t == -1000: c2 = 0 c1 = c_star_max else: additional_condition = abs(max_correlation_with_y/max_correlation_with_t) print("additional_condition", additional_condition) c2 = math.sqrt(c_star_max/additional_condition) c1 = c_star_max/c2""" final_U = _generate_confounder_from_residuals(c1_final, c2_final, d_y, d_t, X) return final_U def _generate_confounder_from_residuals(c1, c2, d_y, d_t, X): """ This function takes the residuals from the treatment and outcome model and their coefficients and simulates the intermediate random variable U by taking the row wise normal distribution corresponding to each residual value and then debiasing the intermediate variable to get the final variable. :param c1: coefficient to the residual from the outcome model :type float :param c2: coefficient to the residual from the treatment model :type float :param d_y: residuals from the outcome model :type list :param d_t: residuals from the treatment model :type list :returns: The simulated values of the unobserved confounder based on the data :type pandas.core.series.Series """ U = [] for j in range(len(d_t)): simulated_variable_mean = c1 * d_y[j] + c2 * d_t[j] simulated_variable_stddev = 1 U.append(np.random.normal(simulated_variable_mean, simulated_variable_stddev, 1)) U = np.array(U) model = sm.OLS(U, X) results = model.fit() U = U.reshape( -1, ) final_U = U - results.fittedvalues.values final_U = pd.Series(U) return final_U def sensitivity_linear_partial_r2( data: pd.DataFrame, estimate: CausalEstimate, treatment_name: str, frac_strength_treatment: float = 1.0, frac_strength_outcome: float = 1.0, percent_change_estimate: float = 1.0, benchmark_common_causes: Optional[List[str]] = None, significance_level: Optional[float] = None, null_hypothesis_effect: Optional[float] = None, plot_estimate: bool = True, ) -> LinearSensitivityAnalyzer: """Add an unobserved confounder for refutation using Linear partial R2 methond (Sensitivity Analysis for linear models). :param data: pd.DataFrame: Data to run the refutation :param estimate: CausalEstimate: Estimate to run the refutation :param treatment_name: str: Name of the treatment :param frac_strength_treatment: float: This parameter decides the effect strength of the simulated confounder as a fraction of the effect strength of observed confounders on treatment. Defaults to 1. :param frac_strength_outcome: float: This parameter decides the effect strength of the simulated confounder as a fraction of the effect strength of observed confounders on outcome. Defaults to 1. :param percent_change_estimate: It is the percentage of reduction of treatment estimate that could alter the results (default = 1). if percent_change_estimate = 1, the robustness value describes the strength of association of confounders with treatment and outcome in order to reduce the estimate by 100% i.e bring it down to 0. (relevant only for Linear Sensitivity Analysis, ignore for rest) :param benchmark_common_causes: names of variables for bounding strength of confounders. (relevant only for partial-r2 based simulation methods) :param significance_level: confidence interval for statistical inference(default = 0.05). (relevant only for partial-r2 based simulation methods) :param null_hypothesis_effect: assumed effect under the null hypothesis. (relevant only for linear-partial-R2, ignore for rest) :param plot_estimate: Generate contour plot for estimate while performing sensitivity analysis. (default = True). (relevant only for partial-r2 based simulation methods) """ if not (isinstance(estimate.estimator, LinearRegressionEstimator)): raise NotImplementedError("Currently only LinearRegressionEstimator is supported for Sensitivity Analysis") if len(estimate.estimator._effect_modifier_names) > 0: raise NotImplementedError("The current implementation does not support effect modifiers") if frac_strength_outcome == 1: frac_strength_outcome = frac_strength_treatment analyzer = LinearSensitivityAnalyzer( estimator=estimate.estimator, data=data, treatment_name=treatment_name, percent_change_estimate=percent_change_estimate, significance_level=significance_level, benchmark_common_causes=benchmark_common_causes, null_hypothesis_effect=null_hypothesis_effect, frac_strength_treatment=frac_strength_treatment, frac_strength_outcome=frac_strength_outcome, common_causes_order=estimate.estimator._observed_common_causes.columns, ) analyzer.check_sensitivity(plot=plot_estimate) return analyzer def sensitivity_non_parametric_partial_r2( estimate: CausalEstimate, kappa_t: Optional[Union[float, np.ndarray]] = None, kappa_y: Optional[Union[float, np.ndarray]] = None, frac_strength_treatment: float = 1.0, frac_strength_outcome: float = 1.0, benchmark_common_causes: Optional[List[str]] = None, plot_estimate: bool = True, alpha_s_estimator_list: Optional[List] = None, alpha_s_estimator_param_list: Optional[List[Dict]] = None, g_s_estimator_list: Optional[List] = None, g_s_estimator_param_list: Optional[List[Dict]] = None, plugin_reisz: bool = False, ) -> Union[PartialLinearSensitivityAnalyzer, NonParametricSensitivityAnalyzer]: """Add an unobserved confounder for refutation using Non-parametric partial R2 methond (Sensitivity Analysis for non-parametric models). :param estimate: CausalEstimate: Estimate to run the refutation :param kappa_t: float, numpy.ndarray: Partial R2 of the unobserved confounder wrt the treatment conditioned on the observed confounders. Only in the case of general non-parametric-partial-R2, it is the fraction of variance in the reisz representer that is explained by the unobserved confounder; specifically (1-r), where r is the ratio of variance of reisz representer, alpha^2, based on observed confounders and that based on all confounders. :param kappa_y: float, numpy.ndarray: Partial R2 of the unobserved confounder wrt the outcome conditioned on the treatment and observed confounders. :param frac_strength_treatment: float: This parameter decides the effect strength of the simulated confounder as a fraction of the effect strength of observed confounders on treatment. Defaults to 1. :param frac_strength_outcome: float: This parameter decides the effect strength of the simulated confounder as a fraction of the effect strength of observed confounders on outcome. Defaults to 1. :param benchmark_common_causes: names of variables for bounding strength of confounders. (relevant only for partial-r2 based simulation methods) :param plot_estimate: Generate contour plot for estimate while performing sensitivity analysis. (default = True). (relevant only for partial-r2 based simulation methods) :param alpha_s_estimator_list: list of estimator objects for estimating alpha_s. These objects should have fit() and predict() methods (relevant only for non-parametric-partial-R2 method) :param alpha_s_estimator_param_list: list of dictionaries with parameters for finding alpha_s. (relevant only for non-parametric-partial-R2 simulation method) :param g_s_estimator_list: list of estimator objects for finding g_s. These objects should have fit() and predict() functions implemented. (relevant only for non-parametric-partial-R2 simulation method) :param g_s_estimator_param_list: list of dictionaries with parameters for tuning respective estimators in "g_s_estimator_list". The order of the dictionaries in the list should be consistent with the estimator objects order in "g_s_estimator_list". (relevant only for non-parametric-partial-R2 simulation method) :plugin_reisz: bool: Flag on whether to use the plugin estimator or the nonparametric estimator for reisz representer function (alpha_s). """ # If the estimator used is LinearDML, partially linear sensitivity analysis will be automatically chosen if isinstance(estimate.estimator, dowhy.causal_estimators.econml.Econml): if estimate.estimator._econml_methodname == "econml.dml.LinearDML": analyzer = PartialLinearSensitivityAnalyzer( estimator=estimate._estimator_object, observed_common_causes=estimate.estimator._observed_common_causes, treatment=estimate.estimator._treatment, outcome=estimate.estimator._outcome, alpha_s_estimator_param_list=alpha_s_estimator_param_list, g_s_estimator_list=g_s_estimator_list, g_s_estimator_param_list=g_s_estimator_param_list, effect_strength_treatment=kappa_t, effect_strength_outcome=kappa_y, benchmark_common_causes=benchmark_common_causes, frac_strength_treatment=frac_strength_treatment, frac_strength_outcome=frac_strength_outcome, ) analyzer.check_sensitivity(plot=plot_estimate) return analyzer analyzer = NonParametricSensitivityAnalyzer( estimator=estimate.estimator, observed_common_causes=estimate.estimator._observed_common_causes, treatment=estimate.estimator._treatment, outcome=estimate.estimator._outcome, alpha_s_estimator_list=alpha_s_estimator_list, alpha_s_estimator_param_list=alpha_s_estimator_param_list, g_s_estimator_list=g_s_estimator_list, g_s_estimator_param_list=g_s_estimator_param_list, effect_strength_treatment=kappa_t, effect_strength_outcome=kappa_y, benchmark_common_causes=benchmark_common_causes, frac_strength_treatment=frac_strength_treatment, frac_strength_outcome=frac_strength_outcome, theta_s=estimate.value, plugin_reisz=plugin_reisz, ) analyzer.check_sensitivity(plot=plot_estimate) return analyzer def sensitivity_e_value( data: pd.DataFrame, target_estimand: IdentifiedEstimand, estimate: CausalEstimate, treatment_name: List[str], outcome_name: List[str], plot_estimate: bool = True, ) -> EValueSensitivityAnalyzer: if not isinstance(estimate.estimator, RegressionEstimator): raise NotImplementedError("E-Value sensitivity analysis is currently only implemented RegressionEstimator.") if len(estimate.estimator._effect_modifier_names) > 0: raise NotImplementedError("The current implementation does not support effect modifiers") analyzer = EValueSensitivityAnalyzer( estimate=estimate, estimand=target_estimand, data=data, treatment_name=treatment_name[0], outcome_name=outcome_name[0], ) analyzer.check_sensitivity(plot=plot_estimate) return analyzer def sensitivity_simulation( data: pd.DataFrame, target_estimand: IdentifiedEstimand, estimate: CausalEstimate, treatment_name: str, outcome_name: str, kappa_t: Optional[Union[float, np.ndarray]] = None, kappa_y: Optional[Union[float, np.ndarray]] = None, confounders_effect_on_treatment: str = "binary_flip", confounders_effect_on_outcome: str = "linear", frac_strength_treatment: float = 1.0, frac_strength_outcome: float = 1.0, plotmethod: Optional[str] = None, show_progress_bar=False, **_, ) -> CausalRefutation: """ This function attempts to add an unobserved common cause to the outcome and the treatment. At present, we have implemented the behavior for one dimensional behaviors for continuous and binary variables. This function can either take single valued inputs or a range of inputs. The function then looks at the data type of the input and then decides on the course of action. :param data: pd.DataFrame: Data to run the refutation :param target_estimand: IdentifiedEstimand: Identified estimand to run the refutation :param estimate: CausalEstimate: Estimate to run the refutation :param treatment_name: str: Name of the treatment :param outcome_name: str: Name of the outcome :param kappa_t: float, numpy.ndarray: Strength of the confounder's effect on treatment. When confounders_effect_on_treatment is linear, it is the regression coefficient. When the confounders_effect_on_treatment is binary flip, it is the probability with which effect of unobserved confounder can invert the value of the treatment. :param kappa_y: float, numpy.ndarray: Strength of the confounder's effect on outcome. Its interpretation depends on confounders_effect_on_outcome and the simulation_method. When simulation_method is direct-simulation, for a linear effect it behaves like the regression coefficient and for a binary flip, it is the probability with which it can invert the value of the outcome. :param confounders_effect_on_treatment: str : The type of effect on the treatment due to the unobserved confounder. Possible values are ['binary_flip', 'linear'] :param confounders_effect_on_outcome: str : The type of effect on the outcome due to the unobserved confounder. Possible values are ['binary_flip', 'linear'] :param frac_strength_treatment: float: This parameter decides the effect strength of the simulated confounder as a fraction of the effect strength of observed confounders on treatment. Defaults to 1. :param frac_strength_outcome: float: This parameter decides the effect strength of the simulated confounder as a fraction of the effect strength of observed confounders on outcome. Defaults to 1. :param plotmethod: string: Type of plot to be shown. If None, no plot is generated. This parameter is used only only when more than one treatment confounder effect values or outcome confounder effect values are provided. Default is "colormesh". Supported values are "contour", "colormesh" when more than one value is provided for both confounder effect value parameters; "line" when provided for only one of them. :return: CausalRefuter: An object that contains the estimated effect and a new effect and the name of the refutation used. """ if kappa_t is None: kappa_t = _infer_default_kappa_t( data, target_estimand, treatment_name, confounders_effect_on_treatment, frac_strength_treatment ) if kappa_y is None: kappa_y = _infer_default_kappa_y( data, target_estimand, outcome_name, confounders_effect_on_outcome, frac_strength_outcome ) if not isinstance(kappa_t, (list, np.ndarray)) and not isinstance( kappa_y, (list, np.ndarray) ): # Deal with single value inputs new_data = copy.deepcopy(data) new_data = _include_confounders_effect( data, new_data, confounders_effect_on_treatment, treatment_name, kappa_t, confounders_effect_on_outcome, outcome_name, kappa_y, ) new_estimator = CausalEstimator.get_estimator_object(new_data, target_estimand, estimate) new_effect = new_estimator.estimate_effect() refute = CausalRefutation( estimate.value, new_effect.value, refutation_type="Refute: Add an Unobserved Common Cause" ) refute.new_effect_array = np.array(new_effect.value) refute.new_effect = new_effect.value return refute else: # Deal with multiple value inputs if isinstance(kappa_t, (list, np.ndarray)) and isinstance( kappa_y, (list, np.ndarray) ): # Deal with range inputs # Get a 2D matrix of values # x,y = np.meshgrid(self.kappa_t, self.kappa_y) # x,y are both MxN results_matrix = np.random.rand(len(kappa_t), len(kappa_y)) # Matrix to hold all the results of NxM orig_data = copy.deepcopy(data) for i in tqdm( range(len(kappa_t)), colour=CausalRefuter.PROGRESS_BAR_COLOR, disable=not show_progress_bar, desc="Refuting Estimates: ", ): for j in range(len(kappa_y)): new_data = _include_confounders_effect( data, orig_data, confounders_effect_on_treatment, treatment_name, kappa_t[i], confounders_effect_on_outcome, outcome_name, kappa_y[j], ) new_estimator = CausalEstimator.get_estimator_object(new_data, target_estimand, estimate) new_effect = new_estimator.estimate_effect() refute = CausalRefutation( estimate.value, new_effect.value, refutation_type="Refute: Add an Unobserved Common Cause", ) results_matrix[i][j] = refute.new_effect # Populate the results refute.new_effect_array = results_matrix refute.new_effect = (np.min(results_matrix), np.max(results_matrix)) # Store the values into the refute object if plotmethod is None: return refute import matplotlib import matplotlib.pyplot as plt fig = plt.figure(figsize=(6, 5)) left, bottom, width, height = 0.1, 0.1, 0.8, 0.8 ax = fig.add_axes([left, bottom, width, height]) oe = estimate.value contour_levels = [oe / 4.0, oe / 2.0, (3.0 / 4) * oe, oe] contour_levels.extend([0, np.min(results_matrix), np.max(results_matrix)]) if plotmethod == "contour": cp = plt.contourf(kappa_y, kappa_t, results_matrix, levels=sorted(contour_levels)) # Adding a label on the contour line for the original estimate fmt = {} trueeffect_index = np.where(cp.levels == oe)[0][0] fmt[cp.levels[trueeffect_index]] = "Estimated Effect" # Label every other level using strings plt.clabel(cp, [cp.levels[trueeffect_index]], inline=True, fmt=fmt) plt.colorbar(cp) elif plotmethod == "colormesh": cp = plt.pcolormesh(kappa_y, kappa_t, results_matrix, shading="nearest") plt.colorbar(cp, ticks=contour_levels) ax.yaxis.set_ticks(kappa_t) ax.xaxis.set_ticks(kappa_y) plt.xticks(rotation=45) ax.set_title("Effect of Unobserved Common Cause") ax.set_ylabel("Value of Linear Constant on Treatment") ax.set_xlabel("Value of Linear Constant on Outcome") plt.show() return refute elif isinstance(kappa_t, (list, np.ndarray)): outcomes = np.random.rand(len(kappa_t)) orig_data = copy.deepcopy(data) for i in tqdm( range(0, len(kappa_t)), colour=CausalRefuter.PROGRESS_BAR_COLOR, disable=not show_progress_bar, desc="Refuting Estimates: ", ): new_data = _include_confounders_effect( data, orig_data, confounders_effect_on_treatment, treatment_name, kappa_t[i], confounders_effect_on_outcome, outcome_name, kappa_y, ) new_estimator = CausalEstimator.get_estimator_object(new_data, target_estimand, estimate) new_effect = new_estimator.estimate_effect() refute = CausalRefutation( estimate.value, new_effect.value, refutation_type="Refute: Add an Unobserved Common Cause" ) logger.debug(refute) outcomes[i] = refute.new_effect # Populate the results refute.new_effect_array = outcomes refute.new_effect = (np.min(outcomes), np.max(outcomes)) if plotmethod is None: return refute import matplotlib import matplotlib.pyplot as plt fig = plt.figure(figsize=(6, 5)) left, bottom, width, height = 0.1, 0.1, 0.8, 0.8 ax = fig.add_axes([left, bottom, width, height]) plt.plot(kappa_t, outcomes) plt.axhline(estimate.value, linestyle="--", color="gray") ax.set_title("Effect of Unobserved Common Cause") ax.set_xlabel("Value of Linear Constant on Treatment") ax.set_ylabel("Estimated Effect after adding the common cause") plt.show() return refute elif isinstance(kappa_y, (list, np.ndarray)): outcomes = np.random.rand(len(kappa_y)) orig_data = copy.deepcopy(data) for i in tqdm( range(0, len(kappa_y)), colour=CausalRefuter.PROGRESS_BAR_COLOR, disable=not show_progress_bar, desc="Refuting Estimates: ", ): new_data = _include_confounders_effect( data, orig_data, confounders_effect_on_treatment, treatment_name, kappa_t, confounders_effect_on_outcome, outcome_name, kappa_y[i], ) new_estimator = CausalEstimator.get_estimator_object(new_data, target_estimand, estimate) new_effect = new_estimator.estimate_effect() refute = CausalRefutation( estimate.value, new_effect.value, refutation_type="Refute: Add an Unobserved Common Cause" ) logger.debug(refute) outcomes[i] = refute.new_effect # Populate the results refute.new_effect_array = outcomes refute.new_effect = (np.min(outcomes), np.max(outcomes)) if plotmethod is None: return refute import matplotlib import matplotlib.pyplot as plt fig = plt.figure(figsize=(6, 5)) left, bottom, width, height = 0.1, 0.1, 0.8, 0.8 ax = fig.add_axes([left, bottom, width, height]) plt.plot(kappa_y, outcomes) plt.axhline(estimate.value, linestyle="--", color="gray") ax.set_title("Effect of Unobserved Common Cause") ax.set_xlabel("Value of Linear Constant on Outcome") ax.set_ylabel("Estimated Effect after adding the common cause") plt.show() return refute

andresmor-ms

133e7b9a4ed32aae8ab5f39a01eb02b3a4d1c0ba

e1652ec3c6606b1bb2dfe91ef830e4b4b566712d

this is the list of estimator objects for estimating alpha_s. These objects should have fit() and predict() methods (relevant only for non-parametric-partial-R2 method)

amit-sharma

py-why/dowhy

Functional api/refute estimate

* Refactor refuters into functions * Rename functional_api notebook for clarity * Add return types to identify_estimate * Update `__init__.py` for imports * Add joblib for bootstrap refuter * Create `refute_estimate` function * Add types for refuter parameters & return types

2022-10-04 16:18:49+00:00

2022-10-07 04:30:22+00:00

dowhy/causal_refuters/add_unobserved_common_cause.py

import copy import logging import math import numpy as np import pandas as pd import scipy.stats import statsmodels.api as sm from sklearn.linear_model import LogisticRegression from sklearn.preprocessing import StandardScaler from tqdm.auto import tqdm import dowhy.causal_estimators.econml from dowhy.causal_estimator import CausalEstimator from dowhy.causal_estimators.linear_regression_estimator import LinearRegressionEstimator from dowhy.causal_estimators.regression_estimator import RegressionEstimator from dowhy.causal_refuter import CausalRefutation, CausalRefuter from dowhy.causal_refuters.evalue_sensitivity_analyzer import EValueSensitivityAnalyzer from dowhy.causal_refuters.linear_sensitivity_analyzer import LinearSensitivityAnalyzer from dowhy.causal_refuters.non_parametric_sensitivity_analyzer import NonParametricSensitivityAnalyzer from dowhy.causal_refuters.partial_linear_sensitivity_analyzer import PartialLinearSensitivityAnalyzer class AddUnobservedCommonCause(CausalRefuter): """Add an unobserved confounder for refutation. AddUnobservedCommonCause class supports three methods: 1) Simulation of an unobserved confounder 2) Linear partial R2 : Sensitivity Analysis for linear models. 3) Non-Parametric partial R2 based : Sensitivity Analyis for non-parametric models. Supports additional parameters that can be specified in the refute_estimate() method. """ def __init__(self, *args, **kwargs): """ Initialize the parameters required for the refuter. For direct_simulation, if effect_strength_on_treatment or effect_strength_on_outcome is not given, it is calculated automatically as a range between the minimum and maximum effect strength of observed confounders on treatment and outcome respectively. :param simulation_method: The method to use for simulating effect of unobserved confounder. Possible values are ["direct-simulation", "linear-partial-R2", "non-parametric-partial-R2", "e-value"]. :param confounders_effect_on_treatment: str : The type of effect on the treatment due to the unobserved confounder. Possible values are ['binary_flip', 'linear'] :param confounders_effect_on_outcome: str : The type of effect on the outcome due to the unobserved confounder. Possible values are ['binary_flip', 'linear'] :param effect_strength_on_treatment: float, numpy.ndarray: [Used when simulation_method="direct-simulation"] Strength of the confounder's effect on treatment. When confounders_effect_on_treatment is linear, it is the regression coefficient. When the confounders_effect_on_treatment is binary flip, it is the probability with which effect of unobserved confounder can invert the value of the treatment. :param effect_strength_on_outcome: float, numpy.ndarray: Strength of the confounder's effect on outcome. Its interpretation depends on confounders_effect_on_outcome and the simulation_method. When simulation_method is direct-simulation, for a linear effect it behaves like the regression coefficient and for a binary flip, it is the probability with which it can invert the value of the outcome. :param partial_r2_confounder_treatment: float, numpy.ndarray: [Used when simulation_method is linear-partial-R2 or non-parametric-partial-R2] Partial R2 of the unobserved confounder wrt the treatment conditioned on the observed confounders. Only in the case of general non-parametric-partial-R2, it is the fraction of variance in the reisz representer that is explained by the unobserved confounder; specifically (1-r), where r is the ratio of variance of reisz representer, alpha^2, based on observed confounders and that based on all confounders. :param partial_r2_confounder_outcome: float, numpy.ndarray: [Used when simulation_method is linear-partial-R2 or non-parametric-partial-R2] Partial R2 of the unobserved confounder wrt the outcome conditioned on the treatment and observed confounders. :param frac_strength_treatment: float: This parameter decides the effect strength of the simulated confounder as a fraction of the effect strength of observed confounders on treatment. Defaults to 1. :param frac_strength_outcome: float: This parameter decides the effect strength of the simulated confounder as a fraction of the effect strength of observed confounders on outcome. Defaults to 1. :param plotmethod: string: Type of plot to be shown. If None, no plot is generated. This parameter is used only only when more than one treatment confounder effect values or outcome confounder effect values are provided. Default is "colormesh". Supported values are "contour", "colormesh" when more than one value is provided for both confounder effect value parameters; "line" when provided for only one of them. :param percent_change_estimate: It is the percentage of reduction of treatment estimate that could alter the results (default = 1). if percent_change_estimate = 1, the robustness value describes the strength of association of confounders with treatment and outcome in order to reduce the estimate by 100% i.e bring it down to 0. (relevant only for Linear Sensitivity Analysis, ignore for rest) :param confounder_increases_estimate: True implies that confounder increases the absolute value of estimate and vice versa. (Default = False). (relevant only for Linear Sensitivity Analysis, ignore for rest) :param benchmark_common_causes: names of variables for bounding strength of confounders. (relevant only for partial-r2 based simulation methods) :param significance_level: confidence interval for statistical inference(default = 0.05). (relevant only for partial-r2 based simulation methods) :param null_hypothesis_effect: assumed effect under the null hypothesis. (relevant only for linear-partial-R2, ignore for rest) :param plot_estimate: Generate contour plot for estimate while performing sensitivity analysis. (default = True). (relevant only for partial-r2 based simulation methods) :param num_splits: number of splits for cross validation. (default = 5). (relevant only for non-parametric-partial-R2 simulation method) :param shuffle_data : shuffle data or not before splitting into folds (default = False). (relevant only for non-parametric-partial-R2 simulation method) :param shuffle_random_seed: seed for randomly shuffling data. (relevant only for non-parametric-partial-R2 simulation method) :param alpha_s_estimator_param_list: list of dictionaries with parameters for finding alpha_s. (relevant only for non-parametric-partial-R2 simulation method) :param g_s_estimator_list: list of estimator objects for finding g_s. These objects should have fit() and predict() functions implemented. (relevant only for non-parametric-partial-R2 simulation method) :param g_s_estimator_param_list: list of dictionaries with parameters for tuning respective estimators in "g_s_estimator_list". The order of the dictionaries in the list should be consistent with the estimator objects order in "g_s_estimator_list". (relevant only for non-parametric-partial-R2 simulation method) """ super().__init__(*args, **kwargs) self.simulation_method = kwargs["simulation_method"] if "simulation_method" in kwargs else "direct-simulation" self.effect_on_t = ( kwargs["confounders_effect_on_treatment"] if "confounders_effect_on_treatment" in kwargs else "binary_flip" ) self.effect_on_y = ( kwargs["confounders_effect_on_outcome"] if "confounders_effect_on_outcome" in kwargs else "linear" ) if self.simulation_method == "direct-simulation": self.kappa_t = kwargs["effect_strength_on_treatment"] if "effect_strength_on_treatment" in kwargs else None self.kappa_y = kwargs["effect_strength_on_outcome"] if "effect_strength_on_outcome" in kwargs else None elif self.simulation_method in ["linear-partial-R2", "non-parametric-partial-R2"]: self.kappa_t = ( kwargs["partial_r2_confounder_treatment"] if "partial_r2_confounder_treatment" in kwargs else None ) self.kappa_y = ( kwargs["partial_r2_confounder_outcome"] if "partial_r2_confounder_outcome" in kwargs else None ) elif self.simulation_method == "e-value": pass else: raise ValueError( "simulation method is not supported. Try direct-simulation, linear-partial-R2, non-parametric-partial-R2, or e-value" ) self.frac_strength_treatment = ( kwargs["effect_fraction_on_treatment"] if "effect_fraction_on_treatment" in kwargs else 1 ) self.frac_strength_outcome = ( kwargs["effect_fraction_on_outcome"] if "effect_fraction_on_outcome" in kwargs else 1 ) self.plotmethod = kwargs["plotmethod"] if "plotmethod" in kwargs else "colormesh" self.percent_change_estimate = kwargs["percent_change_estimate"] if "percent_change_estimate" in kwargs else 1.0 self.significance_level = kwargs["significance_level"] if "significance_level" in kwargs else 0.05 self.confounder_increases_estimate = ( kwargs["confounder_increases_estimate"] if "confounder_increases_estimate" in kwargs else False ) self.benchmark_common_causes = ( kwargs["benchmark_common_causes"] if "benchmark_common_causes" in kwargs else None ) self.null_hypothesis_effect = kwargs["null_hypothesis_effect"] if "null_hypothesis_effect" in kwargs else 0 self.plot_estimate = kwargs["plot_estimate"] if "plot_estimate" in kwargs else True self.num_splits = kwargs["num_splits"] if "num_splits" in kwargs else 5 self.shuffle_data = kwargs["shuffle_data"] if "shuffle_data" in kwargs else False self.shuffle_random_seed = kwargs["shuffle_random_seed"] if "shuffle_random_seed" in kwargs else None self.alpha_s_estimator_param_list = ( kwargs["alpha_s_estimator_param_list"] if "alpha_s_estimator_param_list" in kwargs else None ) self.alpha_s_estimator_list = kwargs["alpha_s_estimator_list"] if "alpha_s_estimator_list" in kwargs else None self.g_s_estimator_list = kwargs["g_s_estimator_list"] if "g_s_estimator_list" in kwargs else None self.g_s_estimator_param_list = ( kwargs["g_s_estimator_param_list"] if "g_s_estimator_param_list" in kwargs else None ) self.plugin_reisz = kwargs["plugin_reisz"] if "plugin_reisz" in kwargs else False self.logger = logging.getLogger(__name__) def infer_default_kappa_t(self, len_kappa_t=10): """Infer default effect strength of simulated confounder on treatment.""" observed_common_causes_names = self._target_estimand.get_backdoor_variables() if len(observed_common_causes_names) > 0: observed_common_causes = self._data[observed_common_causes_names] observed_common_causes = pd.get_dummies(observed_common_causes, drop_first=True) else: raise ValueError( "There needs to be at least one common cause to" + "automatically compute the default value of kappa_t." + " Provide a value for kappa_t" ) t = self._data[self._treatment_name] # Standardizing the data observed_common_causes = StandardScaler().fit_transform(observed_common_causes) if self.effect_on_t == "binary_flip": # Fit a model containing all confounders and compare predictions # using all features compared to all features except a given # confounder. tmodel = LogisticRegression().fit(observed_common_causes, t) tpred = tmodel.predict(observed_common_causes).astype(int) flips = [] for i in range(observed_common_causes.shape[1]): oldval = np.copy(observed_common_causes[:, i]) observed_common_causes[:, i] = 0 tcap = tmodel.predict(observed_common_causes).astype(int) observed_common_causes[:, i] = oldval flips.append(np.sum(abs(tcap - tpred)) / tpred.shape[0]) min_coeff, max_coeff = min(flips), max(flips) elif self.effect_on_t == "linear": # Estimating the regression coefficient from standardized features to t corrcoef_var_t = np.corrcoef(observed_common_causes, t, rowvar=False)[-1, :-1] std_dev_t = np.std(t)[0] max_coeff = max(corrcoef_var_t) * std_dev_t min_coeff = min(corrcoef_var_t) * std_dev_t else: raise NotImplementedError( "'" + self.effect_on_t + "' method not supported for confounders' effect on treatment" ) min_coeff, max_coeff = self._compute_min_max_coeff(min_coeff, max_coeff, self.frac_strength_treatment) # By default, return a plot with 10 points # consider 10 values of the effect of the unobserved confounder step = (max_coeff - min_coeff) / len_kappa_t self.logger.info("(Min, Max) kappa_t for observed common causes, ({0}, {1})".format(min_coeff, max_coeff)) if np.equal(max_coeff, min_coeff): return max_coeff else: return np.arange(min_coeff, max_coeff, step) def _compute_min_max_coeff(self, min_coeff, max_coeff, effect_strength_fraction): max_coeff = effect_strength_fraction * max_coeff min_coeff = effect_strength_fraction * min_coeff return min_coeff, max_coeff def infer_default_kappa_y(self, len_kappa_y=10): """Infer default effect strength of simulated confounder on treatment.""" observed_common_causes_names = self._target_estimand.get_backdoor_variables() if len(observed_common_causes_names) > 0: observed_common_causes = self._data[observed_common_causes_names] observed_common_causes = pd.get_dummies(observed_common_causes, drop_first=True) else: raise ValueError( "There needs to be at least one common cause to" + "automatically compute the default value of kappa_y." + " Provide a value for kappa_y" ) y = self._data[self._outcome_name] # Standardizing the data observed_common_causes = StandardScaler().fit_transform(observed_common_causes) if self.effect_on_y == "binary_flip": # Fit a model containing all confounders and compare predictions # using all features compared to all features except a given # confounder. ymodel = LogisticRegression().fit(observed_common_causes, y) ypred = ymodel.predict(observed_common_causes).astype(int) flips = [] for i in range(observed_common_causes.shape[1]): oldval = np.copy(observed_common_causes[:, i]) observed_common_causes[:, i] = 0 ycap = ymodel.predict(observed_common_causes).astype(int) observed_common_causes[:, i] = oldval flips.append(np.sum(abs(ycap - ypred)) / ypred.shape[0]) min_coeff, max_coeff = min(flips), max(flips) elif self.effect_on_y == "linear": corrcoef_var_y = np.corrcoef(observed_common_causes, y, rowvar=False)[-1, :-1] std_dev_y = np.std(y)[0] max_coeff = max(corrcoef_var_y) * std_dev_y min_coeff = min(corrcoef_var_y) * std_dev_y else: raise NotImplementedError( "'" + self.effect_on_y + "' method not supported for confounders' effect on outcome" ) min_coeff, max_coeff = self._compute_min_max_coeff(min_coeff, max_coeff, self.frac_strength_outcome) # By default, return a plot with 10 points # consider 10 values of the effect of the unobserved confounder step = (max_coeff - min_coeff) / len_kappa_y self.logger.info("(Min, Max) kappa_y for observed common causes, ({0}, {1})".format(min_coeff, max_coeff)) if np.equal(max_coeff, min_coeff): return max_coeff else: return np.arange(min_coeff, max_coeff, step) def refute_estimate(self, show_progress_bar=False): """ This function attempts to add an unobserved common cause to the outcome and the treatment. At present, we have implemented the behavior for one dimensional behaviors for continuous and binary variables. This function can either take single valued inputs or a range of inputs. The function then looks at the data type of the input and then decides on the course of action. :return: CausalRefuter: An object that contains the estimated effect and a new effect and the name of the refutation used. """ if self.simulation_method == "linear-partial-R2": if not (isinstance(self._estimate.estimator, LinearRegressionEstimator)): raise NotImplementedError( "Currently only LinearRegressionEstimator is supported for Sensitivity Analysis" ) if len(self._estimate.estimator._effect_modifier_names) > 0: raise NotImplementedError("The current implementation does not support effect modifiers") if self.frac_strength_outcome == 1: self.frac_strength_outcome = self.frac_strength_treatment analyzer = LinearSensitivityAnalyzer( estimator=self._estimate.estimator, data=self._data, treatment_name=self._treatment_name, percent_change_estimate=self.percent_change_estimate, significance_level=self.significance_level, benchmark_common_causes=self.benchmark_common_causes, null_hypothesis_effect=self.null_hypothesis_effect, frac_strength_treatment=self.frac_strength_treatment, frac_strength_outcome=self.frac_strength_outcome, common_causes_order=self._estimate.estimator._observed_common_causes.columns, ) analyzer.check_sensitivity(plot=self.plot_estimate) return analyzer if self.simulation_method == "non-parametric-partial-R2": # If the estimator used is LinearDML, partially linear sensitivity analysis will be automatically chosen if isinstance(self._estimate.estimator, dowhy.causal_estimators.econml.Econml): if self._estimate.estimator._econml_methodname == "econml.dml.LinearDML": analyzer = PartialLinearSensitivityAnalyzer( estimator=self._estimate._estimator_object, observed_common_causes=self._estimate.estimator._observed_common_causes, treatment=self._estimate.estimator._treatment, outcome=self._estimate.estimator._outcome, alpha_s_estimator_param_list=self.alpha_s_estimator_param_list, g_s_estimator_list=self.g_s_estimator_list, g_s_estimator_param_list=self.g_s_estimator_param_list, effect_strength_treatment=self.kappa_t, effect_strength_outcome=self.kappa_y, benchmark_common_causes=self.benchmark_common_causes, frac_strength_treatment=self.frac_strength_treatment, frac_strength_outcome=self.frac_strength_outcome, ) analyzer.check_sensitivity(plot=self.plot_estimate) return analyzer analyzer = NonParametricSensitivityAnalyzer( estimator=self._estimate.estimator, observed_common_causes=self._estimate.estimator._observed_common_causes, treatment=self._estimate.estimator._treatment, outcome=self._estimate.estimator._outcome, alpha_s_estimator_list=self.alpha_s_estimator_list, alpha_s_estimator_param_list=self.alpha_s_estimator_param_list, g_s_estimator_list=self.g_s_estimator_list, g_s_estimator_param_list=self.g_s_estimator_param_list, effect_strength_treatment=self.kappa_t, effect_strength_outcome=self.kappa_y, benchmark_common_causes=self.benchmark_common_causes, frac_strength_treatment=self.frac_strength_treatment, frac_strength_outcome=self.frac_strength_outcome, theta_s=self._estimate.value, plugin_reisz=self.plugin_reisz, ) analyzer.check_sensitivity(plot=self.plot_estimate) return analyzer if self.simulation_method == "e-value": if not isinstance(self._estimate.estimator, RegressionEstimator): raise NotImplementedError( "E-Value sensitivity analysis is currently only implemented RegressionEstimator." ) if len(self._estimate.estimator._effect_modifier_names) > 0: raise NotImplementedError("The current implementation does not support effect modifiers") analyzer = EValueSensitivityAnalyzer( estimate=self._estimate, estimand=self._target_estimand, data=self._data, treatment_name=self._treatment_name[0], outcome_name=self._outcome_name[0], ) analyzer.check_sensitivity(plot=self.plot_estimate) return analyzer if self.kappa_t is None: self.kappa_t = self.infer_default_kappa_t() if self.kappa_y is None: self.kappa_y = self.infer_default_kappa_y() if not isinstance(self.kappa_t, (list, np.ndarray)) and not isinstance( self.kappa_y, (list, np.ndarray) ): # Deal with single value inputs new_data = copy.deepcopy(self._data) new_data = self.include_confounders_effect(new_data, self.kappa_t, self.kappa_y) new_estimator = CausalEstimator.get_estimator_object(new_data, self._target_estimand, self._estimate) new_effect = new_estimator.estimate_effect() refute = CausalRefutation( self._estimate.value, new_effect.value, refutation_type="Refute: Add an Unobserved Common Cause" ) refute.new_effect_array = np.array(new_effect.value) refute.new_effect = new_effect.value refute.add_refuter(self) return refute else: # Deal with multiple value inputs if isinstance(self.kappa_t, (list, np.ndarray)) and isinstance( self.kappa_y, (list, np.ndarray) ): # Deal with range inputs # Get a 2D matrix of values # x,y = np.meshgrid(self.kappa_t, self.kappa_y) # x,y are both MxN results_matrix = np.random.rand( len(self.kappa_t), len(self.kappa_y) ) # Matrix to hold all the results of NxM orig_data = copy.deepcopy(self._data) for i in tqdm( range(len(self.kappa_t)), colour=CausalRefuter.PROGRESS_BAR_COLOR, disable=not show_progress_bar, desc="Refuting Estimates: ", ): for j in range(len(self.kappa_y)): new_data = self.include_confounders_effect(orig_data, self.kappa_t[i], self.kappa_y[j]) new_estimator = CausalEstimator.get_estimator_object( new_data, self._target_estimand, self._estimate ) new_effect = new_estimator.estimate_effect() refute = CausalRefutation( self._estimate.value, new_effect.value, refutation_type="Refute: Add an Unobserved Common Cause", ) results_matrix[i][j] = refute.new_effect # Populate the results refute.new_effect_array = results_matrix refute.new_effect = (np.min(results_matrix), np.max(results_matrix)) # Store the values into the refute object refute.add_refuter(self) if self.plotmethod is None: return refute import matplotlib import matplotlib.pyplot as plt fig = plt.figure(figsize=(6, 5)) left, bottom, width, height = 0.1, 0.1, 0.8, 0.8 ax = fig.add_axes([left, bottom, width, height]) oe = self._estimate.value contour_levels = [oe / 4.0, oe / 2.0, (3.0 / 4) * oe, oe] contour_levels.extend([0, np.min(results_matrix), np.max(results_matrix)]) if self.plotmethod == "contour": cp = plt.contourf(self.kappa_y, self.kappa_t, results_matrix, levels=sorted(contour_levels)) # Adding a label on the contour line for the original estimate fmt = {} trueeffect_index = np.where(cp.levels == oe)[0][0] fmt[cp.levels[trueeffect_index]] = "Estimated Effect" # Label every other level using strings plt.clabel(cp, [cp.levels[trueeffect_index]], inline=True, fmt=fmt) plt.colorbar(cp) elif self.plotmethod == "colormesh": cp = plt.pcolormesh(self.kappa_y, self.kappa_t, results_matrix, shading="nearest") plt.colorbar(cp, ticks=contour_levels) ax.yaxis.set_ticks(self.kappa_t) ax.xaxis.set_ticks(self.kappa_y) plt.xticks(rotation=45) ax.set_title("Effect of Unobserved Common Cause") ax.set_ylabel("Value of Linear Constant on Treatment") ax.set_xlabel("Value of Linear Constant on Outcome") plt.show() return refute elif isinstance(self.kappa_t, (list, np.ndarray)): outcomes = np.random.rand(len(self.kappa_t)) orig_data = copy.deepcopy(self._data) for i in tqdm( range(0, len(self.kappa_t)), colour=CausalRefuter.PROGRESS_BAR_COLOR, disable=not show_progress_bar, desc="Refuting Estimates: ", ): new_data = self.include_confounders_effect(orig_data, self.kappa_t[i], self.kappa_y) new_estimator = CausalEstimator.get_estimator_object( new_data, self._target_estimand, self._estimate ) new_effect = new_estimator.estimate_effect() refute = CausalRefutation( self._estimate.value, new_effect.value, refutation_type="Refute: Add an Unobserved Common Cause" ) self.logger.debug(refute) outcomes[i] = refute.new_effect # Populate the results refute.new_effect_array = outcomes refute.new_effect = (np.min(outcomes), np.max(outcomes)) refute.add_refuter(self) if self.plotmethod is None: return refute import matplotlib import matplotlib.pyplot as plt fig = plt.figure(figsize=(6, 5)) left, bottom, width, height = 0.1, 0.1, 0.8, 0.8 ax = fig.add_axes([left, bottom, width, height]) plt.plot(self.kappa_t, outcomes) plt.axhline(self._estimate.value, linestyle="--", color="gray") ax.set_title("Effect of Unobserved Common Cause") ax.set_xlabel("Value of Linear Constant on Treatment") ax.set_ylabel("Estimated Effect after adding the common cause") plt.show() return refute elif isinstance(self.kappa_y, (list, np.ndarray)): outcomes = np.random.rand(len(self.kappa_y)) orig_data = copy.deepcopy(self._data) for i in tqdm( range(0, len(self.kappa_y)), colour=CausalRefuter.PROGRESS_BAR_COLOR, disable=not show_progress_bar, desc="Refuting Estimates: ", ): new_data = self.include_confounders_effect(orig_data, self.kappa_t, self.kappa_y[i]) new_estimator = CausalEstimator.get_estimator_object( new_data, self._target_estimand, self._estimate ) new_effect = new_estimator.estimate_effect() refute = CausalRefutation( self._estimate.value, new_effect.value, refutation_type="Refute: Add an Unobserved Common Cause" ) self.logger.debug(refute) outcomes[i] = refute.new_effect # Populate the results refute.new_effect_array = outcomes refute.new_effect = (np.min(outcomes), np.max(outcomes)) refute.add_refuter(self) if self.plotmethod is None: return refute import matplotlib import matplotlib.pyplot as plt fig = plt.figure(figsize=(6, 5)) left, bottom, width, height = 0.1, 0.1, 0.8, 0.8 ax = fig.add_axes([left, bottom, width, height]) plt.plot(self.kappa_y, outcomes) plt.axhline(self._estimate.value, linestyle="--", color="gray") ax.set_title("Effect of Unobserved Common Cause") ax.set_xlabel("Value of Linear Constant on Outcome") ax.set_ylabel("Estimated Effect after adding the common cause") plt.show() return refute def include_confounders_effect(self, new_data, kappa_t, kappa_y): """ This function deals with the change in the value of the data due to the effect of the unobserved confounder. In the case of a binary flip, we flip only if the random number is greater than the threshold set. In the case of a linear effect, we use the variable as the linear regression constant. :param new_data: pandas.DataFrame: The data to be changed due to the effects of the unobserved confounder. :param kappa_t: numpy.float64: The value of the threshold for binary_flip or the value of the regression coefficient for linear effect. :param kappa_y: numpy.float64: The value of the threshold for binary_flip or the value of the regression coefficient for linear effect. :return: pandas.DataFrame: The DataFrame that includes the effects of the unobserved confounder. """ num_rows = self._data.shape[0] stdnorm = scipy.stats.norm() w_random = stdnorm.rvs(num_rows) if self.effect_on_t == "binary_flip": alpha = 2 * kappa_t - 1 if kappa_t >= 0.5 else 1 - 2 * kappa_t interval = stdnorm.interval(alpha) rel_interval = interval[0] if kappa_t >= 0.5 else interval[1] new_data.loc[rel_interval <= w_random, self._treatment_name] = ( 1 - new_data.loc[rel_interval <= w_random, self._treatment_name] ) for tname in self._treatment_name: if pd.api.types.is_bool_dtype(self._data[tname]): new_data = new_data.astype({tname: "bool"}, copy=False) elif self.effect_on_t == "linear": confounder_t_effect = kappa_t * w_random # By default, we add the effect of simulated confounder for treatment. # But subtract it from outcome to create a negative correlation # assuming that the original confounder's effect was positive on both. # This is to remove the effect of the original confounder. new_data[self._treatment_name] = new_data[self._treatment_name].values + np.ndarray( shape=(num_rows, 1), buffer=confounder_t_effect ) else: raise NotImplementedError( "'" + self.effect_on_t + "' method not supported for confounders' effect on treatment" ) if self.effect_on_y == "binary_flip": alpha = 2 * kappa_y - 1 if kappa_y >= 0.5 else 1 - 2 * kappa_y interval = stdnorm.interval(alpha) rel_interval = interval[0] if kappa_y >= 0.5 else interval[1] new_data.loc[rel_interval <= w_random, self._outcome_name] = ( 1 - new_data.loc[rel_interval <= w_random, self._outcome_name] ) for yname in self._outcome_name: if pd.api.types.is_bool_dtype(self._data[yname]): new_data = new_data.astype({yname: "bool"}, copy=False) elif self.effect_on_y == "linear": confounder_y_effect = (-1) * kappa_y * w_random # By default, we add the effect of simulated confounder for treatment. # But subtract it from outcome to create a negative correlation # assuming that the original confounder's effect was positive on both. # This is to remove the effect of the original confounder. new_data[self._outcome_name] = new_data[self._outcome_name].values + np.ndarray( shape=(num_rows, 1), buffer=confounder_y_effect ) else: raise NotImplementedError( "'" + self.effect_on_y + "' method not supported for confounders' effect on outcome" ) return new_data def include_simulated_confounder(self, convergence_threshold=0.1, c_star_max=1000): """ This function simulates an unobserved confounder based on the data using the following steps: 1. It calculates the "residuals" from the treatment and outcome model i.) The outcome model has outcome as the dependent variable and all the observed variables including treatment as independent variables ii.) The treatment model has treatment as the dependent variable and all the observed variables as independent variables. 2. U is an intermediate random variable drawn from the normal distribution with the weighted average of residuals as mean and a unit variance U ~ N(c1*d_y + c2*d_t, 1) where *d_y and d_t are residuals from the treatment and outcome model *c1 and c2 are coefficients to the residuals 3. The final U, which is the simulated unobserved confounder is obtained by debiasing the intermediate variable U by residualising it with X Choosing the coefficients c1 and c2: The coefficients are chosen based on these basic assumptions: 1. There is a hyperbolic relationship satisfying c1*c2 = c_star 2. c_star is chosen from a range of possible values based on the correlation of the obtained simulated variable with outcome and treatment. 3. The product of correlations with treatment and outcome should be at a minimum distance to the maximum correlations with treatment and outcome in any of the observed confounders 4. The ratio of the weights should be such that they maintain the ratio of the maximum possible observed coefficients within some confidence interval :param c_star_max: The maximum possible value for the hyperbolic curve on which the coefficients to the residuals lie. It defaults to 1000 in the code if not specified by the user. :type int :param convergence_threshold: The threshold to check the plateauing of the correlation while selecting a c_star. It defaults to 0.1 in the code if not specified by the user :type float :returns: The simulated values of the unobserved confounder based on the data :type pandas.core.series.Series """ # Obtaining the list of observed variables required_variables = True observed_variables = self.choose_variables(required_variables) observed_variables_with_treatment_and_outcome = observed_variables + self._treatment_name + self._outcome_name # Taking a subset of the dataframe that has only observed variables self._data = self._data[observed_variables_with_treatment_and_outcome] # Residuals from the outcome model obtained by fitting a linear model y = self._data[self._outcome_name[0]] observed_variables_with_treatment = observed_variables + self._treatment_name X = self._data[observed_variables_with_treatment] model = sm.OLS(y, X.astype("float")) results = model.fit() residuals_y = y - results.fittedvalues d_y = list(pd.Series(residuals_y)) # Residuals from the treatment model obtained by fitting a linear model t = self._data[self._treatment_name[0]].astype("int64") X = self._data[observed_variables] model = sm.OLS(t, X) results = model.fit() residuals_t = t - results.fittedvalues d_t = list(pd.Series(residuals_t)) # Initialising product_cor_metric_observed with a really low value as finding maximum product_cor_metric_observed = -10000000000 for i in observed_variables: current_obs_confounder = self._data[i] outcome_values = self._data[self._outcome_name[0]] correlation_y = current_obs_confounder.corr(outcome_values) treatment_values = t correlation_t = current_obs_confounder.corr(treatment_values) product_cor_metric_current = correlation_y * correlation_t if product_cor_metric_current >= product_cor_metric_observed: product_cor_metric_observed = product_cor_metric_current correlation_t_observed = correlation_t correlation_y_observed = correlation_y # The user has an option to give the the effect_strength_on_y and effect_strength_on_t which can be then used instead of maximum correlation with treatment and outcome in the observed variables as it specifies the desired effect. if self.kappa_t is not None: correlation_t_observed = self.kappa_t if self.kappa_y is not None: correlation_y_observed = self.kappa_y # Choosing a c_star based on the data. # The correlations stop increasing upon increasing c_star after a certain value, that is it plateaus and we choose the value of c_star to be the value it plateaus. correlation_y_list = [] correlation_t_list = [] product_cor_metric_simulated_list = [] x_list = [] step = int(c_star_max / 10) for i in range(0, int(c_star_max), step): c1 = math.sqrt(i) c2 = c1 final_U = self.generate_confounder_from_residuals(c1, c2, d_y, d_t, X) current_simulated_confounder = final_U outcome_values = self._data[self._outcome_name[0]] correlation_y = current_simulated_confounder.corr(outcome_values) correlation_y_list.append(correlation_y) treatment_values = t correlation_t = current_simulated_confounder.corr(treatment_values) correlation_t_list.append(correlation_t) product_cor_metric_simulated = correlation_y * correlation_t product_cor_metric_simulated_list.append(product_cor_metric_simulated) x_list.append(i) index = 1 while index < len(correlation_y_list): if (correlation_y_list[index] - correlation_y_list[index - 1]) <= convergence_threshold: c_star = x_list[index] break index = index + 1 # Choosing c1 and c2 based on the hyperbolic relationship once c_star is chosen by going over various combinations of c1 and c2 values and choosing the combination which # which maintains the minimum distance between the product of correlations of the simulated variable and the product of maximum correlations of one of the observed variables # and additionally checks if the ratio of the weights are such that they maintain the ratio of the maximum possible observed coefficients within some confidence interval # c1_final and c2_final are initialised to the values on the hyperbolic curve such that c1_final = c2_final and c1_final*c2_final = c_star c1_final = math.sqrt(c_star) c2_final = math.sqrt(c_star) # initialising min_distance_between_product_cor_metrics to be a value greater than 1 min_distance_between_product_cor_metrics = 1.5 i = 0.05 threshold = c_star / 0.05 while i <= threshold: c2 = i c1 = c_star / c2 final_U = self.generate_confounder_from_residuals(c1, c2, d_y, d_t, X) current_simulated_confounder = final_U outcome_values = self._data[self._outcome_name[0]] correlation_y = current_simulated_confounder.corr(outcome_values) treatment_values = t correlation_t = current_simulated_confounder.corr(treatment_values) product_cor_metric_simulated = correlation_y * correlation_t if min_distance_between_product_cor_metrics >= abs( product_cor_metric_simulated - product_cor_metric_observed ): min_distance_between_product_cor_metrics = abs( product_cor_metric_simulated - product_cor_metric_observed ) additional_condition = correlation_y_observed / correlation_t_observed if ((c1 / c2) <= (additional_condition + 0.3 * additional_condition)) and ( (c1 / c2) >= (additional_condition - 0.3 * additional_condition) ): # choose minimum positive value c1_final = c1 c2_final = c2 i = i * 1.5 """#closed form solution print("c_star_max before closed form", c_star_max) if max_correlation_with_t == -1000: c2 = 0 c1 = c_star_max else: additional_condition = abs(max_correlation_with_y/max_correlation_with_t) print("additional_condition", additional_condition) c2 = math.sqrt(c_star_max/additional_condition) c1 = c_star_max/c2""" final_U = self.generate_confounder_from_residuals(c1_final, c2_final, d_y, d_t, X) return final_U def generate_confounder_from_residuals(self, c1, c2, d_y, d_t, X): """ This function takes the residuals from the treatment and outcome model and their coefficients and simulates the intermediate random variable U by taking the row wise normal distribution corresponding to each residual value and then debiasing the intermediate variable to get the final variable. :param c1: coefficient to the residual from the outcome model :type float :param c2: coefficient to the residual from the treatment model :type float :param d_y: residuals from the outcome model :type list :param d_t: residuals from the treatment model :type list :returns: The simulated values of the unobserved confounder based on the data :type pandas.core.series.Series """ U = [] for j in range(len(d_t)): simulated_variable_mean = c1 * d_y[j] + c2 * d_t[j] simulated_variable_stddev = 1 U.append(np.random.normal(simulated_variable_mean, simulated_variable_stddev, 1)) U = np.array(U) model = sm.OLS(U, X) results = model.fit() U = U.reshape( -1, ) final_U = U - results.fittedvalues.values final_U = pd.Series(U) return final_U

import copy import logging import math from typing import Dict, List, Optional, Union import numpy as np import pandas as pd import scipy.stats import statsmodels.api as sm from sklearn.linear_model import LogisticRegression from sklearn.preprocessing import StandardScaler from tqdm.auto import tqdm import dowhy.causal_estimators.econml from dowhy.causal_estimator import CausalEstimate, CausalEstimator from dowhy.causal_estimators.linear_regression_estimator import LinearRegressionEstimator from dowhy.causal_estimators.regression_estimator import RegressionEstimator from dowhy.causal_identifier.identified_estimand import IdentifiedEstimand from dowhy.causal_refuter import CausalRefutation, CausalRefuter, choose_variables from dowhy.causal_refuters.evalue_sensitivity_analyzer import EValueSensitivityAnalyzer from dowhy.causal_refuters.linear_sensitivity_analyzer import LinearSensitivityAnalyzer from dowhy.causal_refuters.non_parametric_sensitivity_analyzer import NonParametricSensitivityAnalyzer from dowhy.causal_refuters.partial_linear_sensitivity_analyzer import PartialLinearSensitivityAnalyzer logger = logging.getLogger(__name__) class AddUnobservedCommonCause(CausalRefuter): """Add an unobserved confounder for refutation. AddUnobservedCommonCause class supports three methods: 1) Simulation of an unobserved confounder 2) Linear partial R2 : Sensitivity Analysis for linear models. 3) Non-Parametric partial R2 based : Sensitivity Analyis for non-parametric models. Supports additional parameters that can be specified in the refute_estimate() method. """ def __init__(self, *args, **kwargs): """ Initialize the parameters required for the refuter. For direct_simulation, if effect_strength_on_treatment or effect_strength_on_outcome is not given, it is calculated automatically as a range between the minimum and maximum effect strength of observed confounders on treatment and outcome respectively. :param simulation_method: The method to use for simulating effect of unobserved confounder. Possible values are ["direct-simulation", "linear-partial-R2", "non-parametric-partial-R2", "e-value"]. :param confounders_effect_on_treatment: str : The type of effect on the treatment due to the unobserved confounder. Possible values are ['binary_flip', 'linear'] :param confounders_effect_on_outcome: str : The type of effect on the outcome due to the unobserved confounder. Possible values are ['binary_flip', 'linear'] :param effect_strength_on_treatment: float, numpy.ndarray: [Used when simulation_method="direct-simulation"] Strength of the confounder's effect on treatment. When confounders_effect_on_treatment is linear, it is the regression coefficient. When the confounders_effect_on_treatment is binary flip, it is the probability with which effect of unobserved confounder can invert the value of the treatment. :param effect_strength_on_outcome: float, numpy.ndarray: Strength of the confounder's effect on outcome. Its interpretation depends on confounders_effect_on_outcome and the simulation_method. When simulation_method is direct-simulation, for a linear effect it behaves like the regression coefficient and for a binary flip, it is the probability with which it can invert the value of the outcome. :param partial_r2_confounder_treatment: float, numpy.ndarray: [Used when simulation_method is linear-partial-R2 or non-parametric-partial-R2] Partial R2 of the unobserved confounder wrt the treatment conditioned on the observed confounders. Only in the case of general non-parametric-partial-R2, it is the fraction of variance in the reisz representer that is explained by the unobserved confounder; specifically (1-r), where r is the ratio of variance of reisz representer, alpha^2, based on observed confounders and that based on all confounders. :param partial_r2_confounder_outcome: float, numpy.ndarray: [Used when simulation_method is linear-partial-R2 or non-parametric-partial-R2] Partial R2 of the unobserved confounder wrt the outcome conditioned on the treatment and observed confounders. :param frac_strength_treatment: float: This parameter decides the effect strength of the simulated confounder as a fraction of the effect strength of observed confounders on treatment. Defaults to 1. :param frac_strength_outcome: float: This parameter decides the effect strength of the simulated confounder as a fraction of the effect strength of observed confounders on outcome. Defaults to 1. :param plotmethod: string: Type of plot to be shown. If None, no plot is generated. This parameter is used only only when more than one treatment confounder effect values or outcome confounder effect values are provided. Default is "colormesh". Supported values are "contour", "colormesh" when more than one value is provided for both confounder effect value parameters; "line" when provided for only one of them. :param percent_change_estimate: It is the percentage of reduction of treatment estimate that could alter the results (default = 1). if percent_change_estimate = 1, the robustness value describes the strength of association of confounders with treatment and outcome in order to reduce the estimate by 100% i.e bring it down to 0. (relevant only for Linear Sensitivity Analysis, ignore for rest) :param confounder_increases_estimate: True implies that confounder increases the absolute value of estimate and vice versa. (Default = False). (relevant only for Linear Sensitivity Analysis, ignore for rest) :param benchmark_common_causes: names of variables for bounding strength of confounders. (relevant only for partial-r2 based simulation methods) :param significance_level: confidence interval for statistical inference(default = 0.05). (relevant only for partial-r2 based simulation methods) :param null_hypothesis_effect: assumed effect under the null hypothesis. (relevant only for linear-partial-R2, ignore for rest) :param plot_estimate: Generate contour plot for estimate while performing sensitivity analysis. (default = True). (relevant only for partial-r2 based simulation methods) :param num_splits: number of splits for cross validation. (default = 5). (relevant only for non-parametric-partial-R2 simulation method) :param shuffle_data : shuffle data or not before splitting into folds (default = False). (relevant only for non-parametric-partial-R2 simulation method) :param shuffle_random_seed: seed for randomly shuffling data. (relevant only for non-parametric-partial-R2 simulation method) :param alpha_s_estimator_param_list: list of dictionaries with parameters for finding alpha_s. (relevant only for non-parametric-partial-R2 simulation method) :param g_s_estimator_list: list of estimator objects for finding g_s. These objects should have fit() and predict() functions implemented. (relevant only for non-parametric-partial-R2 simulation method) :param g_s_estimator_param_list: list of dictionaries with parameters for tuning respective estimators in "g_s_estimator_list". The order of the dictionaries in the list should be consistent with the estimator objects order in "g_s_estimator_list". (relevant only for non-parametric-partial-R2 simulation method) """ super().__init__(*args, **kwargs) self.simulation_method = kwargs["simulation_method"] if "simulation_method" in kwargs else "direct-simulation" self.effect_on_t = ( kwargs["confounders_effect_on_treatment"] if "confounders_effect_on_treatment" in kwargs else "binary_flip" ) self.effect_on_y = ( kwargs["confounders_effect_on_outcome"] if "confounders_effect_on_outcome" in kwargs else "linear" ) if self.simulation_method == "direct-simulation": self.kappa_t = kwargs["effect_strength_on_treatment"] if "effect_strength_on_treatment" in kwargs else None self.kappa_y = kwargs["effect_strength_on_outcome"] if "effect_strength_on_outcome" in kwargs else None elif self.simulation_method in ["linear-partial-R2", "non-parametric-partial-R2"]: self.kappa_t = ( kwargs["partial_r2_confounder_treatment"] if "partial_r2_confounder_treatment" in kwargs else None ) self.kappa_y = ( kwargs["partial_r2_confounder_outcome"] if "partial_r2_confounder_outcome" in kwargs else None ) elif self.simulation_method == "e-value": pass else: raise ValueError( "simulation method is not supported. Try direct-simulation, linear-partial-R2, non-parametric-partial-R2, or e-value" ) self.frac_strength_treatment = ( kwargs["effect_fraction_on_treatment"] if "effect_fraction_on_treatment" in kwargs else 1 ) self.frac_strength_outcome = ( kwargs["effect_fraction_on_outcome"] if "effect_fraction_on_outcome" in kwargs else 1 ) self.plotmethod = kwargs["plotmethod"] if "plotmethod" in kwargs else "colormesh" self.percent_change_estimate = kwargs["percent_change_estimate"] if "percent_change_estimate" in kwargs else 1.0 self.significance_level = kwargs["significance_level"] if "significance_level" in kwargs else 0.05 self.confounder_increases_estimate = ( kwargs["confounder_increases_estimate"] if "confounder_increases_estimate" in kwargs else False ) self.benchmark_common_causes = ( kwargs["benchmark_common_causes"] if "benchmark_common_causes" in kwargs else None ) self.null_hypothesis_effect = kwargs["null_hypothesis_effect"] if "null_hypothesis_effect" in kwargs else 0 self.plot_estimate = kwargs["plot_estimate"] if "plot_estimate" in kwargs else True self.num_splits = kwargs["num_splits"] if "num_splits" in kwargs else 5 self.shuffle_data = kwargs["shuffle_data"] if "shuffle_data" in kwargs else False self.shuffle_random_seed = kwargs["shuffle_random_seed"] if "shuffle_random_seed" in kwargs else None self.alpha_s_estimator_param_list = ( kwargs["alpha_s_estimator_param_list"] if "alpha_s_estimator_param_list" in kwargs else None ) self.alpha_s_estimator_list = kwargs["alpha_s_estimator_list"] if "alpha_s_estimator_list" in kwargs else None self.g_s_estimator_list = kwargs["g_s_estimator_list"] if "g_s_estimator_list" in kwargs else None self.g_s_estimator_param_list = ( kwargs["g_s_estimator_param_list"] if "g_s_estimator_param_list" in kwargs else None ) self.plugin_reisz = kwargs["plugin_reisz"] if "plugin_reisz" in kwargs else False self.logger = logging.getLogger(__name__) def refute_estimate(self, show_progress_bar=False): if self.simulation_method == "linear-partial-R2": return sensitivity_linear_partial_r2( self._data, self._estimate, self._treatment_name, self.frac_strength_treatment, self.frac_strength_outcome, self.percent_change_estimate, self.benchmark_common_causes, self.significance_level, self.null_hypothesis_effect, self.plot_estimate, ) elif self.simulation_method == "non-parametric-partial-R2": return sensitivity_non_parametric_partial_r2( self._estimate, self.kappa_t, self.kappa_y, self.frac_strength_treatment, self.frac_strength_outcome, self.benchmark_common_causes, self.plot_estimate, self.alpha_s_estimator_list, self.alpha_s_estimator_param_list, self.g_s_estimator_list, self.g_s_estimator_param_list, self.plugin_reisz, ) elif self.simulation_method == "e-value": return sensitivity_e_value( self._data, self._target_estimand, self._estimate, self._treatment_name, self._outcome_name, self.plot_estimate, ) elif self.simulation_method == "direct-simulation": refute = sensitivity_simulation( self._data, self._target_estimand, self._estimate, self._treatment_name, self._outcome_name, self.kappa_t, self.kappa_y, self.effect_on_t, self.effect_on_y, self.frac_strength_treatment, self.frac_strength_outcome, self.plotmethod, show_progress_bar, ) refute.add_refuter(self) return refute def _infer_default_kappa_t( data: pd.DataFrame, target_estimand: IdentifiedEstimand, treatment_name: List[str], effect_on_t: str, frac_strength_treatment: float, len_kappa_t: int = 10, ): """Infer default effect strength of simulated confounder on treatment.""" observed_common_causes_names = target_estimand.get_backdoor_variables() if len(observed_common_causes_names) > 0: observed_common_causes = data[observed_common_causes_names] observed_common_causes = pd.get_dummies(observed_common_causes, drop_first=True) else: raise ValueError( "There needs to be at least one common cause to" + "automatically compute the default value of kappa_t." + " Provide a value for kappa_t" ) t = data[treatment_name] # Standardizing the data observed_common_causes = StandardScaler().fit_transform(observed_common_causes) if effect_on_t == "binary_flip": # Fit a model containing all confounders and compare predictions # using all features compared to all features except a given # confounder. tmodel = LogisticRegression().fit(observed_common_causes, t) tpred = tmodel.predict(observed_common_causes).astype(int) flips = [] for i in range(observed_common_causes.shape[1]): oldval = np.copy(observed_common_causes[:, i]) observed_common_causes[:, i] = 0 tcap = tmodel.predict(observed_common_causes).astype(int) observed_common_causes[:, i] = oldval flips.append(np.sum(abs(tcap - tpred)) / tpred.shape[0]) min_coeff, max_coeff = min(flips), max(flips) elif effect_on_t == "linear": # Estimating the regression coefficient from standardized features to t corrcoef_var_t = np.corrcoef(observed_common_causes, t, rowvar=False)[-1, :-1] std_dev_t = np.std(t)[0] max_coeff = max(corrcoef_var_t) * std_dev_t min_coeff = min(corrcoef_var_t) * std_dev_t else: raise NotImplementedError("'" + effect_on_t + "' method not supported for confounders' effect on treatment") min_coeff, max_coeff = _compute_min_max_coeff(min_coeff, max_coeff, frac_strength_treatment) # By default, return a plot with 10 points # consider 10 values of the effect of the unobserved confounder step = (max_coeff - min_coeff) / len_kappa_t logger.info("(Min, Max) kappa_t for observed common causes, ({0}, {1})".format(min_coeff, max_coeff)) if np.equal(max_coeff, min_coeff): return max_coeff else: return np.arange(min_coeff, max_coeff, step) def _compute_min_max_coeff(min_coeff: float, max_coeff: float, effect_strength_fraction: np.ndarray): max_coeff = effect_strength_fraction * max_coeff min_coeff = effect_strength_fraction * min_coeff return min_coeff, max_coeff def _infer_default_kappa_y( data: pd.DataFrame, target_estimand: IdentifiedEstimand, outcome_name: List[str], effect_on_y: str, frac_strength_outcome: float, len_kappa_y: int = 10, ): """Infer default effect strength of simulated confounder on treatment.""" observed_common_causes_names = target_estimand.get_backdoor_variables() if len(observed_common_causes_names) > 0: observed_common_causes = data[observed_common_causes_names] observed_common_causes = pd.get_dummies(observed_common_causes, drop_first=True) else: raise ValueError( "There needs to be at least one common cause to" + "automatically compute the default value of kappa_y." + " Provide a value for kappa_y" ) y = data[outcome_name] # Standardizing the data observed_common_causes = StandardScaler().fit_transform(observed_common_causes) if effect_on_y == "binary_flip": # Fit a model containing all confounders and compare predictions # using all features compared to all features except a given # confounder. ymodel = LogisticRegression().fit(observed_common_causes, y) ypred = ymodel.predict(observed_common_causes).astype(int) flips = [] for i in range(observed_common_causes.shape[1]): oldval = np.copy(observed_common_causes[:, i]) observed_common_causes[:, i] = 0 ycap = ymodel.predict(observed_common_causes).astype(int) observed_common_causes[:, i] = oldval flips.append(np.sum(abs(ycap - ypred)) / ypred.shape[0]) min_coeff, max_coeff = min(flips), max(flips) elif effect_on_y == "linear": corrcoef_var_y = np.corrcoef(observed_common_causes, y, rowvar=False)[-1, :-1] std_dev_y = np.std(y)[0] max_coeff = max(corrcoef_var_y) * std_dev_y min_coeff = min(corrcoef_var_y) * std_dev_y else: raise NotImplementedError("'" + effect_on_y + "' method not supported for confounders' effect on outcome") min_coeff, max_coeff = _compute_min_max_coeff(min_coeff, max_coeff, frac_strength_outcome) # By default, return a plot with 10 points # consider 10 values of the effect of the unobserved confounder step = (max_coeff - min_coeff) / len_kappa_y logger.info("(Min, Max) kappa_y for observed common causes, ({0}, {1})".format(min_coeff, max_coeff)) if np.equal(max_coeff, min_coeff): return max_coeff else: return np.arange(min_coeff, max_coeff, step) def _include_confounders_effect( data: pd.DataFrame, new_data: pd.DataFrame, effect_on_t: str, treatment_name: str, kappa_t: float, effect_on_y: str, outcome_name: str, kappa_y: float, ): """ This function deals with the change in the value of the data due to the effect of the unobserved confounder. In the case of a binary flip, we flip only if the random number is greater than the threshold set. In the case of a linear effect, we use the variable as the linear regression constant. :param new_data: pandas.DataFrame: The data to be changed due to the effects of the unobserved confounder. :param kappa_t: numpy.float64: The value of the threshold for binary_flip or the value of the regression coefficient for linear effect. :param kappa_y: numpy.float64: The value of the threshold for binary_flip or the value of the regression coefficient for linear effect. :return: pandas.DataFrame: The DataFrame that includes the effects of the unobserved confounder. """ num_rows = data.shape[0] stdnorm = scipy.stats.norm() w_random = stdnorm.rvs(num_rows) if effect_on_t == "binary_flip": alpha = 2 * kappa_t - 1 if kappa_t >= 0.5 else 1 - 2 * kappa_t interval = stdnorm.interval(alpha) rel_interval = interval[0] if kappa_t >= 0.5 else interval[1] new_data.loc[rel_interval <= w_random, treatment_name] = ( 1 - new_data.loc[rel_interval <= w_random, treatment_name] ) for tname in treatment_name: if pd.api.types.is_bool_dtype(data[tname]): new_data = new_data.astype({tname: "bool"}, copy=False) elif effect_on_t == "linear": confounder_t_effect = kappa_t * w_random # By default, we add the effect of simulated confounder for treatment. # But subtract it from outcome to create a negative correlation # assuming that the original confounder's effect was positive on both. # This is to remove the effect of the original confounder. new_data[treatment_name] = new_data[treatment_name].values + np.ndarray( shape=(num_rows, 1), buffer=confounder_t_effect ) else: raise NotImplementedError("'" + effect_on_t + "' method not supported for confounders' effect on treatment") if effect_on_y == "binary_flip": alpha = 2 * kappa_y - 1 if kappa_y >= 0.5 else 1 - 2 * kappa_y interval = stdnorm.interval(alpha) rel_interval = interval[0] if kappa_y >= 0.5 else interval[1] new_data.loc[rel_interval <= w_random, outcome_name] = 1 - new_data.loc[rel_interval <= w_random, outcome_name] for yname in outcome_name: if pd.api.types.is_bool_dtype(data[yname]): new_data = new_data.astype({yname: "bool"}, copy=False) elif effect_on_y == "linear": confounder_y_effect = (-1) * kappa_y * w_random # By default, we add the effect of simulated confounder for treatment. # But subtract it from outcome to create a negative correlation # assuming that the original confounder's effect was positive on both. # This is to remove the effect of the original confounder. new_data[outcome_name] = new_data[outcome_name].values + np.ndarray( shape=(num_rows, 1), buffer=confounder_y_effect ) else: raise NotImplementedError("'" + effect_on_y + "' method not supported for confounders' effect on outcome") return new_data def include_simulated_confounder( data: pd.DataFrame, treatment_name: str, outcome_name: str, kappa_t: float, kappa_y: float, convergence_threshold: float = 0.1, c_star_max: int = 1000, ): """ This function simulates an unobserved confounder based on the data using the following steps: 1. It calculates the "residuals" from the treatment and outcome model i.) The outcome model has outcome as the dependent variable and all the observed variables including treatment as independent variables ii.) The treatment model has treatment as the dependent variable and all the observed variables as independent variables. 2. U is an intermediate random variable drawn from the normal distribution with the weighted average of residuals as mean and a unit variance U ~ N(c1*d_y + c2*d_t, 1) where *d_y and d_t are residuals from the treatment and outcome model *c1 and c2 are coefficients to the residuals 3. The final U, which is the simulated unobserved confounder is obtained by debiasing the intermediate variable U by residualising it with X Choosing the coefficients c1 and c2: The coefficients are chosen based on these basic assumptions: 1. There is a hyperbolic relationship satisfying c1*c2 = c_star 2. c_star is chosen from a range of possible values based on the correlation of the obtained simulated variable with outcome and treatment. 3. The product of correlations with treatment and outcome should be at a minimum distance to the maximum correlations with treatment and outcome in any of the observed confounders 4. The ratio of the weights should be such that they maintain the ratio of the maximum possible observed coefficients within some confidence interval :param c_star_max: The maximum possible value for the hyperbolic curve on which the coefficients to the residuals lie. It defaults to 1000 in the code if not specified by the user. :type int :param convergence_threshold: The threshold to check the plateauing of the correlation while selecting a c_star. It defaults to 0.1 in the code if not specified by the user :type float :returns: The simulated values of the unobserved confounder based on the data :type pandas.core.series.Series """ # Obtaining the list of observed variables required_variables = True observed_variables = choose_variables(required_variables) observed_variables_with_treatment_and_outcome = observed_variables + treatment_name + outcome_name # Taking a subset of the dataframe that has only observed variables data = data[observed_variables_with_treatment_and_outcome] # Residuals from the outcome model obtained by fitting a linear model y = data[outcome_name[0]] observed_variables_with_treatment = observed_variables + treatment_name X = data[observed_variables_with_treatment] model = sm.OLS(y, X.astype("float")) results = model.fit() residuals_y = y - results.fittedvalues d_y = list(pd.Series(residuals_y)) # Residuals from the treatment model obtained by fitting a linear model t = data[treatment_name[0]].astype("int64") X = data[observed_variables] model = sm.OLS(t, X) results = model.fit() residuals_t = t - results.fittedvalues d_t = list(pd.Series(residuals_t)) # Initialising product_cor_metric_observed with a really low value as finding maximum product_cor_metric_observed = -10000000000 for i in observed_variables: current_obs_confounder = data[i] outcome_values = data[outcome_name[0]] correlation_y = current_obs_confounder.corr(outcome_values) treatment_values = t correlation_t = current_obs_confounder.corr(treatment_values) product_cor_metric_current = correlation_y * correlation_t if product_cor_metric_current >= product_cor_metric_observed: product_cor_metric_observed = product_cor_metric_current correlation_t_observed = correlation_t correlation_y_observed = correlation_y # The user has an option to give the the effect_strength_on_y and effect_strength_on_t which can be then used instead of maximum correlation with treatment and outcome in the observed variables as it specifies the desired effect. if kappa_t is not None: correlation_t_observed = kappa_t if kappa_y is not None: correlation_y_observed = kappa_y # Choosing a c_star based on the data. # The correlations stop increasing upon increasing c_star after a certain value, that is it plateaus and we choose the value of c_star to be the value it plateaus. correlation_y_list = [] correlation_t_list = [] product_cor_metric_simulated_list = [] x_list = [] step = int(c_star_max / 10) for i in range(0, int(c_star_max), step): c1 = math.sqrt(i) c2 = c1 final_U = _generate_confounder_from_residuals(c1, c2, d_y, d_t, X) current_simulated_confounder = final_U outcome_values = data[outcome_name[0]] correlation_y = current_simulated_confounder.corr(outcome_values) correlation_y_list.append(correlation_y) treatment_values = t correlation_t = current_simulated_confounder.corr(treatment_values) correlation_t_list.append(correlation_t) product_cor_metric_simulated = correlation_y * correlation_t product_cor_metric_simulated_list.append(product_cor_metric_simulated) x_list.append(i) index = 1 while index < len(correlation_y_list): if (correlation_y_list[index] - correlation_y_list[index - 1]) <= convergence_threshold: c_star = x_list[index] break index = index + 1 # Choosing c1 and c2 based on the hyperbolic relationship once c_star is chosen by going over various combinations of c1 and c2 values and choosing the combination which # which maintains the minimum distance between the product of correlations of the simulated variable and the product of maximum correlations of one of the observed variables # and additionally checks if the ratio of the weights are such that they maintain the ratio of the maximum possible observed coefficients within some confidence interval # c1_final and c2_final are initialised to the values on the hyperbolic curve such that c1_final = c2_final and c1_final*c2_final = c_star c1_final = math.sqrt(c_star) c2_final = math.sqrt(c_star) # initialising min_distance_between_product_cor_metrics to be a value greater than 1 min_distance_between_product_cor_metrics = 1.5 i = 0.05 threshold = c_star / 0.05 while i <= threshold: c2 = i c1 = c_star / c2 final_U = _generate_confounder_from_residuals(c1, c2, d_y, d_t, X) current_simulated_confounder = final_U outcome_values = data[outcome_name[0]] correlation_y = current_simulated_confounder.corr(outcome_values) treatment_values = t correlation_t = current_simulated_confounder.corr(treatment_values) product_cor_metric_simulated = correlation_y * correlation_t if min_distance_between_product_cor_metrics >= abs(product_cor_metric_simulated - product_cor_metric_observed): min_distance_between_product_cor_metrics = abs(product_cor_metric_simulated - product_cor_metric_observed) additional_condition = correlation_y_observed / correlation_t_observed if ((c1 / c2) <= (additional_condition + 0.3 * additional_condition)) and ( (c1 / c2) >= (additional_condition - 0.3 * additional_condition) ): # choose minimum positive value c1_final = c1 c2_final = c2 i = i * 1.5 """#closed form solution print("c_star_max before closed form", c_star_max) if max_correlation_with_t == -1000: c2 = 0 c1 = c_star_max else: additional_condition = abs(max_correlation_with_y/max_correlation_with_t) print("additional_condition", additional_condition) c2 = math.sqrt(c_star_max/additional_condition) c1 = c_star_max/c2""" final_U = _generate_confounder_from_residuals(c1_final, c2_final, d_y, d_t, X) return final_U def _generate_confounder_from_residuals(c1, c2, d_y, d_t, X): """ This function takes the residuals from the treatment and outcome model and their coefficients and simulates the intermediate random variable U by taking the row wise normal distribution corresponding to each residual value and then debiasing the intermediate variable to get the final variable. :param c1: coefficient to the residual from the outcome model :type float :param c2: coefficient to the residual from the treatment model :type float :param d_y: residuals from the outcome model :type list :param d_t: residuals from the treatment model :type list :returns: The simulated values of the unobserved confounder based on the data :type pandas.core.series.Series """ U = [] for j in range(len(d_t)): simulated_variable_mean = c1 * d_y[j] + c2 * d_t[j] simulated_variable_stddev = 1 U.append(np.random.normal(simulated_variable_mean, simulated_variable_stddev, 1)) U = np.array(U) model = sm.OLS(U, X) results = model.fit() U = U.reshape( -1, ) final_U = U - results.fittedvalues.values final_U = pd.Series(U) return final_U def sensitivity_linear_partial_r2( data: pd.DataFrame, estimate: CausalEstimate, treatment_name: str, frac_strength_treatment: float = 1.0, frac_strength_outcome: float = 1.0, percent_change_estimate: float = 1.0, benchmark_common_causes: Optional[List[str]] = None, significance_level: Optional[float] = None, null_hypothesis_effect: Optional[float] = None, plot_estimate: bool = True, ) -> LinearSensitivityAnalyzer: """Add an unobserved confounder for refutation using Linear partial R2 methond (Sensitivity Analysis for linear models). :param data: pd.DataFrame: Data to run the refutation :param estimate: CausalEstimate: Estimate to run the refutation :param treatment_name: str: Name of the treatment :param frac_strength_treatment: float: This parameter decides the effect strength of the simulated confounder as a fraction of the effect strength of observed confounders on treatment. Defaults to 1. :param frac_strength_outcome: float: This parameter decides the effect strength of the simulated confounder as a fraction of the effect strength of observed confounders on outcome. Defaults to 1. :param percent_change_estimate: It is the percentage of reduction of treatment estimate that could alter the results (default = 1). if percent_change_estimate = 1, the robustness value describes the strength of association of confounders with treatment and outcome in order to reduce the estimate by 100% i.e bring it down to 0. (relevant only for Linear Sensitivity Analysis, ignore for rest) :param benchmark_common_causes: names of variables for bounding strength of confounders. (relevant only for partial-r2 based simulation methods) :param significance_level: confidence interval for statistical inference(default = 0.05). (relevant only for partial-r2 based simulation methods) :param null_hypothesis_effect: assumed effect under the null hypothesis. (relevant only for linear-partial-R2, ignore for rest) :param plot_estimate: Generate contour plot for estimate while performing sensitivity analysis. (default = True). (relevant only for partial-r2 based simulation methods) """ if not (isinstance(estimate.estimator, LinearRegressionEstimator)): raise NotImplementedError("Currently only LinearRegressionEstimator is supported for Sensitivity Analysis") if len(estimate.estimator._effect_modifier_names) > 0: raise NotImplementedError("The current implementation does not support effect modifiers") if frac_strength_outcome == 1: frac_strength_outcome = frac_strength_treatment analyzer = LinearSensitivityAnalyzer( estimator=estimate.estimator, data=data, treatment_name=treatment_name, percent_change_estimate=percent_change_estimate, significance_level=significance_level, benchmark_common_causes=benchmark_common_causes, null_hypothesis_effect=null_hypothesis_effect, frac_strength_treatment=frac_strength_treatment, frac_strength_outcome=frac_strength_outcome, common_causes_order=estimate.estimator._observed_common_causes.columns, ) analyzer.check_sensitivity(plot=plot_estimate) return analyzer def sensitivity_non_parametric_partial_r2( estimate: CausalEstimate, kappa_t: Optional[Union[float, np.ndarray]] = None, kappa_y: Optional[Union[float, np.ndarray]] = None, frac_strength_treatment: float = 1.0, frac_strength_outcome: float = 1.0, benchmark_common_causes: Optional[List[str]] = None, plot_estimate: bool = True, alpha_s_estimator_list: Optional[List] = None, alpha_s_estimator_param_list: Optional[List[Dict]] = None, g_s_estimator_list: Optional[List] = None, g_s_estimator_param_list: Optional[List[Dict]] = None, plugin_reisz: bool = False, ) -> Union[PartialLinearSensitivityAnalyzer, NonParametricSensitivityAnalyzer]: """Add an unobserved confounder for refutation using Non-parametric partial R2 methond (Sensitivity Analysis for non-parametric models). :param estimate: CausalEstimate: Estimate to run the refutation :param kappa_t: float, numpy.ndarray: Partial R2 of the unobserved confounder wrt the treatment conditioned on the observed confounders. Only in the case of general non-parametric-partial-R2, it is the fraction of variance in the reisz representer that is explained by the unobserved confounder; specifically (1-r), where r is the ratio of variance of reisz representer, alpha^2, based on observed confounders and that based on all confounders. :param kappa_y: float, numpy.ndarray: Partial R2 of the unobserved confounder wrt the outcome conditioned on the treatment and observed confounders. :param frac_strength_treatment: float: This parameter decides the effect strength of the simulated confounder as a fraction of the effect strength of observed confounders on treatment. Defaults to 1. :param frac_strength_outcome: float: This parameter decides the effect strength of the simulated confounder as a fraction of the effect strength of observed confounders on outcome. Defaults to 1. :param benchmark_common_causes: names of variables for bounding strength of confounders. (relevant only for partial-r2 based simulation methods) :param plot_estimate: Generate contour plot for estimate while performing sensitivity analysis. (default = True). (relevant only for partial-r2 based simulation methods) :param alpha_s_estimator_list: list of estimator objects for estimating alpha_s. These objects should have fit() and predict() methods (relevant only for non-parametric-partial-R2 method) :param alpha_s_estimator_param_list: list of dictionaries with parameters for finding alpha_s. (relevant only for non-parametric-partial-R2 simulation method) :param g_s_estimator_list: list of estimator objects for finding g_s. These objects should have fit() and predict() functions implemented. (relevant only for non-parametric-partial-R2 simulation method) :param g_s_estimator_param_list: list of dictionaries with parameters for tuning respective estimators in "g_s_estimator_list". The order of the dictionaries in the list should be consistent with the estimator objects order in "g_s_estimator_list". (relevant only for non-parametric-partial-R2 simulation method) :plugin_reisz: bool: Flag on whether to use the plugin estimator or the nonparametric estimator for reisz representer function (alpha_s). """ # If the estimator used is LinearDML, partially linear sensitivity analysis will be automatically chosen if isinstance(estimate.estimator, dowhy.causal_estimators.econml.Econml): if estimate.estimator._econml_methodname == "econml.dml.LinearDML": analyzer = PartialLinearSensitivityAnalyzer( estimator=estimate._estimator_object, observed_common_causes=estimate.estimator._observed_common_causes, treatment=estimate.estimator._treatment, outcome=estimate.estimator._outcome, alpha_s_estimator_param_list=alpha_s_estimator_param_list, g_s_estimator_list=g_s_estimator_list, g_s_estimator_param_list=g_s_estimator_param_list, effect_strength_treatment=kappa_t, effect_strength_outcome=kappa_y, benchmark_common_causes=benchmark_common_causes, frac_strength_treatment=frac_strength_treatment, frac_strength_outcome=frac_strength_outcome, ) analyzer.check_sensitivity(plot=plot_estimate) return analyzer analyzer = NonParametricSensitivityAnalyzer( estimator=estimate.estimator, observed_common_causes=estimate.estimator._observed_common_causes, treatment=estimate.estimator._treatment, outcome=estimate.estimator._outcome, alpha_s_estimator_list=alpha_s_estimator_list, alpha_s_estimator_param_list=alpha_s_estimator_param_list, g_s_estimator_list=g_s_estimator_list, g_s_estimator_param_list=g_s_estimator_param_list, effect_strength_treatment=kappa_t, effect_strength_outcome=kappa_y, benchmark_common_causes=benchmark_common_causes, frac_strength_treatment=frac_strength_treatment, frac_strength_outcome=frac_strength_outcome, theta_s=estimate.value, plugin_reisz=plugin_reisz, ) analyzer.check_sensitivity(plot=plot_estimate) return analyzer def sensitivity_e_value( data: pd.DataFrame, target_estimand: IdentifiedEstimand, estimate: CausalEstimate, treatment_name: List[str], outcome_name: List[str], plot_estimate: bool = True, ) -> EValueSensitivityAnalyzer: if not isinstance(estimate.estimator, RegressionEstimator): raise NotImplementedError("E-Value sensitivity analysis is currently only implemented RegressionEstimator.") if len(estimate.estimator._effect_modifier_names) > 0: raise NotImplementedError("The current implementation does not support effect modifiers") analyzer = EValueSensitivityAnalyzer( estimate=estimate, estimand=target_estimand, data=data, treatment_name=treatment_name[0], outcome_name=outcome_name[0], ) analyzer.check_sensitivity(plot=plot_estimate) return analyzer def sensitivity_simulation( data: pd.DataFrame, target_estimand: IdentifiedEstimand, estimate: CausalEstimate, treatment_name: str, outcome_name: str, kappa_t: Optional[Union[float, np.ndarray]] = None, kappa_y: Optional[Union[float, np.ndarray]] = None, confounders_effect_on_treatment: str = "binary_flip", confounders_effect_on_outcome: str = "linear", frac_strength_treatment: float = 1.0, frac_strength_outcome: float = 1.0, plotmethod: Optional[str] = None, show_progress_bar=False, **_, ) -> CausalRefutation: """ This function attempts to add an unobserved common cause to the outcome and the treatment. At present, we have implemented the behavior for one dimensional behaviors for continuous and binary variables. This function can either take single valued inputs or a range of inputs. The function then looks at the data type of the input and then decides on the course of action. :param data: pd.DataFrame: Data to run the refutation :param target_estimand: IdentifiedEstimand: Identified estimand to run the refutation :param estimate: CausalEstimate: Estimate to run the refutation :param treatment_name: str: Name of the treatment :param outcome_name: str: Name of the outcome :param kappa_t: float, numpy.ndarray: Strength of the confounder's effect on treatment. When confounders_effect_on_treatment is linear, it is the regression coefficient. When the confounders_effect_on_treatment is binary flip, it is the probability with which effect of unobserved confounder can invert the value of the treatment. :param kappa_y: float, numpy.ndarray: Strength of the confounder's effect on outcome. Its interpretation depends on confounders_effect_on_outcome and the simulation_method. When simulation_method is direct-simulation, for a linear effect it behaves like the regression coefficient and for a binary flip, it is the probability with which it can invert the value of the outcome. :param confounders_effect_on_treatment: str : The type of effect on the treatment due to the unobserved confounder. Possible values are ['binary_flip', 'linear'] :param confounders_effect_on_outcome: str : The type of effect on the outcome due to the unobserved confounder. Possible values are ['binary_flip', 'linear'] :param frac_strength_treatment: float: This parameter decides the effect strength of the simulated confounder as a fraction of the effect strength of observed confounders on treatment. Defaults to 1. :param frac_strength_outcome: float: This parameter decides the effect strength of the simulated confounder as a fraction of the effect strength of observed confounders on outcome. Defaults to 1. :param plotmethod: string: Type of plot to be shown. If None, no plot is generated. This parameter is used only only when more than one treatment confounder effect values or outcome confounder effect values are provided. Default is "colormesh". Supported values are "contour", "colormesh" when more than one value is provided for both confounder effect value parameters; "line" when provided for only one of them. :return: CausalRefuter: An object that contains the estimated effect and a new effect and the name of the refutation used. """ if kappa_t is None: kappa_t = _infer_default_kappa_t( data, target_estimand, treatment_name, confounders_effect_on_treatment, frac_strength_treatment ) if kappa_y is None: kappa_y = _infer_default_kappa_y( data, target_estimand, outcome_name, confounders_effect_on_outcome, frac_strength_outcome ) if not isinstance(kappa_t, (list, np.ndarray)) and not isinstance( kappa_y, (list, np.ndarray) ): # Deal with single value inputs new_data = copy.deepcopy(data) new_data = _include_confounders_effect( data, new_data, confounders_effect_on_treatment, treatment_name, kappa_t, confounders_effect_on_outcome, outcome_name, kappa_y, ) new_estimator = CausalEstimator.get_estimator_object(new_data, target_estimand, estimate) new_effect = new_estimator.estimate_effect() refute = CausalRefutation( estimate.value, new_effect.value, refutation_type="Refute: Add an Unobserved Common Cause" ) refute.new_effect_array = np.array(new_effect.value) refute.new_effect = new_effect.value return refute else: # Deal with multiple value inputs if isinstance(kappa_t, (list, np.ndarray)) and isinstance( kappa_y, (list, np.ndarray) ): # Deal with range inputs # Get a 2D matrix of values # x,y = np.meshgrid(self.kappa_t, self.kappa_y) # x,y are both MxN results_matrix = np.random.rand(len(kappa_t), len(kappa_y)) # Matrix to hold all the results of NxM orig_data = copy.deepcopy(data) for i in tqdm( range(len(kappa_t)), colour=CausalRefuter.PROGRESS_BAR_COLOR, disable=not show_progress_bar, desc="Refuting Estimates: ", ): for j in range(len(kappa_y)): new_data = _include_confounders_effect( data, orig_data, confounders_effect_on_treatment, treatment_name, kappa_t[i], confounders_effect_on_outcome, outcome_name, kappa_y[j], ) new_estimator = CausalEstimator.get_estimator_object(new_data, target_estimand, estimate) new_effect = new_estimator.estimate_effect() refute = CausalRefutation( estimate.value, new_effect.value, refutation_type="Refute: Add an Unobserved Common Cause", ) results_matrix[i][j] = refute.new_effect # Populate the results refute.new_effect_array = results_matrix refute.new_effect = (np.min(results_matrix), np.max(results_matrix)) # Store the values into the refute object if plotmethod is None: return refute import matplotlib import matplotlib.pyplot as plt fig = plt.figure(figsize=(6, 5)) left, bottom, width, height = 0.1, 0.1, 0.8, 0.8 ax = fig.add_axes([left, bottom, width, height]) oe = estimate.value contour_levels = [oe / 4.0, oe / 2.0, (3.0 / 4) * oe, oe] contour_levels.extend([0, np.min(results_matrix), np.max(results_matrix)]) if plotmethod == "contour": cp = plt.contourf(kappa_y, kappa_t, results_matrix, levels=sorted(contour_levels)) # Adding a label on the contour line for the original estimate fmt = {} trueeffect_index = np.where(cp.levels == oe)[0][0] fmt[cp.levels[trueeffect_index]] = "Estimated Effect" # Label every other level using strings plt.clabel(cp, [cp.levels[trueeffect_index]], inline=True, fmt=fmt) plt.colorbar(cp) elif plotmethod == "colormesh": cp = plt.pcolormesh(kappa_y, kappa_t, results_matrix, shading="nearest") plt.colorbar(cp, ticks=contour_levels) ax.yaxis.set_ticks(kappa_t) ax.xaxis.set_ticks(kappa_y) plt.xticks(rotation=45) ax.set_title("Effect of Unobserved Common Cause") ax.set_ylabel("Value of Linear Constant on Treatment") ax.set_xlabel("Value of Linear Constant on Outcome") plt.show() return refute elif isinstance(kappa_t, (list, np.ndarray)): outcomes = np.random.rand(len(kappa_t)) orig_data = copy.deepcopy(data) for i in tqdm( range(0, len(kappa_t)), colour=CausalRefuter.PROGRESS_BAR_COLOR, disable=not show_progress_bar, desc="Refuting Estimates: ", ): new_data = _include_confounders_effect( data, orig_data, confounders_effect_on_treatment, treatment_name, kappa_t[i], confounders_effect_on_outcome, outcome_name, kappa_y, ) new_estimator = CausalEstimator.get_estimator_object(new_data, target_estimand, estimate) new_effect = new_estimator.estimate_effect() refute = CausalRefutation( estimate.value, new_effect.value, refutation_type="Refute: Add an Unobserved Common Cause" ) logger.debug(refute) outcomes[i] = refute.new_effect # Populate the results refute.new_effect_array = outcomes refute.new_effect = (np.min(outcomes), np.max(outcomes)) if plotmethod is None: return refute import matplotlib import matplotlib.pyplot as plt fig = plt.figure(figsize=(6, 5)) left, bottom, width, height = 0.1, 0.1, 0.8, 0.8 ax = fig.add_axes([left, bottom, width, height]) plt.plot(kappa_t, outcomes) plt.axhline(estimate.value, linestyle="--", color="gray") ax.set_title("Effect of Unobserved Common Cause") ax.set_xlabel("Value of Linear Constant on Treatment") ax.set_ylabel("Estimated Effect after adding the common cause") plt.show() return refute elif isinstance(kappa_y, (list, np.ndarray)): outcomes = np.random.rand(len(kappa_y)) orig_data = copy.deepcopy(data) for i in tqdm( range(0, len(kappa_y)), colour=CausalRefuter.PROGRESS_BAR_COLOR, disable=not show_progress_bar, desc="Refuting Estimates: ", ): new_data = _include_confounders_effect( data, orig_data, confounders_effect_on_treatment, treatment_name, kappa_t, confounders_effect_on_outcome, outcome_name, kappa_y[i], ) new_estimator = CausalEstimator.get_estimator_object(new_data, target_estimand, estimate) new_effect = new_estimator.estimate_effect() refute = CausalRefutation( estimate.value, new_effect.value, refutation_type="Refute: Add an Unobserved Common Cause" ) logger.debug(refute) outcomes[i] = refute.new_effect # Populate the results refute.new_effect_array = outcomes refute.new_effect = (np.min(outcomes), np.max(outcomes)) if plotmethod is None: return refute import matplotlib import matplotlib.pyplot as plt fig = plt.figure(figsize=(6, 5)) left, bottom, width, height = 0.1, 0.1, 0.8, 0.8 ax = fig.add_axes([left, bottom, width, height]) plt.plot(kappa_y, outcomes) plt.axhline(estimate.value, linestyle="--", color="gray") ax.set_title("Effect of Unobserved Common Cause") ax.set_xlabel("Value of Linear Constant on Outcome") ax.set_ylabel("Estimated Effect after adding the common cause") plt.show() return refute

andresmor-ms

133e7b9a4ed32aae8ab5f39a01eb02b3a4d1c0ba

e1652ec3c6606b1bb2dfe91ef830e4b4b566712d

Flag on whether to use the plugin estimator or the nonparametric estimator for reisz representer function (alpha_s).

amit-sharma

py-why/dowhy

Functional api/refute estimate

* Refactor refuters into functions * Rename functional_api notebook for clarity * Add return types to identify_estimate * Update `__init__.py` for imports * Add joblib for bootstrap refuter * Create `refute_estimate` function * Add types for refuter parameters & return types

2022-10-04 16:18:49+00:00

2022-10-07 04:30:22+00:00

dowhy/causal_refuters/add_unobserved_common_cause.py

import copy import logging import math import numpy as np import pandas as pd import scipy.stats import statsmodels.api as sm from sklearn.linear_model import LogisticRegression from sklearn.preprocessing import StandardScaler from tqdm.auto import tqdm import dowhy.causal_estimators.econml from dowhy.causal_estimator import CausalEstimator from dowhy.causal_estimators.linear_regression_estimator import LinearRegressionEstimator from dowhy.causal_estimators.regression_estimator import RegressionEstimator from dowhy.causal_refuter import CausalRefutation, CausalRefuter from dowhy.causal_refuters.evalue_sensitivity_analyzer import EValueSensitivityAnalyzer from dowhy.causal_refuters.linear_sensitivity_analyzer import LinearSensitivityAnalyzer from dowhy.causal_refuters.non_parametric_sensitivity_analyzer import NonParametricSensitivityAnalyzer from dowhy.causal_refuters.partial_linear_sensitivity_analyzer import PartialLinearSensitivityAnalyzer class AddUnobservedCommonCause(CausalRefuter): """Add an unobserved confounder for refutation. AddUnobservedCommonCause class supports three methods: 1) Simulation of an unobserved confounder 2) Linear partial R2 : Sensitivity Analysis for linear models. 3) Non-Parametric partial R2 based : Sensitivity Analyis for non-parametric models. Supports additional parameters that can be specified in the refute_estimate() method. """ def __init__(self, *args, **kwargs): """ Initialize the parameters required for the refuter. For direct_simulation, if effect_strength_on_treatment or effect_strength_on_outcome is not given, it is calculated automatically as a range between the minimum and maximum effect strength of observed confounders on treatment and outcome respectively. :param simulation_method: The method to use for simulating effect of unobserved confounder. Possible values are ["direct-simulation", "linear-partial-R2", "non-parametric-partial-R2", "e-value"]. :param confounders_effect_on_treatment: str : The type of effect on the treatment due to the unobserved confounder. Possible values are ['binary_flip', 'linear'] :param confounders_effect_on_outcome: str : The type of effect on the outcome due to the unobserved confounder. Possible values are ['binary_flip', 'linear'] :param effect_strength_on_treatment: float, numpy.ndarray: [Used when simulation_method="direct-simulation"] Strength of the confounder's effect on treatment. When confounders_effect_on_treatment is linear, it is the regression coefficient. When the confounders_effect_on_treatment is binary flip, it is the probability with which effect of unobserved confounder can invert the value of the treatment. :param effect_strength_on_outcome: float, numpy.ndarray: Strength of the confounder's effect on outcome. Its interpretation depends on confounders_effect_on_outcome and the simulation_method. When simulation_method is direct-simulation, for a linear effect it behaves like the regression coefficient and for a binary flip, it is the probability with which it can invert the value of the outcome. :param partial_r2_confounder_treatment: float, numpy.ndarray: [Used when simulation_method is linear-partial-R2 or non-parametric-partial-R2] Partial R2 of the unobserved confounder wrt the treatment conditioned on the observed confounders. Only in the case of general non-parametric-partial-R2, it is the fraction of variance in the reisz representer that is explained by the unobserved confounder; specifically (1-r), where r is the ratio of variance of reisz representer, alpha^2, based on observed confounders and that based on all confounders. :param partial_r2_confounder_outcome: float, numpy.ndarray: [Used when simulation_method is linear-partial-R2 or non-parametric-partial-R2] Partial R2 of the unobserved confounder wrt the outcome conditioned on the treatment and observed confounders. :param frac_strength_treatment: float: This parameter decides the effect strength of the simulated confounder as a fraction of the effect strength of observed confounders on treatment. Defaults to 1. :param frac_strength_outcome: float: This parameter decides the effect strength of the simulated confounder as a fraction of the effect strength of observed confounders on outcome. Defaults to 1. :param plotmethod: string: Type of plot to be shown. If None, no plot is generated. This parameter is used only only when more than one treatment confounder effect values or outcome confounder effect values are provided. Default is "colormesh". Supported values are "contour", "colormesh" when more than one value is provided for both confounder effect value parameters; "line" when provided for only one of them. :param percent_change_estimate: It is the percentage of reduction of treatment estimate that could alter the results (default = 1). if percent_change_estimate = 1, the robustness value describes the strength of association of confounders with treatment and outcome in order to reduce the estimate by 100% i.e bring it down to 0. (relevant only for Linear Sensitivity Analysis, ignore for rest) :param confounder_increases_estimate: True implies that confounder increases the absolute value of estimate and vice versa. (Default = False). (relevant only for Linear Sensitivity Analysis, ignore for rest) :param benchmark_common_causes: names of variables for bounding strength of confounders. (relevant only for partial-r2 based simulation methods) :param significance_level: confidence interval for statistical inference(default = 0.05). (relevant only for partial-r2 based simulation methods) :param null_hypothesis_effect: assumed effect under the null hypothesis. (relevant only for linear-partial-R2, ignore for rest) :param plot_estimate: Generate contour plot for estimate while performing sensitivity analysis. (default = True). (relevant only for partial-r2 based simulation methods) :param num_splits: number of splits for cross validation. (default = 5). (relevant only for non-parametric-partial-R2 simulation method) :param shuffle_data : shuffle data or not before splitting into folds (default = False). (relevant only for non-parametric-partial-R2 simulation method) :param shuffle_random_seed: seed for randomly shuffling data. (relevant only for non-parametric-partial-R2 simulation method) :param alpha_s_estimator_param_list: list of dictionaries with parameters for finding alpha_s. (relevant only for non-parametric-partial-R2 simulation method) :param g_s_estimator_list: list of estimator objects for finding g_s. These objects should have fit() and predict() functions implemented. (relevant only for non-parametric-partial-R2 simulation method) :param g_s_estimator_param_list: list of dictionaries with parameters for tuning respective estimators in "g_s_estimator_list". The order of the dictionaries in the list should be consistent with the estimator objects order in "g_s_estimator_list". (relevant only for non-parametric-partial-R2 simulation method) """ super().__init__(*args, **kwargs) self.simulation_method = kwargs["simulation_method"] if "simulation_method" in kwargs else "direct-simulation" self.effect_on_t = ( kwargs["confounders_effect_on_treatment"] if "confounders_effect_on_treatment" in kwargs else "binary_flip" ) self.effect_on_y = ( kwargs["confounders_effect_on_outcome"] if "confounders_effect_on_outcome" in kwargs else "linear" ) if self.simulation_method == "direct-simulation": self.kappa_t = kwargs["effect_strength_on_treatment"] if "effect_strength_on_treatment" in kwargs else None self.kappa_y = kwargs["effect_strength_on_outcome"] if "effect_strength_on_outcome" in kwargs else None elif self.simulation_method in ["linear-partial-R2", "non-parametric-partial-R2"]: self.kappa_t = ( kwargs["partial_r2_confounder_treatment"] if "partial_r2_confounder_treatment" in kwargs else None ) self.kappa_y = ( kwargs["partial_r2_confounder_outcome"] if "partial_r2_confounder_outcome" in kwargs else None ) elif self.simulation_method == "e-value": pass else: raise ValueError( "simulation method is not supported. Try direct-simulation, linear-partial-R2, non-parametric-partial-R2, or e-value" ) self.frac_strength_treatment = ( kwargs["effect_fraction_on_treatment"] if "effect_fraction_on_treatment" in kwargs else 1 ) self.frac_strength_outcome = ( kwargs["effect_fraction_on_outcome"] if "effect_fraction_on_outcome" in kwargs else 1 ) self.plotmethod = kwargs["plotmethod"] if "plotmethod" in kwargs else "colormesh" self.percent_change_estimate = kwargs["percent_change_estimate"] if "percent_change_estimate" in kwargs else 1.0 self.significance_level = kwargs["significance_level"] if "significance_level" in kwargs else 0.05 self.confounder_increases_estimate = ( kwargs["confounder_increases_estimate"] if "confounder_increases_estimate" in kwargs else False ) self.benchmark_common_causes = ( kwargs["benchmark_common_causes"] if "benchmark_common_causes" in kwargs else None ) self.null_hypothesis_effect = kwargs["null_hypothesis_effect"] if "null_hypothesis_effect" in kwargs else 0 self.plot_estimate = kwargs["plot_estimate"] if "plot_estimate" in kwargs else True self.num_splits = kwargs["num_splits"] if "num_splits" in kwargs else 5 self.shuffle_data = kwargs["shuffle_data"] if "shuffle_data" in kwargs else False self.shuffle_random_seed = kwargs["shuffle_random_seed"] if "shuffle_random_seed" in kwargs else None self.alpha_s_estimator_param_list = ( kwargs["alpha_s_estimator_param_list"] if "alpha_s_estimator_param_list" in kwargs else None ) self.alpha_s_estimator_list = kwargs["alpha_s_estimator_list"] if "alpha_s_estimator_list" in kwargs else None self.g_s_estimator_list = kwargs["g_s_estimator_list"] if "g_s_estimator_list" in kwargs else None self.g_s_estimator_param_list = ( kwargs["g_s_estimator_param_list"] if "g_s_estimator_param_list" in kwargs else None ) self.plugin_reisz = kwargs["plugin_reisz"] if "plugin_reisz" in kwargs else False self.logger = logging.getLogger(__name__) def infer_default_kappa_t(self, len_kappa_t=10): """Infer default effect strength of simulated confounder on treatment.""" observed_common_causes_names = self._target_estimand.get_backdoor_variables() if len(observed_common_causes_names) > 0: observed_common_causes = self._data[observed_common_causes_names] observed_common_causes = pd.get_dummies(observed_common_causes, drop_first=True) else: raise ValueError( "There needs to be at least one common cause to" + "automatically compute the default value of kappa_t." + " Provide a value for kappa_t" ) t = self._data[self._treatment_name] # Standardizing the data observed_common_causes = StandardScaler().fit_transform(observed_common_causes) if self.effect_on_t == "binary_flip": # Fit a model containing all confounders and compare predictions # using all features compared to all features except a given # confounder. tmodel = LogisticRegression().fit(observed_common_causes, t) tpred = tmodel.predict(observed_common_causes).astype(int) flips = [] for i in range(observed_common_causes.shape[1]): oldval = np.copy(observed_common_causes[:, i]) observed_common_causes[:, i] = 0 tcap = tmodel.predict(observed_common_causes).astype(int) observed_common_causes[:, i] = oldval flips.append(np.sum(abs(tcap - tpred)) / tpred.shape[0]) min_coeff, max_coeff = min(flips), max(flips) elif self.effect_on_t == "linear": # Estimating the regression coefficient from standardized features to t corrcoef_var_t = np.corrcoef(observed_common_causes, t, rowvar=False)[-1, :-1] std_dev_t = np.std(t)[0] max_coeff = max(corrcoef_var_t) * std_dev_t min_coeff = min(corrcoef_var_t) * std_dev_t else: raise NotImplementedError( "'" + self.effect_on_t + "' method not supported for confounders' effect on treatment" ) min_coeff, max_coeff = self._compute_min_max_coeff(min_coeff, max_coeff, self.frac_strength_treatment) # By default, return a plot with 10 points # consider 10 values of the effect of the unobserved confounder step = (max_coeff - min_coeff) / len_kappa_t self.logger.info("(Min, Max) kappa_t for observed common causes, ({0}, {1})".format(min_coeff, max_coeff)) if np.equal(max_coeff, min_coeff): return max_coeff else: return np.arange(min_coeff, max_coeff, step) def _compute_min_max_coeff(self, min_coeff, max_coeff, effect_strength_fraction): max_coeff = effect_strength_fraction * max_coeff min_coeff = effect_strength_fraction * min_coeff return min_coeff, max_coeff def infer_default_kappa_y(self, len_kappa_y=10): """Infer default effect strength of simulated confounder on treatment.""" observed_common_causes_names = self._target_estimand.get_backdoor_variables() if len(observed_common_causes_names) > 0: observed_common_causes = self._data[observed_common_causes_names] observed_common_causes = pd.get_dummies(observed_common_causes, drop_first=True) else: raise ValueError( "There needs to be at least one common cause to" + "automatically compute the default value of kappa_y." + " Provide a value for kappa_y" ) y = self._data[self._outcome_name] # Standardizing the data observed_common_causes = StandardScaler().fit_transform(observed_common_causes) if self.effect_on_y == "binary_flip": # Fit a model containing all confounders and compare predictions # using all features compared to all features except a given # confounder. ymodel = LogisticRegression().fit(observed_common_causes, y) ypred = ymodel.predict(observed_common_causes).astype(int) flips = [] for i in range(observed_common_causes.shape[1]): oldval = np.copy(observed_common_causes[:, i]) observed_common_causes[:, i] = 0 ycap = ymodel.predict(observed_common_causes).astype(int) observed_common_causes[:, i] = oldval flips.append(np.sum(abs(ycap - ypred)) / ypred.shape[0]) min_coeff, max_coeff = min(flips), max(flips) elif self.effect_on_y == "linear": corrcoef_var_y = np.corrcoef(observed_common_causes, y, rowvar=False)[-1, :-1] std_dev_y = np.std(y)[0] max_coeff = max(corrcoef_var_y) * std_dev_y min_coeff = min(corrcoef_var_y) * std_dev_y else: raise NotImplementedError( "'" + self.effect_on_y + "' method not supported for confounders' effect on outcome" ) min_coeff, max_coeff = self._compute_min_max_coeff(min_coeff, max_coeff, self.frac_strength_outcome) # By default, return a plot with 10 points # consider 10 values of the effect of the unobserved confounder step = (max_coeff - min_coeff) / len_kappa_y self.logger.info("(Min, Max) kappa_y for observed common causes, ({0}, {1})".format(min_coeff, max_coeff)) if np.equal(max_coeff, min_coeff): return max_coeff else: return np.arange(min_coeff, max_coeff, step) def refute_estimate(self, show_progress_bar=False): """ This function attempts to add an unobserved common cause to the outcome and the treatment. At present, we have implemented the behavior for one dimensional behaviors for continuous and binary variables. This function can either take single valued inputs or a range of inputs. The function then looks at the data type of the input and then decides on the course of action. :return: CausalRefuter: An object that contains the estimated effect and a new effect and the name of the refutation used. """ if self.simulation_method == "linear-partial-R2": if not (isinstance(self._estimate.estimator, LinearRegressionEstimator)): raise NotImplementedError( "Currently only LinearRegressionEstimator is supported for Sensitivity Analysis" ) if len(self._estimate.estimator._effect_modifier_names) > 0: raise NotImplementedError("The current implementation does not support effect modifiers") if self.frac_strength_outcome == 1: self.frac_strength_outcome = self.frac_strength_treatment analyzer = LinearSensitivityAnalyzer( estimator=self._estimate.estimator, data=self._data, treatment_name=self._treatment_name, percent_change_estimate=self.percent_change_estimate, significance_level=self.significance_level, benchmark_common_causes=self.benchmark_common_causes, null_hypothesis_effect=self.null_hypothesis_effect, frac_strength_treatment=self.frac_strength_treatment, frac_strength_outcome=self.frac_strength_outcome, common_causes_order=self._estimate.estimator._observed_common_causes.columns, ) analyzer.check_sensitivity(plot=self.plot_estimate) return analyzer if self.simulation_method == "non-parametric-partial-R2": # If the estimator used is LinearDML, partially linear sensitivity analysis will be automatically chosen if isinstance(self._estimate.estimator, dowhy.causal_estimators.econml.Econml): if self._estimate.estimator._econml_methodname == "econml.dml.LinearDML": analyzer = PartialLinearSensitivityAnalyzer( estimator=self._estimate._estimator_object, observed_common_causes=self._estimate.estimator._observed_common_causes, treatment=self._estimate.estimator._treatment, outcome=self._estimate.estimator._outcome, alpha_s_estimator_param_list=self.alpha_s_estimator_param_list, g_s_estimator_list=self.g_s_estimator_list, g_s_estimator_param_list=self.g_s_estimator_param_list, effect_strength_treatment=self.kappa_t, effect_strength_outcome=self.kappa_y, benchmark_common_causes=self.benchmark_common_causes, frac_strength_treatment=self.frac_strength_treatment, frac_strength_outcome=self.frac_strength_outcome, ) analyzer.check_sensitivity(plot=self.plot_estimate) return analyzer analyzer = NonParametricSensitivityAnalyzer( estimator=self._estimate.estimator, observed_common_causes=self._estimate.estimator._observed_common_causes, treatment=self._estimate.estimator._treatment, outcome=self._estimate.estimator._outcome, alpha_s_estimator_list=self.alpha_s_estimator_list, alpha_s_estimator_param_list=self.alpha_s_estimator_param_list, g_s_estimator_list=self.g_s_estimator_list, g_s_estimator_param_list=self.g_s_estimator_param_list, effect_strength_treatment=self.kappa_t, effect_strength_outcome=self.kappa_y, benchmark_common_causes=self.benchmark_common_causes, frac_strength_treatment=self.frac_strength_treatment, frac_strength_outcome=self.frac_strength_outcome, theta_s=self._estimate.value, plugin_reisz=self.plugin_reisz, ) analyzer.check_sensitivity(plot=self.plot_estimate) return analyzer if self.simulation_method == "e-value": if not isinstance(self._estimate.estimator, RegressionEstimator): raise NotImplementedError( "E-Value sensitivity analysis is currently only implemented RegressionEstimator." ) if len(self._estimate.estimator._effect_modifier_names) > 0: raise NotImplementedError("The current implementation does not support effect modifiers") analyzer = EValueSensitivityAnalyzer( estimate=self._estimate, estimand=self._target_estimand, data=self._data, treatment_name=self._treatment_name[0], outcome_name=self._outcome_name[0], ) analyzer.check_sensitivity(plot=self.plot_estimate) return analyzer if self.kappa_t is None: self.kappa_t = self.infer_default_kappa_t() if self.kappa_y is None: self.kappa_y = self.infer_default_kappa_y() if not isinstance(self.kappa_t, (list, np.ndarray)) and not isinstance( self.kappa_y, (list, np.ndarray) ): # Deal with single value inputs new_data = copy.deepcopy(self._data) new_data = self.include_confounders_effect(new_data, self.kappa_t, self.kappa_y) new_estimator = CausalEstimator.get_estimator_object(new_data, self._target_estimand, self._estimate) new_effect = new_estimator.estimate_effect() refute = CausalRefutation( self._estimate.value, new_effect.value, refutation_type="Refute: Add an Unobserved Common Cause" ) refute.new_effect_array = np.array(new_effect.value) refute.new_effect = new_effect.value refute.add_refuter(self) return refute else: # Deal with multiple value inputs if isinstance(self.kappa_t, (list, np.ndarray)) and isinstance( self.kappa_y, (list, np.ndarray) ): # Deal with range inputs # Get a 2D matrix of values # x,y = np.meshgrid(self.kappa_t, self.kappa_y) # x,y are both MxN results_matrix = np.random.rand( len(self.kappa_t), len(self.kappa_y) ) # Matrix to hold all the results of NxM orig_data = copy.deepcopy(self._data) for i in tqdm( range(len(self.kappa_t)), colour=CausalRefuter.PROGRESS_BAR_COLOR, disable=not show_progress_bar, desc="Refuting Estimates: ", ): for j in range(len(self.kappa_y)): new_data = self.include_confounders_effect(orig_data, self.kappa_t[i], self.kappa_y[j]) new_estimator = CausalEstimator.get_estimator_object( new_data, self._target_estimand, self._estimate ) new_effect = new_estimator.estimate_effect() refute = CausalRefutation( self._estimate.value, new_effect.value, refutation_type="Refute: Add an Unobserved Common Cause", ) results_matrix[i][j] = refute.new_effect # Populate the results refute.new_effect_array = results_matrix refute.new_effect = (np.min(results_matrix), np.max(results_matrix)) # Store the values into the refute object refute.add_refuter(self) if self.plotmethod is None: return refute import matplotlib import matplotlib.pyplot as plt fig = plt.figure(figsize=(6, 5)) left, bottom, width, height = 0.1, 0.1, 0.8, 0.8 ax = fig.add_axes([left, bottom, width, height]) oe = self._estimate.value contour_levels = [oe / 4.0, oe / 2.0, (3.0 / 4) * oe, oe] contour_levels.extend([0, np.min(results_matrix), np.max(results_matrix)]) if self.plotmethod == "contour": cp = plt.contourf(self.kappa_y, self.kappa_t, results_matrix, levels=sorted(contour_levels)) # Adding a label on the contour line for the original estimate fmt = {} trueeffect_index = np.where(cp.levels == oe)[0][0] fmt[cp.levels[trueeffect_index]] = "Estimated Effect" # Label every other level using strings plt.clabel(cp, [cp.levels[trueeffect_index]], inline=True, fmt=fmt) plt.colorbar(cp) elif self.plotmethod == "colormesh": cp = plt.pcolormesh(self.kappa_y, self.kappa_t, results_matrix, shading="nearest") plt.colorbar(cp, ticks=contour_levels) ax.yaxis.set_ticks(self.kappa_t) ax.xaxis.set_ticks(self.kappa_y) plt.xticks(rotation=45) ax.set_title("Effect of Unobserved Common Cause") ax.set_ylabel("Value of Linear Constant on Treatment") ax.set_xlabel("Value of Linear Constant on Outcome") plt.show() return refute elif isinstance(self.kappa_t, (list, np.ndarray)): outcomes = np.random.rand(len(self.kappa_t)) orig_data = copy.deepcopy(self._data) for i in tqdm( range(0, len(self.kappa_t)), colour=CausalRefuter.PROGRESS_BAR_COLOR, disable=not show_progress_bar, desc="Refuting Estimates: ", ): new_data = self.include_confounders_effect(orig_data, self.kappa_t[i], self.kappa_y) new_estimator = CausalEstimator.get_estimator_object( new_data, self._target_estimand, self._estimate ) new_effect = new_estimator.estimate_effect() refute = CausalRefutation( self._estimate.value, new_effect.value, refutation_type="Refute: Add an Unobserved Common Cause" ) self.logger.debug(refute) outcomes[i] = refute.new_effect # Populate the results refute.new_effect_array = outcomes refute.new_effect = (np.min(outcomes), np.max(outcomes)) refute.add_refuter(self) if self.plotmethod is None: return refute import matplotlib import matplotlib.pyplot as plt fig = plt.figure(figsize=(6, 5)) left, bottom, width, height = 0.1, 0.1, 0.8, 0.8 ax = fig.add_axes([left, bottom, width, height]) plt.plot(self.kappa_t, outcomes) plt.axhline(self._estimate.value, linestyle="--", color="gray") ax.set_title("Effect of Unobserved Common Cause") ax.set_xlabel("Value of Linear Constant on Treatment") ax.set_ylabel("Estimated Effect after adding the common cause") plt.show() return refute elif isinstance(self.kappa_y, (list, np.ndarray)): outcomes = np.random.rand(len(self.kappa_y)) orig_data = copy.deepcopy(self._data) for i in tqdm( range(0, len(self.kappa_y)), colour=CausalRefuter.PROGRESS_BAR_COLOR, disable=not show_progress_bar, desc="Refuting Estimates: ", ): new_data = self.include_confounders_effect(orig_data, self.kappa_t, self.kappa_y[i]) new_estimator = CausalEstimator.get_estimator_object( new_data, self._target_estimand, self._estimate ) new_effect = new_estimator.estimate_effect() refute = CausalRefutation( self._estimate.value, new_effect.value, refutation_type="Refute: Add an Unobserved Common Cause" ) self.logger.debug(refute) outcomes[i] = refute.new_effect # Populate the results refute.new_effect_array = outcomes refute.new_effect = (np.min(outcomes), np.max(outcomes)) refute.add_refuter(self) if self.plotmethod is None: return refute import matplotlib import matplotlib.pyplot as plt fig = plt.figure(figsize=(6, 5)) left, bottom, width, height = 0.1, 0.1, 0.8, 0.8 ax = fig.add_axes([left, bottom, width, height]) plt.plot(self.kappa_y, outcomes) plt.axhline(self._estimate.value, linestyle="--", color="gray") ax.set_title("Effect of Unobserved Common Cause") ax.set_xlabel("Value of Linear Constant on Outcome") ax.set_ylabel("Estimated Effect after adding the common cause") plt.show() return refute def include_confounders_effect(self, new_data, kappa_t, kappa_y): """ This function deals with the change in the value of the data due to the effect of the unobserved confounder. In the case of a binary flip, we flip only if the random number is greater than the threshold set. In the case of a linear effect, we use the variable as the linear regression constant. :param new_data: pandas.DataFrame: The data to be changed due to the effects of the unobserved confounder. :param kappa_t: numpy.float64: The value of the threshold for binary_flip or the value of the regression coefficient for linear effect. :param kappa_y: numpy.float64: The value of the threshold for binary_flip or the value of the regression coefficient for linear effect. :return: pandas.DataFrame: The DataFrame that includes the effects of the unobserved confounder. """ num_rows = self._data.shape[0] stdnorm = scipy.stats.norm() w_random = stdnorm.rvs(num_rows) if self.effect_on_t == "binary_flip": alpha = 2 * kappa_t - 1 if kappa_t >= 0.5 else 1 - 2 * kappa_t interval = stdnorm.interval(alpha) rel_interval = interval[0] if kappa_t >= 0.5 else interval[1] new_data.loc[rel_interval <= w_random, self._treatment_name] = ( 1 - new_data.loc[rel_interval <= w_random, self._treatment_name] ) for tname in self._treatment_name: if pd.api.types.is_bool_dtype(self._data[tname]): new_data = new_data.astype({tname: "bool"}, copy=False) elif self.effect_on_t == "linear": confounder_t_effect = kappa_t * w_random # By default, we add the effect of simulated confounder for treatment. # But subtract it from outcome to create a negative correlation # assuming that the original confounder's effect was positive on both. # This is to remove the effect of the original confounder. new_data[self._treatment_name] = new_data[self._treatment_name].values + np.ndarray( shape=(num_rows, 1), buffer=confounder_t_effect ) else: raise NotImplementedError( "'" + self.effect_on_t + "' method not supported for confounders' effect on treatment" ) if self.effect_on_y == "binary_flip": alpha = 2 * kappa_y - 1 if kappa_y >= 0.5 else 1 - 2 * kappa_y interval = stdnorm.interval(alpha) rel_interval = interval[0] if kappa_y >= 0.5 else interval[1] new_data.loc[rel_interval <= w_random, self._outcome_name] = ( 1 - new_data.loc[rel_interval <= w_random, self._outcome_name] ) for yname in self._outcome_name: if pd.api.types.is_bool_dtype(self._data[yname]): new_data = new_data.astype({yname: "bool"}, copy=False) elif self.effect_on_y == "linear": confounder_y_effect = (-1) * kappa_y * w_random # By default, we add the effect of simulated confounder for treatment. # But subtract it from outcome to create a negative correlation # assuming that the original confounder's effect was positive on both. # This is to remove the effect of the original confounder. new_data[self._outcome_name] = new_data[self._outcome_name].values + np.ndarray( shape=(num_rows, 1), buffer=confounder_y_effect ) else: raise NotImplementedError( "'" + self.effect_on_y + "' method not supported for confounders' effect on outcome" ) return new_data def include_simulated_confounder(self, convergence_threshold=0.1, c_star_max=1000): """ This function simulates an unobserved confounder based on the data using the following steps: 1. It calculates the "residuals" from the treatment and outcome model i.) The outcome model has outcome as the dependent variable and all the observed variables including treatment as independent variables ii.) The treatment model has treatment as the dependent variable and all the observed variables as independent variables. 2. U is an intermediate random variable drawn from the normal distribution with the weighted average of residuals as mean and a unit variance U ~ N(c1*d_y + c2*d_t, 1) where *d_y and d_t are residuals from the treatment and outcome model *c1 and c2 are coefficients to the residuals 3. The final U, which is the simulated unobserved confounder is obtained by debiasing the intermediate variable U by residualising it with X Choosing the coefficients c1 and c2: The coefficients are chosen based on these basic assumptions: 1. There is a hyperbolic relationship satisfying c1*c2 = c_star 2. c_star is chosen from a range of possible values based on the correlation of the obtained simulated variable with outcome and treatment. 3. The product of correlations with treatment and outcome should be at a minimum distance to the maximum correlations with treatment and outcome in any of the observed confounders 4. The ratio of the weights should be such that they maintain the ratio of the maximum possible observed coefficients within some confidence interval :param c_star_max: The maximum possible value for the hyperbolic curve on which the coefficients to the residuals lie. It defaults to 1000 in the code if not specified by the user. :type int :param convergence_threshold: The threshold to check the plateauing of the correlation while selecting a c_star. It defaults to 0.1 in the code if not specified by the user :type float :returns: The simulated values of the unobserved confounder based on the data :type pandas.core.series.Series """ # Obtaining the list of observed variables required_variables = True observed_variables = self.choose_variables(required_variables) observed_variables_with_treatment_and_outcome = observed_variables + self._treatment_name + self._outcome_name # Taking a subset of the dataframe that has only observed variables self._data = self._data[observed_variables_with_treatment_and_outcome] # Residuals from the outcome model obtained by fitting a linear model y = self._data[self._outcome_name[0]] observed_variables_with_treatment = observed_variables + self._treatment_name X = self._data[observed_variables_with_treatment] model = sm.OLS(y, X.astype("float")) results = model.fit() residuals_y = y - results.fittedvalues d_y = list(pd.Series(residuals_y)) # Residuals from the treatment model obtained by fitting a linear model t = self._data[self._treatment_name[0]].astype("int64") X = self._data[observed_variables] model = sm.OLS(t, X) results = model.fit() residuals_t = t - results.fittedvalues d_t = list(pd.Series(residuals_t)) # Initialising product_cor_metric_observed with a really low value as finding maximum product_cor_metric_observed = -10000000000 for i in observed_variables: current_obs_confounder = self._data[i] outcome_values = self._data[self._outcome_name[0]] correlation_y = current_obs_confounder.corr(outcome_values) treatment_values = t correlation_t = current_obs_confounder.corr(treatment_values) product_cor_metric_current = correlation_y * correlation_t if product_cor_metric_current >= product_cor_metric_observed: product_cor_metric_observed = product_cor_metric_current correlation_t_observed = correlation_t correlation_y_observed = correlation_y # The user has an option to give the the effect_strength_on_y and effect_strength_on_t which can be then used instead of maximum correlation with treatment and outcome in the observed variables as it specifies the desired effect. if self.kappa_t is not None: correlation_t_observed = self.kappa_t if self.kappa_y is not None: correlation_y_observed = self.kappa_y # Choosing a c_star based on the data. # The correlations stop increasing upon increasing c_star after a certain value, that is it plateaus and we choose the value of c_star to be the value it plateaus. correlation_y_list = [] correlation_t_list = [] product_cor_metric_simulated_list = [] x_list = [] step = int(c_star_max / 10) for i in range(0, int(c_star_max), step): c1 = math.sqrt(i) c2 = c1 final_U = self.generate_confounder_from_residuals(c1, c2, d_y, d_t, X) current_simulated_confounder = final_U outcome_values = self._data[self._outcome_name[0]] correlation_y = current_simulated_confounder.corr(outcome_values) correlation_y_list.append(correlation_y) treatment_values = t correlation_t = current_simulated_confounder.corr(treatment_values) correlation_t_list.append(correlation_t) product_cor_metric_simulated = correlation_y * correlation_t product_cor_metric_simulated_list.append(product_cor_metric_simulated) x_list.append(i) index = 1 while index < len(correlation_y_list): if (correlation_y_list[index] - correlation_y_list[index - 1]) <= convergence_threshold: c_star = x_list[index] break index = index + 1 # Choosing c1 and c2 based on the hyperbolic relationship once c_star is chosen by going over various combinations of c1 and c2 values and choosing the combination which # which maintains the minimum distance between the product of correlations of the simulated variable and the product of maximum correlations of one of the observed variables # and additionally checks if the ratio of the weights are such that they maintain the ratio of the maximum possible observed coefficients within some confidence interval # c1_final and c2_final are initialised to the values on the hyperbolic curve such that c1_final = c2_final and c1_final*c2_final = c_star c1_final = math.sqrt(c_star) c2_final = math.sqrt(c_star) # initialising min_distance_between_product_cor_metrics to be a value greater than 1 min_distance_between_product_cor_metrics = 1.5 i = 0.05 threshold = c_star / 0.05 while i <= threshold: c2 = i c1 = c_star / c2 final_U = self.generate_confounder_from_residuals(c1, c2, d_y, d_t, X) current_simulated_confounder = final_U outcome_values = self._data[self._outcome_name[0]] correlation_y = current_simulated_confounder.corr(outcome_values) treatment_values = t correlation_t = current_simulated_confounder.corr(treatment_values) product_cor_metric_simulated = correlation_y * correlation_t if min_distance_between_product_cor_metrics >= abs( product_cor_metric_simulated - product_cor_metric_observed ): min_distance_between_product_cor_metrics = abs( product_cor_metric_simulated - product_cor_metric_observed ) additional_condition = correlation_y_observed / correlation_t_observed if ((c1 / c2) <= (additional_condition + 0.3 * additional_condition)) and ( (c1 / c2) >= (additional_condition - 0.3 * additional_condition) ): # choose minimum positive value c1_final = c1 c2_final = c2 i = i * 1.5 """#closed form solution print("c_star_max before closed form", c_star_max) if max_correlation_with_t == -1000: c2 = 0 c1 = c_star_max else: additional_condition = abs(max_correlation_with_y/max_correlation_with_t) print("additional_condition", additional_condition) c2 = math.sqrt(c_star_max/additional_condition) c1 = c_star_max/c2""" final_U = self.generate_confounder_from_residuals(c1_final, c2_final, d_y, d_t, X) return final_U def generate_confounder_from_residuals(self, c1, c2, d_y, d_t, X): """ This function takes the residuals from the treatment and outcome model and their coefficients and simulates the intermediate random variable U by taking the row wise normal distribution corresponding to each residual value and then debiasing the intermediate variable to get the final variable. :param c1: coefficient to the residual from the outcome model :type float :param c2: coefficient to the residual from the treatment model :type float :param d_y: residuals from the outcome model :type list :param d_t: residuals from the treatment model :type list :returns: The simulated values of the unobserved confounder based on the data :type pandas.core.series.Series """ U = [] for j in range(len(d_t)): simulated_variable_mean = c1 * d_y[j] + c2 * d_t[j] simulated_variable_stddev = 1 U.append(np.random.normal(simulated_variable_mean, simulated_variable_stddev, 1)) U = np.array(U) model = sm.OLS(U, X) results = model.fit() U = U.reshape( -1, ) final_U = U - results.fittedvalues.values final_U = pd.Series(U) return final_U

import copy import logging import math from typing import Dict, List, Optional, Union import numpy as np import pandas as pd import scipy.stats import statsmodels.api as sm from sklearn.linear_model import LogisticRegression from sklearn.preprocessing import StandardScaler from tqdm.auto import tqdm import dowhy.causal_estimators.econml from dowhy.causal_estimator import CausalEstimate, CausalEstimator from dowhy.causal_estimators.linear_regression_estimator import LinearRegressionEstimator from dowhy.causal_estimators.regression_estimator import RegressionEstimator from dowhy.causal_identifier.identified_estimand import IdentifiedEstimand from dowhy.causal_refuter import CausalRefutation, CausalRefuter, choose_variables from dowhy.causal_refuters.evalue_sensitivity_analyzer import EValueSensitivityAnalyzer from dowhy.causal_refuters.linear_sensitivity_analyzer import LinearSensitivityAnalyzer from dowhy.causal_refuters.non_parametric_sensitivity_analyzer import NonParametricSensitivityAnalyzer from dowhy.causal_refuters.partial_linear_sensitivity_analyzer import PartialLinearSensitivityAnalyzer logger = logging.getLogger(__name__) class AddUnobservedCommonCause(CausalRefuter): """Add an unobserved confounder for refutation. AddUnobservedCommonCause class supports three methods: 1) Simulation of an unobserved confounder 2) Linear partial R2 : Sensitivity Analysis for linear models. 3) Non-Parametric partial R2 based : Sensitivity Analyis for non-parametric models. Supports additional parameters that can be specified in the refute_estimate() method. """ def __init__(self, *args, **kwargs): """ Initialize the parameters required for the refuter. For direct_simulation, if effect_strength_on_treatment or effect_strength_on_outcome is not given, it is calculated automatically as a range between the minimum and maximum effect strength of observed confounders on treatment and outcome respectively. :param simulation_method: The method to use for simulating effect of unobserved confounder. Possible values are ["direct-simulation", "linear-partial-R2", "non-parametric-partial-R2", "e-value"]. :param confounders_effect_on_treatment: str : The type of effect on the treatment due to the unobserved confounder. Possible values are ['binary_flip', 'linear'] :param confounders_effect_on_outcome: str : The type of effect on the outcome due to the unobserved confounder. Possible values are ['binary_flip', 'linear'] :param effect_strength_on_treatment: float, numpy.ndarray: [Used when simulation_method="direct-simulation"] Strength of the confounder's effect on treatment. When confounders_effect_on_treatment is linear, it is the regression coefficient. When the confounders_effect_on_treatment is binary flip, it is the probability with which effect of unobserved confounder can invert the value of the treatment. :param effect_strength_on_outcome: float, numpy.ndarray: Strength of the confounder's effect on outcome. Its interpretation depends on confounders_effect_on_outcome and the simulation_method. When simulation_method is direct-simulation, for a linear effect it behaves like the regression coefficient and for a binary flip, it is the probability with which it can invert the value of the outcome. :param partial_r2_confounder_treatment: float, numpy.ndarray: [Used when simulation_method is linear-partial-R2 or non-parametric-partial-R2] Partial R2 of the unobserved confounder wrt the treatment conditioned on the observed confounders. Only in the case of general non-parametric-partial-R2, it is the fraction of variance in the reisz representer that is explained by the unobserved confounder; specifically (1-r), where r is the ratio of variance of reisz representer, alpha^2, based on observed confounders and that based on all confounders. :param partial_r2_confounder_outcome: float, numpy.ndarray: [Used when simulation_method is linear-partial-R2 or non-parametric-partial-R2] Partial R2 of the unobserved confounder wrt the outcome conditioned on the treatment and observed confounders. :param frac_strength_treatment: float: This parameter decides the effect strength of the simulated confounder as a fraction of the effect strength of observed confounders on treatment. Defaults to 1. :param frac_strength_outcome: float: This parameter decides the effect strength of the simulated confounder as a fraction of the effect strength of observed confounders on outcome. Defaults to 1. :param plotmethod: string: Type of plot to be shown. If None, no plot is generated. This parameter is used only only when more than one treatment confounder effect values or outcome confounder effect values are provided. Default is "colormesh". Supported values are "contour", "colormesh" when more than one value is provided for both confounder effect value parameters; "line" when provided for only one of them. :param percent_change_estimate: It is the percentage of reduction of treatment estimate that could alter the results (default = 1). if percent_change_estimate = 1, the robustness value describes the strength of association of confounders with treatment and outcome in order to reduce the estimate by 100% i.e bring it down to 0. (relevant only for Linear Sensitivity Analysis, ignore for rest) :param confounder_increases_estimate: True implies that confounder increases the absolute value of estimate and vice versa. (Default = False). (relevant only for Linear Sensitivity Analysis, ignore for rest) :param benchmark_common_causes: names of variables for bounding strength of confounders. (relevant only for partial-r2 based simulation methods) :param significance_level: confidence interval for statistical inference(default = 0.05). (relevant only for partial-r2 based simulation methods) :param null_hypothesis_effect: assumed effect under the null hypothesis. (relevant only for linear-partial-R2, ignore for rest) :param plot_estimate: Generate contour plot for estimate while performing sensitivity analysis. (default = True). (relevant only for partial-r2 based simulation methods) :param num_splits: number of splits for cross validation. (default = 5). (relevant only for non-parametric-partial-R2 simulation method) :param shuffle_data : shuffle data or not before splitting into folds (default = False). (relevant only for non-parametric-partial-R2 simulation method) :param shuffle_random_seed: seed for randomly shuffling data. (relevant only for non-parametric-partial-R2 simulation method) :param alpha_s_estimator_param_list: list of dictionaries with parameters for finding alpha_s. (relevant only for non-parametric-partial-R2 simulation method) :param g_s_estimator_list: list of estimator objects for finding g_s. These objects should have fit() and predict() functions implemented. (relevant only for non-parametric-partial-R2 simulation method) :param g_s_estimator_param_list: list of dictionaries with parameters for tuning respective estimators in "g_s_estimator_list". The order of the dictionaries in the list should be consistent with the estimator objects order in "g_s_estimator_list". (relevant only for non-parametric-partial-R2 simulation method) """ super().__init__(*args, **kwargs) self.simulation_method = kwargs["simulation_method"] if "simulation_method" in kwargs else "direct-simulation" self.effect_on_t = ( kwargs["confounders_effect_on_treatment"] if "confounders_effect_on_treatment" in kwargs else "binary_flip" ) self.effect_on_y = ( kwargs["confounders_effect_on_outcome"] if "confounders_effect_on_outcome" in kwargs else "linear" ) if self.simulation_method == "direct-simulation": self.kappa_t = kwargs["effect_strength_on_treatment"] if "effect_strength_on_treatment" in kwargs else None self.kappa_y = kwargs["effect_strength_on_outcome"] if "effect_strength_on_outcome" in kwargs else None elif self.simulation_method in ["linear-partial-R2", "non-parametric-partial-R2"]: self.kappa_t = ( kwargs["partial_r2_confounder_treatment"] if "partial_r2_confounder_treatment" in kwargs else None ) self.kappa_y = ( kwargs["partial_r2_confounder_outcome"] if "partial_r2_confounder_outcome" in kwargs else None ) elif self.simulation_method == "e-value": pass else: raise ValueError( "simulation method is not supported. Try direct-simulation, linear-partial-R2, non-parametric-partial-R2, or e-value" ) self.frac_strength_treatment = ( kwargs["effect_fraction_on_treatment"] if "effect_fraction_on_treatment" in kwargs else 1 ) self.frac_strength_outcome = ( kwargs["effect_fraction_on_outcome"] if "effect_fraction_on_outcome" in kwargs else 1 ) self.plotmethod = kwargs["plotmethod"] if "plotmethod" in kwargs else "colormesh" self.percent_change_estimate = kwargs["percent_change_estimate"] if "percent_change_estimate" in kwargs else 1.0 self.significance_level = kwargs["significance_level"] if "significance_level" in kwargs else 0.05 self.confounder_increases_estimate = ( kwargs["confounder_increases_estimate"] if "confounder_increases_estimate" in kwargs else False ) self.benchmark_common_causes = ( kwargs["benchmark_common_causes"] if "benchmark_common_causes" in kwargs else None ) self.null_hypothesis_effect = kwargs["null_hypothesis_effect"] if "null_hypothesis_effect" in kwargs else 0 self.plot_estimate = kwargs["plot_estimate"] if "plot_estimate" in kwargs else True self.num_splits = kwargs["num_splits"] if "num_splits" in kwargs else 5 self.shuffle_data = kwargs["shuffle_data"] if "shuffle_data" in kwargs else False self.shuffle_random_seed = kwargs["shuffle_random_seed"] if "shuffle_random_seed" in kwargs else None self.alpha_s_estimator_param_list = ( kwargs["alpha_s_estimator_param_list"] if "alpha_s_estimator_param_list" in kwargs else None ) self.alpha_s_estimator_list = kwargs["alpha_s_estimator_list"] if "alpha_s_estimator_list" in kwargs else None self.g_s_estimator_list = kwargs["g_s_estimator_list"] if "g_s_estimator_list" in kwargs else None self.g_s_estimator_param_list = ( kwargs["g_s_estimator_param_list"] if "g_s_estimator_param_list" in kwargs else None ) self.plugin_reisz = kwargs["plugin_reisz"] if "plugin_reisz" in kwargs else False self.logger = logging.getLogger(__name__) def refute_estimate(self, show_progress_bar=False): if self.simulation_method == "linear-partial-R2": return sensitivity_linear_partial_r2( self._data, self._estimate, self._treatment_name, self.frac_strength_treatment, self.frac_strength_outcome, self.percent_change_estimate, self.benchmark_common_causes, self.significance_level, self.null_hypothesis_effect, self.plot_estimate, ) elif self.simulation_method == "non-parametric-partial-R2": return sensitivity_non_parametric_partial_r2( self._estimate, self.kappa_t, self.kappa_y, self.frac_strength_treatment, self.frac_strength_outcome, self.benchmark_common_causes, self.plot_estimate, self.alpha_s_estimator_list, self.alpha_s_estimator_param_list, self.g_s_estimator_list, self.g_s_estimator_param_list, self.plugin_reisz, ) elif self.simulation_method == "e-value": return sensitivity_e_value( self._data, self._target_estimand, self._estimate, self._treatment_name, self._outcome_name, self.plot_estimate, ) elif self.simulation_method == "direct-simulation": refute = sensitivity_simulation( self._data, self._target_estimand, self._estimate, self._treatment_name, self._outcome_name, self.kappa_t, self.kappa_y, self.effect_on_t, self.effect_on_y, self.frac_strength_treatment, self.frac_strength_outcome, self.plotmethod, show_progress_bar, ) refute.add_refuter(self) return refute def _infer_default_kappa_t( data: pd.DataFrame, target_estimand: IdentifiedEstimand, treatment_name: List[str], effect_on_t: str, frac_strength_treatment: float, len_kappa_t: int = 10, ): """Infer default effect strength of simulated confounder on treatment.""" observed_common_causes_names = target_estimand.get_backdoor_variables() if len(observed_common_causes_names) > 0: observed_common_causes = data[observed_common_causes_names] observed_common_causes = pd.get_dummies(observed_common_causes, drop_first=True) else: raise ValueError( "There needs to be at least one common cause to" + "automatically compute the default value of kappa_t." + " Provide a value for kappa_t" ) t = data[treatment_name] # Standardizing the data observed_common_causes = StandardScaler().fit_transform(observed_common_causes) if effect_on_t == "binary_flip": # Fit a model containing all confounders and compare predictions # using all features compared to all features except a given # confounder. tmodel = LogisticRegression().fit(observed_common_causes, t) tpred = tmodel.predict(observed_common_causes).astype(int) flips = [] for i in range(observed_common_causes.shape[1]): oldval = np.copy(observed_common_causes[:, i]) observed_common_causes[:, i] = 0 tcap = tmodel.predict(observed_common_causes).astype(int) observed_common_causes[:, i] = oldval flips.append(np.sum(abs(tcap - tpred)) / tpred.shape[0]) min_coeff, max_coeff = min(flips), max(flips) elif effect_on_t == "linear": # Estimating the regression coefficient from standardized features to t corrcoef_var_t = np.corrcoef(observed_common_causes, t, rowvar=False)[-1, :-1] std_dev_t = np.std(t)[0] max_coeff = max(corrcoef_var_t) * std_dev_t min_coeff = min(corrcoef_var_t) * std_dev_t else: raise NotImplementedError("'" + effect_on_t + "' method not supported for confounders' effect on treatment") min_coeff, max_coeff = _compute_min_max_coeff(min_coeff, max_coeff, frac_strength_treatment) # By default, return a plot with 10 points # consider 10 values of the effect of the unobserved confounder step = (max_coeff - min_coeff) / len_kappa_t logger.info("(Min, Max) kappa_t for observed common causes, ({0}, {1})".format(min_coeff, max_coeff)) if np.equal(max_coeff, min_coeff): return max_coeff else: return np.arange(min_coeff, max_coeff, step) def _compute_min_max_coeff(min_coeff: float, max_coeff: float, effect_strength_fraction: np.ndarray): max_coeff = effect_strength_fraction * max_coeff min_coeff = effect_strength_fraction * min_coeff return min_coeff, max_coeff def _infer_default_kappa_y( data: pd.DataFrame, target_estimand: IdentifiedEstimand, outcome_name: List[str], effect_on_y: str, frac_strength_outcome: float, len_kappa_y: int = 10, ): """Infer default effect strength of simulated confounder on treatment.""" observed_common_causes_names = target_estimand.get_backdoor_variables() if len(observed_common_causes_names) > 0: observed_common_causes = data[observed_common_causes_names] observed_common_causes = pd.get_dummies(observed_common_causes, drop_first=True) else: raise ValueError( "There needs to be at least one common cause to" + "automatically compute the default value of kappa_y." + " Provide a value for kappa_y" ) y = data[outcome_name] # Standardizing the data observed_common_causes = StandardScaler().fit_transform(observed_common_causes) if effect_on_y == "binary_flip": # Fit a model containing all confounders and compare predictions # using all features compared to all features except a given # confounder. ymodel = LogisticRegression().fit(observed_common_causes, y) ypred = ymodel.predict(observed_common_causes).astype(int) flips = [] for i in range(observed_common_causes.shape[1]): oldval = np.copy(observed_common_causes[:, i]) observed_common_causes[:, i] = 0 ycap = ymodel.predict(observed_common_causes).astype(int) observed_common_causes[:, i] = oldval flips.append(np.sum(abs(ycap - ypred)) / ypred.shape[0]) min_coeff, max_coeff = min(flips), max(flips) elif effect_on_y == "linear": corrcoef_var_y = np.corrcoef(observed_common_causes, y, rowvar=False)[-1, :-1] std_dev_y = np.std(y)[0] max_coeff = max(corrcoef_var_y) * std_dev_y min_coeff = min(corrcoef_var_y) * std_dev_y else: raise NotImplementedError("'" + effect_on_y + "' method not supported for confounders' effect on outcome") min_coeff, max_coeff = _compute_min_max_coeff(min_coeff, max_coeff, frac_strength_outcome) # By default, return a plot with 10 points # consider 10 values of the effect of the unobserved confounder step = (max_coeff - min_coeff) / len_kappa_y logger.info("(Min, Max) kappa_y for observed common causes, ({0}, {1})".format(min_coeff, max_coeff)) if np.equal(max_coeff, min_coeff): return max_coeff else: return np.arange(min_coeff, max_coeff, step) def _include_confounders_effect( data: pd.DataFrame, new_data: pd.DataFrame, effect_on_t: str, treatment_name: str, kappa_t: float, effect_on_y: str, outcome_name: str, kappa_y: float, ): """ This function deals with the change in the value of the data due to the effect of the unobserved confounder. In the case of a binary flip, we flip only if the random number is greater than the threshold set. In the case of a linear effect, we use the variable as the linear regression constant. :param new_data: pandas.DataFrame: The data to be changed due to the effects of the unobserved confounder. :param kappa_t: numpy.float64: The value of the threshold for binary_flip or the value of the regression coefficient for linear effect. :param kappa_y: numpy.float64: The value of the threshold for binary_flip or the value of the regression coefficient for linear effect. :return: pandas.DataFrame: The DataFrame that includes the effects of the unobserved confounder. """ num_rows = data.shape[0] stdnorm = scipy.stats.norm() w_random = stdnorm.rvs(num_rows) if effect_on_t == "binary_flip": alpha = 2 * kappa_t - 1 if kappa_t >= 0.5 else 1 - 2 * kappa_t interval = stdnorm.interval(alpha) rel_interval = interval[0] if kappa_t >= 0.5 else interval[1] new_data.loc[rel_interval <= w_random, treatment_name] = ( 1 - new_data.loc[rel_interval <= w_random, treatment_name] ) for tname in treatment_name: if pd.api.types.is_bool_dtype(data[tname]): new_data = new_data.astype({tname: "bool"}, copy=False) elif effect_on_t == "linear": confounder_t_effect = kappa_t * w_random # By default, we add the effect of simulated confounder for treatment. # But subtract it from outcome to create a negative correlation # assuming that the original confounder's effect was positive on both. # This is to remove the effect of the original confounder. new_data[treatment_name] = new_data[treatment_name].values + np.ndarray( shape=(num_rows, 1), buffer=confounder_t_effect ) else: raise NotImplementedError("'" + effect_on_t + "' method not supported for confounders' effect on treatment") if effect_on_y == "binary_flip": alpha = 2 * kappa_y - 1 if kappa_y >= 0.5 else 1 - 2 * kappa_y interval = stdnorm.interval(alpha) rel_interval = interval[0] if kappa_y >= 0.5 else interval[1] new_data.loc[rel_interval <= w_random, outcome_name] = 1 - new_data.loc[rel_interval <= w_random, outcome_name] for yname in outcome_name: if pd.api.types.is_bool_dtype(data[yname]): new_data = new_data.astype({yname: "bool"}, copy=False) elif effect_on_y == "linear": confounder_y_effect = (-1) * kappa_y * w_random # By default, we add the effect of simulated confounder for treatment. # But subtract it from outcome to create a negative correlation # assuming that the original confounder's effect was positive on both. # This is to remove the effect of the original confounder. new_data[outcome_name] = new_data[outcome_name].values + np.ndarray( shape=(num_rows, 1), buffer=confounder_y_effect ) else: raise NotImplementedError("'" + effect_on_y + "' method not supported for confounders' effect on outcome") return new_data def include_simulated_confounder( data: pd.DataFrame, treatment_name: str, outcome_name: str, kappa_t: float, kappa_y: float, convergence_threshold: float = 0.1, c_star_max: int = 1000, ): """ This function simulates an unobserved confounder based on the data using the following steps: 1. It calculates the "residuals" from the treatment and outcome model i.) The outcome model has outcome as the dependent variable and all the observed variables including treatment as independent variables ii.) The treatment model has treatment as the dependent variable and all the observed variables as independent variables. 2. U is an intermediate random variable drawn from the normal distribution with the weighted average of residuals as mean and a unit variance U ~ N(c1*d_y + c2*d_t, 1) where *d_y and d_t are residuals from the treatment and outcome model *c1 and c2 are coefficients to the residuals 3. The final U, which is the simulated unobserved confounder is obtained by debiasing the intermediate variable U by residualising it with X Choosing the coefficients c1 and c2: The coefficients are chosen based on these basic assumptions: 1. There is a hyperbolic relationship satisfying c1*c2 = c_star 2. c_star is chosen from a range of possible values based on the correlation of the obtained simulated variable with outcome and treatment. 3. The product of correlations with treatment and outcome should be at a minimum distance to the maximum correlations with treatment and outcome in any of the observed confounders 4. The ratio of the weights should be such that they maintain the ratio of the maximum possible observed coefficients within some confidence interval :param c_star_max: The maximum possible value for the hyperbolic curve on which the coefficients to the residuals lie. It defaults to 1000 in the code if not specified by the user. :type int :param convergence_threshold: The threshold to check the plateauing of the correlation while selecting a c_star. It defaults to 0.1 in the code if not specified by the user :type float :returns: The simulated values of the unobserved confounder based on the data :type pandas.core.series.Series """ # Obtaining the list of observed variables required_variables = True observed_variables = choose_variables(required_variables) observed_variables_with_treatment_and_outcome = observed_variables + treatment_name + outcome_name # Taking a subset of the dataframe that has only observed variables data = data[observed_variables_with_treatment_and_outcome] # Residuals from the outcome model obtained by fitting a linear model y = data[outcome_name[0]] observed_variables_with_treatment = observed_variables + treatment_name X = data[observed_variables_with_treatment] model = sm.OLS(y, X.astype("float")) results = model.fit() residuals_y = y - results.fittedvalues d_y = list(pd.Series(residuals_y)) # Residuals from the treatment model obtained by fitting a linear model t = data[treatment_name[0]].astype("int64") X = data[observed_variables] model = sm.OLS(t, X) results = model.fit() residuals_t = t - results.fittedvalues d_t = list(pd.Series(residuals_t)) # Initialising product_cor_metric_observed with a really low value as finding maximum product_cor_metric_observed = -10000000000 for i in observed_variables: current_obs_confounder = data[i] outcome_values = data[outcome_name[0]] correlation_y = current_obs_confounder.corr(outcome_values) treatment_values = t correlation_t = current_obs_confounder.corr(treatment_values) product_cor_metric_current = correlation_y * correlation_t if product_cor_metric_current >= product_cor_metric_observed: product_cor_metric_observed = product_cor_metric_current correlation_t_observed = correlation_t correlation_y_observed = correlation_y # The user has an option to give the the effect_strength_on_y and effect_strength_on_t which can be then used instead of maximum correlation with treatment and outcome in the observed variables as it specifies the desired effect. if kappa_t is not None: correlation_t_observed = kappa_t if kappa_y is not None: correlation_y_observed = kappa_y # Choosing a c_star based on the data. # The correlations stop increasing upon increasing c_star after a certain value, that is it plateaus and we choose the value of c_star to be the value it plateaus. correlation_y_list = [] correlation_t_list = [] product_cor_metric_simulated_list = [] x_list = [] step = int(c_star_max / 10) for i in range(0, int(c_star_max), step): c1 = math.sqrt(i) c2 = c1 final_U = _generate_confounder_from_residuals(c1, c2, d_y, d_t, X) current_simulated_confounder = final_U outcome_values = data[outcome_name[0]] correlation_y = current_simulated_confounder.corr(outcome_values) correlation_y_list.append(correlation_y) treatment_values = t correlation_t = current_simulated_confounder.corr(treatment_values) correlation_t_list.append(correlation_t) product_cor_metric_simulated = correlation_y * correlation_t product_cor_metric_simulated_list.append(product_cor_metric_simulated) x_list.append(i) index = 1 while index < len(correlation_y_list): if (correlation_y_list[index] - correlation_y_list[index - 1]) <= convergence_threshold: c_star = x_list[index] break index = index + 1 # Choosing c1 and c2 based on the hyperbolic relationship once c_star is chosen by going over various combinations of c1 and c2 values and choosing the combination which # which maintains the minimum distance between the product of correlations of the simulated variable and the product of maximum correlations of one of the observed variables # and additionally checks if the ratio of the weights are such that they maintain the ratio of the maximum possible observed coefficients within some confidence interval # c1_final and c2_final are initialised to the values on the hyperbolic curve such that c1_final = c2_final and c1_final*c2_final = c_star c1_final = math.sqrt(c_star) c2_final = math.sqrt(c_star) # initialising min_distance_between_product_cor_metrics to be a value greater than 1 min_distance_between_product_cor_metrics = 1.5 i = 0.05 threshold = c_star / 0.05 while i <= threshold: c2 = i c1 = c_star / c2 final_U = _generate_confounder_from_residuals(c1, c2, d_y, d_t, X) current_simulated_confounder = final_U outcome_values = data[outcome_name[0]] correlation_y = current_simulated_confounder.corr(outcome_values) treatment_values = t correlation_t = current_simulated_confounder.corr(treatment_values) product_cor_metric_simulated = correlation_y * correlation_t if min_distance_between_product_cor_metrics >= abs(product_cor_metric_simulated - product_cor_metric_observed): min_distance_between_product_cor_metrics = abs(product_cor_metric_simulated - product_cor_metric_observed) additional_condition = correlation_y_observed / correlation_t_observed if ((c1 / c2) <= (additional_condition + 0.3 * additional_condition)) and ( (c1 / c2) >= (additional_condition - 0.3 * additional_condition) ): # choose minimum positive value c1_final = c1 c2_final = c2 i = i * 1.5 """#closed form solution print("c_star_max before closed form", c_star_max) if max_correlation_with_t == -1000: c2 = 0 c1 = c_star_max else: additional_condition = abs(max_correlation_with_y/max_correlation_with_t) print("additional_condition", additional_condition) c2 = math.sqrt(c_star_max/additional_condition) c1 = c_star_max/c2""" final_U = _generate_confounder_from_residuals(c1_final, c2_final, d_y, d_t, X) return final_U def _generate_confounder_from_residuals(c1, c2, d_y, d_t, X): """ This function takes the residuals from the treatment and outcome model and their coefficients and simulates the intermediate random variable U by taking the row wise normal distribution corresponding to each residual value and then debiasing the intermediate variable to get the final variable. :param c1: coefficient to the residual from the outcome model :type float :param c2: coefficient to the residual from the treatment model :type float :param d_y: residuals from the outcome model :type list :param d_t: residuals from the treatment model :type list :returns: The simulated values of the unobserved confounder based on the data :type pandas.core.series.Series """ U = [] for j in range(len(d_t)): simulated_variable_mean = c1 * d_y[j] + c2 * d_t[j] simulated_variable_stddev = 1 U.append(np.random.normal(simulated_variable_mean, simulated_variable_stddev, 1)) U = np.array(U) model = sm.OLS(U, X) results = model.fit() U = U.reshape( -1, ) final_U = U - results.fittedvalues.values final_U = pd.Series(U) return final_U def sensitivity_linear_partial_r2( data: pd.DataFrame, estimate: CausalEstimate, treatment_name: str, frac_strength_treatment: float = 1.0, frac_strength_outcome: float = 1.0, percent_change_estimate: float = 1.0, benchmark_common_causes: Optional[List[str]] = None, significance_level: Optional[float] = None, null_hypothesis_effect: Optional[float] = None, plot_estimate: bool = True, ) -> LinearSensitivityAnalyzer: """Add an unobserved confounder for refutation using Linear partial R2 methond (Sensitivity Analysis for linear models). :param data: pd.DataFrame: Data to run the refutation :param estimate: CausalEstimate: Estimate to run the refutation :param treatment_name: str: Name of the treatment :param frac_strength_treatment: float: This parameter decides the effect strength of the simulated confounder as a fraction of the effect strength of observed confounders on treatment. Defaults to 1. :param frac_strength_outcome: float: This parameter decides the effect strength of the simulated confounder as a fraction of the effect strength of observed confounders on outcome. Defaults to 1. :param percent_change_estimate: It is the percentage of reduction of treatment estimate that could alter the results (default = 1). if percent_change_estimate = 1, the robustness value describes the strength of association of confounders with treatment and outcome in order to reduce the estimate by 100% i.e bring it down to 0. (relevant only for Linear Sensitivity Analysis, ignore for rest) :param benchmark_common_causes: names of variables for bounding strength of confounders. (relevant only for partial-r2 based simulation methods) :param significance_level: confidence interval for statistical inference(default = 0.05). (relevant only for partial-r2 based simulation methods) :param null_hypothesis_effect: assumed effect under the null hypothesis. (relevant only for linear-partial-R2, ignore for rest) :param plot_estimate: Generate contour plot for estimate while performing sensitivity analysis. (default = True). (relevant only for partial-r2 based simulation methods) """ if not (isinstance(estimate.estimator, LinearRegressionEstimator)): raise NotImplementedError("Currently only LinearRegressionEstimator is supported for Sensitivity Analysis") if len(estimate.estimator._effect_modifier_names) > 0: raise NotImplementedError("The current implementation does not support effect modifiers") if frac_strength_outcome == 1: frac_strength_outcome = frac_strength_treatment analyzer = LinearSensitivityAnalyzer( estimator=estimate.estimator, data=data, treatment_name=treatment_name, percent_change_estimate=percent_change_estimate, significance_level=significance_level, benchmark_common_causes=benchmark_common_causes, null_hypothesis_effect=null_hypothesis_effect, frac_strength_treatment=frac_strength_treatment, frac_strength_outcome=frac_strength_outcome, common_causes_order=estimate.estimator._observed_common_causes.columns, ) analyzer.check_sensitivity(plot=plot_estimate) return analyzer def sensitivity_non_parametric_partial_r2( estimate: CausalEstimate, kappa_t: Optional[Union[float, np.ndarray]] = None, kappa_y: Optional[Union[float, np.ndarray]] = None, frac_strength_treatment: float = 1.0, frac_strength_outcome: float = 1.0, benchmark_common_causes: Optional[List[str]] = None, plot_estimate: bool = True, alpha_s_estimator_list: Optional[List] = None, alpha_s_estimator_param_list: Optional[List[Dict]] = None, g_s_estimator_list: Optional[List] = None, g_s_estimator_param_list: Optional[List[Dict]] = None, plugin_reisz: bool = False, ) -> Union[PartialLinearSensitivityAnalyzer, NonParametricSensitivityAnalyzer]: """Add an unobserved confounder for refutation using Non-parametric partial R2 methond (Sensitivity Analysis for non-parametric models). :param estimate: CausalEstimate: Estimate to run the refutation :param kappa_t: float, numpy.ndarray: Partial R2 of the unobserved confounder wrt the treatment conditioned on the observed confounders. Only in the case of general non-parametric-partial-R2, it is the fraction of variance in the reisz representer that is explained by the unobserved confounder; specifically (1-r), where r is the ratio of variance of reisz representer, alpha^2, based on observed confounders and that based on all confounders. :param kappa_y: float, numpy.ndarray: Partial R2 of the unobserved confounder wrt the outcome conditioned on the treatment and observed confounders. :param frac_strength_treatment: float: This parameter decides the effect strength of the simulated confounder as a fraction of the effect strength of observed confounders on treatment. Defaults to 1. :param frac_strength_outcome: float: This parameter decides the effect strength of the simulated confounder as a fraction of the effect strength of observed confounders on outcome. Defaults to 1. :param benchmark_common_causes: names of variables for bounding strength of confounders. (relevant only for partial-r2 based simulation methods) :param plot_estimate: Generate contour plot for estimate while performing sensitivity analysis. (default = True). (relevant only for partial-r2 based simulation methods) :param alpha_s_estimator_list: list of estimator objects for estimating alpha_s. These objects should have fit() and predict() methods (relevant only for non-parametric-partial-R2 method) :param alpha_s_estimator_param_list: list of dictionaries with parameters for finding alpha_s. (relevant only for non-parametric-partial-R2 simulation method) :param g_s_estimator_list: list of estimator objects for finding g_s. These objects should have fit() and predict() functions implemented. (relevant only for non-parametric-partial-R2 simulation method) :param g_s_estimator_param_list: list of dictionaries with parameters for tuning respective estimators in "g_s_estimator_list". The order of the dictionaries in the list should be consistent with the estimator objects order in "g_s_estimator_list". (relevant only for non-parametric-partial-R2 simulation method) :plugin_reisz: bool: Flag on whether to use the plugin estimator or the nonparametric estimator for reisz representer function (alpha_s). """ # If the estimator used is LinearDML, partially linear sensitivity analysis will be automatically chosen if isinstance(estimate.estimator, dowhy.causal_estimators.econml.Econml): if estimate.estimator._econml_methodname == "econml.dml.LinearDML": analyzer = PartialLinearSensitivityAnalyzer( estimator=estimate._estimator_object, observed_common_causes=estimate.estimator._observed_common_causes, treatment=estimate.estimator._treatment, outcome=estimate.estimator._outcome, alpha_s_estimator_param_list=alpha_s_estimator_param_list, g_s_estimator_list=g_s_estimator_list, g_s_estimator_param_list=g_s_estimator_param_list, effect_strength_treatment=kappa_t, effect_strength_outcome=kappa_y, benchmark_common_causes=benchmark_common_causes, frac_strength_treatment=frac_strength_treatment, frac_strength_outcome=frac_strength_outcome, ) analyzer.check_sensitivity(plot=plot_estimate) return analyzer analyzer = NonParametricSensitivityAnalyzer( estimator=estimate.estimator, observed_common_causes=estimate.estimator._observed_common_causes, treatment=estimate.estimator._treatment, outcome=estimate.estimator._outcome, alpha_s_estimator_list=alpha_s_estimator_list, alpha_s_estimator_param_list=alpha_s_estimator_param_list, g_s_estimator_list=g_s_estimator_list, g_s_estimator_param_list=g_s_estimator_param_list, effect_strength_treatment=kappa_t, effect_strength_outcome=kappa_y, benchmark_common_causes=benchmark_common_causes, frac_strength_treatment=frac_strength_treatment, frac_strength_outcome=frac_strength_outcome, theta_s=estimate.value, plugin_reisz=plugin_reisz, ) analyzer.check_sensitivity(plot=plot_estimate) return analyzer def sensitivity_e_value( data: pd.DataFrame, target_estimand: IdentifiedEstimand, estimate: CausalEstimate, treatment_name: List[str], outcome_name: List[str], plot_estimate: bool = True, ) -> EValueSensitivityAnalyzer: if not isinstance(estimate.estimator, RegressionEstimator): raise NotImplementedError("E-Value sensitivity analysis is currently only implemented RegressionEstimator.") if len(estimate.estimator._effect_modifier_names) > 0: raise NotImplementedError("The current implementation does not support effect modifiers") analyzer = EValueSensitivityAnalyzer( estimate=estimate, estimand=target_estimand, data=data, treatment_name=treatment_name[0], outcome_name=outcome_name[0], ) analyzer.check_sensitivity(plot=plot_estimate) return analyzer def sensitivity_simulation( data: pd.DataFrame, target_estimand: IdentifiedEstimand, estimate: CausalEstimate, treatment_name: str, outcome_name: str, kappa_t: Optional[Union[float, np.ndarray]] = None, kappa_y: Optional[Union[float, np.ndarray]] = None, confounders_effect_on_treatment: str = "binary_flip", confounders_effect_on_outcome: str = "linear", frac_strength_treatment: float = 1.0, frac_strength_outcome: float = 1.0, plotmethod: Optional[str] = None, show_progress_bar=False, **_, ) -> CausalRefutation: """ This function attempts to add an unobserved common cause to the outcome and the treatment. At present, we have implemented the behavior for one dimensional behaviors for continuous and binary variables. This function can either take single valued inputs or a range of inputs. The function then looks at the data type of the input and then decides on the course of action. :param data: pd.DataFrame: Data to run the refutation :param target_estimand: IdentifiedEstimand: Identified estimand to run the refutation :param estimate: CausalEstimate: Estimate to run the refutation :param treatment_name: str: Name of the treatment :param outcome_name: str: Name of the outcome :param kappa_t: float, numpy.ndarray: Strength of the confounder's effect on treatment. When confounders_effect_on_treatment is linear, it is the regression coefficient. When the confounders_effect_on_treatment is binary flip, it is the probability with which effect of unobserved confounder can invert the value of the treatment. :param kappa_y: float, numpy.ndarray: Strength of the confounder's effect on outcome. Its interpretation depends on confounders_effect_on_outcome and the simulation_method. When simulation_method is direct-simulation, for a linear effect it behaves like the regression coefficient and for a binary flip, it is the probability with which it can invert the value of the outcome. :param confounders_effect_on_treatment: str : The type of effect on the treatment due to the unobserved confounder. Possible values are ['binary_flip', 'linear'] :param confounders_effect_on_outcome: str : The type of effect on the outcome due to the unobserved confounder. Possible values are ['binary_flip', 'linear'] :param frac_strength_treatment: float: This parameter decides the effect strength of the simulated confounder as a fraction of the effect strength of observed confounders on treatment. Defaults to 1. :param frac_strength_outcome: float: This parameter decides the effect strength of the simulated confounder as a fraction of the effect strength of observed confounders on outcome. Defaults to 1. :param plotmethod: string: Type of plot to be shown. If None, no plot is generated. This parameter is used only only when more than one treatment confounder effect values or outcome confounder effect values are provided. Default is "colormesh". Supported values are "contour", "colormesh" when more than one value is provided for both confounder effect value parameters; "line" when provided for only one of them. :return: CausalRefuter: An object that contains the estimated effect and a new effect and the name of the refutation used. """ if kappa_t is None: kappa_t = _infer_default_kappa_t( data, target_estimand, treatment_name, confounders_effect_on_treatment, frac_strength_treatment ) if kappa_y is None: kappa_y = _infer_default_kappa_y( data, target_estimand, outcome_name, confounders_effect_on_outcome, frac_strength_outcome ) if not isinstance(kappa_t, (list, np.ndarray)) and not isinstance( kappa_y, (list, np.ndarray) ): # Deal with single value inputs new_data = copy.deepcopy(data) new_data = _include_confounders_effect( data, new_data, confounders_effect_on_treatment, treatment_name, kappa_t, confounders_effect_on_outcome, outcome_name, kappa_y, ) new_estimator = CausalEstimator.get_estimator_object(new_data, target_estimand, estimate) new_effect = new_estimator.estimate_effect() refute = CausalRefutation( estimate.value, new_effect.value, refutation_type="Refute: Add an Unobserved Common Cause" ) refute.new_effect_array = np.array(new_effect.value) refute.new_effect = new_effect.value return refute else: # Deal with multiple value inputs if isinstance(kappa_t, (list, np.ndarray)) and isinstance( kappa_y, (list, np.ndarray) ): # Deal with range inputs # Get a 2D matrix of values # x,y = np.meshgrid(self.kappa_t, self.kappa_y) # x,y are both MxN results_matrix = np.random.rand(len(kappa_t), len(kappa_y)) # Matrix to hold all the results of NxM orig_data = copy.deepcopy(data) for i in tqdm( range(len(kappa_t)), colour=CausalRefuter.PROGRESS_BAR_COLOR, disable=not show_progress_bar, desc="Refuting Estimates: ", ): for j in range(len(kappa_y)): new_data = _include_confounders_effect( data, orig_data, confounders_effect_on_treatment, treatment_name, kappa_t[i], confounders_effect_on_outcome, outcome_name, kappa_y[j], ) new_estimator = CausalEstimator.get_estimator_object(new_data, target_estimand, estimate) new_effect = new_estimator.estimate_effect() refute = CausalRefutation( estimate.value, new_effect.value, refutation_type="Refute: Add an Unobserved Common Cause", ) results_matrix[i][j] = refute.new_effect # Populate the results refute.new_effect_array = results_matrix refute.new_effect = (np.min(results_matrix), np.max(results_matrix)) # Store the values into the refute object if plotmethod is None: return refute import matplotlib import matplotlib.pyplot as plt fig = plt.figure(figsize=(6, 5)) left, bottom, width, height = 0.1, 0.1, 0.8, 0.8 ax = fig.add_axes([left, bottom, width, height]) oe = estimate.value contour_levels = [oe / 4.0, oe / 2.0, (3.0 / 4) * oe, oe] contour_levels.extend([0, np.min(results_matrix), np.max(results_matrix)]) if plotmethod == "contour": cp = plt.contourf(kappa_y, kappa_t, results_matrix, levels=sorted(contour_levels)) # Adding a label on the contour line for the original estimate fmt = {} trueeffect_index = np.where(cp.levels == oe)[0][0] fmt[cp.levels[trueeffect_index]] = "Estimated Effect" # Label every other level using strings plt.clabel(cp, [cp.levels[trueeffect_index]], inline=True, fmt=fmt) plt.colorbar(cp) elif plotmethod == "colormesh": cp = plt.pcolormesh(kappa_y, kappa_t, results_matrix, shading="nearest") plt.colorbar(cp, ticks=contour_levels) ax.yaxis.set_ticks(kappa_t) ax.xaxis.set_ticks(kappa_y) plt.xticks(rotation=45) ax.set_title("Effect of Unobserved Common Cause") ax.set_ylabel("Value of Linear Constant on Treatment") ax.set_xlabel("Value of Linear Constant on Outcome") plt.show() return refute elif isinstance(kappa_t, (list, np.ndarray)): outcomes = np.random.rand(len(kappa_t)) orig_data = copy.deepcopy(data) for i in tqdm( range(0, len(kappa_t)), colour=CausalRefuter.PROGRESS_BAR_COLOR, disable=not show_progress_bar, desc="Refuting Estimates: ", ): new_data = _include_confounders_effect( data, orig_data, confounders_effect_on_treatment, treatment_name, kappa_t[i], confounders_effect_on_outcome, outcome_name, kappa_y, ) new_estimator = CausalEstimator.get_estimator_object(new_data, target_estimand, estimate) new_effect = new_estimator.estimate_effect() refute = CausalRefutation( estimate.value, new_effect.value, refutation_type="Refute: Add an Unobserved Common Cause" ) logger.debug(refute) outcomes[i] = refute.new_effect # Populate the results refute.new_effect_array = outcomes refute.new_effect = (np.min(outcomes), np.max(outcomes)) if plotmethod is None: return refute import matplotlib import matplotlib.pyplot as plt fig = plt.figure(figsize=(6, 5)) left, bottom, width, height = 0.1, 0.1, 0.8, 0.8 ax = fig.add_axes([left, bottom, width, height]) plt.plot(kappa_t, outcomes) plt.axhline(estimate.value, linestyle="--", color="gray") ax.set_title("Effect of Unobserved Common Cause") ax.set_xlabel("Value of Linear Constant on Treatment") ax.set_ylabel("Estimated Effect after adding the common cause") plt.show() return refute elif isinstance(kappa_y, (list, np.ndarray)): outcomes = np.random.rand(len(kappa_y)) orig_data = copy.deepcopy(data) for i in tqdm( range(0, len(kappa_y)), colour=CausalRefuter.PROGRESS_BAR_COLOR, disable=not show_progress_bar, desc="Refuting Estimates: ", ): new_data = _include_confounders_effect( data, orig_data, confounders_effect_on_treatment, treatment_name, kappa_t, confounders_effect_on_outcome, outcome_name, kappa_y[i], ) new_estimator = CausalEstimator.get_estimator_object(new_data, target_estimand, estimate) new_effect = new_estimator.estimate_effect() refute = CausalRefutation( estimate.value, new_effect.value, refutation_type="Refute: Add an Unobserved Common Cause" ) logger.debug(refute) outcomes[i] = refute.new_effect # Populate the results refute.new_effect_array = outcomes refute.new_effect = (np.min(outcomes), np.max(outcomes)) if plotmethod is None: return refute import matplotlib import matplotlib.pyplot as plt fig = plt.figure(figsize=(6, 5)) left, bottom, width, height = 0.1, 0.1, 0.8, 0.8 ax = fig.add_axes([left, bottom, width, height]) plt.plot(kappa_y, outcomes) plt.axhline(estimate.value, linestyle="--", color="gray") ax.set_title("Effect of Unobserved Common Cause") ax.set_xlabel("Value of Linear Constant on Outcome") ax.set_ylabel("Estimated Effect after adding the common cause") plt.show() return refute

andresmor-ms

133e7b9a4ed32aae8ab5f39a01eb02b3a4d1c0ba

e1652ec3c6606b1bb2dfe91ef830e4b4b566712d

with the functional API, is there a way to ensure that any future refuter functions follow the same basic signature? E.g., all refute functions should have a data, target_estimand and estimate? I'm thinking of making it easier to for new contributors to know the basic protocol that they need to adhere to. something like `def refute_*(data, target_estimand, estimate, *args, **kwargs)`

amit-sharma

py-why/dowhy

Functional api/refute estimate

* Refactor refuters into functions * Rename functional_api notebook for clarity * Add return types to identify_estimate * Update `__init__.py` for imports * Add joblib for bootstrap refuter * Create `refute_estimate` function * Add types for refuter parameters & return types

2022-10-04 16:18:49+00:00

2022-10-07 04:30:22+00:00

dowhy/causal_refuters/add_unobserved_common_cause.py

import copy import logging import math import numpy as np import pandas as pd import scipy.stats import statsmodels.api as sm from sklearn.linear_model import LogisticRegression from sklearn.preprocessing import StandardScaler from tqdm.auto import tqdm import dowhy.causal_estimators.econml from dowhy.causal_estimator import CausalEstimator from dowhy.causal_estimators.linear_regression_estimator import LinearRegressionEstimator from dowhy.causal_estimators.regression_estimator import RegressionEstimator from dowhy.causal_refuter import CausalRefutation, CausalRefuter from dowhy.causal_refuters.evalue_sensitivity_analyzer import EValueSensitivityAnalyzer from dowhy.causal_refuters.linear_sensitivity_analyzer import LinearSensitivityAnalyzer from dowhy.causal_refuters.non_parametric_sensitivity_analyzer import NonParametricSensitivityAnalyzer from dowhy.causal_refuters.partial_linear_sensitivity_analyzer import PartialLinearSensitivityAnalyzer class AddUnobservedCommonCause(CausalRefuter): """Add an unobserved confounder for refutation. AddUnobservedCommonCause class supports three methods: 1) Simulation of an unobserved confounder 2) Linear partial R2 : Sensitivity Analysis for linear models. 3) Non-Parametric partial R2 based : Sensitivity Analyis for non-parametric models. Supports additional parameters that can be specified in the refute_estimate() method. """ def __init__(self, *args, **kwargs): """ Initialize the parameters required for the refuter. For direct_simulation, if effect_strength_on_treatment or effect_strength_on_outcome is not given, it is calculated automatically as a range between the minimum and maximum effect strength of observed confounders on treatment and outcome respectively. :param simulation_method: The method to use for simulating effect of unobserved confounder. Possible values are ["direct-simulation", "linear-partial-R2", "non-parametric-partial-R2", "e-value"]. :param confounders_effect_on_treatment: str : The type of effect on the treatment due to the unobserved confounder. Possible values are ['binary_flip', 'linear'] :param confounders_effect_on_outcome: str : The type of effect on the outcome due to the unobserved confounder. Possible values are ['binary_flip', 'linear'] :param effect_strength_on_treatment: float, numpy.ndarray: [Used when simulation_method="direct-simulation"] Strength of the confounder's effect on treatment. When confounders_effect_on_treatment is linear, it is the regression coefficient. When the confounders_effect_on_treatment is binary flip, it is the probability with which effect of unobserved confounder can invert the value of the treatment. :param effect_strength_on_outcome: float, numpy.ndarray: Strength of the confounder's effect on outcome. Its interpretation depends on confounders_effect_on_outcome and the simulation_method. When simulation_method is direct-simulation, for a linear effect it behaves like the regression coefficient and for a binary flip, it is the probability with which it can invert the value of the outcome. :param partial_r2_confounder_treatment: float, numpy.ndarray: [Used when simulation_method is linear-partial-R2 or non-parametric-partial-R2] Partial R2 of the unobserved confounder wrt the treatment conditioned on the observed confounders. Only in the case of general non-parametric-partial-R2, it is the fraction of variance in the reisz representer that is explained by the unobserved confounder; specifically (1-r), where r is the ratio of variance of reisz representer, alpha^2, based on observed confounders and that based on all confounders. :param partial_r2_confounder_outcome: float, numpy.ndarray: [Used when simulation_method is linear-partial-R2 or non-parametric-partial-R2] Partial R2 of the unobserved confounder wrt the outcome conditioned on the treatment and observed confounders. :param frac_strength_treatment: float: This parameter decides the effect strength of the simulated confounder as a fraction of the effect strength of observed confounders on treatment. Defaults to 1. :param frac_strength_outcome: float: This parameter decides the effect strength of the simulated confounder as a fraction of the effect strength of observed confounders on outcome. Defaults to 1. :param plotmethod: string: Type of plot to be shown. If None, no plot is generated. This parameter is used only only when more than one treatment confounder effect values or outcome confounder effect values are provided. Default is "colormesh". Supported values are "contour", "colormesh" when more than one value is provided for both confounder effect value parameters; "line" when provided for only one of them. :param percent_change_estimate: It is the percentage of reduction of treatment estimate that could alter the results (default = 1). if percent_change_estimate = 1, the robustness value describes the strength of association of confounders with treatment and outcome in order to reduce the estimate by 100% i.e bring it down to 0. (relevant only for Linear Sensitivity Analysis, ignore for rest) :param confounder_increases_estimate: True implies that confounder increases the absolute value of estimate and vice versa. (Default = False). (relevant only for Linear Sensitivity Analysis, ignore for rest) :param benchmark_common_causes: names of variables for bounding strength of confounders. (relevant only for partial-r2 based simulation methods) :param significance_level: confidence interval for statistical inference(default = 0.05). (relevant only for partial-r2 based simulation methods) :param null_hypothesis_effect: assumed effect under the null hypothesis. (relevant only for linear-partial-R2, ignore for rest) :param plot_estimate: Generate contour plot for estimate while performing sensitivity analysis. (default = True). (relevant only for partial-r2 based simulation methods) :param num_splits: number of splits for cross validation. (default = 5). (relevant only for non-parametric-partial-R2 simulation method) :param shuffle_data : shuffle data or not before splitting into folds (default = False). (relevant only for non-parametric-partial-R2 simulation method) :param shuffle_random_seed: seed for randomly shuffling data. (relevant only for non-parametric-partial-R2 simulation method) :param alpha_s_estimator_param_list: list of dictionaries with parameters for finding alpha_s. (relevant only for non-parametric-partial-R2 simulation method) :param g_s_estimator_list: list of estimator objects for finding g_s. These objects should have fit() and predict() functions implemented. (relevant only for non-parametric-partial-R2 simulation method) :param g_s_estimator_param_list: list of dictionaries with parameters for tuning respective estimators in "g_s_estimator_list". The order of the dictionaries in the list should be consistent with the estimator objects order in "g_s_estimator_list". (relevant only for non-parametric-partial-R2 simulation method) """ super().__init__(*args, **kwargs) self.simulation_method = kwargs["simulation_method"] if "simulation_method" in kwargs else "direct-simulation" self.effect_on_t = ( kwargs["confounders_effect_on_treatment"] if "confounders_effect_on_treatment" in kwargs else "binary_flip" ) self.effect_on_y = ( kwargs["confounders_effect_on_outcome"] if "confounders_effect_on_outcome" in kwargs else "linear" ) if self.simulation_method == "direct-simulation": self.kappa_t = kwargs["effect_strength_on_treatment"] if "effect_strength_on_treatment" in kwargs else None self.kappa_y = kwargs["effect_strength_on_outcome"] if "effect_strength_on_outcome" in kwargs else None elif self.simulation_method in ["linear-partial-R2", "non-parametric-partial-R2"]: self.kappa_t = ( kwargs["partial_r2_confounder_treatment"] if "partial_r2_confounder_treatment" in kwargs else None ) self.kappa_y = ( kwargs["partial_r2_confounder_outcome"] if "partial_r2_confounder_outcome" in kwargs else None ) elif self.simulation_method == "e-value": pass else: raise ValueError( "simulation method is not supported. Try direct-simulation, linear-partial-R2, non-parametric-partial-R2, or e-value" ) self.frac_strength_treatment = ( kwargs["effect_fraction_on_treatment"] if "effect_fraction_on_treatment" in kwargs else 1 ) self.frac_strength_outcome = ( kwargs["effect_fraction_on_outcome"] if "effect_fraction_on_outcome" in kwargs else 1 ) self.plotmethod = kwargs["plotmethod"] if "plotmethod" in kwargs else "colormesh" self.percent_change_estimate = kwargs["percent_change_estimate"] if "percent_change_estimate" in kwargs else 1.0 self.significance_level = kwargs["significance_level"] if "significance_level" in kwargs else 0.05 self.confounder_increases_estimate = ( kwargs["confounder_increases_estimate"] if "confounder_increases_estimate" in kwargs else False ) self.benchmark_common_causes = ( kwargs["benchmark_common_causes"] if "benchmark_common_causes" in kwargs else None ) self.null_hypothesis_effect = kwargs["null_hypothesis_effect"] if "null_hypothesis_effect" in kwargs else 0 self.plot_estimate = kwargs["plot_estimate"] if "plot_estimate" in kwargs else True self.num_splits = kwargs["num_splits"] if "num_splits" in kwargs else 5 self.shuffle_data = kwargs["shuffle_data"] if "shuffle_data" in kwargs else False self.shuffle_random_seed = kwargs["shuffle_random_seed"] if "shuffle_random_seed" in kwargs else None self.alpha_s_estimator_param_list = ( kwargs["alpha_s_estimator_param_list"] if "alpha_s_estimator_param_list" in kwargs else None ) self.alpha_s_estimator_list = kwargs["alpha_s_estimator_list"] if "alpha_s_estimator_list" in kwargs else None self.g_s_estimator_list = kwargs["g_s_estimator_list"] if "g_s_estimator_list" in kwargs else None self.g_s_estimator_param_list = ( kwargs["g_s_estimator_param_list"] if "g_s_estimator_param_list" in kwargs else None ) self.plugin_reisz = kwargs["plugin_reisz"] if "plugin_reisz" in kwargs else False self.logger = logging.getLogger(__name__) def infer_default_kappa_t(self, len_kappa_t=10): """Infer default effect strength of simulated confounder on treatment.""" observed_common_causes_names = self._target_estimand.get_backdoor_variables() if len(observed_common_causes_names) > 0: observed_common_causes = self._data[observed_common_causes_names] observed_common_causes = pd.get_dummies(observed_common_causes, drop_first=True) else: raise ValueError( "There needs to be at least one common cause to" + "automatically compute the default value of kappa_t." + " Provide a value for kappa_t" ) t = self._data[self._treatment_name] # Standardizing the data observed_common_causes = StandardScaler().fit_transform(observed_common_causes) if self.effect_on_t == "binary_flip": # Fit a model containing all confounders and compare predictions # using all features compared to all features except a given # confounder. tmodel = LogisticRegression().fit(observed_common_causes, t) tpred = tmodel.predict(observed_common_causes).astype(int) flips = [] for i in range(observed_common_causes.shape[1]): oldval = np.copy(observed_common_causes[:, i]) observed_common_causes[:, i] = 0 tcap = tmodel.predict(observed_common_causes).astype(int) observed_common_causes[:, i] = oldval flips.append(np.sum(abs(tcap - tpred)) / tpred.shape[0]) min_coeff, max_coeff = min(flips), max(flips) elif self.effect_on_t == "linear": # Estimating the regression coefficient from standardized features to t corrcoef_var_t = np.corrcoef(observed_common_causes, t, rowvar=False)[-1, :-1] std_dev_t = np.std(t)[0] max_coeff = max(corrcoef_var_t) * std_dev_t min_coeff = min(corrcoef_var_t) * std_dev_t else: raise NotImplementedError( "'" + self.effect_on_t + "' method not supported for confounders' effect on treatment" ) min_coeff, max_coeff = self._compute_min_max_coeff(min_coeff, max_coeff, self.frac_strength_treatment) # By default, return a plot with 10 points # consider 10 values of the effect of the unobserved confounder step = (max_coeff - min_coeff) / len_kappa_t self.logger.info("(Min, Max) kappa_t for observed common causes, ({0}, {1})".format(min_coeff, max_coeff)) if np.equal(max_coeff, min_coeff): return max_coeff else: return np.arange(min_coeff, max_coeff, step) def _compute_min_max_coeff(self, min_coeff, max_coeff, effect_strength_fraction): max_coeff = effect_strength_fraction * max_coeff min_coeff = effect_strength_fraction * min_coeff return min_coeff, max_coeff def infer_default_kappa_y(self, len_kappa_y=10): """Infer default effect strength of simulated confounder on treatment.""" observed_common_causes_names = self._target_estimand.get_backdoor_variables() if len(observed_common_causes_names) > 0: observed_common_causes = self._data[observed_common_causes_names] observed_common_causes = pd.get_dummies(observed_common_causes, drop_first=True) else: raise ValueError( "There needs to be at least one common cause to" + "automatically compute the default value of kappa_y." + " Provide a value for kappa_y" ) y = self._data[self._outcome_name] # Standardizing the data observed_common_causes = StandardScaler().fit_transform(observed_common_causes) if self.effect_on_y == "binary_flip": # Fit a model containing all confounders and compare predictions # using all features compared to all features except a given # confounder. ymodel = LogisticRegression().fit(observed_common_causes, y) ypred = ymodel.predict(observed_common_causes).astype(int) flips = [] for i in range(observed_common_causes.shape[1]): oldval = np.copy(observed_common_causes[:, i]) observed_common_causes[:, i] = 0 ycap = ymodel.predict(observed_common_causes).astype(int) observed_common_causes[:, i] = oldval flips.append(np.sum(abs(ycap - ypred)) / ypred.shape[0]) min_coeff, max_coeff = min(flips), max(flips) elif self.effect_on_y == "linear": corrcoef_var_y = np.corrcoef(observed_common_causes, y, rowvar=False)[-1, :-1] std_dev_y = np.std(y)[0] max_coeff = max(corrcoef_var_y) * std_dev_y min_coeff = min(corrcoef_var_y) * std_dev_y else: raise NotImplementedError( "'" + self.effect_on_y + "' method not supported for confounders' effect on outcome" ) min_coeff, max_coeff = self._compute_min_max_coeff(min_coeff, max_coeff, self.frac_strength_outcome) # By default, return a plot with 10 points # consider 10 values of the effect of the unobserved confounder step = (max_coeff - min_coeff) / len_kappa_y self.logger.info("(Min, Max) kappa_y for observed common causes, ({0}, {1})".format(min_coeff, max_coeff)) if np.equal(max_coeff, min_coeff): return max_coeff else: return np.arange(min_coeff, max_coeff, step) def refute_estimate(self, show_progress_bar=False): """ This function attempts to add an unobserved common cause to the outcome and the treatment. At present, we have implemented the behavior for one dimensional behaviors for continuous and binary variables. This function can either take single valued inputs or a range of inputs. The function then looks at the data type of the input and then decides on the course of action. :return: CausalRefuter: An object that contains the estimated effect and a new effect and the name of the refutation used. """ if self.simulation_method == "linear-partial-R2": if not (isinstance(self._estimate.estimator, LinearRegressionEstimator)): raise NotImplementedError( "Currently only LinearRegressionEstimator is supported for Sensitivity Analysis" ) if len(self._estimate.estimator._effect_modifier_names) > 0: raise NotImplementedError("The current implementation does not support effect modifiers") if self.frac_strength_outcome == 1: self.frac_strength_outcome = self.frac_strength_treatment analyzer = LinearSensitivityAnalyzer( estimator=self._estimate.estimator, data=self._data, treatment_name=self._treatment_name, percent_change_estimate=self.percent_change_estimate, significance_level=self.significance_level, benchmark_common_causes=self.benchmark_common_causes, null_hypothesis_effect=self.null_hypothesis_effect, frac_strength_treatment=self.frac_strength_treatment, frac_strength_outcome=self.frac_strength_outcome, common_causes_order=self._estimate.estimator._observed_common_causes.columns, ) analyzer.check_sensitivity(plot=self.plot_estimate) return analyzer if self.simulation_method == "non-parametric-partial-R2": # If the estimator used is LinearDML, partially linear sensitivity analysis will be automatically chosen if isinstance(self._estimate.estimator, dowhy.causal_estimators.econml.Econml): if self._estimate.estimator._econml_methodname == "econml.dml.LinearDML": analyzer = PartialLinearSensitivityAnalyzer( estimator=self._estimate._estimator_object, observed_common_causes=self._estimate.estimator._observed_common_causes, treatment=self._estimate.estimator._treatment, outcome=self._estimate.estimator._outcome, alpha_s_estimator_param_list=self.alpha_s_estimator_param_list, g_s_estimator_list=self.g_s_estimator_list, g_s_estimator_param_list=self.g_s_estimator_param_list, effect_strength_treatment=self.kappa_t, effect_strength_outcome=self.kappa_y, benchmark_common_causes=self.benchmark_common_causes, frac_strength_treatment=self.frac_strength_treatment, frac_strength_outcome=self.frac_strength_outcome, ) analyzer.check_sensitivity(plot=self.plot_estimate) return analyzer analyzer = NonParametricSensitivityAnalyzer( estimator=self._estimate.estimator, observed_common_causes=self._estimate.estimator._observed_common_causes, treatment=self._estimate.estimator._treatment, outcome=self._estimate.estimator._outcome, alpha_s_estimator_list=self.alpha_s_estimator_list, alpha_s_estimator_param_list=self.alpha_s_estimator_param_list, g_s_estimator_list=self.g_s_estimator_list, g_s_estimator_param_list=self.g_s_estimator_param_list, effect_strength_treatment=self.kappa_t, effect_strength_outcome=self.kappa_y, benchmark_common_causes=self.benchmark_common_causes, frac_strength_treatment=self.frac_strength_treatment, frac_strength_outcome=self.frac_strength_outcome, theta_s=self._estimate.value, plugin_reisz=self.plugin_reisz, ) analyzer.check_sensitivity(plot=self.plot_estimate) return analyzer if self.simulation_method == "e-value": if not isinstance(self._estimate.estimator, RegressionEstimator): raise NotImplementedError( "E-Value sensitivity analysis is currently only implemented RegressionEstimator." ) if len(self._estimate.estimator._effect_modifier_names) > 0: raise NotImplementedError("The current implementation does not support effect modifiers") analyzer = EValueSensitivityAnalyzer( estimate=self._estimate, estimand=self._target_estimand, data=self._data, treatment_name=self._treatment_name[0], outcome_name=self._outcome_name[0], ) analyzer.check_sensitivity(plot=self.plot_estimate) return analyzer if self.kappa_t is None: self.kappa_t = self.infer_default_kappa_t() if self.kappa_y is None: self.kappa_y = self.infer_default_kappa_y() if not isinstance(self.kappa_t, (list, np.ndarray)) and not isinstance( self.kappa_y, (list, np.ndarray) ): # Deal with single value inputs new_data = copy.deepcopy(self._data) new_data = self.include_confounders_effect(new_data, self.kappa_t, self.kappa_y) new_estimator = CausalEstimator.get_estimator_object(new_data, self._target_estimand, self._estimate) new_effect = new_estimator.estimate_effect() refute = CausalRefutation( self._estimate.value, new_effect.value, refutation_type="Refute: Add an Unobserved Common Cause" ) refute.new_effect_array = np.array(new_effect.value) refute.new_effect = new_effect.value refute.add_refuter(self) return refute else: # Deal with multiple value inputs if isinstance(self.kappa_t, (list, np.ndarray)) and isinstance( self.kappa_y, (list, np.ndarray) ): # Deal with range inputs # Get a 2D matrix of values # x,y = np.meshgrid(self.kappa_t, self.kappa_y) # x,y are both MxN results_matrix = np.random.rand( len(self.kappa_t), len(self.kappa_y) ) # Matrix to hold all the results of NxM orig_data = copy.deepcopy(self._data) for i in tqdm( range(len(self.kappa_t)), colour=CausalRefuter.PROGRESS_BAR_COLOR, disable=not show_progress_bar, desc="Refuting Estimates: ", ): for j in range(len(self.kappa_y)): new_data = self.include_confounders_effect(orig_data, self.kappa_t[i], self.kappa_y[j]) new_estimator = CausalEstimator.get_estimator_object( new_data, self._target_estimand, self._estimate ) new_effect = new_estimator.estimate_effect() refute = CausalRefutation( self._estimate.value, new_effect.value, refutation_type="Refute: Add an Unobserved Common Cause", ) results_matrix[i][j] = refute.new_effect # Populate the results refute.new_effect_array = results_matrix refute.new_effect = (np.min(results_matrix), np.max(results_matrix)) # Store the values into the refute object refute.add_refuter(self) if self.plotmethod is None: return refute import matplotlib import matplotlib.pyplot as plt fig = plt.figure(figsize=(6, 5)) left, bottom, width, height = 0.1, 0.1, 0.8, 0.8 ax = fig.add_axes([left, bottom, width, height]) oe = self._estimate.value contour_levels = [oe / 4.0, oe / 2.0, (3.0 / 4) * oe, oe] contour_levels.extend([0, np.min(results_matrix), np.max(results_matrix)]) if self.plotmethod == "contour": cp = plt.contourf(self.kappa_y, self.kappa_t, results_matrix, levels=sorted(contour_levels)) # Adding a label on the contour line for the original estimate fmt = {} trueeffect_index = np.where(cp.levels == oe)[0][0] fmt[cp.levels[trueeffect_index]] = "Estimated Effect" # Label every other level using strings plt.clabel(cp, [cp.levels[trueeffect_index]], inline=True, fmt=fmt) plt.colorbar(cp) elif self.plotmethod == "colormesh": cp = plt.pcolormesh(self.kappa_y, self.kappa_t, results_matrix, shading="nearest") plt.colorbar(cp, ticks=contour_levels) ax.yaxis.set_ticks(self.kappa_t) ax.xaxis.set_ticks(self.kappa_y) plt.xticks(rotation=45) ax.set_title("Effect of Unobserved Common Cause") ax.set_ylabel("Value of Linear Constant on Treatment") ax.set_xlabel("Value of Linear Constant on Outcome") plt.show() return refute elif isinstance(self.kappa_t, (list, np.ndarray)): outcomes = np.random.rand(len(self.kappa_t)) orig_data = copy.deepcopy(self._data) for i in tqdm( range(0, len(self.kappa_t)), colour=CausalRefuter.PROGRESS_BAR_COLOR, disable=not show_progress_bar, desc="Refuting Estimates: ", ): new_data = self.include_confounders_effect(orig_data, self.kappa_t[i], self.kappa_y) new_estimator = CausalEstimator.get_estimator_object( new_data, self._target_estimand, self._estimate ) new_effect = new_estimator.estimate_effect() refute = CausalRefutation( self._estimate.value, new_effect.value, refutation_type="Refute: Add an Unobserved Common Cause" ) self.logger.debug(refute) outcomes[i] = refute.new_effect # Populate the results refute.new_effect_array = outcomes refute.new_effect = (np.min(outcomes), np.max(outcomes)) refute.add_refuter(self) if self.plotmethod is None: return refute import matplotlib import matplotlib.pyplot as plt fig = plt.figure(figsize=(6, 5)) left, bottom, width, height = 0.1, 0.1, 0.8, 0.8 ax = fig.add_axes([left, bottom, width, height]) plt.plot(self.kappa_t, outcomes) plt.axhline(self._estimate.value, linestyle="--", color="gray") ax.set_title("Effect of Unobserved Common Cause") ax.set_xlabel("Value of Linear Constant on Treatment") ax.set_ylabel("Estimated Effect after adding the common cause") plt.show() return refute elif isinstance(self.kappa_y, (list, np.ndarray)): outcomes = np.random.rand(len(self.kappa_y)) orig_data = copy.deepcopy(self._data) for i in tqdm( range(0, len(self.kappa_y)), colour=CausalRefuter.PROGRESS_BAR_COLOR, disable=not show_progress_bar, desc="Refuting Estimates: ", ): new_data = self.include_confounders_effect(orig_data, self.kappa_t, self.kappa_y[i]) new_estimator = CausalEstimator.get_estimator_object( new_data, self._target_estimand, self._estimate ) new_effect = new_estimator.estimate_effect() refute = CausalRefutation( self._estimate.value, new_effect.value, refutation_type="Refute: Add an Unobserved Common Cause" ) self.logger.debug(refute) outcomes[i] = refute.new_effect # Populate the results refute.new_effect_array = outcomes refute.new_effect = (np.min(outcomes), np.max(outcomes)) refute.add_refuter(self) if self.plotmethod is None: return refute import matplotlib import matplotlib.pyplot as plt fig = plt.figure(figsize=(6, 5)) left, bottom, width, height = 0.1, 0.1, 0.8, 0.8 ax = fig.add_axes([left, bottom, width, height]) plt.plot(self.kappa_y, outcomes) plt.axhline(self._estimate.value, linestyle="--", color="gray") ax.set_title("Effect of Unobserved Common Cause") ax.set_xlabel("Value of Linear Constant on Outcome") ax.set_ylabel("Estimated Effect after adding the common cause") plt.show() return refute def include_confounders_effect(self, new_data, kappa_t, kappa_y): """ This function deals with the change in the value of the data due to the effect of the unobserved confounder. In the case of a binary flip, we flip only if the random number is greater than the threshold set. In the case of a linear effect, we use the variable as the linear regression constant. :param new_data: pandas.DataFrame: The data to be changed due to the effects of the unobserved confounder. :param kappa_t: numpy.float64: The value of the threshold for binary_flip or the value of the regression coefficient for linear effect. :param kappa_y: numpy.float64: The value of the threshold for binary_flip or the value of the regression coefficient for linear effect. :return: pandas.DataFrame: The DataFrame that includes the effects of the unobserved confounder. """ num_rows = self._data.shape[0] stdnorm = scipy.stats.norm() w_random = stdnorm.rvs(num_rows) if self.effect_on_t == "binary_flip": alpha = 2 * kappa_t - 1 if kappa_t >= 0.5 else 1 - 2 * kappa_t interval = stdnorm.interval(alpha) rel_interval = interval[0] if kappa_t >= 0.5 else interval[1] new_data.loc[rel_interval <= w_random, self._treatment_name] = ( 1 - new_data.loc[rel_interval <= w_random, self._treatment_name] ) for tname in self._treatment_name: if pd.api.types.is_bool_dtype(self._data[tname]): new_data = new_data.astype({tname: "bool"}, copy=False) elif self.effect_on_t == "linear": confounder_t_effect = kappa_t * w_random # By default, we add the effect of simulated confounder for treatment. # But subtract it from outcome to create a negative correlation # assuming that the original confounder's effect was positive on both. # This is to remove the effect of the original confounder. new_data[self._treatment_name] = new_data[self._treatment_name].values + np.ndarray( shape=(num_rows, 1), buffer=confounder_t_effect ) else: raise NotImplementedError( "'" + self.effect_on_t + "' method not supported for confounders' effect on treatment" ) if self.effect_on_y == "binary_flip": alpha = 2 * kappa_y - 1 if kappa_y >= 0.5 else 1 - 2 * kappa_y interval = stdnorm.interval(alpha) rel_interval = interval[0] if kappa_y >= 0.5 else interval[1] new_data.loc[rel_interval <= w_random, self._outcome_name] = ( 1 - new_data.loc[rel_interval <= w_random, self._outcome_name] ) for yname in self._outcome_name: if pd.api.types.is_bool_dtype(self._data[yname]): new_data = new_data.astype({yname: "bool"}, copy=False) elif self.effect_on_y == "linear": confounder_y_effect = (-1) * kappa_y * w_random # By default, we add the effect of simulated confounder for treatment. # But subtract it from outcome to create a negative correlation # assuming that the original confounder's effect was positive on both. # This is to remove the effect of the original confounder. new_data[self._outcome_name] = new_data[self._outcome_name].values + np.ndarray( shape=(num_rows, 1), buffer=confounder_y_effect ) else: raise NotImplementedError( "'" + self.effect_on_y + "' method not supported for confounders' effect on outcome" ) return new_data def include_simulated_confounder(self, convergence_threshold=0.1, c_star_max=1000): """ This function simulates an unobserved confounder based on the data using the following steps: 1. It calculates the "residuals" from the treatment and outcome model i.) The outcome model has outcome as the dependent variable and all the observed variables including treatment as independent variables ii.) The treatment model has treatment as the dependent variable and all the observed variables as independent variables. 2. U is an intermediate random variable drawn from the normal distribution with the weighted average of residuals as mean and a unit variance U ~ N(c1*d_y + c2*d_t, 1) where *d_y and d_t are residuals from the treatment and outcome model *c1 and c2 are coefficients to the residuals 3. The final U, which is the simulated unobserved confounder is obtained by debiasing the intermediate variable U by residualising it with X Choosing the coefficients c1 and c2: The coefficients are chosen based on these basic assumptions: 1. There is a hyperbolic relationship satisfying c1*c2 = c_star 2. c_star is chosen from a range of possible values based on the correlation of the obtained simulated variable with outcome and treatment. 3. The product of correlations with treatment and outcome should be at a minimum distance to the maximum correlations with treatment and outcome in any of the observed confounders 4. The ratio of the weights should be such that they maintain the ratio of the maximum possible observed coefficients within some confidence interval :param c_star_max: The maximum possible value for the hyperbolic curve on which the coefficients to the residuals lie. It defaults to 1000 in the code if not specified by the user. :type int :param convergence_threshold: The threshold to check the plateauing of the correlation while selecting a c_star. It defaults to 0.1 in the code if not specified by the user :type float :returns: The simulated values of the unobserved confounder based on the data :type pandas.core.series.Series """ # Obtaining the list of observed variables required_variables = True observed_variables = self.choose_variables(required_variables) observed_variables_with_treatment_and_outcome = observed_variables + self._treatment_name + self._outcome_name # Taking a subset of the dataframe that has only observed variables self._data = self._data[observed_variables_with_treatment_and_outcome] # Residuals from the outcome model obtained by fitting a linear model y = self._data[self._outcome_name[0]] observed_variables_with_treatment = observed_variables + self._treatment_name X = self._data[observed_variables_with_treatment] model = sm.OLS(y, X.astype("float")) results = model.fit() residuals_y = y - results.fittedvalues d_y = list(pd.Series(residuals_y)) # Residuals from the treatment model obtained by fitting a linear model t = self._data[self._treatment_name[0]].astype("int64") X = self._data[observed_variables] model = sm.OLS(t, X) results = model.fit() residuals_t = t - results.fittedvalues d_t = list(pd.Series(residuals_t)) # Initialising product_cor_metric_observed with a really low value as finding maximum product_cor_metric_observed = -10000000000 for i in observed_variables: current_obs_confounder = self._data[i] outcome_values = self._data[self._outcome_name[0]] correlation_y = current_obs_confounder.corr(outcome_values) treatment_values = t correlation_t = current_obs_confounder.corr(treatment_values) product_cor_metric_current = correlation_y * correlation_t if product_cor_metric_current >= product_cor_metric_observed: product_cor_metric_observed = product_cor_metric_current correlation_t_observed = correlation_t correlation_y_observed = correlation_y # The user has an option to give the the effect_strength_on_y and effect_strength_on_t which can be then used instead of maximum correlation with treatment and outcome in the observed variables as it specifies the desired effect. if self.kappa_t is not None: correlation_t_observed = self.kappa_t if self.kappa_y is not None: correlation_y_observed = self.kappa_y # Choosing a c_star based on the data. # The correlations stop increasing upon increasing c_star after a certain value, that is it plateaus and we choose the value of c_star to be the value it plateaus. correlation_y_list = [] correlation_t_list = [] product_cor_metric_simulated_list = [] x_list = [] step = int(c_star_max / 10) for i in range(0, int(c_star_max), step): c1 = math.sqrt(i) c2 = c1 final_U = self.generate_confounder_from_residuals(c1, c2, d_y, d_t, X) current_simulated_confounder = final_U outcome_values = self._data[self._outcome_name[0]] correlation_y = current_simulated_confounder.corr(outcome_values) correlation_y_list.append(correlation_y) treatment_values = t correlation_t = current_simulated_confounder.corr(treatment_values) correlation_t_list.append(correlation_t) product_cor_metric_simulated = correlation_y * correlation_t product_cor_metric_simulated_list.append(product_cor_metric_simulated) x_list.append(i) index = 1 while index < len(correlation_y_list): if (correlation_y_list[index] - correlation_y_list[index - 1]) <= convergence_threshold: c_star = x_list[index] break index = index + 1 # Choosing c1 and c2 based on the hyperbolic relationship once c_star is chosen by going over various combinations of c1 and c2 values and choosing the combination which # which maintains the minimum distance between the product of correlations of the simulated variable and the product of maximum correlations of one of the observed variables # and additionally checks if the ratio of the weights are such that they maintain the ratio of the maximum possible observed coefficients within some confidence interval # c1_final and c2_final are initialised to the values on the hyperbolic curve such that c1_final = c2_final and c1_final*c2_final = c_star c1_final = math.sqrt(c_star) c2_final = math.sqrt(c_star) # initialising min_distance_between_product_cor_metrics to be a value greater than 1 min_distance_between_product_cor_metrics = 1.5 i = 0.05 threshold = c_star / 0.05 while i <= threshold: c2 = i c1 = c_star / c2 final_U = self.generate_confounder_from_residuals(c1, c2, d_y, d_t, X) current_simulated_confounder = final_U outcome_values = self._data[self._outcome_name[0]] correlation_y = current_simulated_confounder.corr(outcome_values) treatment_values = t correlation_t = current_simulated_confounder.corr(treatment_values) product_cor_metric_simulated = correlation_y * correlation_t if min_distance_between_product_cor_metrics >= abs( product_cor_metric_simulated - product_cor_metric_observed ): min_distance_between_product_cor_metrics = abs( product_cor_metric_simulated - product_cor_metric_observed ) additional_condition = correlation_y_observed / correlation_t_observed if ((c1 / c2) <= (additional_condition + 0.3 * additional_condition)) and ( (c1 / c2) >= (additional_condition - 0.3 * additional_condition) ): # choose minimum positive value c1_final = c1 c2_final = c2 i = i * 1.5 """#closed form solution print("c_star_max before closed form", c_star_max) if max_correlation_with_t == -1000: c2 = 0 c1 = c_star_max else: additional_condition = abs(max_correlation_with_y/max_correlation_with_t) print("additional_condition", additional_condition) c2 = math.sqrt(c_star_max/additional_condition) c1 = c_star_max/c2""" final_U = self.generate_confounder_from_residuals(c1_final, c2_final, d_y, d_t, X) return final_U def generate_confounder_from_residuals(self, c1, c2, d_y, d_t, X): """ This function takes the residuals from the treatment and outcome model and their coefficients and simulates the intermediate random variable U by taking the row wise normal distribution corresponding to each residual value and then debiasing the intermediate variable to get the final variable. :param c1: coefficient to the residual from the outcome model :type float :param c2: coefficient to the residual from the treatment model :type float :param d_y: residuals from the outcome model :type list :param d_t: residuals from the treatment model :type list :returns: The simulated values of the unobserved confounder based on the data :type pandas.core.series.Series """ U = [] for j in range(len(d_t)): simulated_variable_mean = c1 * d_y[j] + c2 * d_t[j] simulated_variable_stddev = 1 U.append(np.random.normal(simulated_variable_mean, simulated_variable_stddev, 1)) U = np.array(U) model = sm.OLS(U, X) results = model.fit() U = U.reshape( -1, ) final_U = U - results.fittedvalues.values final_U = pd.Series(U) return final_U

import copy import logging import math from typing import Dict, List, Optional, Union import numpy as np import pandas as pd import scipy.stats import statsmodels.api as sm from sklearn.linear_model import LogisticRegression from sklearn.preprocessing import StandardScaler from tqdm.auto import tqdm import dowhy.causal_estimators.econml from dowhy.causal_estimator import CausalEstimate, CausalEstimator from dowhy.causal_estimators.linear_regression_estimator import LinearRegressionEstimator from dowhy.causal_estimators.regression_estimator import RegressionEstimator from dowhy.causal_identifier.identified_estimand import IdentifiedEstimand from dowhy.causal_refuter import CausalRefutation, CausalRefuter, choose_variables from dowhy.causal_refuters.evalue_sensitivity_analyzer import EValueSensitivityAnalyzer from dowhy.causal_refuters.linear_sensitivity_analyzer import LinearSensitivityAnalyzer from dowhy.causal_refuters.non_parametric_sensitivity_analyzer import NonParametricSensitivityAnalyzer from dowhy.causal_refuters.partial_linear_sensitivity_analyzer import PartialLinearSensitivityAnalyzer logger = logging.getLogger(__name__) class AddUnobservedCommonCause(CausalRefuter): """Add an unobserved confounder for refutation. AddUnobservedCommonCause class supports three methods: 1) Simulation of an unobserved confounder 2) Linear partial R2 : Sensitivity Analysis for linear models. 3) Non-Parametric partial R2 based : Sensitivity Analyis for non-parametric models. Supports additional parameters that can be specified in the refute_estimate() method. """ def __init__(self, *args, **kwargs): """ Initialize the parameters required for the refuter. For direct_simulation, if effect_strength_on_treatment or effect_strength_on_outcome is not given, it is calculated automatically as a range between the minimum and maximum effect strength of observed confounders on treatment and outcome respectively. :param simulation_method: The method to use for simulating effect of unobserved confounder. Possible values are ["direct-simulation", "linear-partial-R2", "non-parametric-partial-R2", "e-value"]. :param confounders_effect_on_treatment: str : The type of effect on the treatment due to the unobserved confounder. Possible values are ['binary_flip', 'linear'] :param confounders_effect_on_outcome: str : The type of effect on the outcome due to the unobserved confounder. Possible values are ['binary_flip', 'linear'] :param effect_strength_on_treatment: float, numpy.ndarray: [Used when simulation_method="direct-simulation"] Strength of the confounder's effect on treatment. When confounders_effect_on_treatment is linear, it is the regression coefficient. When the confounders_effect_on_treatment is binary flip, it is the probability with which effect of unobserved confounder can invert the value of the treatment. :param effect_strength_on_outcome: float, numpy.ndarray: Strength of the confounder's effect on outcome. Its interpretation depends on confounders_effect_on_outcome and the simulation_method. When simulation_method is direct-simulation, for a linear effect it behaves like the regression coefficient and for a binary flip, it is the probability with which it can invert the value of the outcome. :param partial_r2_confounder_treatment: float, numpy.ndarray: [Used when simulation_method is linear-partial-R2 or non-parametric-partial-R2] Partial R2 of the unobserved confounder wrt the treatment conditioned on the observed confounders. Only in the case of general non-parametric-partial-R2, it is the fraction of variance in the reisz representer that is explained by the unobserved confounder; specifically (1-r), where r is the ratio of variance of reisz representer, alpha^2, based on observed confounders and that based on all confounders. :param partial_r2_confounder_outcome: float, numpy.ndarray: [Used when simulation_method is linear-partial-R2 or non-parametric-partial-R2] Partial R2 of the unobserved confounder wrt the outcome conditioned on the treatment and observed confounders. :param frac_strength_treatment: float: This parameter decides the effect strength of the simulated confounder as a fraction of the effect strength of observed confounders on treatment. Defaults to 1. :param frac_strength_outcome: float: This parameter decides the effect strength of the simulated confounder as a fraction of the effect strength of observed confounders on outcome. Defaults to 1. :param plotmethod: string: Type of plot to be shown. If None, no plot is generated. This parameter is used only only when more than one treatment confounder effect values or outcome confounder effect values are provided. Default is "colormesh". Supported values are "contour", "colormesh" when more than one value is provided for both confounder effect value parameters; "line" when provided for only one of them. :param percent_change_estimate: It is the percentage of reduction of treatment estimate that could alter the results (default = 1). if percent_change_estimate = 1, the robustness value describes the strength of association of confounders with treatment and outcome in order to reduce the estimate by 100% i.e bring it down to 0. (relevant only for Linear Sensitivity Analysis, ignore for rest) :param confounder_increases_estimate: True implies that confounder increases the absolute value of estimate and vice versa. (Default = False). (relevant only for Linear Sensitivity Analysis, ignore for rest) :param benchmark_common_causes: names of variables for bounding strength of confounders. (relevant only for partial-r2 based simulation methods) :param significance_level: confidence interval for statistical inference(default = 0.05). (relevant only for partial-r2 based simulation methods) :param null_hypothesis_effect: assumed effect under the null hypothesis. (relevant only for linear-partial-R2, ignore for rest) :param plot_estimate: Generate contour plot for estimate while performing sensitivity analysis. (default = True). (relevant only for partial-r2 based simulation methods) :param num_splits: number of splits for cross validation. (default = 5). (relevant only for non-parametric-partial-R2 simulation method) :param shuffle_data : shuffle data or not before splitting into folds (default = False). (relevant only for non-parametric-partial-R2 simulation method) :param shuffle_random_seed: seed for randomly shuffling data. (relevant only for non-parametric-partial-R2 simulation method) :param alpha_s_estimator_param_list: list of dictionaries with parameters for finding alpha_s. (relevant only for non-parametric-partial-R2 simulation method) :param g_s_estimator_list: list of estimator objects for finding g_s. These objects should have fit() and predict() functions implemented. (relevant only for non-parametric-partial-R2 simulation method) :param g_s_estimator_param_list: list of dictionaries with parameters for tuning respective estimators in "g_s_estimator_list". The order of the dictionaries in the list should be consistent with the estimator objects order in "g_s_estimator_list". (relevant only for non-parametric-partial-R2 simulation method) """ super().__init__(*args, **kwargs) self.simulation_method = kwargs["simulation_method"] if "simulation_method" in kwargs else "direct-simulation" self.effect_on_t = ( kwargs["confounders_effect_on_treatment"] if "confounders_effect_on_treatment" in kwargs else "binary_flip" ) self.effect_on_y = ( kwargs["confounders_effect_on_outcome"] if "confounders_effect_on_outcome" in kwargs else "linear" ) if self.simulation_method == "direct-simulation": self.kappa_t = kwargs["effect_strength_on_treatment"] if "effect_strength_on_treatment" in kwargs else None self.kappa_y = kwargs["effect_strength_on_outcome"] if "effect_strength_on_outcome" in kwargs else None elif self.simulation_method in ["linear-partial-R2", "non-parametric-partial-R2"]: self.kappa_t = ( kwargs["partial_r2_confounder_treatment"] if "partial_r2_confounder_treatment" in kwargs else None ) self.kappa_y = ( kwargs["partial_r2_confounder_outcome"] if "partial_r2_confounder_outcome" in kwargs else None ) elif self.simulation_method == "e-value": pass else: raise ValueError( "simulation method is not supported. Try direct-simulation, linear-partial-R2, non-parametric-partial-R2, or e-value" ) self.frac_strength_treatment = ( kwargs["effect_fraction_on_treatment"] if "effect_fraction_on_treatment" in kwargs else 1 ) self.frac_strength_outcome = ( kwargs["effect_fraction_on_outcome"] if "effect_fraction_on_outcome" in kwargs else 1 ) self.plotmethod = kwargs["plotmethod"] if "plotmethod" in kwargs else "colormesh" self.percent_change_estimate = kwargs["percent_change_estimate"] if "percent_change_estimate" in kwargs else 1.0 self.significance_level = kwargs["significance_level"] if "significance_level" in kwargs else 0.05 self.confounder_increases_estimate = ( kwargs["confounder_increases_estimate"] if "confounder_increases_estimate" in kwargs else False ) self.benchmark_common_causes = ( kwargs["benchmark_common_causes"] if "benchmark_common_causes" in kwargs else None ) self.null_hypothesis_effect = kwargs["null_hypothesis_effect"] if "null_hypothesis_effect" in kwargs else 0 self.plot_estimate = kwargs["plot_estimate"] if "plot_estimate" in kwargs else True self.num_splits = kwargs["num_splits"] if "num_splits" in kwargs else 5 self.shuffle_data = kwargs["shuffle_data"] if "shuffle_data" in kwargs else False self.shuffle_random_seed = kwargs["shuffle_random_seed"] if "shuffle_random_seed" in kwargs else None self.alpha_s_estimator_param_list = ( kwargs["alpha_s_estimator_param_list"] if "alpha_s_estimator_param_list" in kwargs else None ) self.alpha_s_estimator_list = kwargs["alpha_s_estimator_list"] if "alpha_s_estimator_list" in kwargs else None self.g_s_estimator_list = kwargs["g_s_estimator_list"] if "g_s_estimator_list" in kwargs else None self.g_s_estimator_param_list = ( kwargs["g_s_estimator_param_list"] if "g_s_estimator_param_list" in kwargs else None ) self.plugin_reisz = kwargs["plugin_reisz"] if "plugin_reisz" in kwargs else False self.logger = logging.getLogger(__name__) def refute_estimate(self, show_progress_bar=False): if self.simulation_method == "linear-partial-R2": return sensitivity_linear_partial_r2( self._data, self._estimate, self._treatment_name, self.frac_strength_treatment, self.frac_strength_outcome, self.percent_change_estimate, self.benchmark_common_causes, self.significance_level, self.null_hypothesis_effect, self.plot_estimate, ) elif self.simulation_method == "non-parametric-partial-R2": return sensitivity_non_parametric_partial_r2( self._estimate, self.kappa_t, self.kappa_y, self.frac_strength_treatment, self.frac_strength_outcome, self.benchmark_common_causes, self.plot_estimate, self.alpha_s_estimator_list, self.alpha_s_estimator_param_list, self.g_s_estimator_list, self.g_s_estimator_param_list, self.plugin_reisz, ) elif self.simulation_method == "e-value": return sensitivity_e_value( self._data, self._target_estimand, self._estimate, self._treatment_name, self._outcome_name, self.plot_estimate, ) elif self.simulation_method == "direct-simulation": refute = sensitivity_simulation( self._data, self._target_estimand, self._estimate, self._treatment_name, self._outcome_name, self.kappa_t, self.kappa_y, self.effect_on_t, self.effect_on_y, self.frac_strength_treatment, self.frac_strength_outcome, self.plotmethod, show_progress_bar, ) refute.add_refuter(self) return refute def _infer_default_kappa_t( data: pd.DataFrame, target_estimand: IdentifiedEstimand, treatment_name: List[str], effect_on_t: str, frac_strength_treatment: float, len_kappa_t: int = 10, ): """Infer default effect strength of simulated confounder on treatment.""" observed_common_causes_names = target_estimand.get_backdoor_variables() if len(observed_common_causes_names) > 0: observed_common_causes = data[observed_common_causes_names] observed_common_causes = pd.get_dummies(observed_common_causes, drop_first=True) else: raise ValueError( "There needs to be at least one common cause to" + "automatically compute the default value of kappa_t." + " Provide a value for kappa_t" ) t = data[treatment_name] # Standardizing the data observed_common_causes = StandardScaler().fit_transform(observed_common_causes) if effect_on_t == "binary_flip": # Fit a model containing all confounders and compare predictions # using all features compared to all features except a given # confounder. tmodel = LogisticRegression().fit(observed_common_causes, t) tpred = tmodel.predict(observed_common_causes).astype(int) flips = [] for i in range(observed_common_causes.shape[1]): oldval = np.copy(observed_common_causes[:, i]) observed_common_causes[:, i] = 0 tcap = tmodel.predict(observed_common_causes).astype(int) observed_common_causes[:, i] = oldval flips.append(np.sum(abs(tcap - tpred)) / tpred.shape[0]) min_coeff, max_coeff = min(flips), max(flips) elif effect_on_t == "linear": # Estimating the regression coefficient from standardized features to t corrcoef_var_t = np.corrcoef(observed_common_causes, t, rowvar=False)[-1, :-1] std_dev_t = np.std(t)[0] max_coeff = max(corrcoef_var_t) * std_dev_t min_coeff = min(corrcoef_var_t) * std_dev_t else: raise NotImplementedError("'" + effect_on_t + "' method not supported for confounders' effect on treatment") min_coeff, max_coeff = _compute_min_max_coeff(min_coeff, max_coeff, frac_strength_treatment) # By default, return a plot with 10 points # consider 10 values of the effect of the unobserved confounder step = (max_coeff - min_coeff) / len_kappa_t logger.info("(Min, Max) kappa_t for observed common causes, ({0}, {1})".format(min_coeff, max_coeff)) if np.equal(max_coeff, min_coeff): return max_coeff else: return np.arange(min_coeff, max_coeff, step) def _compute_min_max_coeff(min_coeff: float, max_coeff: float, effect_strength_fraction: np.ndarray): max_coeff = effect_strength_fraction * max_coeff min_coeff = effect_strength_fraction * min_coeff return min_coeff, max_coeff def _infer_default_kappa_y( data: pd.DataFrame, target_estimand: IdentifiedEstimand, outcome_name: List[str], effect_on_y: str, frac_strength_outcome: float, len_kappa_y: int = 10, ): """Infer default effect strength of simulated confounder on treatment.""" observed_common_causes_names = target_estimand.get_backdoor_variables() if len(observed_common_causes_names) > 0: observed_common_causes = data[observed_common_causes_names] observed_common_causes = pd.get_dummies(observed_common_causes, drop_first=True) else: raise ValueError( "There needs to be at least one common cause to" + "automatically compute the default value of kappa_y." + " Provide a value for kappa_y" ) y = data[outcome_name] # Standardizing the data observed_common_causes = StandardScaler().fit_transform(observed_common_causes) if effect_on_y == "binary_flip": # Fit a model containing all confounders and compare predictions # using all features compared to all features except a given # confounder. ymodel = LogisticRegression().fit(observed_common_causes, y) ypred = ymodel.predict(observed_common_causes).astype(int) flips = [] for i in range(observed_common_causes.shape[1]): oldval = np.copy(observed_common_causes[:, i]) observed_common_causes[:, i] = 0 ycap = ymodel.predict(observed_common_causes).astype(int) observed_common_causes[:, i] = oldval flips.append(np.sum(abs(ycap - ypred)) / ypred.shape[0]) min_coeff, max_coeff = min(flips), max(flips) elif effect_on_y == "linear": corrcoef_var_y = np.corrcoef(observed_common_causes, y, rowvar=False)[-1, :-1] std_dev_y = np.std(y)[0] max_coeff = max(corrcoef_var_y) * std_dev_y min_coeff = min(corrcoef_var_y) * std_dev_y else: raise NotImplementedError("'" + effect_on_y + "' method not supported for confounders' effect on outcome") min_coeff, max_coeff = _compute_min_max_coeff(min_coeff, max_coeff, frac_strength_outcome) # By default, return a plot with 10 points # consider 10 values of the effect of the unobserved confounder step = (max_coeff - min_coeff) / len_kappa_y logger.info("(Min, Max) kappa_y for observed common causes, ({0}, {1})".format(min_coeff, max_coeff)) if np.equal(max_coeff, min_coeff): return max_coeff else: return np.arange(min_coeff, max_coeff, step) def _include_confounders_effect( data: pd.DataFrame, new_data: pd.DataFrame, effect_on_t: str, treatment_name: str, kappa_t: float, effect_on_y: str, outcome_name: str, kappa_y: float, ): """ This function deals with the change in the value of the data due to the effect of the unobserved confounder. In the case of a binary flip, we flip only if the random number is greater than the threshold set. In the case of a linear effect, we use the variable as the linear regression constant. :param new_data: pandas.DataFrame: The data to be changed due to the effects of the unobserved confounder. :param kappa_t: numpy.float64: The value of the threshold for binary_flip or the value of the regression coefficient for linear effect. :param kappa_y: numpy.float64: The value of the threshold for binary_flip or the value of the regression coefficient for linear effect. :return: pandas.DataFrame: The DataFrame that includes the effects of the unobserved confounder. """ num_rows = data.shape[0] stdnorm = scipy.stats.norm() w_random = stdnorm.rvs(num_rows) if effect_on_t == "binary_flip": alpha = 2 * kappa_t - 1 if kappa_t >= 0.5 else 1 - 2 * kappa_t interval = stdnorm.interval(alpha) rel_interval = interval[0] if kappa_t >= 0.5 else interval[1] new_data.loc[rel_interval <= w_random, treatment_name] = ( 1 - new_data.loc[rel_interval <= w_random, treatment_name] ) for tname in treatment_name: if pd.api.types.is_bool_dtype(data[tname]): new_data = new_data.astype({tname: "bool"}, copy=False) elif effect_on_t == "linear": confounder_t_effect = kappa_t * w_random # By default, we add the effect of simulated confounder for treatment. # But subtract it from outcome to create a negative correlation # assuming that the original confounder's effect was positive on both. # This is to remove the effect of the original confounder. new_data[treatment_name] = new_data[treatment_name].values + np.ndarray( shape=(num_rows, 1), buffer=confounder_t_effect ) else: raise NotImplementedError("'" + effect_on_t + "' method not supported for confounders' effect on treatment") if effect_on_y == "binary_flip": alpha = 2 * kappa_y - 1 if kappa_y >= 0.5 else 1 - 2 * kappa_y interval = stdnorm.interval(alpha) rel_interval = interval[0] if kappa_y >= 0.5 else interval[1] new_data.loc[rel_interval <= w_random, outcome_name] = 1 - new_data.loc[rel_interval <= w_random, outcome_name] for yname in outcome_name: if pd.api.types.is_bool_dtype(data[yname]): new_data = new_data.astype({yname: "bool"}, copy=False) elif effect_on_y == "linear": confounder_y_effect = (-1) * kappa_y * w_random # By default, we add the effect of simulated confounder for treatment. # But subtract it from outcome to create a negative correlation # assuming that the original confounder's effect was positive on both. # This is to remove the effect of the original confounder. new_data[outcome_name] = new_data[outcome_name].values + np.ndarray( shape=(num_rows, 1), buffer=confounder_y_effect ) else: raise NotImplementedError("'" + effect_on_y + "' method not supported for confounders' effect on outcome") return new_data def include_simulated_confounder( data: pd.DataFrame, treatment_name: str, outcome_name: str, kappa_t: float, kappa_y: float, convergence_threshold: float = 0.1, c_star_max: int = 1000, ): """ This function simulates an unobserved confounder based on the data using the following steps: 1. It calculates the "residuals" from the treatment and outcome model i.) The outcome model has outcome as the dependent variable and all the observed variables including treatment as independent variables ii.) The treatment model has treatment as the dependent variable and all the observed variables as independent variables. 2. U is an intermediate random variable drawn from the normal distribution with the weighted average of residuals as mean and a unit variance U ~ N(c1*d_y + c2*d_t, 1) where *d_y and d_t are residuals from the treatment and outcome model *c1 and c2 are coefficients to the residuals 3. The final U, which is the simulated unobserved confounder is obtained by debiasing the intermediate variable U by residualising it with X Choosing the coefficients c1 and c2: The coefficients are chosen based on these basic assumptions: 1. There is a hyperbolic relationship satisfying c1*c2 = c_star 2. c_star is chosen from a range of possible values based on the correlation of the obtained simulated variable with outcome and treatment. 3. The product of correlations with treatment and outcome should be at a minimum distance to the maximum correlations with treatment and outcome in any of the observed confounders 4. The ratio of the weights should be such that they maintain the ratio of the maximum possible observed coefficients within some confidence interval :param c_star_max: The maximum possible value for the hyperbolic curve on which the coefficients to the residuals lie. It defaults to 1000 in the code if not specified by the user. :type int :param convergence_threshold: The threshold to check the plateauing of the correlation while selecting a c_star. It defaults to 0.1 in the code if not specified by the user :type float :returns: The simulated values of the unobserved confounder based on the data :type pandas.core.series.Series """ # Obtaining the list of observed variables required_variables = True observed_variables = choose_variables(required_variables) observed_variables_with_treatment_and_outcome = observed_variables + treatment_name + outcome_name # Taking a subset of the dataframe that has only observed variables data = data[observed_variables_with_treatment_and_outcome] # Residuals from the outcome model obtained by fitting a linear model y = data[outcome_name[0]] observed_variables_with_treatment = observed_variables + treatment_name X = data[observed_variables_with_treatment] model = sm.OLS(y, X.astype("float")) results = model.fit() residuals_y = y - results.fittedvalues d_y = list(pd.Series(residuals_y)) # Residuals from the treatment model obtained by fitting a linear model t = data[treatment_name[0]].astype("int64") X = data[observed_variables] model = sm.OLS(t, X) results = model.fit() residuals_t = t - results.fittedvalues d_t = list(pd.Series(residuals_t)) # Initialising product_cor_metric_observed with a really low value as finding maximum product_cor_metric_observed = -10000000000 for i in observed_variables: current_obs_confounder = data[i] outcome_values = data[outcome_name[0]] correlation_y = current_obs_confounder.corr(outcome_values) treatment_values = t correlation_t = current_obs_confounder.corr(treatment_values) product_cor_metric_current = correlation_y * correlation_t if product_cor_metric_current >= product_cor_metric_observed: product_cor_metric_observed = product_cor_metric_current correlation_t_observed = correlation_t correlation_y_observed = correlation_y # The user has an option to give the the effect_strength_on_y and effect_strength_on_t which can be then used instead of maximum correlation with treatment and outcome in the observed variables as it specifies the desired effect. if kappa_t is not None: correlation_t_observed = kappa_t if kappa_y is not None: correlation_y_observed = kappa_y # Choosing a c_star based on the data. # The correlations stop increasing upon increasing c_star after a certain value, that is it plateaus and we choose the value of c_star to be the value it plateaus. correlation_y_list = [] correlation_t_list = [] product_cor_metric_simulated_list = [] x_list = [] step = int(c_star_max / 10) for i in range(0, int(c_star_max), step): c1 = math.sqrt(i) c2 = c1 final_U = _generate_confounder_from_residuals(c1, c2, d_y, d_t, X) current_simulated_confounder = final_U outcome_values = data[outcome_name[0]] correlation_y = current_simulated_confounder.corr(outcome_values) correlation_y_list.append(correlation_y) treatment_values = t correlation_t = current_simulated_confounder.corr(treatment_values) correlation_t_list.append(correlation_t) product_cor_metric_simulated = correlation_y * correlation_t product_cor_metric_simulated_list.append(product_cor_metric_simulated) x_list.append(i) index = 1 while index < len(correlation_y_list): if (correlation_y_list[index] - correlation_y_list[index - 1]) <= convergence_threshold: c_star = x_list[index] break index = index + 1 # Choosing c1 and c2 based on the hyperbolic relationship once c_star is chosen by going over various combinations of c1 and c2 values and choosing the combination which # which maintains the minimum distance between the product of correlations of the simulated variable and the product of maximum correlations of one of the observed variables # and additionally checks if the ratio of the weights are such that they maintain the ratio of the maximum possible observed coefficients within some confidence interval # c1_final and c2_final are initialised to the values on the hyperbolic curve such that c1_final = c2_final and c1_final*c2_final = c_star c1_final = math.sqrt(c_star) c2_final = math.sqrt(c_star) # initialising min_distance_between_product_cor_metrics to be a value greater than 1 min_distance_between_product_cor_metrics = 1.5 i = 0.05 threshold = c_star / 0.05 while i <= threshold: c2 = i c1 = c_star / c2 final_U = _generate_confounder_from_residuals(c1, c2, d_y, d_t, X) current_simulated_confounder = final_U outcome_values = data[outcome_name[0]] correlation_y = current_simulated_confounder.corr(outcome_values) treatment_values = t correlation_t = current_simulated_confounder.corr(treatment_values) product_cor_metric_simulated = correlation_y * correlation_t if min_distance_between_product_cor_metrics >= abs(product_cor_metric_simulated - product_cor_metric_observed): min_distance_between_product_cor_metrics = abs(product_cor_metric_simulated - product_cor_metric_observed) additional_condition = correlation_y_observed / correlation_t_observed if ((c1 / c2) <= (additional_condition + 0.3 * additional_condition)) and ( (c1 / c2) >= (additional_condition - 0.3 * additional_condition) ): # choose minimum positive value c1_final = c1 c2_final = c2 i = i * 1.5 """#closed form solution print("c_star_max before closed form", c_star_max) if max_correlation_with_t == -1000: c2 = 0 c1 = c_star_max else: additional_condition = abs(max_correlation_with_y/max_correlation_with_t) print("additional_condition", additional_condition) c2 = math.sqrt(c_star_max/additional_condition) c1 = c_star_max/c2""" final_U = _generate_confounder_from_residuals(c1_final, c2_final, d_y, d_t, X) return final_U def _generate_confounder_from_residuals(c1, c2, d_y, d_t, X): """ This function takes the residuals from the treatment and outcome model and their coefficients and simulates the intermediate random variable U by taking the row wise normal distribution corresponding to each residual value and then debiasing the intermediate variable to get the final variable. :param c1: coefficient to the residual from the outcome model :type float :param c2: coefficient to the residual from the treatment model :type float :param d_y: residuals from the outcome model :type list :param d_t: residuals from the treatment model :type list :returns: The simulated values of the unobserved confounder based on the data :type pandas.core.series.Series """ U = [] for j in range(len(d_t)): simulated_variable_mean = c1 * d_y[j] + c2 * d_t[j] simulated_variable_stddev = 1 U.append(np.random.normal(simulated_variable_mean, simulated_variable_stddev, 1)) U = np.array(U) model = sm.OLS(U, X) results = model.fit() U = U.reshape( -1, ) final_U = U - results.fittedvalues.values final_U = pd.Series(U) return final_U def sensitivity_linear_partial_r2( data: pd.DataFrame, estimate: CausalEstimate, treatment_name: str, frac_strength_treatment: float = 1.0, frac_strength_outcome: float = 1.0, percent_change_estimate: float = 1.0, benchmark_common_causes: Optional[List[str]] = None, significance_level: Optional[float] = None, null_hypothesis_effect: Optional[float] = None, plot_estimate: bool = True, ) -> LinearSensitivityAnalyzer: """Add an unobserved confounder for refutation using Linear partial R2 methond (Sensitivity Analysis for linear models). :param data: pd.DataFrame: Data to run the refutation :param estimate: CausalEstimate: Estimate to run the refutation :param treatment_name: str: Name of the treatment :param frac_strength_treatment: float: This parameter decides the effect strength of the simulated confounder as a fraction of the effect strength of observed confounders on treatment. Defaults to 1. :param frac_strength_outcome: float: This parameter decides the effect strength of the simulated confounder as a fraction of the effect strength of observed confounders on outcome. Defaults to 1. :param percent_change_estimate: It is the percentage of reduction of treatment estimate that could alter the results (default = 1). if percent_change_estimate = 1, the robustness value describes the strength of association of confounders with treatment and outcome in order to reduce the estimate by 100% i.e bring it down to 0. (relevant only for Linear Sensitivity Analysis, ignore for rest) :param benchmark_common_causes: names of variables for bounding strength of confounders. (relevant only for partial-r2 based simulation methods) :param significance_level: confidence interval for statistical inference(default = 0.05). (relevant only for partial-r2 based simulation methods) :param null_hypothesis_effect: assumed effect under the null hypothesis. (relevant only for linear-partial-R2, ignore for rest) :param plot_estimate: Generate contour plot for estimate while performing sensitivity analysis. (default = True). (relevant only for partial-r2 based simulation methods) """ if not (isinstance(estimate.estimator, LinearRegressionEstimator)): raise NotImplementedError("Currently only LinearRegressionEstimator is supported for Sensitivity Analysis") if len(estimate.estimator._effect_modifier_names) > 0: raise NotImplementedError("The current implementation does not support effect modifiers") if frac_strength_outcome == 1: frac_strength_outcome = frac_strength_treatment analyzer = LinearSensitivityAnalyzer( estimator=estimate.estimator, data=data, treatment_name=treatment_name, percent_change_estimate=percent_change_estimate, significance_level=significance_level, benchmark_common_causes=benchmark_common_causes, null_hypothesis_effect=null_hypothesis_effect, frac_strength_treatment=frac_strength_treatment, frac_strength_outcome=frac_strength_outcome, common_causes_order=estimate.estimator._observed_common_causes.columns, ) analyzer.check_sensitivity(plot=plot_estimate) return analyzer def sensitivity_non_parametric_partial_r2( estimate: CausalEstimate, kappa_t: Optional[Union[float, np.ndarray]] = None, kappa_y: Optional[Union[float, np.ndarray]] = None, frac_strength_treatment: float = 1.0, frac_strength_outcome: float = 1.0, benchmark_common_causes: Optional[List[str]] = None, plot_estimate: bool = True, alpha_s_estimator_list: Optional[List] = None, alpha_s_estimator_param_list: Optional[List[Dict]] = None, g_s_estimator_list: Optional[List] = None, g_s_estimator_param_list: Optional[List[Dict]] = None, plugin_reisz: bool = False, ) -> Union[PartialLinearSensitivityAnalyzer, NonParametricSensitivityAnalyzer]: """Add an unobserved confounder for refutation using Non-parametric partial R2 methond (Sensitivity Analysis for non-parametric models). :param estimate: CausalEstimate: Estimate to run the refutation :param kappa_t: float, numpy.ndarray: Partial R2 of the unobserved confounder wrt the treatment conditioned on the observed confounders. Only in the case of general non-parametric-partial-R2, it is the fraction of variance in the reisz representer that is explained by the unobserved confounder; specifically (1-r), where r is the ratio of variance of reisz representer, alpha^2, based on observed confounders and that based on all confounders. :param kappa_y: float, numpy.ndarray: Partial R2 of the unobserved confounder wrt the outcome conditioned on the treatment and observed confounders. :param frac_strength_treatment: float: This parameter decides the effect strength of the simulated confounder as a fraction of the effect strength of observed confounders on treatment. Defaults to 1. :param frac_strength_outcome: float: This parameter decides the effect strength of the simulated confounder as a fraction of the effect strength of observed confounders on outcome. Defaults to 1. :param benchmark_common_causes: names of variables for bounding strength of confounders. (relevant only for partial-r2 based simulation methods) :param plot_estimate: Generate contour plot for estimate while performing sensitivity analysis. (default = True). (relevant only for partial-r2 based simulation methods) :param alpha_s_estimator_list: list of estimator objects for estimating alpha_s. These objects should have fit() and predict() methods (relevant only for non-parametric-partial-R2 method) :param alpha_s_estimator_param_list: list of dictionaries with parameters for finding alpha_s. (relevant only for non-parametric-partial-R2 simulation method) :param g_s_estimator_list: list of estimator objects for finding g_s. These objects should have fit() and predict() functions implemented. (relevant only for non-parametric-partial-R2 simulation method) :param g_s_estimator_param_list: list of dictionaries with parameters for tuning respective estimators in "g_s_estimator_list". The order of the dictionaries in the list should be consistent with the estimator objects order in "g_s_estimator_list". (relevant only for non-parametric-partial-R2 simulation method) :plugin_reisz: bool: Flag on whether to use the plugin estimator or the nonparametric estimator for reisz representer function (alpha_s). """ # If the estimator used is LinearDML, partially linear sensitivity analysis will be automatically chosen if isinstance(estimate.estimator, dowhy.causal_estimators.econml.Econml): if estimate.estimator._econml_methodname == "econml.dml.LinearDML": analyzer = PartialLinearSensitivityAnalyzer( estimator=estimate._estimator_object, observed_common_causes=estimate.estimator._observed_common_causes, treatment=estimate.estimator._treatment, outcome=estimate.estimator._outcome, alpha_s_estimator_param_list=alpha_s_estimator_param_list, g_s_estimator_list=g_s_estimator_list, g_s_estimator_param_list=g_s_estimator_param_list, effect_strength_treatment=kappa_t, effect_strength_outcome=kappa_y, benchmark_common_causes=benchmark_common_causes, frac_strength_treatment=frac_strength_treatment, frac_strength_outcome=frac_strength_outcome, ) analyzer.check_sensitivity(plot=plot_estimate) return analyzer analyzer = NonParametricSensitivityAnalyzer( estimator=estimate.estimator, observed_common_causes=estimate.estimator._observed_common_causes, treatment=estimate.estimator._treatment, outcome=estimate.estimator._outcome, alpha_s_estimator_list=alpha_s_estimator_list, alpha_s_estimator_param_list=alpha_s_estimator_param_list, g_s_estimator_list=g_s_estimator_list, g_s_estimator_param_list=g_s_estimator_param_list, effect_strength_treatment=kappa_t, effect_strength_outcome=kappa_y, benchmark_common_causes=benchmark_common_causes, frac_strength_treatment=frac_strength_treatment, frac_strength_outcome=frac_strength_outcome, theta_s=estimate.value, plugin_reisz=plugin_reisz, ) analyzer.check_sensitivity(plot=plot_estimate) return analyzer def sensitivity_e_value( data: pd.DataFrame, target_estimand: IdentifiedEstimand, estimate: CausalEstimate, treatment_name: List[str], outcome_name: List[str], plot_estimate: bool = True, ) -> EValueSensitivityAnalyzer: if not isinstance(estimate.estimator, RegressionEstimator): raise NotImplementedError("E-Value sensitivity analysis is currently only implemented RegressionEstimator.") if len(estimate.estimator._effect_modifier_names) > 0: raise NotImplementedError("The current implementation does not support effect modifiers") analyzer = EValueSensitivityAnalyzer( estimate=estimate, estimand=target_estimand, data=data, treatment_name=treatment_name[0], outcome_name=outcome_name[0], ) analyzer.check_sensitivity(plot=plot_estimate) return analyzer def sensitivity_simulation( data: pd.DataFrame, target_estimand: IdentifiedEstimand, estimate: CausalEstimate, treatment_name: str, outcome_name: str, kappa_t: Optional[Union[float, np.ndarray]] = None, kappa_y: Optional[Union[float, np.ndarray]] = None, confounders_effect_on_treatment: str = "binary_flip", confounders_effect_on_outcome: str = "linear", frac_strength_treatment: float = 1.0, frac_strength_outcome: float = 1.0, plotmethod: Optional[str] = None, show_progress_bar=False, **_, ) -> CausalRefutation: """ This function attempts to add an unobserved common cause to the outcome and the treatment. At present, we have implemented the behavior for one dimensional behaviors for continuous and binary variables. This function can either take single valued inputs or a range of inputs. The function then looks at the data type of the input and then decides on the course of action. :param data: pd.DataFrame: Data to run the refutation :param target_estimand: IdentifiedEstimand: Identified estimand to run the refutation :param estimate: CausalEstimate: Estimate to run the refutation :param treatment_name: str: Name of the treatment :param outcome_name: str: Name of the outcome :param kappa_t: float, numpy.ndarray: Strength of the confounder's effect on treatment. When confounders_effect_on_treatment is linear, it is the regression coefficient. When the confounders_effect_on_treatment is binary flip, it is the probability with which effect of unobserved confounder can invert the value of the treatment. :param kappa_y: float, numpy.ndarray: Strength of the confounder's effect on outcome. Its interpretation depends on confounders_effect_on_outcome and the simulation_method. When simulation_method is direct-simulation, for a linear effect it behaves like the regression coefficient and for a binary flip, it is the probability with which it can invert the value of the outcome. :param confounders_effect_on_treatment: str : The type of effect on the treatment due to the unobserved confounder. Possible values are ['binary_flip', 'linear'] :param confounders_effect_on_outcome: str : The type of effect on the outcome due to the unobserved confounder. Possible values are ['binary_flip', 'linear'] :param frac_strength_treatment: float: This parameter decides the effect strength of the simulated confounder as a fraction of the effect strength of observed confounders on treatment. Defaults to 1. :param frac_strength_outcome: float: This parameter decides the effect strength of the simulated confounder as a fraction of the effect strength of observed confounders on outcome. Defaults to 1. :param plotmethod: string: Type of plot to be shown. If None, no plot is generated. This parameter is used only only when more than one treatment confounder effect values or outcome confounder effect values are provided. Default is "colormesh". Supported values are "contour", "colormesh" when more than one value is provided for both confounder effect value parameters; "line" when provided for only one of them. :return: CausalRefuter: An object that contains the estimated effect and a new effect and the name of the refutation used. """ if kappa_t is None: kappa_t = _infer_default_kappa_t( data, target_estimand, treatment_name, confounders_effect_on_treatment, frac_strength_treatment ) if kappa_y is None: kappa_y = _infer_default_kappa_y( data, target_estimand, outcome_name, confounders_effect_on_outcome, frac_strength_outcome ) if not isinstance(kappa_t, (list, np.ndarray)) and not isinstance( kappa_y, (list, np.ndarray) ): # Deal with single value inputs new_data = copy.deepcopy(data) new_data = _include_confounders_effect( data, new_data, confounders_effect_on_treatment, treatment_name, kappa_t, confounders_effect_on_outcome, outcome_name, kappa_y, ) new_estimator = CausalEstimator.get_estimator_object(new_data, target_estimand, estimate) new_effect = new_estimator.estimate_effect() refute = CausalRefutation( estimate.value, new_effect.value, refutation_type="Refute: Add an Unobserved Common Cause" ) refute.new_effect_array = np.array(new_effect.value) refute.new_effect = new_effect.value return refute else: # Deal with multiple value inputs if isinstance(kappa_t, (list, np.ndarray)) and isinstance( kappa_y, (list, np.ndarray) ): # Deal with range inputs # Get a 2D matrix of values # x,y = np.meshgrid(self.kappa_t, self.kappa_y) # x,y are both MxN results_matrix = np.random.rand(len(kappa_t), len(kappa_y)) # Matrix to hold all the results of NxM orig_data = copy.deepcopy(data) for i in tqdm( range(len(kappa_t)), colour=CausalRefuter.PROGRESS_BAR_COLOR, disable=not show_progress_bar, desc="Refuting Estimates: ", ): for j in range(len(kappa_y)): new_data = _include_confounders_effect( data, orig_data, confounders_effect_on_treatment, treatment_name, kappa_t[i], confounders_effect_on_outcome, outcome_name, kappa_y[j], ) new_estimator = CausalEstimator.get_estimator_object(new_data, target_estimand, estimate) new_effect = new_estimator.estimate_effect() refute = CausalRefutation( estimate.value, new_effect.value, refutation_type="Refute: Add an Unobserved Common Cause", ) results_matrix[i][j] = refute.new_effect # Populate the results refute.new_effect_array = results_matrix refute.new_effect = (np.min(results_matrix), np.max(results_matrix)) # Store the values into the refute object if plotmethod is None: return refute import matplotlib import matplotlib.pyplot as plt fig = plt.figure(figsize=(6, 5)) left, bottom, width, height = 0.1, 0.1, 0.8, 0.8 ax = fig.add_axes([left, bottom, width, height]) oe = estimate.value contour_levels = [oe / 4.0, oe / 2.0, (3.0 / 4) * oe, oe] contour_levels.extend([0, np.min(results_matrix), np.max(results_matrix)]) if plotmethod == "contour": cp = plt.contourf(kappa_y, kappa_t, results_matrix, levels=sorted(contour_levels)) # Adding a label on the contour line for the original estimate fmt = {} trueeffect_index = np.where(cp.levels == oe)[0][0] fmt[cp.levels[trueeffect_index]] = "Estimated Effect" # Label every other level using strings plt.clabel(cp, [cp.levels[trueeffect_index]], inline=True, fmt=fmt) plt.colorbar(cp) elif plotmethod == "colormesh": cp = plt.pcolormesh(kappa_y, kappa_t, results_matrix, shading="nearest") plt.colorbar(cp, ticks=contour_levels) ax.yaxis.set_ticks(kappa_t) ax.xaxis.set_ticks(kappa_y) plt.xticks(rotation=45) ax.set_title("Effect of Unobserved Common Cause") ax.set_ylabel("Value of Linear Constant on Treatment") ax.set_xlabel("Value of Linear Constant on Outcome") plt.show() return refute elif isinstance(kappa_t, (list, np.ndarray)): outcomes = np.random.rand(len(kappa_t)) orig_data = copy.deepcopy(data) for i in tqdm( range(0, len(kappa_t)), colour=CausalRefuter.PROGRESS_BAR_COLOR, disable=not show_progress_bar, desc="Refuting Estimates: ", ): new_data = _include_confounders_effect( data, orig_data, confounders_effect_on_treatment, treatment_name, kappa_t[i], confounders_effect_on_outcome, outcome_name, kappa_y, ) new_estimator = CausalEstimator.get_estimator_object(new_data, target_estimand, estimate) new_effect = new_estimator.estimate_effect() refute = CausalRefutation( estimate.value, new_effect.value, refutation_type="Refute: Add an Unobserved Common Cause" ) logger.debug(refute) outcomes[i] = refute.new_effect # Populate the results refute.new_effect_array = outcomes refute.new_effect = (np.min(outcomes), np.max(outcomes)) if plotmethod is None: return refute import matplotlib import matplotlib.pyplot as plt fig = plt.figure(figsize=(6, 5)) left, bottom, width, height = 0.1, 0.1, 0.8, 0.8 ax = fig.add_axes([left, bottom, width, height]) plt.plot(kappa_t, outcomes) plt.axhline(estimate.value, linestyle="--", color="gray") ax.set_title("Effect of Unobserved Common Cause") ax.set_xlabel("Value of Linear Constant on Treatment") ax.set_ylabel("Estimated Effect after adding the common cause") plt.show() return refute elif isinstance(kappa_y, (list, np.ndarray)): outcomes = np.random.rand(len(kappa_y)) orig_data = copy.deepcopy(data) for i in tqdm( range(0, len(kappa_y)), colour=CausalRefuter.PROGRESS_BAR_COLOR, disable=not show_progress_bar, desc="Refuting Estimates: ", ): new_data = _include_confounders_effect( data, orig_data, confounders_effect_on_treatment, treatment_name, kappa_t, confounders_effect_on_outcome, outcome_name, kappa_y[i], ) new_estimator = CausalEstimator.get_estimator_object(new_data, target_estimand, estimate) new_effect = new_estimator.estimate_effect() refute = CausalRefutation( estimate.value, new_effect.value, refutation_type="Refute: Add an Unobserved Common Cause" ) logger.debug(refute) outcomes[i] = refute.new_effect # Populate the results refute.new_effect_array = outcomes refute.new_effect = (np.min(outcomes), np.max(outcomes)) if plotmethod is None: return refute import matplotlib import matplotlib.pyplot as plt fig = plt.figure(figsize=(6, 5)) left, bottom, width, height = 0.1, 0.1, 0.8, 0.8 ax = fig.add_axes([left, bottom, width, height]) plt.plot(kappa_y, outcomes) plt.axhline(estimate.value, linestyle="--", color="gray") ax.set_title("Effect of Unobserved Common Cause") ax.set_xlabel("Value of Linear Constant on Outcome") ax.set_ylabel("Estimated Effect after adding the common cause") plt.show() return refute

andresmor-ms

133e7b9a4ed32aae8ab5f39a01eb02b3a4d1c0ba

e1652ec3c6606b1bb2dfe91ef830e4b4b566712d

I'm adding the `_` everywhere I see a non-public function/method, also I'm adding the public facing functions into the `__init__.py` file of the module. I guess that's the pythonic way, I don't think there's a way to prevent the user from importing/using those functions.

andresmor-ms

py-why/dowhy

Functional api/refute estimate

* Refactor refuters into functions * Rename functional_api notebook for clarity * Add return types to identify_estimate * Update `__init__.py` for imports * Add joblib for bootstrap refuter * Create `refute_estimate` function * Add types for refuter parameters & return types

2022-10-04 16:18:49+00:00

2022-10-07 04:30:22+00:00

dowhy/causal_refuters/add_unobserved_common_cause.py

import copy import logging import math import numpy as np import pandas as pd import scipy.stats import statsmodels.api as sm from sklearn.linear_model import LogisticRegression from sklearn.preprocessing import StandardScaler from tqdm.auto import tqdm import dowhy.causal_estimators.econml from dowhy.causal_estimator import CausalEstimator from dowhy.causal_estimators.linear_regression_estimator import LinearRegressionEstimator from dowhy.causal_estimators.regression_estimator import RegressionEstimator from dowhy.causal_refuter import CausalRefutation, CausalRefuter from dowhy.causal_refuters.evalue_sensitivity_analyzer import EValueSensitivityAnalyzer from dowhy.causal_refuters.linear_sensitivity_analyzer import LinearSensitivityAnalyzer from dowhy.causal_refuters.non_parametric_sensitivity_analyzer import NonParametricSensitivityAnalyzer from dowhy.causal_refuters.partial_linear_sensitivity_analyzer import PartialLinearSensitivityAnalyzer class AddUnobservedCommonCause(CausalRefuter): """Add an unobserved confounder for refutation. AddUnobservedCommonCause class supports three methods: 1) Simulation of an unobserved confounder 2) Linear partial R2 : Sensitivity Analysis for linear models. 3) Non-Parametric partial R2 based : Sensitivity Analyis for non-parametric models. Supports additional parameters that can be specified in the refute_estimate() method. """ def __init__(self, *args, **kwargs): """ Initialize the parameters required for the refuter. For direct_simulation, if effect_strength_on_treatment or effect_strength_on_outcome is not given, it is calculated automatically as a range between the minimum and maximum effect strength of observed confounders on treatment and outcome respectively. :param simulation_method: The method to use for simulating effect of unobserved confounder. Possible values are ["direct-simulation", "linear-partial-R2", "non-parametric-partial-R2", "e-value"]. :param confounders_effect_on_treatment: str : The type of effect on the treatment due to the unobserved confounder. Possible values are ['binary_flip', 'linear'] :param confounders_effect_on_outcome: str : The type of effect on the outcome due to the unobserved confounder. Possible values are ['binary_flip', 'linear'] :param effect_strength_on_treatment: float, numpy.ndarray: [Used when simulation_method="direct-simulation"] Strength of the confounder's effect on treatment. When confounders_effect_on_treatment is linear, it is the regression coefficient. When the confounders_effect_on_treatment is binary flip, it is the probability with which effect of unobserved confounder can invert the value of the treatment. :param effect_strength_on_outcome: float, numpy.ndarray: Strength of the confounder's effect on outcome. Its interpretation depends on confounders_effect_on_outcome and the simulation_method. When simulation_method is direct-simulation, for a linear effect it behaves like the regression coefficient and for a binary flip, it is the probability with which it can invert the value of the outcome. :param partial_r2_confounder_treatment: float, numpy.ndarray: [Used when simulation_method is linear-partial-R2 or non-parametric-partial-R2] Partial R2 of the unobserved confounder wrt the treatment conditioned on the observed confounders. Only in the case of general non-parametric-partial-R2, it is the fraction of variance in the reisz representer that is explained by the unobserved confounder; specifically (1-r), where r is the ratio of variance of reisz representer, alpha^2, based on observed confounders and that based on all confounders. :param partial_r2_confounder_outcome: float, numpy.ndarray: [Used when simulation_method is linear-partial-R2 or non-parametric-partial-R2] Partial R2 of the unobserved confounder wrt the outcome conditioned on the treatment and observed confounders. :param frac_strength_treatment: float: This parameter decides the effect strength of the simulated confounder as a fraction of the effect strength of observed confounders on treatment. Defaults to 1. :param frac_strength_outcome: float: This parameter decides the effect strength of the simulated confounder as a fraction of the effect strength of observed confounders on outcome. Defaults to 1. :param plotmethod: string: Type of plot to be shown. If None, no plot is generated. This parameter is used only only when more than one treatment confounder effect values or outcome confounder effect values are provided. Default is "colormesh". Supported values are "contour", "colormesh" when more than one value is provided for both confounder effect value parameters; "line" when provided for only one of them. :param percent_change_estimate: It is the percentage of reduction of treatment estimate that could alter the results (default = 1). if percent_change_estimate = 1, the robustness value describes the strength of association of confounders with treatment and outcome in order to reduce the estimate by 100% i.e bring it down to 0. (relevant only for Linear Sensitivity Analysis, ignore for rest) :param confounder_increases_estimate: True implies that confounder increases the absolute value of estimate and vice versa. (Default = False). (relevant only for Linear Sensitivity Analysis, ignore for rest) :param benchmark_common_causes: names of variables for bounding strength of confounders. (relevant only for partial-r2 based simulation methods) :param significance_level: confidence interval for statistical inference(default = 0.05). (relevant only for partial-r2 based simulation methods) :param null_hypothesis_effect: assumed effect under the null hypothesis. (relevant only for linear-partial-R2, ignore for rest) :param plot_estimate: Generate contour plot for estimate while performing sensitivity analysis. (default = True). (relevant only for partial-r2 based simulation methods) :param num_splits: number of splits for cross validation. (default = 5). (relevant only for non-parametric-partial-R2 simulation method) :param shuffle_data : shuffle data or not before splitting into folds (default = False). (relevant only for non-parametric-partial-R2 simulation method) :param shuffle_random_seed: seed for randomly shuffling data. (relevant only for non-parametric-partial-R2 simulation method) :param alpha_s_estimator_param_list: list of dictionaries with parameters for finding alpha_s. (relevant only for non-parametric-partial-R2 simulation method) :param g_s_estimator_list: list of estimator objects for finding g_s. These objects should have fit() and predict() functions implemented. (relevant only for non-parametric-partial-R2 simulation method) :param g_s_estimator_param_list: list of dictionaries with parameters for tuning respective estimators in "g_s_estimator_list". The order of the dictionaries in the list should be consistent with the estimator objects order in "g_s_estimator_list". (relevant only for non-parametric-partial-R2 simulation method) """ super().__init__(*args, **kwargs) self.simulation_method = kwargs["simulation_method"] if "simulation_method" in kwargs else "direct-simulation" self.effect_on_t = ( kwargs["confounders_effect_on_treatment"] if "confounders_effect_on_treatment" in kwargs else "binary_flip" ) self.effect_on_y = ( kwargs["confounders_effect_on_outcome"] if "confounders_effect_on_outcome" in kwargs else "linear" ) if self.simulation_method == "direct-simulation": self.kappa_t = kwargs["effect_strength_on_treatment"] if "effect_strength_on_treatment" in kwargs else None self.kappa_y = kwargs["effect_strength_on_outcome"] if "effect_strength_on_outcome" in kwargs else None elif self.simulation_method in ["linear-partial-R2", "non-parametric-partial-R2"]: self.kappa_t = ( kwargs["partial_r2_confounder_treatment"] if "partial_r2_confounder_treatment" in kwargs else None ) self.kappa_y = ( kwargs["partial_r2_confounder_outcome"] if "partial_r2_confounder_outcome" in kwargs else None ) elif self.simulation_method == "e-value": pass else: raise ValueError( "simulation method is not supported. Try direct-simulation, linear-partial-R2, non-parametric-partial-R2, or e-value" ) self.frac_strength_treatment = ( kwargs["effect_fraction_on_treatment"] if "effect_fraction_on_treatment" in kwargs else 1 ) self.frac_strength_outcome = ( kwargs["effect_fraction_on_outcome"] if "effect_fraction_on_outcome" in kwargs else 1 ) self.plotmethod = kwargs["plotmethod"] if "plotmethod" in kwargs else "colormesh" self.percent_change_estimate = kwargs["percent_change_estimate"] if "percent_change_estimate" in kwargs else 1.0 self.significance_level = kwargs["significance_level"] if "significance_level" in kwargs else 0.05 self.confounder_increases_estimate = ( kwargs["confounder_increases_estimate"] if "confounder_increases_estimate" in kwargs else False ) self.benchmark_common_causes = ( kwargs["benchmark_common_causes"] if "benchmark_common_causes" in kwargs else None ) self.null_hypothesis_effect = kwargs["null_hypothesis_effect"] if "null_hypothesis_effect" in kwargs else 0 self.plot_estimate = kwargs["plot_estimate"] if "plot_estimate" in kwargs else True self.num_splits = kwargs["num_splits"] if "num_splits" in kwargs else 5 self.shuffle_data = kwargs["shuffle_data"] if "shuffle_data" in kwargs else False self.shuffle_random_seed = kwargs["shuffle_random_seed"] if "shuffle_random_seed" in kwargs else None self.alpha_s_estimator_param_list = ( kwargs["alpha_s_estimator_param_list"] if "alpha_s_estimator_param_list" in kwargs else None ) self.alpha_s_estimator_list = kwargs["alpha_s_estimator_list"] if "alpha_s_estimator_list" in kwargs else None self.g_s_estimator_list = kwargs["g_s_estimator_list"] if "g_s_estimator_list" in kwargs else None self.g_s_estimator_param_list = ( kwargs["g_s_estimator_param_list"] if "g_s_estimator_param_list" in kwargs else None ) self.plugin_reisz = kwargs["plugin_reisz"] if "plugin_reisz" in kwargs else False self.logger = logging.getLogger(__name__) def infer_default_kappa_t(self, len_kappa_t=10): """Infer default effect strength of simulated confounder on treatment.""" observed_common_causes_names = self._target_estimand.get_backdoor_variables() if len(observed_common_causes_names) > 0: observed_common_causes = self._data[observed_common_causes_names] observed_common_causes = pd.get_dummies(observed_common_causes, drop_first=True) else: raise ValueError( "There needs to be at least one common cause to" + "automatically compute the default value of kappa_t." + " Provide a value for kappa_t" ) t = self._data[self._treatment_name] # Standardizing the data observed_common_causes = StandardScaler().fit_transform(observed_common_causes) if self.effect_on_t == "binary_flip": # Fit a model containing all confounders and compare predictions # using all features compared to all features except a given # confounder. tmodel = LogisticRegression().fit(observed_common_causes, t) tpred = tmodel.predict(observed_common_causes).astype(int) flips = [] for i in range(observed_common_causes.shape[1]): oldval = np.copy(observed_common_causes[:, i]) observed_common_causes[:, i] = 0 tcap = tmodel.predict(observed_common_causes).astype(int) observed_common_causes[:, i] = oldval flips.append(np.sum(abs(tcap - tpred)) / tpred.shape[0]) min_coeff, max_coeff = min(flips), max(flips) elif self.effect_on_t == "linear": # Estimating the regression coefficient from standardized features to t corrcoef_var_t = np.corrcoef(observed_common_causes, t, rowvar=False)[-1, :-1] std_dev_t = np.std(t)[0] max_coeff = max(corrcoef_var_t) * std_dev_t min_coeff = min(corrcoef_var_t) * std_dev_t else: raise NotImplementedError( "'" + self.effect_on_t + "' method not supported for confounders' effect on treatment" ) min_coeff, max_coeff = self._compute_min_max_coeff(min_coeff, max_coeff, self.frac_strength_treatment) # By default, return a plot with 10 points # consider 10 values of the effect of the unobserved confounder step = (max_coeff - min_coeff) / len_kappa_t self.logger.info("(Min, Max) kappa_t for observed common causes, ({0}, {1})".format(min_coeff, max_coeff)) if np.equal(max_coeff, min_coeff): return max_coeff else: return np.arange(min_coeff, max_coeff, step) def _compute_min_max_coeff(self, min_coeff, max_coeff, effect_strength_fraction): max_coeff = effect_strength_fraction * max_coeff min_coeff = effect_strength_fraction * min_coeff return min_coeff, max_coeff def infer_default_kappa_y(self, len_kappa_y=10): """Infer default effect strength of simulated confounder on treatment.""" observed_common_causes_names = self._target_estimand.get_backdoor_variables() if len(observed_common_causes_names) > 0: observed_common_causes = self._data[observed_common_causes_names] observed_common_causes = pd.get_dummies(observed_common_causes, drop_first=True) else: raise ValueError( "There needs to be at least one common cause to" + "automatically compute the default value of kappa_y." + " Provide a value for kappa_y" ) y = self._data[self._outcome_name] # Standardizing the data observed_common_causes = StandardScaler().fit_transform(observed_common_causes) if self.effect_on_y == "binary_flip": # Fit a model containing all confounders and compare predictions # using all features compared to all features except a given # confounder. ymodel = LogisticRegression().fit(observed_common_causes, y) ypred = ymodel.predict(observed_common_causes).astype(int) flips = [] for i in range(observed_common_causes.shape[1]): oldval = np.copy(observed_common_causes[:, i]) observed_common_causes[:, i] = 0 ycap = ymodel.predict(observed_common_causes).astype(int) observed_common_causes[:, i] = oldval flips.append(np.sum(abs(ycap - ypred)) / ypred.shape[0]) min_coeff, max_coeff = min(flips), max(flips) elif self.effect_on_y == "linear": corrcoef_var_y = np.corrcoef(observed_common_causes, y, rowvar=False)[-1, :-1] std_dev_y = np.std(y)[0] max_coeff = max(corrcoef_var_y) * std_dev_y min_coeff = min(corrcoef_var_y) * std_dev_y else: raise NotImplementedError( "'" + self.effect_on_y + "' method not supported for confounders' effect on outcome" ) min_coeff, max_coeff = self._compute_min_max_coeff(min_coeff, max_coeff, self.frac_strength_outcome) # By default, return a plot with 10 points # consider 10 values of the effect of the unobserved confounder step = (max_coeff - min_coeff) / len_kappa_y self.logger.info("(Min, Max) kappa_y for observed common causes, ({0}, {1})".format(min_coeff, max_coeff)) if np.equal(max_coeff, min_coeff): return max_coeff else: return np.arange(min_coeff, max_coeff, step) def refute_estimate(self, show_progress_bar=False): """ This function attempts to add an unobserved common cause to the outcome and the treatment. At present, we have implemented the behavior for one dimensional behaviors for continuous and binary variables. This function can either take single valued inputs or a range of inputs. The function then looks at the data type of the input and then decides on the course of action. :return: CausalRefuter: An object that contains the estimated effect and a new effect and the name of the refutation used. """ if self.simulation_method == "linear-partial-R2": if not (isinstance(self._estimate.estimator, LinearRegressionEstimator)): raise NotImplementedError( "Currently only LinearRegressionEstimator is supported for Sensitivity Analysis" ) if len(self._estimate.estimator._effect_modifier_names) > 0: raise NotImplementedError("The current implementation does not support effect modifiers") if self.frac_strength_outcome == 1: self.frac_strength_outcome = self.frac_strength_treatment analyzer = LinearSensitivityAnalyzer( estimator=self._estimate.estimator, data=self._data, treatment_name=self._treatment_name, percent_change_estimate=self.percent_change_estimate, significance_level=self.significance_level, benchmark_common_causes=self.benchmark_common_causes, null_hypothesis_effect=self.null_hypothesis_effect, frac_strength_treatment=self.frac_strength_treatment, frac_strength_outcome=self.frac_strength_outcome, common_causes_order=self._estimate.estimator._observed_common_causes.columns, ) analyzer.check_sensitivity(plot=self.plot_estimate) return analyzer if self.simulation_method == "non-parametric-partial-R2": # If the estimator used is LinearDML, partially linear sensitivity analysis will be automatically chosen if isinstance(self._estimate.estimator, dowhy.causal_estimators.econml.Econml): if self._estimate.estimator._econml_methodname == "econml.dml.LinearDML": analyzer = PartialLinearSensitivityAnalyzer( estimator=self._estimate._estimator_object, observed_common_causes=self._estimate.estimator._observed_common_causes, treatment=self._estimate.estimator._treatment, outcome=self._estimate.estimator._outcome, alpha_s_estimator_param_list=self.alpha_s_estimator_param_list, g_s_estimator_list=self.g_s_estimator_list, g_s_estimator_param_list=self.g_s_estimator_param_list, effect_strength_treatment=self.kappa_t, effect_strength_outcome=self.kappa_y, benchmark_common_causes=self.benchmark_common_causes, frac_strength_treatment=self.frac_strength_treatment, frac_strength_outcome=self.frac_strength_outcome, ) analyzer.check_sensitivity(plot=self.plot_estimate) return analyzer analyzer = NonParametricSensitivityAnalyzer( estimator=self._estimate.estimator, observed_common_causes=self._estimate.estimator._observed_common_causes, treatment=self._estimate.estimator._treatment, outcome=self._estimate.estimator._outcome, alpha_s_estimator_list=self.alpha_s_estimator_list, alpha_s_estimator_param_list=self.alpha_s_estimator_param_list, g_s_estimator_list=self.g_s_estimator_list, g_s_estimator_param_list=self.g_s_estimator_param_list, effect_strength_treatment=self.kappa_t, effect_strength_outcome=self.kappa_y, benchmark_common_causes=self.benchmark_common_causes, frac_strength_treatment=self.frac_strength_treatment, frac_strength_outcome=self.frac_strength_outcome, theta_s=self._estimate.value, plugin_reisz=self.plugin_reisz, ) analyzer.check_sensitivity(plot=self.plot_estimate) return analyzer if self.simulation_method == "e-value": if not isinstance(self._estimate.estimator, RegressionEstimator): raise NotImplementedError( "E-Value sensitivity analysis is currently only implemented RegressionEstimator." ) if len(self._estimate.estimator._effect_modifier_names) > 0: raise NotImplementedError("The current implementation does not support effect modifiers") analyzer = EValueSensitivityAnalyzer( estimate=self._estimate, estimand=self._target_estimand, data=self._data, treatment_name=self._treatment_name[0], outcome_name=self._outcome_name[0], ) analyzer.check_sensitivity(plot=self.plot_estimate) return analyzer if self.kappa_t is None: self.kappa_t = self.infer_default_kappa_t() if self.kappa_y is None: self.kappa_y = self.infer_default_kappa_y() if not isinstance(self.kappa_t, (list, np.ndarray)) and not isinstance( self.kappa_y, (list, np.ndarray) ): # Deal with single value inputs new_data = copy.deepcopy(self._data) new_data = self.include_confounders_effect(new_data, self.kappa_t, self.kappa_y) new_estimator = CausalEstimator.get_estimator_object(new_data, self._target_estimand, self._estimate) new_effect = new_estimator.estimate_effect() refute = CausalRefutation( self._estimate.value, new_effect.value, refutation_type="Refute: Add an Unobserved Common Cause" ) refute.new_effect_array = np.array(new_effect.value) refute.new_effect = new_effect.value refute.add_refuter(self) return refute else: # Deal with multiple value inputs if isinstance(self.kappa_t, (list, np.ndarray)) and isinstance( self.kappa_y, (list, np.ndarray) ): # Deal with range inputs # Get a 2D matrix of values # x,y = np.meshgrid(self.kappa_t, self.kappa_y) # x,y are both MxN results_matrix = np.random.rand( len(self.kappa_t), len(self.kappa_y) ) # Matrix to hold all the results of NxM orig_data = copy.deepcopy(self._data) for i in tqdm( range(len(self.kappa_t)), colour=CausalRefuter.PROGRESS_BAR_COLOR, disable=not show_progress_bar, desc="Refuting Estimates: ", ): for j in range(len(self.kappa_y)): new_data = self.include_confounders_effect(orig_data, self.kappa_t[i], self.kappa_y[j]) new_estimator = CausalEstimator.get_estimator_object( new_data, self._target_estimand, self._estimate ) new_effect = new_estimator.estimate_effect() refute = CausalRefutation( self._estimate.value, new_effect.value, refutation_type="Refute: Add an Unobserved Common Cause", ) results_matrix[i][j] = refute.new_effect # Populate the results refute.new_effect_array = results_matrix refute.new_effect = (np.min(results_matrix), np.max(results_matrix)) # Store the values into the refute object refute.add_refuter(self) if self.plotmethod is None: return refute import matplotlib import matplotlib.pyplot as plt fig = plt.figure(figsize=(6, 5)) left, bottom, width, height = 0.1, 0.1, 0.8, 0.8 ax = fig.add_axes([left, bottom, width, height]) oe = self._estimate.value contour_levels = [oe / 4.0, oe / 2.0, (3.0 / 4) * oe, oe] contour_levels.extend([0, np.min(results_matrix), np.max(results_matrix)]) if self.plotmethod == "contour": cp = plt.contourf(self.kappa_y, self.kappa_t, results_matrix, levels=sorted(contour_levels)) # Adding a label on the contour line for the original estimate fmt = {} trueeffect_index = np.where(cp.levels == oe)[0][0] fmt[cp.levels[trueeffect_index]] = "Estimated Effect" # Label every other level using strings plt.clabel(cp, [cp.levels[trueeffect_index]], inline=True, fmt=fmt) plt.colorbar(cp) elif self.plotmethod == "colormesh": cp = plt.pcolormesh(self.kappa_y, self.kappa_t, results_matrix, shading="nearest") plt.colorbar(cp, ticks=contour_levels) ax.yaxis.set_ticks(self.kappa_t) ax.xaxis.set_ticks(self.kappa_y) plt.xticks(rotation=45) ax.set_title("Effect of Unobserved Common Cause") ax.set_ylabel("Value of Linear Constant on Treatment") ax.set_xlabel("Value of Linear Constant on Outcome") plt.show() return refute elif isinstance(self.kappa_t, (list, np.ndarray)): outcomes = np.random.rand(len(self.kappa_t)) orig_data = copy.deepcopy(self._data) for i in tqdm( range(0, len(self.kappa_t)), colour=CausalRefuter.PROGRESS_BAR_COLOR, disable=not show_progress_bar, desc="Refuting Estimates: ", ): new_data = self.include_confounders_effect(orig_data, self.kappa_t[i], self.kappa_y) new_estimator = CausalEstimator.get_estimator_object( new_data, self._target_estimand, self._estimate ) new_effect = new_estimator.estimate_effect() refute = CausalRefutation( self._estimate.value, new_effect.value, refutation_type="Refute: Add an Unobserved Common Cause" ) self.logger.debug(refute) outcomes[i] = refute.new_effect # Populate the results refute.new_effect_array = outcomes refute.new_effect = (np.min(outcomes), np.max(outcomes)) refute.add_refuter(self) if self.plotmethod is None: return refute import matplotlib import matplotlib.pyplot as plt fig = plt.figure(figsize=(6, 5)) left, bottom, width, height = 0.1, 0.1, 0.8, 0.8 ax = fig.add_axes([left, bottom, width, height]) plt.plot(self.kappa_t, outcomes) plt.axhline(self._estimate.value, linestyle="--", color="gray") ax.set_title("Effect of Unobserved Common Cause") ax.set_xlabel("Value of Linear Constant on Treatment") ax.set_ylabel("Estimated Effect after adding the common cause") plt.show() return refute elif isinstance(self.kappa_y, (list, np.ndarray)): outcomes = np.random.rand(len(self.kappa_y)) orig_data = copy.deepcopy(self._data) for i in tqdm( range(0, len(self.kappa_y)), colour=CausalRefuter.PROGRESS_BAR_COLOR, disable=not show_progress_bar, desc="Refuting Estimates: ", ): new_data = self.include_confounders_effect(orig_data, self.kappa_t, self.kappa_y[i]) new_estimator = CausalEstimator.get_estimator_object( new_data, self._target_estimand, self._estimate ) new_effect = new_estimator.estimate_effect() refute = CausalRefutation( self._estimate.value, new_effect.value, refutation_type="Refute: Add an Unobserved Common Cause" ) self.logger.debug(refute) outcomes[i] = refute.new_effect # Populate the results refute.new_effect_array = outcomes refute.new_effect = (np.min(outcomes), np.max(outcomes)) refute.add_refuter(self) if self.plotmethod is None: return refute import matplotlib import matplotlib.pyplot as plt fig = plt.figure(figsize=(6, 5)) left, bottom, width, height = 0.1, 0.1, 0.8, 0.8 ax = fig.add_axes([left, bottom, width, height]) plt.plot(self.kappa_y, outcomes) plt.axhline(self._estimate.value, linestyle="--", color="gray") ax.set_title("Effect of Unobserved Common Cause") ax.set_xlabel("Value of Linear Constant on Outcome") ax.set_ylabel("Estimated Effect after adding the common cause") plt.show() return refute def include_confounders_effect(self, new_data, kappa_t, kappa_y): """ This function deals with the change in the value of the data due to the effect of the unobserved confounder. In the case of a binary flip, we flip only if the random number is greater than the threshold set. In the case of a linear effect, we use the variable as the linear regression constant. :param new_data: pandas.DataFrame: The data to be changed due to the effects of the unobserved confounder. :param kappa_t: numpy.float64: The value of the threshold for binary_flip or the value of the regression coefficient for linear effect. :param kappa_y: numpy.float64: The value of the threshold for binary_flip or the value of the regression coefficient for linear effect. :return: pandas.DataFrame: The DataFrame that includes the effects of the unobserved confounder. """ num_rows = self._data.shape[0] stdnorm = scipy.stats.norm() w_random = stdnorm.rvs(num_rows) if self.effect_on_t == "binary_flip": alpha = 2 * kappa_t - 1 if kappa_t >= 0.5 else 1 - 2 * kappa_t interval = stdnorm.interval(alpha) rel_interval = interval[0] if kappa_t >= 0.5 else interval[1] new_data.loc[rel_interval <= w_random, self._treatment_name] = ( 1 - new_data.loc[rel_interval <= w_random, self._treatment_name] ) for tname in self._treatment_name: if pd.api.types.is_bool_dtype(self._data[tname]): new_data = new_data.astype({tname: "bool"}, copy=False) elif self.effect_on_t == "linear": confounder_t_effect = kappa_t * w_random # By default, we add the effect of simulated confounder for treatment. # But subtract it from outcome to create a negative correlation # assuming that the original confounder's effect was positive on both. # This is to remove the effect of the original confounder. new_data[self._treatment_name] = new_data[self._treatment_name].values + np.ndarray( shape=(num_rows, 1), buffer=confounder_t_effect ) else: raise NotImplementedError( "'" + self.effect_on_t + "' method not supported for confounders' effect on treatment" ) if self.effect_on_y == "binary_flip": alpha = 2 * kappa_y - 1 if kappa_y >= 0.5 else 1 - 2 * kappa_y interval = stdnorm.interval(alpha) rel_interval = interval[0] if kappa_y >= 0.5 else interval[1] new_data.loc[rel_interval <= w_random, self._outcome_name] = ( 1 - new_data.loc[rel_interval <= w_random, self._outcome_name] ) for yname in self._outcome_name: if pd.api.types.is_bool_dtype(self._data[yname]): new_data = new_data.astype({yname: "bool"}, copy=False) elif self.effect_on_y == "linear": confounder_y_effect = (-1) * kappa_y * w_random # By default, we add the effect of simulated confounder for treatment. # But subtract it from outcome to create a negative correlation # assuming that the original confounder's effect was positive on both. # This is to remove the effect of the original confounder. new_data[self._outcome_name] = new_data[self._outcome_name].values + np.ndarray( shape=(num_rows, 1), buffer=confounder_y_effect ) else: raise NotImplementedError( "'" + self.effect_on_y + "' method not supported for confounders' effect on outcome" ) return new_data def include_simulated_confounder(self, convergence_threshold=0.1, c_star_max=1000): """ This function simulates an unobserved confounder based on the data using the following steps: 1. It calculates the "residuals" from the treatment and outcome model i.) The outcome model has outcome as the dependent variable and all the observed variables including treatment as independent variables ii.) The treatment model has treatment as the dependent variable and all the observed variables as independent variables. 2. U is an intermediate random variable drawn from the normal distribution with the weighted average of residuals as mean and a unit variance U ~ N(c1*d_y + c2*d_t, 1) where *d_y and d_t are residuals from the treatment and outcome model *c1 and c2 are coefficients to the residuals 3. The final U, which is the simulated unobserved confounder is obtained by debiasing the intermediate variable U by residualising it with X Choosing the coefficients c1 and c2: The coefficients are chosen based on these basic assumptions: 1. There is a hyperbolic relationship satisfying c1*c2 = c_star 2. c_star is chosen from a range of possible values based on the correlation of the obtained simulated variable with outcome and treatment. 3. The product of correlations with treatment and outcome should be at a minimum distance to the maximum correlations with treatment and outcome in any of the observed confounders 4. The ratio of the weights should be such that they maintain the ratio of the maximum possible observed coefficients within some confidence interval :param c_star_max: The maximum possible value for the hyperbolic curve on which the coefficients to the residuals lie. It defaults to 1000 in the code if not specified by the user. :type int :param convergence_threshold: The threshold to check the plateauing of the correlation while selecting a c_star. It defaults to 0.1 in the code if not specified by the user :type float :returns: The simulated values of the unobserved confounder based on the data :type pandas.core.series.Series """ # Obtaining the list of observed variables required_variables = True observed_variables = self.choose_variables(required_variables) observed_variables_with_treatment_and_outcome = observed_variables + self._treatment_name + self._outcome_name # Taking a subset of the dataframe that has only observed variables self._data = self._data[observed_variables_with_treatment_and_outcome] # Residuals from the outcome model obtained by fitting a linear model y = self._data[self._outcome_name[0]] observed_variables_with_treatment = observed_variables + self._treatment_name X = self._data[observed_variables_with_treatment] model = sm.OLS(y, X.astype("float")) results = model.fit() residuals_y = y - results.fittedvalues d_y = list(pd.Series(residuals_y)) # Residuals from the treatment model obtained by fitting a linear model t = self._data[self._treatment_name[0]].astype("int64") X = self._data[observed_variables] model = sm.OLS(t, X) results = model.fit() residuals_t = t - results.fittedvalues d_t = list(pd.Series(residuals_t)) # Initialising product_cor_metric_observed with a really low value as finding maximum product_cor_metric_observed = -10000000000 for i in observed_variables: current_obs_confounder = self._data[i] outcome_values = self._data[self._outcome_name[0]] correlation_y = current_obs_confounder.corr(outcome_values) treatment_values = t correlation_t = current_obs_confounder.corr(treatment_values) product_cor_metric_current = correlation_y * correlation_t if product_cor_metric_current >= product_cor_metric_observed: product_cor_metric_observed = product_cor_metric_current correlation_t_observed = correlation_t correlation_y_observed = correlation_y # The user has an option to give the the effect_strength_on_y and effect_strength_on_t which can be then used instead of maximum correlation with treatment and outcome in the observed variables as it specifies the desired effect. if self.kappa_t is not None: correlation_t_observed = self.kappa_t if self.kappa_y is not None: correlation_y_observed = self.kappa_y # Choosing a c_star based on the data. # The correlations stop increasing upon increasing c_star after a certain value, that is it plateaus and we choose the value of c_star to be the value it plateaus. correlation_y_list = [] correlation_t_list = [] product_cor_metric_simulated_list = [] x_list = [] step = int(c_star_max / 10) for i in range(0, int(c_star_max), step): c1 = math.sqrt(i) c2 = c1 final_U = self.generate_confounder_from_residuals(c1, c2, d_y, d_t, X) current_simulated_confounder = final_U outcome_values = self._data[self._outcome_name[0]] correlation_y = current_simulated_confounder.corr(outcome_values) correlation_y_list.append(correlation_y) treatment_values = t correlation_t = current_simulated_confounder.corr(treatment_values) correlation_t_list.append(correlation_t) product_cor_metric_simulated = correlation_y * correlation_t product_cor_metric_simulated_list.append(product_cor_metric_simulated) x_list.append(i) index = 1 while index < len(correlation_y_list): if (correlation_y_list[index] - correlation_y_list[index - 1]) <= convergence_threshold: c_star = x_list[index] break index = index + 1 # Choosing c1 and c2 based on the hyperbolic relationship once c_star is chosen by going over various combinations of c1 and c2 values and choosing the combination which # which maintains the minimum distance between the product of correlations of the simulated variable and the product of maximum correlations of one of the observed variables # and additionally checks if the ratio of the weights are such that they maintain the ratio of the maximum possible observed coefficients within some confidence interval # c1_final and c2_final are initialised to the values on the hyperbolic curve such that c1_final = c2_final and c1_final*c2_final = c_star c1_final = math.sqrt(c_star) c2_final = math.sqrt(c_star) # initialising min_distance_between_product_cor_metrics to be a value greater than 1 min_distance_between_product_cor_metrics = 1.5 i = 0.05 threshold = c_star / 0.05 while i <= threshold: c2 = i c1 = c_star / c2 final_U = self.generate_confounder_from_residuals(c1, c2, d_y, d_t, X) current_simulated_confounder = final_U outcome_values = self._data[self._outcome_name[0]] correlation_y = current_simulated_confounder.corr(outcome_values) treatment_values = t correlation_t = current_simulated_confounder.corr(treatment_values) product_cor_metric_simulated = correlation_y * correlation_t if min_distance_between_product_cor_metrics >= abs( product_cor_metric_simulated - product_cor_metric_observed ): min_distance_between_product_cor_metrics = abs( product_cor_metric_simulated - product_cor_metric_observed ) additional_condition = correlation_y_observed / correlation_t_observed if ((c1 / c2) <= (additional_condition + 0.3 * additional_condition)) and ( (c1 / c2) >= (additional_condition - 0.3 * additional_condition) ): # choose minimum positive value c1_final = c1 c2_final = c2 i = i * 1.5 """#closed form solution print("c_star_max before closed form", c_star_max) if max_correlation_with_t == -1000: c2 = 0 c1 = c_star_max else: additional_condition = abs(max_correlation_with_y/max_correlation_with_t) print("additional_condition", additional_condition) c2 = math.sqrt(c_star_max/additional_condition) c1 = c_star_max/c2""" final_U = self.generate_confounder_from_residuals(c1_final, c2_final, d_y, d_t, X) return final_U def generate_confounder_from_residuals(self, c1, c2, d_y, d_t, X): """ This function takes the residuals from the treatment and outcome model and their coefficients and simulates the intermediate random variable U by taking the row wise normal distribution corresponding to each residual value and then debiasing the intermediate variable to get the final variable. :param c1: coefficient to the residual from the outcome model :type float :param c2: coefficient to the residual from the treatment model :type float :param d_y: residuals from the outcome model :type list :param d_t: residuals from the treatment model :type list :returns: The simulated values of the unobserved confounder based on the data :type pandas.core.series.Series """ U = [] for j in range(len(d_t)): simulated_variable_mean = c1 * d_y[j] + c2 * d_t[j] simulated_variable_stddev = 1 U.append(np.random.normal(simulated_variable_mean, simulated_variable_stddev, 1)) U = np.array(U) model = sm.OLS(U, X) results = model.fit() U = U.reshape( -1, ) final_U = U - results.fittedvalues.values final_U = pd.Series(U) return final_U

import copy import logging import math from typing import Dict, List, Optional, Union import numpy as np import pandas as pd import scipy.stats import statsmodels.api as sm from sklearn.linear_model import LogisticRegression from sklearn.preprocessing import StandardScaler from tqdm.auto import tqdm import dowhy.causal_estimators.econml from dowhy.causal_estimator import CausalEstimate, CausalEstimator from dowhy.causal_estimators.linear_regression_estimator import LinearRegressionEstimator from dowhy.causal_estimators.regression_estimator import RegressionEstimator from dowhy.causal_identifier.identified_estimand import IdentifiedEstimand from dowhy.causal_refuter import CausalRefutation, CausalRefuter, choose_variables from dowhy.causal_refuters.evalue_sensitivity_analyzer import EValueSensitivityAnalyzer from dowhy.causal_refuters.linear_sensitivity_analyzer import LinearSensitivityAnalyzer from dowhy.causal_refuters.non_parametric_sensitivity_analyzer import NonParametricSensitivityAnalyzer from dowhy.causal_refuters.partial_linear_sensitivity_analyzer import PartialLinearSensitivityAnalyzer logger = logging.getLogger(__name__) class AddUnobservedCommonCause(CausalRefuter): """Add an unobserved confounder for refutation. AddUnobservedCommonCause class supports three methods: 1) Simulation of an unobserved confounder 2) Linear partial R2 : Sensitivity Analysis for linear models. 3) Non-Parametric partial R2 based : Sensitivity Analyis for non-parametric models. Supports additional parameters that can be specified in the refute_estimate() method. """ def __init__(self, *args, **kwargs): """ Initialize the parameters required for the refuter. For direct_simulation, if effect_strength_on_treatment or effect_strength_on_outcome is not given, it is calculated automatically as a range between the minimum and maximum effect strength of observed confounders on treatment and outcome respectively. :param simulation_method: The method to use for simulating effect of unobserved confounder. Possible values are ["direct-simulation", "linear-partial-R2", "non-parametric-partial-R2", "e-value"]. :param confounders_effect_on_treatment: str : The type of effect on the treatment due to the unobserved confounder. Possible values are ['binary_flip', 'linear'] :param confounders_effect_on_outcome: str : The type of effect on the outcome due to the unobserved confounder. Possible values are ['binary_flip', 'linear'] :param effect_strength_on_treatment: float, numpy.ndarray: [Used when simulation_method="direct-simulation"] Strength of the confounder's effect on treatment. When confounders_effect_on_treatment is linear, it is the regression coefficient. When the confounders_effect_on_treatment is binary flip, it is the probability with which effect of unobserved confounder can invert the value of the treatment. :param effect_strength_on_outcome: float, numpy.ndarray: Strength of the confounder's effect on outcome. Its interpretation depends on confounders_effect_on_outcome and the simulation_method. When simulation_method is direct-simulation, for a linear effect it behaves like the regression coefficient and for a binary flip, it is the probability with which it can invert the value of the outcome. :param partial_r2_confounder_treatment: float, numpy.ndarray: [Used when simulation_method is linear-partial-R2 or non-parametric-partial-R2] Partial R2 of the unobserved confounder wrt the treatment conditioned on the observed confounders. Only in the case of general non-parametric-partial-R2, it is the fraction of variance in the reisz representer that is explained by the unobserved confounder; specifically (1-r), where r is the ratio of variance of reisz representer, alpha^2, based on observed confounders and that based on all confounders. :param partial_r2_confounder_outcome: float, numpy.ndarray: [Used when simulation_method is linear-partial-R2 or non-parametric-partial-R2] Partial R2 of the unobserved confounder wrt the outcome conditioned on the treatment and observed confounders. :param frac_strength_treatment: float: This parameter decides the effect strength of the simulated confounder as a fraction of the effect strength of observed confounders on treatment. Defaults to 1. :param frac_strength_outcome: float: This parameter decides the effect strength of the simulated confounder as a fraction of the effect strength of observed confounders on outcome. Defaults to 1. :param plotmethod: string: Type of plot to be shown. If None, no plot is generated. This parameter is used only only when more than one treatment confounder effect values or outcome confounder effect values are provided. Default is "colormesh". Supported values are "contour", "colormesh" when more than one value is provided for both confounder effect value parameters; "line" when provided for only one of them. :param percent_change_estimate: It is the percentage of reduction of treatment estimate that could alter the results (default = 1). if percent_change_estimate = 1, the robustness value describes the strength of association of confounders with treatment and outcome in order to reduce the estimate by 100% i.e bring it down to 0. (relevant only for Linear Sensitivity Analysis, ignore for rest) :param confounder_increases_estimate: True implies that confounder increases the absolute value of estimate and vice versa. (Default = False). (relevant only for Linear Sensitivity Analysis, ignore for rest) :param benchmark_common_causes: names of variables for bounding strength of confounders. (relevant only for partial-r2 based simulation methods) :param significance_level: confidence interval for statistical inference(default = 0.05). (relevant only for partial-r2 based simulation methods) :param null_hypothesis_effect: assumed effect under the null hypothesis. (relevant only for linear-partial-R2, ignore for rest) :param plot_estimate: Generate contour plot for estimate while performing sensitivity analysis. (default = True). (relevant only for partial-r2 based simulation methods) :param num_splits: number of splits for cross validation. (default = 5). (relevant only for non-parametric-partial-R2 simulation method) :param shuffle_data : shuffle data or not before splitting into folds (default = False). (relevant only for non-parametric-partial-R2 simulation method) :param shuffle_random_seed: seed for randomly shuffling data. (relevant only for non-parametric-partial-R2 simulation method) :param alpha_s_estimator_param_list: list of dictionaries with parameters for finding alpha_s. (relevant only for non-parametric-partial-R2 simulation method) :param g_s_estimator_list: list of estimator objects for finding g_s. These objects should have fit() and predict() functions implemented. (relevant only for non-parametric-partial-R2 simulation method) :param g_s_estimator_param_list: list of dictionaries with parameters for tuning respective estimators in "g_s_estimator_list". The order of the dictionaries in the list should be consistent with the estimator objects order in "g_s_estimator_list". (relevant only for non-parametric-partial-R2 simulation method) """ super().__init__(*args, **kwargs) self.simulation_method = kwargs["simulation_method"] if "simulation_method" in kwargs else "direct-simulation" self.effect_on_t = ( kwargs["confounders_effect_on_treatment"] if "confounders_effect_on_treatment" in kwargs else "binary_flip" ) self.effect_on_y = ( kwargs["confounders_effect_on_outcome"] if "confounders_effect_on_outcome" in kwargs else "linear" ) if self.simulation_method == "direct-simulation": self.kappa_t = kwargs["effect_strength_on_treatment"] if "effect_strength_on_treatment" in kwargs else None self.kappa_y = kwargs["effect_strength_on_outcome"] if "effect_strength_on_outcome" in kwargs else None elif self.simulation_method in ["linear-partial-R2", "non-parametric-partial-R2"]: self.kappa_t = ( kwargs["partial_r2_confounder_treatment"] if "partial_r2_confounder_treatment" in kwargs else None ) self.kappa_y = ( kwargs["partial_r2_confounder_outcome"] if "partial_r2_confounder_outcome" in kwargs else None ) elif self.simulation_method == "e-value": pass else: raise ValueError( "simulation method is not supported. Try direct-simulation, linear-partial-R2, non-parametric-partial-R2, or e-value" ) self.frac_strength_treatment = ( kwargs["effect_fraction_on_treatment"] if "effect_fraction_on_treatment" in kwargs else 1 ) self.frac_strength_outcome = ( kwargs["effect_fraction_on_outcome"] if "effect_fraction_on_outcome" in kwargs else 1 ) self.plotmethod = kwargs["plotmethod"] if "plotmethod" in kwargs else "colormesh" self.percent_change_estimate = kwargs["percent_change_estimate"] if "percent_change_estimate" in kwargs else 1.0 self.significance_level = kwargs["significance_level"] if "significance_level" in kwargs else 0.05 self.confounder_increases_estimate = ( kwargs["confounder_increases_estimate"] if "confounder_increases_estimate" in kwargs else False ) self.benchmark_common_causes = ( kwargs["benchmark_common_causes"] if "benchmark_common_causes" in kwargs else None ) self.null_hypothesis_effect = kwargs["null_hypothesis_effect"] if "null_hypothesis_effect" in kwargs else 0 self.plot_estimate = kwargs["plot_estimate"] if "plot_estimate" in kwargs else True self.num_splits = kwargs["num_splits"] if "num_splits" in kwargs else 5 self.shuffle_data = kwargs["shuffle_data"] if "shuffle_data" in kwargs else False self.shuffle_random_seed = kwargs["shuffle_random_seed"] if "shuffle_random_seed" in kwargs else None self.alpha_s_estimator_param_list = ( kwargs["alpha_s_estimator_param_list"] if "alpha_s_estimator_param_list" in kwargs else None ) self.alpha_s_estimator_list = kwargs["alpha_s_estimator_list"] if "alpha_s_estimator_list" in kwargs else None self.g_s_estimator_list = kwargs["g_s_estimator_list"] if "g_s_estimator_list" in kwargs else None self.g_s_estimator_param_list = ( kwargs["g_s_estimator_param_list"] if "g_s_estimator_param_list" in kwargs else None ) self.plugin_reisz = kwargs["plugin_reisz"] if "plugin_reisz" in kwargs else False self.logger = logging.getLogger(__name__) def refute_estimate(self, show_progress_bar=False): if self.simulation_method == "linear-partial-R2": return sensitivity_linear_partial_r2( self._data, self._estimate, self._treatment_name, self.frac_strength_treatment, self.frac_strength_outcome, self.percent_change_estimate, self.benchmark_common_causes, self.significance_level, self.null_hypothesis_effect, self.plot_estimate, ) elif self.simulation_method == "non-parametric-partial-R2": return sensitivity_non_parametric_partial_r2( self._estimate, self.kappa_t, self.kappa_y, self.frac_strength_treatment, self.frac_strength_outcome, self.benchmark_common_causes, self.plot_estimate, self.alpha_s_estimator_list, self.alpha_s_estimator_param_list, self.g_s_estimator_list, self.g_s_estimator_param_list, self.plugin_reisz, ) elif self.simulation_method == "e-value": return sensitivity_e_value( self._data, self._target_estimand, self._estimate, self._treatment_name, self._outcome_name, self.plot_estimate, ) elif self.simulation_method == "direct-simulation": refute = sensitivity_simulation( self._data, self._target_estimand, self._estimate, self._treatment_name, self._outcome_name, self.kappa_t, self.kappa_y, self.effect_on_t, self.effect_on_y, self.frac_strength_treatment, self.frac_strength_outcome, self.plotmethod, show_progress_bar, ) refute.add_refuter(self) return refute def _infer_default_kappa_t( data: pd.DataFrame, target_estimand: IdentifiedEstimand, treatment_name: List[str], effect_on_t: str, frac_strength_treatment: float, len_kappa_t: int = 10, ): """Infer default effect strength of simulated confounder on treatment.""" observed_common_causes_names = target_estimand.get_backdoor_variables() if len(observed_common_causes_names) > 0: observed_common_causes = data[observed_common_causes_names] observed_common_causes = pd.get_dummies(observed_common_causes, drop_first=True) else: raise ValueError( "There needs to be at least one common cause to" + "automatically compute the default value of kappa_t." + " Provide a value for kappa_t" ) t = data[treatment_name] # Standardizing the data observed_common_causes = StandardScaler().fit_transform(observed_common_causes) if effect_on_t == "binary_flip": # Fit a model containing all confounders and compare predictions # using all features compared to all features except a given # confounder. tmodel = LogisticRegression().fit(observed_common_causes, t) tpred = tmodel.predict(observed_common_causes).astype(int) flips = [] for i in range(observed_common_causes.shape[1]): oldval = np.copy(observed_common_causes[:, i]) observed_common_causes[:, i] = 0 tcap = tmodel.predict(observed_common_causes).astype(int) observed_common_causes[:, i] = oldval flips.append(np.sum(abs(tcap - tpred)) / tpred.shape[0]) min_coeff, max_coeff = min(flips), max(flips) elif effect_on_t == "linear": # Estimating the regression coefficient from standardized features to t corrcoef_var_t = np.corrcoef(observed_common_causes, t, rowvar=False)[-1, :-1] std_dev_t = np.std(t)[0] max_coeff = max(corrcoef_var_t) * std_dev_t min_coeff = min(corrcoef_var_t) * std_dev_t else: raise NotImplementedError("'" + effect_on_t + "' method not supported for confounders' effect on treatment") min_coeff, max_coeff = _compute_min_max_coeff(min_coeff, max_coeff, frac_strength_treatment) # By default, return a plot with 10 points # consider 10 values of the effect of the unobserved confounder step = (max_coeff - min_coeff) / len_kappa_t logger.info("(Min, Max) kappa_t for observed common causes, ({0}, {1})".format(min_coeff, max_coeff)) if np.equal(max_coeff, min_coeff): return max_coeff else: return np.arange(min_coeff, max_coeff, step) def _compute_min_max_coeff(min_coeff: float, max_coeff: float, effect_strength_fraction: np.ndarray): max_coeff = effect_strength_fraction * max_coeff min_coeff = effect_strength_fraction * min_coeff return min_coeff, max_coeff def _infer_default_kappa_y( data: pd.DataFrame, target_estimand: IdentifiedEstimand, outcome_name: List[str], effect_on_y: str, frac_strength_outcome: float, len_kappa_y: int = 10, ): """Infer default effect strength of simulated confounder on treatment.""" observed_common_causes_names = target_estimand.get_backdoor_variables() if len(observed_common_causes_names) > 0: observed_common_causes = data[observed_common_causes_names] observed_common_causes = pd.get_dummies(observed_common_causes, drop_first=True) else: raise ValueError( "There needs to be at least one common cause to" + "automatically compute the default value of kappa_y." + " Provide a value for kappa_y" ) y = data[outcome_name] # Standardizing the data observed_common_causes = StandardScaler().fit_transform(observed_common_causes) if effect_on_y == "binary_flip": # Fit a model containing all confounders and compare predictions # using all features compared to all features except a given # confounder. ymodel = LogisticRegression().fit(observed_common_causes, y) ypred = ymodel.predict(observed_common_causes).astype(int) flips = [] for i in range(observed_common_causes.shape[1]): oldval = np.copy(observed_common_causes[:, i]) observed_common_causes[:, i] = 0 ycap = ymodel.predict(observed_common_causes).astype(int) observed_common_causes[:, i] = oldval flips.append(np.sum(abs(ycap - ypred)) / ypred.shape[0]) min_coeff, max_coeff = min(flips), max(flips) elif effect_on_y == "linear": corrcoef_var_y = np.corrcoef(observed_common_causes, y, rowvar=False)[-1, :-1] std_dev_y = np.std(y)[0] max_coeff = max(corrcoef_var_y) * std_dev_y min_coeff = min(corrcoef_var_y) * std_dev_y else: raise NotImplementedError("'" + effect_on_y + "' method not supported for confounders' effect on outcome") min_coeff, max_coeff = _compute_min_max_coeff(min_coeff, max_coeff, frac_strength_outcome) # By default, return a plot with 10 points # consider 10 values of the effect of the unobserved confounder step = (max_coeff - min_coeff) / len_kappa_y logger.info("(Min, Max) kappa_y for observed common causes, ({0}, {1})".format(min_coeff, max_coeff)) if np.equal(max_coeff, min_coeff): return max_coeff else: return np.arange(min_coeff, max_coeff, step) def _include_confounders_effect( data: pd.DataFrame, new_data: pd.DataFrame, effect_on_t: str, treatment_name: str, kappa_t: float, effect_on_y: str, outcome_name: str, kappa_y: float, ): """ This function deals with the change in the value of the data due to the effect of the unobserved confounder. In the case of a binary flip, we flip only if the random number is greater than the threshold set. In the case of a linear effect, we use the variable as the linear regression constant. :param new_data: pandas.DataFrame: The data to be changed due to the effects of the unobserved confounder. :param kappa_t: numpy.float64: The value of the threshold for binary_flip or the value of the regression coefficient for linear effect. :param kappa_y: numpy.float64: The value of the threshold for binary_flip or the value of the regression coefficient for linear effect. :return: pandas.DataFrame: The DataFrame that includes the effects of the unobserved confounder. """ num_rows = data.shape[0] stdnorm = scipy.stats.norm() w_random = stdnorm.rvs(num_rows) if effect_on_t == "binary_flip": alpha = 2 * kappa_t - 1 if kappa_t >= 0.5 else 1 - 2 * kappa_t interval = stdnorm.interval(alpha) rel_interval = interval[0] if kappa_t >= 0.5 else interval[1] new_data.loc[rel_interval <= w_random, treatment_name] = ( 1 - new_data.loc[rel_interval <= w_random, treatment_name] ) for tname in treatment_name: if pd.api.types.is_bool_dtype(data[tname]): new_data = new_data.astype({tname: "bool"}, copy=False) elif effect_on_t == "linear": confounder_t_effect = kappa_t * w_random # By default, we add the effect of simulated confounder for treatment. # But subtract it from outcome to create a negative correlation # assuming that the original confounder's effect was positive on both. # This is to remove the effect of the original confounder. new_data[treatment_name] = new_data[treatment_name].values + np.ndarray( shape=(num_rows, 1), buffer=confounder_t_effect ) else: raise NotImplementedError("'" + effect_on_t + "' method not supported for confounders' effect on treatment") if effect_on_y == "binary_flip": alpha = 2 * kappa_y - 1 if kappa_y >= 0.5 else 1 - 2 * kappa_y interval = stdnorm.interval(alpha) rel_interval = interval[0] if kappa_y >= 0.5 else interval[1] new_data.loc[rel_interval <= w_random, outcome_name] = 1 - new_data.loc[rel_interval <= w_random, outcome_name] for yname in outcome_name: if pd.api.types.is_bool_dtype(data[yname]): new_data = new_data.astype({yname: "bool"}, copy=False) elif effect_on_y == "linear": confounder_y_effect = (-1) * kappa_y * w_random # By default, we add the effect of simulated confounder for treatment. # But subtract it from outcome to create a negative correlation # assuming that the original confounder's effect was positive on both. # This is to remove the effect of the original confounder. new_data[outcome_name] = new_data[outcome_name].values + np.ndarray( shape=(num_rows, 1), buffer=confounder_y_effect ) else: raise NotImplementedError("'" + effect_on_y + "' method not supported for confounders' effect on outcome") return new_data def include_simulated_confounder( data: pd.DataFrame, treatment_name: str, outcome_name: str, kappa_t: float, kappa_y: float, convergence_threshold: float = 0.1, c_star_max: int = 1000, ): """ This function simulates an unobserved confounder based on the data using the following steps: 1. It calculates the "residuals" from the treatment and outcome model i.) The outcome model has outcome as the dependent variable and all the observed variables including treatment as independent variables ii.) The treatment model has treatment as the dependent variable and all the observed variables as independent variables. 2. U is an intermediate random variable drawn from the normal distribution with the weighted average of residuals as mean and a unit variance U ~ N(c1*d_y + c2*d_t, 1) where *d_y and d_t are residuals from the treatment and outcome model *c1 and c2 are coefficients to the residuals 3. The final U, which is the simulated unobserved confounder is obtained by debiasing the intermediate variable U by residualising it with X Choosing the coefficients c1 and c2: The coefficients are chosen based on these basic assumptions: 1. There is a hyperbolic relationship satisfying c1*c2 = c_star 2. c_star is chosen from a range of possible values based on the correlation of the obtained simulated variable with outcome and treatment. 3. The product of correlations with treatment and outcome should be at a minimum distance to the maximum correlations with treatment and outcome in any of the observed confounders 4. The ratio of the weights should be such that they maintain the ratio of the maximum possible observed coefficients within some confidence interval :param c_star_max: The maximum possible value for the hyperbolic curve on which the coefficients to the residuals lie. It defaults to 1000 in the code if not specified by the user. :type int :param convergence_threshold: The threshold to check the plateauing of the correlation while selecting a c_star. It defaults to 0.1 in the code if not specified by the user :type float :returns: The simulated values of the unobserved confounder based on the data :type pandas.core.series.Series """ # Obtaining the list of observed variables required_variables = True observed_variables = choose_variables(required_variables) observed_variables_with_treatment_and_outcome = observed_variables + treatment_name + outcome_name # Taking a subset of the dataframe that has only observed variables data = data[observed_variables_with_treatment_and_outcome] # Residuals from the outcome model obtained by fitting a linear model y = data[outcome_name[0]] observed_variables_with_treatment = observed_variables + treatment_name X = data[observed_variables_with_treatment] model = sm.OLS(y, X.astype("float")) results = model.fit() residuals_y = y - results.fittedvalues d_y = list(pd.Series(residuals_y)) # Residuals from the treatment model obtained by fitting a linear model t = data[treatment_name[0]].astype("int64") X = data[observed_variables] model = sm.OLS(t, X) results = model.fit() residuals_t = t - results.fittedvalues d_t = list(pd.Series(residuals_t)) # Initialising product_cor_metric_observed with a really low value as finding maximum product_cor_metric_observed = -10000000000 for i in observed_variables: current_obs_confounder = data[i] outcome_values = data[outcome_name[0]] correlation_y = current_obs_confounder.corr(outcome_values) treatment_values = t correlation_t = current_obs_confounder.corr(treatment_values) product_cor_metric_current = correlation_y * correlation_t if product_cor_metric_current >= product_cor_metric_observed: product_cor_metric_observed = product_cor_metric_current correlation_t_observed = correlation_t correlation_y_observed = correlation_y # The user has an option to give the the effect_strength_on_y and effect_strength_on_t which can be then used instead of maximum correlation with treatment and outcome in the observed variables as it specifies the desired effect. if kappa_t is not None: correlation_t_observed = kappa_t if kappa_y is not None: correlation_y_observed = kappa_y # Choosing a c_star based on the data. # The correlations stop increasing upon increasing c_star after a certain value, that is it plateaus and we choose the value of c_star to be the value it plateaus. correlation_y_list = [] correlation_t_list = [] product_cor_metric_simulated_list = [] x_list = [] step = int(c_star_max / 10) for i in range(0, int(c_star_max), step): c1 = math.sqrt(i) c2 = c1 final_U = _generate_confounder_from_residuals(c1, c2, d_y, d_t, X) current_simulated_confounder = final_U outcome_values = data[outcome_name[0]] correlation_y = current_simulated_confounder.corr(outcome_values) correlation_y_list.append(correlation_y) treatment_values = t correlation_t = current_simulated_confounder.corr(treatment_values) correlation_t_list.append(correlation_t) product_cor_metric_simulated = correlation_y * correlation_t product_cor_metric_simulated_list.append(product_cor_metric_simulated) x_list.append(i) index = 1 while index < len(correlation_y_list): if (correlation_y_list[index] - correlation_y_list[index - 1]) <= convergence_threshold: c_star = x_list[index] break index = index + 1 # Choosing c1 and c2 based on the hyperbolic relationship once c_star is chosen by going over various combinations of c1 and c2 values and choosing the combination which # which maintains the minimum distance between the product of correlations of the simulated variable and the product of maximum correlations of one of the observed variables # and additionally checks if the ratio of the weights are such that they maintain the ratio of the maximum possible observed coefficients within some confidence interval # c1_final and c2_final are initialised to the values on the hyperbolic curve such that c1_final = c2_final and c1_final*c2_final = c_star c1_final = math.sqrt(c_star) c2_final = math.sqrt(c_star) # initialising min_distance_between_product_cor_metrics to be a value greater than 1 min_distance_between_product_cor_metrics = 1.5 i = 0.05 threshold = c_star / 0.05 while i <= threshold: c2 = i c1 = c_star / c2 final_U = _generate_confounder_from_residuals(c1, c2, d_y, d_t, X) current_simulated_confounder = final_U outcome_values = data[outcome_name[0]] correlation_y = current_simulated_confounder.corr(outcome_values) treatment_values = t correlation_t = current_simulated_confounder.corr(treatment_values) product_cor_metric_simulated = correlation_y * correlation_t if min_distance_between_product_cor_metrics >= abs(product_cor_metric_simulated - product_cor_metric_observed): min_distance_between_product_cor_metrics = abs(product_cor_metric_simulated - product_cor_metric_observed) additional_condition = correlation_y_observed / correlation_t_observed if ((c1 / c2) <= (additional_condition + 0.3 * additional_condition)) and ( (c1 / c2) >= (additional_condition - 0.3 * additional_condition) ): # choose minimum positive value c1_final = c1 c2_final = c2 i = i * 1.5 """#closed form solution print("c_star_max before closed form", c_star_max) if max_correlation_with_t == -1000: c2 = 0 c1 = c_star_max else: additional_condition = abs(max_correlation_with_y/max_correlation_with_t) print("additional_condition", additional_condition) c2 = math.sqrt(c_star_max/additional_condition) c1 = c_star_max/c2""" final_U = _generate_confounder_from_residuals(c1_final, c2_final, d_y, d_t, X) return final_U def _generate_confounder_from_residuals(c1, c2, d_y, d_t, X): """ This function takes the residuals from the treatment and outcome model and their coefficients and simulates the intermediate random variable U by taking the row wise normal distribution corresponding to each residual value and then debiasing the intermediate variable to get the final variable. :param c1: coefficient to the residual from the outcome model :type float :param c2: coefficient to the residual from the treatment model :type float :param d_y: residuals from the outcome model :type list :param d_t: residuals from the treatment model :type list :returns: The simulated values of the unobserved confounder based on the data :type pandas.core.series.Series """ U = [] for j in range(len(d_t)): simulated_variable_mean = c1 * d_y[j] + c2 * d_t[j] simulated_variable_stddev = 1 U.append(np.random.normal(simulated_variable_mean, simulated_variable_stddev, 1)) U = np.array(U) model = sm.OLS(U, X) results = model.fit() U = U.reshape( -1, ) final_U = U - results.fittedvalues.values final_U = pd.Series(U) return final_U def sensitivity_linear_partial_r2( data: pd.DataFrame, estimate: CausalEstimate, treatment_name: str, frac_strength_treatment: float = 1.0, frac_strength_outcome: float = 1.0, percent_change_estimate: float = 1.0, benchmark_common_causes: Optional[List[str]] = None, significance_level: Optional[float] = None, null_hypothesis_effect: Optional[float] = None, plot_estimate: bool = True, ) -> LinearSensitivityAnalyzer: """Add an unobserved confounder for refutation using Linear partial R2 methond (Sensitivity Analysis for linear models). :param data: pd.DataFrame: Data to run the refutation :param estimate: CausalEstimate: Estimate to run the refutation :param treatment_name: str: Name of the treatment :param frac_strength_treatment: float: This parameter decides the effect strength of the simulated confounder as a fraction of the effect strength of observed confounders on treatment. Defaults to 1. :param frac_strength_outcome: float: This parameter decides the effect strength of the simulated confounder as a fraction of the effect strength of observed confounders on outcome. Defaults to 1. :param percent_change_estimate: It is the percentage of reduction of treatment estimate that could alter the results (default = 1). if percent_change_estimate = 1, the robustness value describes the strength of association of confounders with treatment and outcome in order to reduce the estimate by 100% i.e bring it down to 0. (relevant only for Linear Sensitivity Analysis, ignore for rest) :param benchmark_common_causes: names of variables for bounding strength of confounders. (relevant only for partial-r2 based simulation methods) :param significance_level: confidence interval for statistical inference(default = 0.05). (relevant only for partial-r2 based simulation methods) :param null_hypothesis_effect: assumed effect under the null hypothesis. (relevant only for linear-partial-R2, ignore for rest) :param plot_estimate: Generate contour plot for estimate while performing sensitivity analysis. (default = True). (relevant only for partial-r2 based simulation methods) """ if not (isinstance(estimate.estimator, LinearRegressionEstimator)): raise NotImplementedError("Currently only LinearRegressionEstimator is supported for Sensitivity Analysis") if len(estimate.estimator._effect_modifier_names) > 0: raise NotImplementedError("The current implementation does not support effect modifiers") if frac_strength_outcome == 1: frac_strength_outcome = frac_strength_treatment analyzer = LinearSensitivityAnalyzer( estimator=estimate.estimator, data=data, treatment_name=treatment_name, percent_change_estimate=percent_change_estimate, significance_level=significance_level, benchmark_common_causes=benchmark_common_causes, null_hypothesis_effect=null_hypothesis_effect, frac_strength_treatment=frac_strength_treatment, frac_strength_outcome=frac_strength_outcome, common_causes_order=estimate.estimator._observed_common_causes.columns, ) analyzer.check_sensitivity(plot=plot_estimate) return analyzer def sensitivity_non_parametric_partial_r2( estimate: CausalEstimate, kappa_t: Optional[Union[float, np.ndarray]] = None, kappa_y: Optional[Union[float, np.ndarray]] = None, frac_strength_treatment: float = 1.0, frac_strength_outcome: float = 1.0, benchmark_common_causes: Optional[List[str]] = None, plot_estimate: bool = True, alpha_s_estimator_list: Optional[List] = None, alpha_s_estimator_param_list: Optional[List[Dict]] = None, g_s_estimator_list: Optional[List] = None, g_s_estimator_param_list: Optional[List[Dict]] = None, plugin_reisz: bool = False, ) -> Union[PartialLinearSensitivityAnalyzer, NonParametricSensitivityAnalyzer]: """Add an unobserved confounder for refutation using Non-parametric partial R2 methond (Sensitivity Analysis for non-parametric models). :param estimate: CausalEstimate: Estimate to run the refutation :param kappa_t: float, numpy.ndarray: Partial R2 of the unobserved confounder wrt the treatment conditioned on the observed confounders. Only in the case of general non-parametric-partial-R2, it is the fraction of variance in the reisz representer that is explained by the unobserved confounder; specifically (1-r), where r is the ratio of variance of reisz representer, alpha^2, based on observed confounders and that based on all confounders. :param kappa_y: float, numpy.ndarray: Partial R2 of the unobserved confounder wrt the outcome conditioned on the treatment and observed confounders. :param frac_strength_treatment: float: This parameter decides the effect strength of the simulated confounder as a fraction of the effect strength of observed confounders on treatment. Defaults to 1. :param frac_strength_outcome: float: This parameter decides the effect strength of the simulated confounder as a fraction of the effect strength of observed confounders on outcome. Defaults to 1. :param benchmark_common_causes: names of variables for bounding strength of confounders. (relevant only for partial-r2 based simulation methods) :param plot_estimate: Generate contour plot for estimate while performing sensitivity analysis. (default = True). (relevant only for partial-r2 based simulation methods) :param alpha_s_estimator_list: list of estimator objects for estimating alpha_s. These objects should have fit() and predict() methods (relevant only for non-parametric-partial-R2 method) :param alpha_s_estimator_param_list: list of dictionaries with parameters for finding alpha_s. (relevant only for non-parametric-partial-R2 simulation method) :param g_s_estimator_list: list of estimator objects for finding g_s. These objects should have fit() and predict() functions implemented. (relevant only for non-parametric-partial-R2 simulation method) :param g_s_estimator_param_list: list of dictionaries with parameters for tuning respective estimators in "g_s_estimator_list". The order of the dictionaries in the list should be consistent with the estimator objects order in "g_s_estimator_list". (relevant only for non-parametric-partial-R2 simulation method) :plugin_reisz: bool: Flag on whether to use the plugin estimator or the nonparametric estimator for reisz representer function (alpha_s). """ # If the estimator used is LinearDML, partially linear sensitivity analysis will be automatically chosen if isinstance(estimate.estimator, dowhy.causal_estimators.econml.Econml): if estimate.estimator._econml_methodname == "econml.dml.LinearDML": analyzer = PartialLinearSensitivityAnalyzer( estimator=estimate._estimator_object, observed_common_causes=estimate.estimator._observed_common_causes, treatment=estimate.estimator._treatment, outcome=estimate.estimator._outcome, alpha_s_estimator_param_list=alpha_s_estimator_param_list, g_s_estimator_list=g_s_estimator_list, g_s_estimator_param_list=g_s_estimator_param_list, effect_strength_treatment=kappa_t, effect_strength_outcome=kappa_y, benchmark_common_causes=benchmark_common_causes, frac_strength_treatment=frac_strength_treatment, frac_strength_outcome=frac_strength_outcome, ) analyzer.check_sensitivity(plot=plot_estimate) return analyzer analyzer = NonParametricSensitivityAnalyzer( estimator=estimate.estimator, observed_common_causes=estimate.estimator._observed_common_causes, treatment=estimate.estimator._treatment, outcome=estimate.estimator._outcome, alpha_s_estimator_list=alpha_s_estimator_list, alpha_s_estimator_param_list=alpha_s_estimator_param_list, g_s_estimator_list=g_s_estimator_list, g_s_estimator_param_list=g_s_estimator_param_list, effect_strength_treatment=kappa_t, effect_strength_outcome=kappa_y, benchmark_common_causes=benchmark_common_causes, frac_strength_treatment=frac_strength_treatment, frac_strength_outcome=frac_strength_outcome, theta_s=estimate.value, plugin_reisz=plugin_reisz, ) analyzer.check_sensitivity(plot=plot_estimate) return analyzer def sensitivity_e_value( data: pd.DataFrame, target_estimand: IdentifiedEstimand, estimate: CausalEstimate, treatment_name: List[str], outcome_name: List[str], plot_estimate: bool = True, ) -> EValueSensitivityAnalyzer: if not isinstance(estimate.estimator, RegressionEstimator): raise NotImplementedError("E-Value sensitivity analysis is currently only implemented RegressionEstimator.") if len(estimate.estimator._effect_modifier_names) > 0: raise NotImplementedError("The current implementation does not support effect modifiers") analyzer = EValueSensitivityAnalyzer( estimate=estimate, estimand=target_estimand, data=data, treatment_name=treatment_name[0], outcome_name=outcome_name[0], ) analyzer.check_sensitivity(plot=plot_estimate) return analyzer def sensitivity_simulation( data: pd.DataFrame, target_estimand: IdentifiedEstimand, estimate: CausalEstimate, treatment_name: str, outcome_name: str, kappa_t: Optional[Union[float, np.ndarray]] = None, kappa_y: Optional[Union[float, np.ndarray]] = None, confounders_effect_on_treatment: str = "binary_flip", confounders_effect_on_outcome: str = "linear", frac_strength_treatment: float = 1.0, frac_strength_outcome: float = 1.0, plotmethod: Optional[str] = None, show_progress_bar=False, **_, ) -> CausalRefutation: """ This function attempts to add an unobserved common cause to the outcome and the treatment. At present, we have implemented the behavior for one dimensional behaviors for continuous and binary variables. This function can either take single valued inputs or a range of inputs. The function then looks at the data type of the input and then decides on the course of action. :param data: pd.DataFrame: Data to run the refutation :param target_estimand: IdentifiedEstimand: Identified estimand to run the refutation :param estimate: CausalEstimate: Estimate to run the refutation :param treatment_name: str: Name of the treatment :param outcome_name: str: Name of the outcome :param kappa_t: float, numpy.ndarray: Strength of the confounder's effect on treatment. When confounders_effect_on_treatment is linear, it is the regression coefficient. When the confounders_effect_on_treatment is binary flip, it is the probability with which effect of unobserved confounder can invert the value of the treatment. :param kappa_y: float, numpy.ndarray: Strength of the confounder's effect on outcome. Its interpretation depends on confounders_effect_on_outcome and the simulation_method. When simulation_method is direct-simulation, for a linear effect it behaves like the regression coefficient and for a binary flip, it is the probability with which it can invert the value of the outcome. :param confounders_effect_on_treatment: str : The type of effect on the treatment due to the unobserved confounder. Possible values are ['binary_flip', 'linear'] :param confounders_effect_on_outcome: str : The type of effect on the outcome due to the unobserved confounder. Possible values are ['binary_flip', 'linear'] :param frac_strength_treatment: float: This parameter decides the effect strength of the simulated confounder as a fraction of the effect strength of observed confounders on treatment. Defaults to 1. :param frac_strength_outcome: float: This parameter decides the effect strength of the simulated confounder as a fraction of the effect strength of observed confounders on outcome. Defaults to 1. :param plotmethod: string: Type of plot to be shown. If None, no plot is generated. This parameter is used only only when more than one treatment confounder effect values or outcome confounder effect values are provided. Default is "colormesh". Supported values are "contour", "colormesh" when more than one value is provided for both confounder effect value parameters; "line" when provided for only one of them. :return: CausalRefuter: An object that contains the estimated effect and a new effect and the name of the refutation used. """ if kappa_t is None: kappa_t = _infer_default_kappa_t( data, target_estimand, treatment_name, confounders_effect_on_treatment, frac_strength_treatment ) if kappa_y is None: kappa_y = _infer_default_kappa_y( data, target_estimand, outcome_name, confounders_effect_on_outcome, frac_strength_outcome ) if not isinstance(kappa_t, (list, np.ndarray)) and not isinstance( kappa_y, (list, np.ndarray) ): # Deal with single value inputs new_data = copy.deepcopy(data) new_data = _include_confounders_effect( data, new_data, confounders_effect_on_treatment, treatment_name, kappa_t, confounders_effect_on_outcome, outcome_name, kappa_y, ) new_estimator = CausalEstimator.get_estimator_object(new_data, target_estimand, estimate) new_effect = new_estimator.estimate_effect() refute = CausalRefutation( estimate.value, new_effect.value, refutation_type="Refute: Add an Unobserved Common Cause" ) refute.new_effect_array = np.array(new_effect.value) refute.new_effect = new_effect.value return refute else: # Deal with multiple value inputs if isinstance(kappa_t, (list, np.ndarray)) and isinstance( kappa_y, (list, np.ndarray) ): # Deal with range inputs # Get a 2D matrix of values # x,y = np.meshgrid(self.kappa_t, self.kappa_y) # x,y are both MxN results_matrix = np.random.rand(len(kappa_t), len(kappa_y)) # Matrix to hold all the results of NxM orig_data = copy.deepcopy(data) for i in tqdm( range(len(kappa_t)), colour=CausalRefuter.PROGRESS_BAR_COLOR, disable=not show_progress_bar, desc="Refuting Estimates: ", ): for j in range(len(kappa_y)): new_data = _include_confounders_effect( data, orig_data, confounders_effect_on_treatment, treatment_name, kappa_t[i], confounders_effect_on_outcome, outcome_name, kappa_y[j], ) new_estimator = CausalEstimator.get_estimator_object(new_data, target_estimand, estimate) new_effect = new_estimator.estimate_effect() refute = CausalRefutation( estimate.value, new_effect.value, refutation_type="Refute: Add an Unobserved Common Cause", ) results_matrix[i][j] = refute.new_effect # Populate the results refute.new_effect_array = results_matrix refute.new_effect = (np.min(results_matrix), np.max(results_matrix)) # Store the values into the refute object if plotmethod is None: return refute import matplotlib import matplotlib.pyplot as plt fig = plt.figure(figsize=(6, 5)) left, bottom, width, height = 0.1, 0.1, 0.8, 0.8 ax = fig.add_axes([left, bottom, width, height]) oe = estimate.value contour_levels = [oe / 4.0, oe / 2.0, (3.0 / 4) * oe, oe] contour_levels.extend([0, np.min(results_matrix), np.max(results_matrix)]) if plotmethod == "contour": cp = plt.contourf(kappa_y, kappa_t, results_matrix, levels=sorted(contour_levels)) # Adding a label on the contour line for the original estimate fmt = {} trueeffect_index = np.where(cp.levels == oe)[0][0] fmt[cp.levels[trueeffect_index]] = "Estimated Effect" # Label every other level using strings plt.clabel(cp, [cp.levels[trueeffect_index]], inline=True, fmt=fmt) plt.colorbar(cp) elif plotmethod == "colormesh": cp = plt.pcolormesh(kappa_y, kappa_t, results_matrix, shading="nearest") plt.colorbar(cp, ticks=contour_levels) ax.yaxis.set_ticks(kappa_t) ax.xaxis.set_ticks(kappa_y) plt.xticks(rotation=45) ax.set_title("Effect of Unobserved Common Cause") ax.set_ylabel("Value of Linear Constant on Treatment") ax.set_xlabel("Value of Linear Constant on Outcome") plt.show() return refute elif isinstance(kappa_t, (list, np.ndarray)): outcomes = np.random.rand(len(kappa_t)) orig_data = copy.deepcopy(data) for i in tqdm( range(0, len(kappa_t)), colour=CausalRefuter.PROGRESS_BAR_COLOR, disable=not show_progress_bar, desc="Refuting Estimates: ", ): new_data = _include_confounders_effect( data, orig_data, confounders_effect_on_treatment, treatment_name, kappa_t[i], confounders_effect_on_outcome, outcome_name, kappa_y, ) new_estimator = CausalEstimator.get_estimator_object(new_data, target_estimand, estimate) new_effect = new_estimator.estimate_effect() refute = CausalRefutation( estimate.value, new_effect.value, refutation_type="Refute: Add an Unobserved Common Cause" ) logger.debug(refute) outcomes[i] = refute.new_effect # Populate the results refute.new_effect_array = outcomes refute.new_effect = (np.min(outcomes), np.max(outcomes)) if plotmethod is None: return refute import matplotlib import matplotlib.pyplot as plt fig = plt.figure(figsize=(6, 5)) left, bottom, width, height = 0.1, 0.1, 0.8, 0.8 ax = fig.add_axes([left, bottom, width, height]) plt.plot(kappa_t, outcomes) plt.axhline(estimate.value, linestyle="--", color="gray") ax.set_title("Effect of Unobserved Common Cause") ax.set_xlabel("Value of Linear Constant on Treatment") ax.set_ylabel("Estimated Effect after adding the common cause") plt.show() return refute elif isinstance(kappa_y, (list, np.ndarray)): outcomes = np.random.rand(len(kappa_y)) orig_data = copy.deepcopy(data) for i in tqdm( range(0, len(kappa_y)), colour=CausalRefuter.PROGRESS_BAR_COLOR, disable=not show_progress_bar, desc="Refuting Estimates: ", ): new_data = _include_confounders_effect( data, orig_data, confounders_effect_on_treatment, treatment_name, kappa_t, confounders_effect_on_outcome, outcome_name, kappa_y[i], ) new_estimator = CausalEstimator.get_estimator_object(new_data, target_estimand, estimate) new_effect = new_estimator.estimate_effect() refute = CausalRefutation( estimate.value, new_effect.value, refutation_type="Refute: Add an Unobserved Common Cause" ) logger.debug(refute) outcomes[i] = refute.new_effect # Populate the results refute.new_effect_array = outcomes refute.new_effect = (np.min(outcomes), np.max(outcomes)) if plotmethod is None: return refute import matplotlib import matplotlib.pyplot as plt fig = plt.figure(figsize=(6, 5)) left, bottom, width, height = 0.1, 0.1, 0.8, 0.8 ax = fig.add_axes([left, bottom, width, height]) plt.plot(kappa_y, outcomes) plt.axhline(estimate.value, linestyle="--", color="gray") ax.set_title("Effect of Unobserved Common Cause") ax.set_xlabel("Value of Linear Constant on Outcome") ax.set_ylabel("Estimated Effect after adding the common cause") plt.show() return refute

andresmor-ms

133e7b9a4ed32aae8ab5f39a01eb02b3a4d1c0ba

e1652ec3c6606b1bb2dfe91ef830e4b4b566712d

I believe there is not a specific way of doing this, however the main `refute_estimate(data, target_estimand, estimate, ...)` partially serves this purpose, in the future if any developer wants the refuter to be callable through this function then the signature must comply with the type: `Callable[..., Union[CausalRefutation, List[CausalRefutation]]]`, which at least hints the developer to return a CausalRefutation or list of CausalRefutation as result. Or we can create as you say a protocol like this: ```python class Refuter(Protocol): def __call__(self, data: pd.DataFrame, target_estimand: IdentifiedEstimand, estimate: CausalEstimate, *args, **kwargs) -> Union[CausalRefutation, List[CausalRefutation]] ``` and then use it as the type hint in the `refute_estimate(..., refuters=List[Refuter])` https://mypy.readthedocs.io/en/latest/protocols.html#callback-protocols I don't really think this is super useful as we also have PR mechanism that we could use to enforce compatibility, but if you consider we should add it like this, then let me know and I'll include it in this PR.

andresmor-ms

py-why/dowhy

Functional api/refute estimate

* Refactor refuters into functions * Rename functional_api notebook for clarity * Add return types to identify_estimate * Update `__init__.py` for imports * Add joblib for bootstrap refuter * Create `refute_estimate` function * Add types for refuter parameters & return types

2022-10-04 16:18:49+00:00

2022-10-07 04:30:22+00:00

dowhy/causal_refuters/add_unobserved_common_cause.py

import copy import logging import math import numpy as np import pandas as pd import scipy.stats import statsmodels.api as sm from sklearn.linear_model import LogisticRegression from sklearn.preprocessing import StandardScaler from tqdm.auto import tqdm import dowhy.causal_estimators.econml from dowhy.causal_estimator import CausalEstimator from dowhy.causal_estimators.linear_regression_estimator import LinearRegressionEstimator from dowhy.causal_estimators.regression_estimator import RegressionEstimator from dowhy.causal_refuter import CausalRefutation, CausalRefuter from dowhy.causal_refuters.evalue_sensitivity_analyzer import EValueSensitivityAnalyzer from dowhy.causal_refuters.linear_sensitivity_analyzer import LinearSensitivityAnalyzer from dowhy.causal_refuters.non_parametric_sensitivity_analyzer import NonParametricSensitivityAnalyzer from dowhy.causal_refuters.partial_linear_sensitivity_analyzer import PartialLinearSensitivityAnalyzer class AddUnobservedCommonCause(CausalRefuter): """Add an unobserved confounder for refutation. AddUnobservedCommonCause class supports three methods: 1) Simulation of an unobserved confounder 2) Linear partial R2 : Sensitivity Analysis for linear models. 3) Non-Parametric partial R2 based : Sensitivity Analyis for non-parametric models. Supports additional parameters that can be specified in the refute_estimate() method. """ def __init__(self, *args, **kwargs): """ Initialize the parameters required for the refuter. For direct_simulation, if effect_strength_on_treatment or effect_strength_on_outcome is not given, it is calculated automatically as a range between the minimum and maximum effect strength of observed confounders on treatment and outcome respectively. :param simulation_method: The method to use for simulating effect of unobserved confounder. Possible values are ["direct-simulation", "linear-partial-R2", "non-parametric-partial-R2", "e-value"]. :param confounders_effect_on_treatment: str : The type of effect on the treatment due to the unobserved confounder. Possible values are ['binary_flip', 'linear'] :param confounders_effect_on_outcome: str : The type of effect on the outcome due to the unobserved confounder. Possible values are ['binary_flip', 'linear'] :param effect_strength_on_treatment: float, numpy.ndarray: [Used when simulation_method="direct-simulation"] Strength of the confounder's effect on treatment. When confounders_effect_on_treatment is linear, it is the regression coefficient. When the confounders_effect_on_treatment is binary flip, it is the probability with which effect of unobserved confounder can invert the value of the treatment. :param effect_strength_on_outcome: float, numpy.ndarray: Strength of the confounder's effect on outcome. Its interpretation depends on confounders_effect_on_outcome and the simulation_method. When simulation_method is direct-simulation, for a linear effect it behaves like the regression coefficient and for a binary flip, it is the probability with which it can invert the value of the outcome. :param partial_r2_confounder_treatment: float, numpy.ndarray: [Used when simulation_method is linear-partial-R2 or non-parametric-partial-R2] Partial R2 of the unobserved confounder wrt the treatment conditioned on the observed confounders. Only in the case of general non-parametric-partial-R2, it is the fraction of variance in the reisz representer that is explained by the unobserved confounder; specifically (1-r), where r is the ratio of variance of reisz representer, alpha^2, based on observed confounders and that based on all confounders. :param partial_r2_confounder_outcome: float, numpy.ndarray: [Used when simulation_method is linear-partial-R2 or non-parametric-partial-R2] Partial R2 of the unobserved confounder wrt the outcome conditioned on the treatment and observed confounders. :param frac_strength_treatment: float: This parameter decides the effect strength of the simulated confounder as a fraction of the effect strength of observed confounders on treatment. Defaults to 1. :param frac_strength_outcome: float: This parameter decides the effect strength of the simulated confounder as a fraction of the effect strength of observed confounders on outcome. Defaults to 1. :param plotmethod: string: Type of plot to be shown. If None, no plot is generated. This parameter is used only only when more than one treatment confounder effect values or outcome confounder effect values are provided. Default is "colormesh". Supported values are "contour", "colormesh" when more than one value is provided for both confounder effect value parameters; "line" when provided for only one of them. :param percent_change_estimate: It is the percentage of reduction of treatment estimate that could alter the results (default = 1). if percent_change_estimate = 1, the robustness value describes the strength of association of confounders with treatment and outcome in order to reduce the estimate by 100% i.e bring it down to 0. (relevant only for Linear Sensitivity Analysis, ignore for rest) :param confounder_increases_estimate: True implies that confounder increases the absolute value of estimate and vice versa. (Default = False). (relevant only for Linear Sensitivity Analysis, ignore for rest) :param benchmark_common_causes: names of variables for bounding strength of confounders. (relevant only for partial-r2 based simulation methods) :param significance_level: confidence interval for statistical inference(default = 0.05). (relevant only for partial-r2 based simulation methods) :param null_hypothesis_effect: assumed effect under the null hypothesis. (relevant only for linear-partial-R2, ignore for rest) :param plot_estimate: Generate contour plot for estimate while performing sensitivity analysis. (default = True). (relevant only for partial-r2 based simulation methods) :param num_splits: number of splits for cross validation. (default = 5). (relevant only for non-parametric-partial-R2 simulation method) :param shuffle_data : shuffle data or not before splitting into folds (default = False). (relevant only for non-parametric-partial-R2 simulation method) :param shuffle_random_seed: seed for randomly shuffling data. (relevant only for non-parametric-partial-R2 simulation method) :param alpha_s_estimator_param_list: list of dictionaries with parameters for finding alpha_s. (relevant only for non-parametric-partial-R2 simulation method) :param g_s_estimator_list: list of estimator objects for finding g_s. These objects should have fit() and predict() functions implemented. (relevant only for non-parametric-partial-R2 simulation method) :param g_s_estimator_param_list: list of dictionaries with parameters for tuning respective estimators in "g_s_estimator_list". The order of the dictionaries in the list should be consistent with the estimator objects order in "g_s_estimator_list". (relevant only for non-parametric-partial-R2 simulation method) """ super().__init__(*args, **kwargs) self.simulation_method = kwargs["simulation_method"] if "simulation_method" in kwargs else "direct-simulation" self.effect_on_t = ( kwargs["confounders_effect_on_treatment"] if "confounders_effect_on_treatment" in kwargs else "binary_flip" ) self.effect_on_y = ( kwargs["confounders_effect_on_outcome"] if "confounders_effect_on_outcome" in kwargs else "linear" ) if self.simulation_method == "direct-simulation": self.kappa_t = kwargs["effect_strength_on_treatment"] if "effect_strength_on_treatment" in kwargs else None self.kappa_y = kwargs["effect_strength_on_outcome"] if "effect_strength_on_outcome" in kwargs else None elif self.simulation_method in ["linear-partial-R2", "non-parametric-partial-R2"]: self.kappa_t = ( kwargs["partial_r2_confounder_treatment"] if "partial_r2_confounder_treatment" in kwargs else None ) self.kappa_y = ( kwargs["partial_r2_confounder_outcome"] if "partial_r2_confounder_outcome" in kwargs else None ) elif self.simulation_method == "e-value": pass else: raise ValueError( "simulation method is not supported. Try direct-simulation, linear-partial-R2, non-parametric-partial-R2, or e-value" ) self.frac_strength_treatment = ( kwargs["effect_fraction_on_treatment"] if "effect_fraction_on_treatment" in kwargs else 1 ) self.frac_strength_outcome = ( kwargs["effect_fraction_on_outcome"] if "effect_fraction_on_outcome" in kwargs else 1 ) self.plotmethod = kwargs["plotmethod"] if "plotmethod" in kwargs else "colormesh" self.percent_change_estimate = kwargs["percent_change_estimate"] if "percent_change_estimate" in kwargs else 1.0 self.significance_level = kwargs["significance_level"] if "significance_level" in kwargs else 0.05 self.confounder_increases_estimate = ( kwargs["confounder_increases_estimate"] if "confounder_increases_estimate" in kwargs else False ) self.benchmark_common_causes = ( kwargs["benchmark_common_causes"] if "benchmark_common_causes" in kwargs else None ) self.null_hypothesis_effect = kwargs["null_hypothesis_effect"] if "null_hypothesis_effect" in kwargs else 0 self.plot_estimate = kwargs["plot_estimate"] if "plot_estimate" in kwargs else True self.num_splits = kwargs["num_splits"] if "num_splits" in kwargs else 5 self.shuffle_data = kwargs["shuffle_data"] if "shuffle_data" in kwargs else False self.shuffle_random_seed = kwargs["shuffle_random_seed"] if "shuffle_random_seed" in kwargs else None self.alpha_s_estimator_param_list = ( kwargs["alpha_s_estimator_param_list"] if "alpha_s_estimator_param_list" in kwargs else None ) self.alpha_s_estimator_list = kwargs["alpha_s_estimator_list"] if "alpha_s_estimator_list" in kwargs else None self.g_s_estimator_list = kwargs["g_s_estimator_list"] if "g_s_estimator_list" in kwargs else None self.g_s_estimator_param_list = ( kwargs["g_s_estimator_param_list"] if "g_s_estimator_param_list" in kwargs else None ) self.plugin_reisz = kwargs["plugin_reisz"] if "plugin_reisz" in kwargs else False self.logger = logging.getLogger(__name__) def infer_default_kappa_t(self, len_kappa_t=10): """Infer default effect strength of simulated confounder on treatment.""" observed_common_causes_names = self._target_estimand.get_backdoor_variables() if len(observed_common_causes_names) > 0: observed_common_causes = self._data[observed_common_causes_names] observed_common_causes = pd.get_dummies(observed_common_causes, drop_first=True) else: raise ValueError( "There needs to be at least one common cause to" + "automatically compute the default value of kappa_t." + " Provide a value for kappa_t" ) t = self._data[self._treatment_name] # Standardizing the data observed_common_causes = StandardScaler().fit_transform(observed_common_causes) if self.effect_on_t == "binary_flip": # Fit a model containing all confounders and compare predictions # using all features compared to all features except a given # confounder. tmodel = LogisticRegression().fit(observed_common_causes, t) tpred = tmodel.predict(observed_common_causes).astype(int) flips = [] for i in range(observed_common_causes.shape[1]): oldval = np.copy(observed_common_causes[:, i]) observed_common_causes[:, i] = 0 tcap = tmodel.predict(observed_common_causes).astype(int) observed_common_causes[:, i] = oldval flips.append(np.sum(abs(tcap - tpred)) / tpred.shape[0]) min_coeff, max_coeff = min(flips), max(flips) elif self.effect_on_t == "linear": # Estimating the regression coefficient from standardized features to t corrcoef_var_t = np.corrcoef(observed_common_causes, t, rowvar=False)[-1, :-1] std_dev_t = np.std(t)[0] max_coeff = max(corrcoef_var_t) * std_dev_t min_coeff = min(corrcoef_var_t) * std_dev_t else: raise NotImplementedError( "'" + self.effect_on_t + "' method not supported for confounders' effect on treatment" ) min_coeff, max_coeff = self._compute_min_max_coeff(min_coeff, max_coeff, self.frac_strength_treatment) # By default, return a plot with 10 points # consider 10 values of the effect of the unobserved confounder step = (max_coeff - min_coeff) / len_kappa_t self.logger.info("(Min, Max) kappa_t for observed common causes, ({0}, {1})".format(min_coeff, max_coeff)) if np.equal(max_coeff, min_coeff): return max_coeff else: return np.arange(min_coeff, max_coeff, step) def _compute_min_max_coeff(self, min_coeff, max_coeff, effect_strength_fraction): max_coeff = effect_strength_fraction * max_coeff min_coeff = effect_strength_fraction * min_coeff return min_coeff, max_coeff def infer_default_kappa_y(self, len_kappa_y=10): """Infer default effect strength of simulated confounder on treatment.""" observed_common_causes_names = self._target_estimand.get_backdoor_variables() if len(observed_common_causes_names) > 0: observed_common_causes = self._data[observed_common_causes_names] observed_common_causes = pd.get_dummies(observed_common_causes, drop_first=True) else: raise ValueError( "There needs to be at least one common cause to" + "automatically compute the default value of kappa_y." + " Provide a value for kappa_y" ) y = self._data[self._outcome_name] # Standardizing the data observed_common_causes = StandardScaler().fit_transform(observed_common_causes) if self.effect_on_y == "binary_flip": # Fit a model containing all confounders and compare predictions # using all features compared to all features except a given # confounder. ymodel = LogisticRegression().fit(observed_common_causes, y) ypred = ymodel.predict(observed_common_causes).astype(int) flips = [] for i in range(observed_common_causes.shape[1]): oldval = np.copy(observed_common_causes[:, i]) observed_common_causes[:, i] = 0 ycap = ymodel.predict(observed_common_causes).astype(int) observed_common_causes[:, i] = oldval flips.append(np.sum(abs(ycap - ypred)) / ypred.shape[0]) min_coeff, max_coeff = min(flips), max(flips) elif self.effect_on_y == "linear": corrcoef_var_y = np.corrcoef(observed_common_causes, y, rowvar=False)[-1, :-1] std_dev_y = np.std(y)[0] max_coeff = max(corrcoef_var_y) * std_dev_y min_coeff = min(corrcoef_var_y) * std_dev_y else: raise NotImplementedError( "'" + self.effect_on_y + "' method not supported for confounders' effect on outcome" ) min_coeff, max_coeff = self._compute_min_max_coeff(min_coeff, max_coeff, self.frac_strength_outcome) # By default, return a plot with 10 points # consider 10 values of the effect of the unobserved confounder step = (max_coeff - min_coeff) / len_kappa_y self.logger.info("(Min, Max) kappa_y for observed common causes, ({0}, {1})".format(min_coeff, max_coeff)) if np.equal(max_coeff, min_coeff): return max_coeff else: return np.arange(min_coeff, max_coeff, step) def refute_estimate(self, show_progress_bar=False): """ This function attempts to add an unobserved common cause to the outcome and the treatment. At present, we have implemented the behavior for one dimensional behaviors for continuous and binary variables. This function can either take single valued inputs or a range of inputs. The function then looks at the data type of the input and then decides on the course of action. :return: CausalRefuter: An object that contains the estimated effect and a new effect and the name of the refutation used. """ if self.simulation_method == "linear-partial-R2": if not (isinstance(self._estimate.estimator, LinearRegressionEstimator)): raise NotImplementedError( "Currently only LinearRegressionEstimator is supported for Sensitivity Analysis" ) if len(self._estimate.estimator._effect_modifier_names) > 0: raise NotImplementedError("The current implementation does not support effect modifiers") if self.frac_strength_outcome == 1: self.frac_strength_outcome = self.frac_strength_treatment analyzer = LinearSensitivityAnalyzer( estimator=self._estimate.estimator, data=self._data, treatment_name=self._treatment_name, percent_change_estimate=self.percent_change_estimate, significance_level=self.significance_level, benchmark_common_causes=self.benchmark_common_causes, null_hypothesis_effect=self.null_hypothesis_effect, frac_strength_treatment=self.frac_strength_treatment, frac_strength_outcome=self.frac_strength_outcome, common_causes_order=self._estimate.estimator._observed_common_causes.columns, ) analyzer.check_sensitivity(plot=self.plot_estimate) return analyzer if self.simulation_method == "non-parametric-partial-R2": # If the estimator used is LinearDML, partially linear sensitivity analysis will be automatically chosen if isinstance(self._estimate.estimator, dowhy.causal_estimators.econml.Econml): if self._estimate.estimator._econml_methodname == "econml.dml.LinearDML": analyzer = PartialLinearSensitivityAnalyzer( estimator=self._estimate._estimator_object, observed_common_causes=self._estimate.estimator._observed_common_causes, treatment=self._estimate.estimator._treatment, outcome=self._estimate.estimator._outcome, alpha_s_estimator_param_list=self.alpha_s_estimator_param_list, g_s_estimator_list=self.g_s_estimator_list, g_s_estimator_param_list=self.g_s_estimator_param_list, effect_strength_treatment=self.kappa_t, effect_strength_outcome=self.kappa_y, benchmark_common_causes=self.benchmark_common_causes, frac_strength_treatment=self.frac_strength_treatment, frac_strength_outcome=self.frac_strength_outcome, ) analyzer.check_sensitivity(plot=self.plot_estimate) return analyzer analyzer = NonParametricSensitivityAnalyzer( estimator=self._estimate.estimator, observed_common_causes=self._estimate.estimator._observed_common_causes, treatment=self._estimate.estimator._treatment, outcome=self._estimate.estimator._outcome, alpha_s_estimator_list=self.alpha_s_estimator_list, alpha_s_estimator_param_list=self.alpha_s_estimator_param_list, g_s_estimator_list=self.g_s_estimator_list, g_s_estimator_param_list=self.g_s_estimator_param_list, effect_strength_treatment=self.kappa_t, effect_strength_outcome=self.kappa_y, benchmark_common_causes=self.benchmark_common_causes, frac_strength_treatment=self.frac_strength_treatment, frac_strength_outcome=self.frac_strength_outcome, theta_s=self._estimate.value, plugin_reisz=self.plugin_reisz, ) analyzer.check_sensitivity(plot=self.plot_estimate) return analyzer if self.simulation_method == "e-value": if not isinstance(self._estimate.estimator, RegressionEstimator): raise NotImplementedError( "E-Value sensitivity analysis is currently only implemented RegressionEstimator." ) if len(self._estimate.estimator._effect_modifier_names) > 0: raise NotImplementedError("The current implementation does not support effect modifiers") analyzer = EValueSensitivityAnalyzer( estimate=self._estimate, estimand=self._target_estimand, data=self._data, treatment_name=self._treatment_name[0], outcome_name=self._outcome_name[0], ) analyzer.check_sensitivity(plot=self.plot_estimate) return analyzer if self.kappa_t is None: self.kappa_t = self.infer_default_kappa_t() if self.kappa_y is None: self.kappa_y = self.infer_default_kappa_y() if not isinstance(self.kappa_t, (list, np.ndarray)) and not isinstance( self.kappa_y, (list, np.ndarray) ): # Deal with single value inputs new_data = copy.deepcopy(self._data) new_data = self.include_confounders_effect(new_data, self.kappa_t, self.kappa_y) new_estimator = CausalEstimator.get_estimator_object(new_data, self._target_estimand, self._estimate) new_effect = new_estimator.estimate_effect() refute = CausalRefutation( self._estimate.value, new_effect.value, refutation_type="Refute: Add an Unobserved Common Cause" ) refute.new_effect_array = np.array(new_effect.value) refute.new_effect = new_effect.value refute.add_refuter(self) return refute else: # Deal with multiple value inputs if isinstance(self.kappa_t, (list, np.ndarray)) and isinstance( self.kappa_y, (list, np.ndarray) ): # Deal with range inputs # Get a 2D matrix of values # x,y = np.meshgrid(self.kappa_t, self.kappa_y) # x,y are both MxN results_matrix = np.random.rand( len(self.kappa_t), len(self.kappa_y) ) # Matrix to hold all the results of NxM orig_data = copy.deepcopy(self._data) for i in tqdm( range(len(self.kappa_t)), colour=CausalRefuter.PROGRESS_BAR_COLOR, disable=not show_progress_bar, desc="Refuting Estimates: ", ): for j in range(len(self.kappa_y)): new_data = self.include_confounders_effect(orig_data, self.kappa_t[i], self.kappa_y[j]) new_estimator = CausalEstimator.get_estimator_object( new_data, self._target_estimand, self._estimate ) new_effect = new_estimator.estimate_effect() refute = CausalRefutation( self._estimate.value, new_effect.value, refutation_type="Refute: Add an Unobserved Common Cause", ) results_matrix[i][j] = refute.new_effect # Populate the results refute.new_effect_array = results_matrix refute.new_effect = (np.min(results_matrix), np.max(results_matrix)) # Store the values into the refute object refute.add_refuter(self) if self.plotmethod is None: return refute import matplotlib import matplotlib.pyplot as plt fig = plt.figure(figsize=(6, 5)) left, bottom, width, height = 0.1, 0.1, 0.8, 0.8 ax = fig.add_axes([left, bottom, width, height]) oe = self._estimate.value contour_levels = [oe / 4.0, oe / 2.0, (3.0 / 4) * oe, oe] contour_levels.extend([0, np.min(results_matrix), np.max(results_matrix)]) if self.plotmethod == "contour": cp = plt.contourf(self.kappa_y, self.kappa_t, results_matrix, levels=sorted(contour_levels)) # Adding a label on the contour line for the original estimate fmt = {} trueeffect_index = np.where(cp.levels == oe)[0][0] fmt[cp.levels[trueeffect_index]] = "Estimated Effect" # Label every other level using strings plt.clabel(cp, [cp.levels[trueeffect_index]], inline=True, fmt=fmt) plt.colorbar(cp) elif self.plotmethod == "colormesh": cp = plt.pcolormesh(self.kappa_y, self.kappa_t, results_matrix, shading="nearest") plt.colorbar(cp, ticks=contour_levels) ax.yaxis.set_ticks(self.kappa_t) ax.xaxis.set_ticks(self.kappa_y) plt.xticks(rotation=45) ax.set_title("Effect of Unobserved Common Cause") ax.set_ylabel("Value of Linear Constant on Treatment") ax.set_xlabel("Value of Linear Constant on Outcome") plt.show() return refute elif isinstance(self.kappa_t, (list, np.ndarray)): outcomes = np.random.rand(len(self.kappa_t)) orig_data = copy.deepcopy(self._data) for i in tqdm( range(0, len(self.kappa_t)), colour=CausalRefuter.PROGRESS_BAR_COLOR, disable=not show_progress_bar, desc="Refuting Estimates: ", ): new_data = self.include_confounders_effect(orig_data, self.kappa_t[i], self.kappa_y) new_estimator = CausalEstimator.get_estimator_object( new_data, self._target_estimand, self._estimate ) new_effect = new_estimator.estimate_effect() refute = CausalRefutation( self._estimate.value, new_effect.value, refutation_type="Refute: Add an Unobserved Common Cause" ) self.logger.debug(refute) outcomes[i] = refute.new_effect # Populate the results refute.new_effect_array = outcomes refute.new_effect = (np.min(outcomes), np.max(outcomes)) refute.add_refuter(self) if self.plotmethod is None: return refute import matplotlib import matplotlib.pyplot as plt fig = plt.figure(figsize=(6, 5)) left, bottom, width, height = 0.1, 0.1, 0.8, 0.8 ax = fig.add_axes([left, bottom, width, height]) plt.plot(self.kappa_t, outcomes) plt.axhline(self._estimate.value, linestyle="--", color="gray") ax.set_title("Effect of Unobserved Common Cause") ax.set_xlabel("Value of Linear Constant on Treatment") ax.set_ylabel("Estimated Effect after adding the common cause") plt.show() return refute elif isinstance(self.kappa_y, (list, np.ndarray)): outcomes = np.random.rand(len(self.kappa_y)) orig_data = copy.deepcopy(self._data) for i in tqdm( range(0, len(self.kappa_y)), colour=CausalRefuter.PROGRESS_BAR_COLOR, disable=not show_progress_bar, desc="Refuting Estimates: ", ): new_data = self.include_confounders_effect(orig_data, self.kappa_t, self.kappa_y[i]) new_estimator = CausalEstimator.get_estimator_object( new_data, self._target_estimand, self._estimate ) new_effect = new_estimator.estimate_effect() refute = CausalRefutation( self._estimate.value, new_effect.value, refutation_type="Refute: Add an Unobserved Common Cause" ) self.logger.debug(refute) outcomes[i] = refute.new_effect # Populate the results refute.new_effect_array = outcomes refute.new_effect = (np.min(outcomes), np.max(outcomes)) refute.add_refuter(self) if self.plotmethod is None: return refute import matplotlib import matplotlib.pyplot as plt fig = plt.figure(figsize=(6, 5)) left, bottom, width, height = 0.1, 0.1, 0.8, 0.8 ax = fig.add_axes([left, bottom, width, height]) plt.plot(self.kappa_y, outcomes) plt.axhline(self._estimate.value, linestyle="--", color="gray") ax.set_title("Effect of Unobserved Common Cause") ax.set_xlabel("Value of Linear Constant on Outcome") ax.set_ylabel("Estimated Effect after adding the common cause") plt.show() return refute def include_confounders_effect(self, new_data, kappa_t, kappa_y): """ This function deals with the change in the value of the data due to the effect of the unobserved confounder. In the case of a binary flip, we flip only if the random number is greater than the threshold set. In the case of a linear effect, we use the variable as the linear regression constant. :param new_data: pandas.DataFrame: The data to be changed due to the effects of the unobserved confounder. :param kappa_t: numpy.float64: The value of the threshold for binary_flip or the value of the regression coefficient for linear effect. :param kappa_y: numpy.float64: The value of the threshold for binary_flip or the value of the regression coefficient for linear effect. :return: pandas.DataFrame: The DataFrame that includes the effects of the unobserved confounder. """ num_rows = self._data.shape[0] stdnorm = scipy.stats.norm() w_random = stdnorm.rvs(num_rows) if self.effect_on_t == "binary_flip": alpha = 2 * kappa_t - 1 if kappa_t >= 0.5 else 1 - 2 * kappa_t interval = stdnorm.interval(alpha) rel_interval = interval[0] if kappa_t >= 0.5 else interval[1] new_data.loc[rel_interval <= w_random, self._treatment_name] = ( 1 - new_data.loc[rel_interval <= w_random, self._treatment_name] ) for tname in self._treatment_name: if pd.api.types.is_bool_dtype(self._data[tname]): new_data = new_data.astype({tname: "bool"}, copy=False) elif self.effect_on_t == "linear": confounder_t_effect = kappa_t * w_random # By default, we add the effect of simulated confounder for treatment. # But subtract it from outcome to create a negative correlation # assuming that the original confounder's effect was positive on both. # This is to remove the effect of the original confounder. new_data[self._treatment_name] = new_data[self._treatment_name].values + np.ndarray( shape=(num_rows, 1), buffer=confounder_t_effect ) else: raise NotImplementedError( "'" + self.effect_on_t + "' method not supported for confounders' effect on treatment" ) if self.effect_on_y == "binary_flip": alpha = 2 * kappa_y - 1 if kappa_y >= 0.5 else 1 - 2 * kappa_y interval = stdnorm.interval(alpha) rel_interval = interval[0] if kappa_y >= 0.5 else interval[1] new_data.loc[rel_interval <= w_random, self._outcome_name] = ( 1 - new_data.loc[rel_interval <= w_random, self._outcome_name] ) for yname in self._outcome_name: if pd.api.types.is_bool_dtype(self._data[yname]): new_data = new_data.astype({yname: "bool"}, copy=False) elif self.effect_on_y == "linear": confounder_y_effect = (-1) * kappa_y * w_random # By default, we add the effect of simulated confounder for treatment. # But subtract it from outcome to create a negative correlation # assuming that the original confounder's effect was positive on both. # This is to remove the effect of the original confounder. new_data[self._outcome_name] = new_data[self._outcome_name].values + np.ndarray( shape=(num_rows, 1), buffer=confounder_y_effect ) else: raise NotImplementedError( "'" + self.effect_on_y + "' method not supported for confounders' effect on outcome" ) return new_data def include_simulated_confounder(self, convergence_threshold=0.1, c_star_max=1000): """ This function simulates an unobserved confounder based on the data using the following steps: 1. It calculates the "residuals" from the treatment and outcome model i.) The outcome model has outcome as the dependent variable and all the observed variables including treatment as independent variables ii.) The treatment model has treatment as the dependent variable and all the observed variables as independent variables. 2. U is an intermediate random variable drawn from the normal distribution with the weighted average of residuals as mean and a unit variance U ~ N(c1*d_y + c2*d_t, 1) where *d_y and d_t are residuals from the treatment and outcome model *c1 and c2 are coefficients to the residuals 3. The final U, which is the simulated unobserved confounder is obtained by debiasing the intermediate variable U by residualising it with X Choosing the coefficients c1 and c2: The coefficients are chosen based on these basic assumptions: 1. There is a hyperbolic relationship satisfying c1*c2 = c_star 2. c_star is chosen from a range of possible values based on the correlation of the obtained simulated variable with outcome and treatment. 3. The product of correlations with treatment and outcome should be at a minimum distance to the maximum correlations with treatment and outcome in any of the observed confounders 4. The ratio of the weights should be such that they maintain the ratio of the maximum possible observed coefficients within some confidence interval :param c_star_max: The maximum possible value for the hyperbolic curve on which the coefficients to the residuals lie. It defaults to 1000 in the code if not specified by the user. :type int :param convergence_threshold: The threshold to check the plateauing of the correlation while selecting a c_star. It defaults to 0.1 in the code if not specified by the user :type float :returns: The simulated values of the unobserved confounder based on the data :type pandas.core.series.Series """ # Obtaining the list of observed variables required_variables = True observed_variables = self.choose_variables(required_variables) observed_variables_with_treatment_and_outcome = observed_variables + self._treatment_name + self._outcome_name # Taking a subset of the dataframe that has only observed variables self._data = self._data[observed_variables_with_treatment_and_outcome] # Residuals from the outcome model obtained by fitting a linear model y = self._data[self._outcome_name[0]] observed_variables_with_treatment = observed_variables + self._treatment_name X = self._data[observed_variables_with_treatment] model = sm.OLS(y, X.astype("float")) results = model.fit() residuals_y = y - results.fittedvalues d_y = list(pd.Series(residuals_y)) # Residuals from the treatment model obtained by fitting a linear model t = self._data[self._treatment_name[0]].astype("int64") X = self._data[observed_variables] model = sm.OLS(t, X) results = model.fit() residuals_t = t - results.fittedvalues d_t = list(pd.Series(residuals_t)) # Initialising product_cor_metric_observed with a really low value as finding maximum product_cor_metric_observed = -10000000000 for i in observed_variables: current_obs_confounder = self._data[i] outcome_values = self._data[self._outcome_name[0]] correlation_y = current_obs_confounder.corr(outcome_values) treatment_values = t correlation_t = current_obs_confounder.corr(treatment_values) product_cor_metric_current = correlation_y * correlation_t if product_cor_metric_current >= product_cor_metric_observed: product_cor_metric_observed = product_cor_metric_current correlation_t_observed = correlation_t correlation_y_observed = correlation_y # The user has an option to give the the effect_strength_on_y and effect_strength_on_t which can be then used instead of maximum correlation with treatment and outcome in the observed variables as it specifies the desired effect. if self.kappa_t is not None: correlation_t_observed = self.kappa_t if self.kappa_y is not None: correlation_y_observed = self.kappa_y # Choosing a c_star based on the data. # The correlations stop increasing upon increasing c_star after a certain value, that is it plateaus and we choose the value of c_star to be the value it plateaus. correlation_y_list = [] correlation_t_list = [] product_cor_metric_simulated_list = [] x_list = [] step = int(c_star_max / 10) for i in range(0, int(c_star_max), step): c1 = math.sqrt(i) c2 = c1 final_U = self.generate_confounder_from_residuals(c1, c2, d_y, d_t, X) current_simulated_confounder = final_U outcome_values = self._data[self._outcome_name[0]] correlation_y = current_simulated_confounder.corr(outcome_values) correlation_y_list.append(correlation_y) treatment_values = t correlation_t = current_simulated_confounder.corr(treatment_values) correlation_t_list.append(correlation_t) product_cor_metric_simulated = correlation_y * correlation_t product_cor_metric_simulated_list.append(product_cor_metric_simulated) x_list.append(i) index = 1 while index < len(correlation_y_list): if (correlation_y_list[index] - correlation_y_list[index - 1]) <= convergence_threshold: c_star = x_list[index] break index = index + 1 # Choosing c1 and c2 based on the hyperbolic relationship once c_star is chosen by going over various combinations of c1 and c2 values and choosing the combination which # which maintains the minimum distance between the product of correlations of the simulated variable and the product of maximum correlations of one of the observed variables # and additionally checks if the ratio of the weights are such that they maintain the ratio of the maximum possible observed coefficients within some confidence interval # c1_final and c2_final are initialised to the values on the hyperbolic curve such that c1_final = c2_final and c1_final*c2_final = c_star c1_final = math.sqrt(c_star) c2_final = math.sqrt(c_star) # initialising min_distance_between_product_cor_metrics to be a value greater than 1 min_distance_between_product_cor_metrics = 1.5 i = 0.05 threshold = c_star / 0.05 while i <= threshold: c2 = i c1 = c_star / c2 final_U = self.generate_confounder_from_residuals(c1, c2, d_y, d_t, X) current_simulated_confounder = final_U outcome_values = self._data[self._outcome_name[0]] correlation_y = current_simulated_confounder.corr(outcome_values) treatment_values = t correlation_t = current_simulated_confounder.corr(treatment_values) product_cor_metric_simulated = correlation_y * correlation_t if min_distance_between_product_cor_metrics >= abs( product_cor_metric_simulated - product_cor_metric_observed ): min_distance_between_product_cor_metrics = abs( product_cor_metric_simulated - product_cor_metric_observed ) additional_condition = correlation_y_observed / correlation_t_observed if ((c1 / c2) <= (additional_condition + 0.3 * additional_condition)) and ( (c1 / c2) >= (additional_condition - 0.3 * additional_condition) ): # choose minimum positive value c1_final = c1 c2_final = c2 i = i * 1.5 """#closed form solution print("c_star_max before closed form", c_star_max) if max_correlation_with_t == -1000: c2 = 0 c1 = c_star_max else: additional_condition = abs(max_correlation_with_y/max_correlation_with_t) print("additional_condition", additional_condition) c2 = math.sqrt(c_star_max/additional_condition) c1 = c_star_max/c2""" final_U = self.generate_confounder_from_residuals(c1_final, c2_final, d_y, d_t, X) return final_U def generate_confounder_from_residuals(self, c1, c2, d_y, d_t, X): """ This function takes the residuals from the treatment and outcome model and their coefficients and simulates the intermediate random variable U by taking the row wise normal distribution corresponding to each residual value and then debiasing the intermediate variable to get the final variable. :param c1: coefficient to the residual from the outcome model :type float :param c2: coefficient to the residual from the treatment model :type float :param d_y: residuals from the outcome model :type list :param d_t: residuals from the treatment model :type list :returns: The simulated values of the unobserved confounder based on the data :type pandas.core.series.Series """ U = [] for j in range(len(d_t)): simulated_variable_mean = c1 * d_y[j] + c2 * d_t[j] simulated_variable_stddev = 1 U.append(np.random.normal(simulated_variable_mean, simulated_variable_stddev, 1)) U = np.array(U) model = sm.OLS(U, X) results = model.fit() U = U.reshape( -1, ) final_U = U - results.fittedvalues.values final_U = pd.Series(U) return final_U

import copy import logging import math from typing import Dict, List, Optional, Union import numpy as np import pandas as pd import scipy.stats import statsmodels.api as sm from sklearn.linear_model import LogisticRegression from sklearn.preprocessing import StandardScaler from tqdm.auto import tqdm import dowhy.causal_estimators.econml from dowhy.causal_estimator import CausalEstimate, CausalEstimator from dowhy.causal_estimators.linear_regression_estimator import LinearRegressionEstimator from dowhy.causal_estimators.regression_estimator import RegressionEstimator from dowhy.causal_identifier.identified_estimand import IdentifiedEstimand from dowhy.causal_refuter import CausalRefutation, CausalRefuter, choose_variables from dowhy.causal_refuters.evalue_sensitivity_analyzer import EValueSensitivityAnalyzer from dowhy.causal_refuters.linear_sensitivity_analyzer import LinearSensitivityAnalyzer from dowhy.causal_refuters.non_parametric_sensitivity_analyzer import NonParametricSensitivityAnalyzer from dowhy.causal_refuters.partial_linear_sensitivity_analyzer import PartialLinearSensitivityAnalyzer logger = logging.getLogger(__name__) class AddUnobservedCommonCause(CausalRefuter): """Add an unobserved confounder for refutation. AddUnobservedCommonCause class supports three methods: 1) Simulation of an unobserved confounder 2) Linear partial R2 : Sensitivity Analysis for linear models. 3) Non-Parametric partial R2 based : Sensitivity Analyis for non-parametric models. Supports additional parameters that can be specified in the refute_estimate() method. """ def __init__(self, *args, **kwargs): """ Initialize the parameters required for the refuter. For direct_simulation, if effect_strength_on_treatment or effect_strength_on_outcome is not given, it is calculated automatically as a range between the minimum and maximum effect strength of observed confounders on treatment and outcome respectively. :param simulation_method: The method to use for simulating effect of unobserved confounder. Possible values are ["direct-simulation", "linear-partial-R2", "non-parametric-partial-R2", "e-value"]. :param confounders_effect_on_treatment: str : The type of effect on the treatment due to the unobserved confounder. Possible values are ['binary_flip', 'linear'] :param confounders_effect_on_outcome: str : The type of effect on the outcome due to the unobserved confounder. Possible values are ['binary_flip', 'linear'] :param effect_strength_on_treatment: float, numpy.ndarray: [Used when simulation_method="direct-simulation"] Strength of the confounder's effect on treatment. When confounders_effect_on_treatment is linear, it is the regression coefficient. When the confounders_effect_on_treatment is binary flip, it is the probability with which effect of unobserved confounder can invert the value of the treatment. :param effect_strength_on_outcome: float, numpy.ndarray: Strength of the confounder's effect on outcome. Its interpretation depends on confounders_effect_on_outcome and the simulation_method. When simulation_method is direct-simulation, for a linear effect it behaves like the regression coefficient and for a binary flip, it is the probability with which it can invert the value of the outcome. :param partial_r2_confounder_treatment: float, numpy.ndarray: [Used when simulation_method is linear-partial-R2 or non-parametric-partial-R2] Partial R2 of the unobserved confounder wrt the treatment conditioned on the observed confounders. Only in the case of general non-parametric-partial-R2, it is the fraction of variance in the reisz representer that is explained by the unobserved confounder; specifically (1-r), where r is the ratio of variance of reisz representer, alpha^2, based on observed confounders and that based on all confounders. :param partial_r2_confounder_outcome: float, numpy.ndarray: [Used when simulation_method is linear-partial-R2 or non-parametric-partial-R2] Partial R2 of the unobserved confounder wrt the outcome conditioned on the treatment and observed confounders. :param frac_strength_treatment: float: This parameter decides the effect strength of the simulated confounder as a fraction of the effect strength of observed confounders on treatment. Defaults to 1. :param frac_strength_outcome: float: This parameter decides the effect strength of the simulated confounder as a fraction of the effect strength of observed confounders on outcome. Defaults to 1. :param plotmethod: string: Type of plot to be shown. If None, no plot is generated. This parameter is used only only when more than one treatment confounder effect values or outcome confounder effect values are provided. Default is "colormesh". Supported values are "contour", "colormesh" when more than one value is provided for both confounder effect value parameters; "line" when provided for only one of them. :param percent_change_estimate: It is the percentage of reduction of treatment estimate that could alter the results (default = 1). if percent_change_estimate = 1, the robustness value describes the strength of association of confounders with treatment and outcome in order to reduce the estimate by 100% i.e bring it down to 0. (relevant only for Linear Sensitivity Analysis, ignore for rest) :param confounder_increases_estimate: True implies that confounder increases the absolute value of estimate and vice versa. (Default = False). (relevant only for Linear Sensitivity Analysis, ignore for rest) :param benchmark_common_causes: names of variables for bounding strength of confounders. (relevant only for partial-r2 based simulation methods) :param significance_level: confidence interval for statistical inference(default = 0.05). (relevant only for partial-r2 based simulation methods) :param null_hypothesis_effect: assumed effect under the null hypothesis. (relevant only for linear-partial-R2, ignore for rest) :param plot_estimate: Generate contour plot for estimate while performing sensitivity analysis. (default = True). (relevant only for partial-r2 based simulation methods) :param num_splits: number of splits for cross validation. (default = 5). (relevant only for non-parametric-partial-R2 simulation method) :param shuffle_data : shuffle data or not before splitting into folds (default = False). (relevant only for non-parametric-partial-R2 simulation method) :param shuffle_random_seed: seed for randomly shuffling data. (relevant only for non-parametric-partial-R2 simulation method) :param alpha_s_estimator_param_list: list of dictionaries with parameters for finding alpha_s. (relevant only for non-parametric-partial-R2 simulation method) :param g_s_estimator_list: list of estimator objects for finding g_s. These objects should have fit() and predict() functions implemented. (relevant only for non-parametric-partial-R2 simulation method) :param g_s_estimator_param_list: list of dictionaries with parameters for tuning respective estimators in "g_s_estimator_list". The order of the dictionaries in the list should be consistent with the estimator objects order in "g_s_estimator_list". (relevant only for non-parametric-partial-R2 simulation method) """ super().__init__(*args, **kwargs) self.simulation_method = kwargs["simulation_method"] if "simulation_method" in kwargs else "direct-simulation" self.effect_on_t = ( kwargs["confounders_effect_on_treatment"] if "confounders_effect_on_treatment" in kwargs else "binary_flip" ) self.effect_on_y = ( kwargs["confounders_effect_on_outcome"] if "confounders_effect_on_outcome" in kwargs else "linear" ) if self.simulation_method == "direct-simulation": self.kappa_t = kwargs["effect_strength_on_treatment"] if "effect_strength_on_treatment" in kwargs else None self.kappa_y = kwargs["effect_strength_on_outcome"] if "effect_strength_on_outcome" in kwargs else None elif self.simulation_method in ["linear-partial-R2", "non-parametric-partial-R2"]: self.kappa_t = ( kwargs["partial_r2_confounder_treatment"] if "partial_r2_confounder_treatment" in kwargs else None ) self.kappa_y = ( kwargs["partial_r2_confounder_outcome"] if "partial_r2_confounder_outcome" in kwargs else None ) elif self.simulation_method == "e-value": pass else: raise ValueError( "simulation method is not supported. Try direct-simulation, linear-partial-R2, non-parametric-partial-R2, or e-value" ) self.frac_strength_treatment = ( kwargs["effect_fraction_on_treatment"] if "effect_fraction_on_treatment" in kwargs else 1 ) self.frac_strength_outcome = ( kwargs["effect_fraction_on_outcome"] if "effect_fraction_on_outcome" in kwargs else 1 ) self.plotmethod = kwargs["plotmethod"] if "plotmethod" in kwargs else "colormesh" self.percent_change_estimate = kwargs["percent_change_estimate"] if "percent_change_estimate" in kwargs else 1.0 self.significance_level = kwargs["significance_level"] if "significance_level" in kwargs else 0.05 self.confounder_increases_estimate = ( kwargs["confounder_increases_estimate"] if "confounder_increases_estimate" in kwargs else False ) self.benchmark_common_causes = ( kwargs["benchmark_common_causes"] if "benchmark_common_causes" in kwargs else None ) self.null_hypothesis_effect = kwargs["null_hypothesis_effect"] if "null_hypothesis_effect" in kwargs else 0 self.plot_estimate = kwargs["plot_estimate"] if "plot_estimate" in kwargs else True self.num_splits = kwargs["num_splits"] if "num_splits" in kwargs else 5 self.shuffle_data = kwargs["shuffle_data"] if "shuffle_data" in kwargs else False self.shuffle_random_seed = kwargs["shuffle_random_seed"] if "shuffle_random_seed" in kwargs else None self.alpha_s_estimator_param_list = ( kwargs["alpha_s_estimator_param_list"] if "alpha_s_estimator_param_list" in kwargs else None ) self.alpha_s_estimator_list = kwargs["alpha_s_estimator_list"] if "alpha_s_estimator_list" in kwargs else None self.g_s_estimator_list = kwargs["g_s_estimator_list"] if "g_s_estimator_list" in kwargs else None self.g_s_estimator_param_list = ( kwargs["g_s_estimator_param_list"] if "g_s_estimator_param_list" in kwargs else None ) self.plugin_reisz = kwargs["plugin_reisz"] if "plugin_reisz" in kwargs else False self.logger = logging.getLogger(__name__) def refute_estimate(self, show_progress_bar=False): if self.simulation_method == "linear-partial-R2": return sensitivity_linear_partial_r2( self._data, self._estimate, self._treatment_name, self.frac_strength_treatment, self.frac_strength_outcome, self.percent_change_estimate, self.benchmark_common_causes, self.significance_level, self.null_hypothesis_effect, self.plot_estimate, ) elif self.simulation_method == "non-parametric-partial-R2": return sensitivity_non_parametric_partial_r2( self._estimate, self.kappa_t, self.kappa_y, self.frac_strength_treatment, self.frac_strength_outcome, self.benchmark_common_causes, self.plot_estimate, self.alpha_s_estimator_list, self.alpha_s_estimator_param_list, self.g_s_estimator_list, self.g_s_estimator_param_list, self.plugin_reisz, ) elif self.simulation_method == "e-value": return sensitivity_e_value( self._data, self._target_estimand, self._estimate, self._treatment_name, self._outcome_name, self.plot_estimate, ) elif self.simulation_method == "direct-simulation": refute = sensitivity_simulation( self._data, self._target_estimand, self._estimate, self._treatment_name, self._outcome_name, self.kappa_t, self.kappa_y, self.effect_on_t, self.effect_on_y, self.frac_strength_treatment, self.frac_strength_outcome, self.plotmethod, show_progress_bar, ) refute.add_refuter(self) return refute def _infer_default_kappa_t( data: pd.DataFrame, target_estimand: IdentifiedEstimand, treatment_name: List[str], effect_on_t: str, frac_strength_treatment: float, len_kappa_t: int = 10, ): """Infer default effect strength of simulated confounder on treatment.""" observed_common_causes_names = target_estimand.get_backdoor_variables() if len(observed_common_causes_names) > 0: observed_common_causes = data[observed_common_causes_names] observed_common_causes = pd.get_dummies(observed_common_causes, drop_first=True) else: raise ValueError( "There needs to be at least one common cause to" + "automatically compute the default value of kappa_t." + " Provide a value for kappa_t" ) t = data[treatment_name] # Standardizing the data observed_common_causes = StandardScaler().fit_transform(observed_common_causes) if effect_on_t == "binary_flip": # Fit a model containing all confounders and compare predictions # using all features compared to all features except a given # confounder. tmodel = LogisticRegression().fit(observed_common_causes, t) tpred = tmodel.predict(observed_common_causes).astype(int) flips = [] for i in range(observed_common_causes.shape[1]): oldval = np.copy(observed_common_causes[:, i]) observed_common_causes[:, i] = 0 tcap = tmodel.predict(observed_common_causes).astype(int) observed_common_causes[:, i] = oldval flips.append(np.sum(abs(tcap - tpred)) / tpred.shape[0]) min_coeff, max_coeff = min(flips), max(flips) elif effect_on_t == "linear": # Estimating the regression coefficient from standardized features to t corrcoef_var_t = np.corrcoef(observed_common_causes, t, rowvar=False)[-1, :-1] std_dev_t = np.std(t)[0] max_coeff = max(corrcoef_var_t) * std_dev_t min_coeff = min(corrcoef_var_t) * std_dev_t else: raise NotImplementedError("'" + effect_on_t + "' method not supported for confounders' effect on treatment") min_coeff, max_coeff = _compute_min_max_coeff(min_coeff, max_coeff, frac_strength_treatment) # By default, return a plot with 10 points # consider 10 values of the effect of the unobserved confounder step = (max_coeff - min_coeff) / len_kappa_t logger.info("(Min, Max) kappa_t for observed common causes, ({0}, {1})".format(min_coeff, max_coeff)) if np.equal(max_coeff, min_coeff): return max_coeff else: return np.arange(min_coeff, max_coeff, step) def _compute_min_max_coeff(min_coeff: float, max_coeff: float, effect_strength_fraction: np.ndarray): max_coeff = effect_strength_fraction * max_coeff min_coeff = effect_strength_fraction * min_coeff return min_coeff, max_coeff def _infer_default_kappa_y( data: pd.DataFrame, target_estimand: IdentifiedEstimand, outcome_name: List[str], effect_on_y: str, frac_strength_outcome: float, len_kappa_y: int = 10, ): """Infer default effect strength of simulated confounder on treatment.""" observed_common_causes_names = target_estimand.get_backdoor_variables() if len(observed_common_causes_names) > 0: observed_common_causes = data[observed_common_causes_names] observed_common_causes = pd.get_dummies(observed_common_causes, drop_first=True) else: raise ValueError( "There needs to be at least one common cause to" + "automatically compute the default value of kappa_y." + " Provide a value for kappa_y" ) y = data[outcome_name] # Standardizing the data observed_common_causes = StandardScaler().fit_transform(observed_common_causes) if effect_on_y == "binary_flip": # Fit a model containing all confounders and compare predictions # using all features compared to all features except a given # confounder. ymodel = LogisticRegression().fit(observed_common_causes, y) ypred = ymodel.predict(observed_common_causes).astype(int) flips = [] for i in range(observed_common_causes.shape[1]): oldval = np.copy(observed_common_causes[:, i]) observed_common_causes[:, i] = 0 ycap = ymodel.predict(observed_common_causes).astype(int) observed_common_causes[:, i] = oldval flips.append(np.sum(abs(ycap - ypred)) / ypred.shape[0]) min_coeff, max_coeff = min(flips), max(flips) elif effect_on_y == "linear": corrcoef_var_y = np.corrcoef(observed_common_causes, y, rowvar=False)[-1, :-1] std_dev_y = np.std(y)[0] max_coeff = max(corrcoef_var_y) * std_dev_y min_coeff = min(corrcoef_var_y) * std_dev_y else: raise NotImplementedError("'" + effect_on_y + "' method not supported for confounders' effect on outcome") min_coeff, max_coeff = _compute_min_max_coeff(min_coeff, max_coeff, frac_strength_outcome) # By default, return a plot with 10 points # consider 10 values of the effect of the unobserved confounder step = (max_coeff - min_coeff) / len_kappa_y logger.info("(Min, Max) kappa_y for observed common causes, ({0}, {1})".format(min_coeff, max_coeff)) if np.equal(max_coeff, min_coeff): return max_coeff else: return np.arange(min_coeff, max_coeff, step) def _include_confounders_effect( data: pd.DataFrame, new_data: pd.DataFrame, effect_on_t: str, treatment_name: str, kappa_t: float, effect_on_y: str, outcome_name: str, kappa_y: float, ): """ This function deals with the change in the value of the data due to the effect of the unobserved confounder. In the case of a binary flip, we flip only if the random number is greater than the threshold set. In the case of a linear effect, we use the variable as the linear regression constant. :param new_data: pandas.DataFrame: The data to be changed due to the effects of the unobserved confounder. :param kappa_t: numpy.float64: The value of the threshold for binary_flip or the value of the regression coefficient for linear effect. :param kappa_y: numpy.float64: The value of the threshold for binary_flip or the value of the regression coefficient for linear effect. :return: pandas.DataFrame: The DataFrame that includes the effects of the unobserved confounder. """ num_rows = data.shape[0] stdnorm = scipy.stats.norm() w_random = stdnorm.rvs(num_rows) if effect_on_t == "binary_flip": alpha = 2 * kappa_t - 1 if kappa_t >= 0.5 else 1 - 2 * kappa_t interval = stdnorm.interval(alpha) rel_interval = interval[0] if kappa_t >= 0.5 else interval[1] new_data.loc[rel_interval <= w_random, treatment_name] = ( 1 - new_data.loc[rel_interval <= w_random, treatment_name] ) for tname in treatment_name: if pd.api.types.is_bool_dtype(data[tname]): new_data = new_data.astype({tname: "bool"}, copy=False) elif effect_on_t == "linear": confounder_t_effect = kappa_t * w_random # By default, we add the effect of simulated confounder for treatment. # But subtract it from outcome to create a negative correlation # assuming that the original confounder's effect was positive on both. # This is to remove the effect of the original confounder. new_data[treatment_name] = new_data[treatment_name].values + np.ndarray( shape=(num_rows, 1), buffer=confounder_t_effect ) else: raise NotImplementedError("'" + effect_on_t + "' method not supported for confounders' effect on treatment") if effect_on_y == "binary_flip": alpha = 2 * kappa_y - 1 if kappa_y >= 0.5 else 1 - 2 * kappa_y interval = stdnorm.interval(alpha) rel_interval = interval[0] if kappa_y >= 0.5 else interval[1] new_data.loc[rel_interval <= w_random, outcome_name] = 1 - new_data.loc[rel_interval <= w_random, outcome_name] for yname in outcome_name: if pd.api.types.is_bool_dtype(data[yname]): new_data = new_data.astype({yname: "bool"}, copy=False) elif effect_on_y == "linear": confounder_y_effect = (-1) * kappa_y * w_random # By default, we add the effect of simulated confounder for treatment. # But subtract it from outcome to create a negative correlation # assuming that the original confounder's effect was positive on both. # This is to remove the effect of the original confounder. new_data[outcome_name] = new_data[outcome_name].values + np.ndarray( shape=(num_rows, 1), buffer=confounder_y_effect ) else: raise NotImplementedError("'" + effect_on_y + "' method not supported for confounders' effect on outcome") return new_data def include_simulated_confounder( data: pd.DataFrame, treatment_name: str, outcome_name: str, kappa_t: float, kappa_y: float, convergence_threshold: float = 0.1, c_star_max: int = 1000, ): """ This function simulates an unobserved confounder based on the data using the following steps: 1. It calculates the "residuals" from the treatment and outcome model i.) The outcome model has outcome as the dependent variable and all the observed variables including treatment as independent variables ii.) The treatment model has treatment as the dependent variable and all the observed variables as independent variables. 2. U is an intermediate random variable drawn from the normal distribution with the weighted average of residuals as mean and a unit variance U ~ N(c1*d_y + c2*d_t, 1) where *d_y and d_t are residuals from the treatment and outcome model *c1 and c2 are coefficients to the residuals 3. The final U, which is the simulated unobserved confounder is obtained by debiasing the intermediate variable U by residualising it with X Choosing the coefficients c1 and c2: The coefficients are chosen based on these basic assumptions: 1. There is a hyperbolic relationship satisfying c1*c2 = c_star 2. c_star is chosen from a range of possible values based on the correlation of the obtained simulated variable with outcome and treatment. 3. The product of correlations with treatment and outcome should be at a minimum distance to the maximum correlations with treatment and outcome in any of the observed confounders 4. The ratio of the weights should be such that they maintain the ratio of the maximum possible observed coefficients within some confidence interval :param c_star_max: The maximum possible value for the hyperbolic curve on which the coefficients to the residuals lie. It defaults to 1000 in the code if not specified by the user. :type int :param convergence_threshold: The threshold to check the plateauing of the correlation while selecting a c_star. It defaults to 0.1 in the code if not specified by the user :type float :returns: The simulated values of the unobserved confounder based on the data :type pandas.core.series.Series """ # Obtaining the list of observed variables required_variables = True observed_variables = choose_variables(required_variables) observed_variables_with_treatment_and_outcome = observed_variables + treatment_name + outcome_name # Taking a subset of the dataframe that has only observed variables data = data[observed_variables_with_treatment_and_outcome] # Residuals from the outcome model obtained by fitting a linear model y = data[outcome_name[0]] observed_variables_with_treatment = observed_variables + treatment_name X = data[observed_variables_with_treatment] model = sm.OLS(y, X.astype("float")) results = model.fit() residuals_y = y - results.fittedvalues d_y = list(pd.Series(residuals_y)) # Residuals from the treatment model obtained by fitting a linear model t = data[treatment_name[0]].astype("int64") X = data[observed_variables] model = sm.OLS(t, X) results = model.fit() residuals_t = t - results.fittedvalues d_t = list(pd.Series(residuals_t)) # Initialising product_cor_metric_observed with a really low value as finding maximum product_cor_metric_observed = -10000000000 for i in observed_variables: current_obs_confounder = data[i] outcome_values = data[outcome_name[0]] correlation_y = current_obs_confounder.corr(outcome_values) treatment_values = t correlation_t = current_obs_confounder.corr(treatment_values) product_cor_metric_current = correlation_y * correlation_t if product_cor_metric_current >= product_cor_metric_observed: product_cor_metric_observed = product_cor_metric_current correlation_t_observed = correlation_t correlation_y_observed = correlation_y # The user has an option to give the the effect_strength_on_y and effect_strength_on_t which can be then used instead of maximum correlation with treatment and outcome in the observed variables as it specifies the desired effect. if kappa_t is not None: correlation_t_observed = kappa_t if kappa_y is not None: correlation_y_observed = kappa_y # Choosing a c_star based on the data. # The correlations stop increasing upon increasing c_star after a certain value, that is it plateaus and we choose the value of c_star to be the value it plateaus. correlation_y_list = [] correlation_t_list = [] product_cor_metric_simulated_list = [] x_list = [] step = int(c_star_max / 10) for i in range(0, int(c_star_max), step): c1 = math.sqrt(i) c2 = c1 final_U = _generate_confounder_from_residuals(c1, c2, d_y, d_t, X) current_simulated_confounder = final_U outcome_values = data[outcome_name[0]] correlation_y = current_simulated_confounder.corr(outcome_values) correlation_y_list.append(correlation_y) treatment_values = t correlation_t = current_simulated_confounder.corr(treatment_values) correlation_t_list.append(correlation_t) product_cor_metric_simulated = correlation_y * correlation_t product_cor_metric_simulated_list.append(product_cor_metric_simulated) x_list.append(i) index = 1 while index < len(correlation_y_list): if (correlation_y_list[index] - correlation_y_list[index - 1]) <= convergence_threshold: c_star = x_list[index] break index = index + 1 # Choosing c1 and c2 based on the hyperbolic relationship once c_star is chosen by going over various combinations of c1 and c2 values and choosing the combination which # which maintains the minimum distance between the product of correlations of the simulated variable and the product of maximum correlations of one of the observed variables # and additionally checks if the ratio of the weights are such that they maintain the ratio of the maximum possible observed coefficients within some confidence interval # c1_final and c2_final are initialised to the values on the hyperbolic curve such that c1_final = c2_final and c1_final*c2_final = c_star c1_final = math.sqrt(c_star) c2_final = math.sqrt(c_star) # initialising min_distance_between_product_cor_metrics to be a value greater than 1 min_distance_between_product_cor_metrics = 1.5 i = 0.05 threshold = c_star / 0.05 while i <= threshold: c2 = i c1 = c_star / c2 final_U = _generate_confounder_from_residuals(c1, c2, d_y, d_t, X) current_simulated_confounder = final_U outcome_values = data[outcome_name[0]] correlation_y = current_simulated_confounder.corr(outcome_values) treatment_values = t correlation_t = current_simulated_confounder.corr(treatment_values) product_cor_metric_simulated = correlation_y * correlation_t if min_distance_between_product_cor_metrics >= abs(product_cor_metric_simulated - product_cor_metric_observed): min_distance_between_product_cor_metrics = abs(product_cor_metric_simulated - product_cor_metric_observed) additional_condition = correlation_y_observed / correlation_t_observed if ((c1 / c2) <= (additional_condition + 0.3 * additional_condition)) and ( (c1 / c2) >= (additional_condition - 0.3 * additional_condition) ): # choose minimum positive value c1_final = c1 c2_final = c2 i = i * 1.5 """#closed form solution print("c_star_max before closed form", c_star_max) if max_correlation_with_t == -1000: c2 = 0 c1 = c_star_max else: additional_condition = abs(max_correlation_with_y/max_correlation_with_t) print("additional_condition", additional_condition) c2 = math.sqrt(c_star_max/additional_condition) c1 = c_star_max/c2""" final_U = _generate_confounder_from_residuals(c1_final, c2_final, d_y, d_t, X) return final_U def _generate_confounder_from_residuals(c1, c2, d_y, d_t, X): """ This function takes the residuals from the treatment and outcome model and their coefficients and simulates the intermediate random variable U by taking the row wise normal distribution corresponding to each residual value and then debiasing the intermediate variable to get the final variable. :param c1: coefficient to the residual from the outcome model :type float :param c2: coefficient to the residual from the treatment model :type float :param d_y: residuals from the outcome model :type list :param d_t: residuals from the treatment model :type list :returns: The simulated values of the unobserved confounder based on the data :type pandas.core.series.Series """ U = [] for j in range(len(d_t)): simulated_variable_mean = c1 * d_y[j] + c2 * d_t[j] simulated_variable_stddev = 1 U.append(np.random.normal(simulated_variable_mean, simulated_variable_stddev, 1)) U = np.array(U) model = sm.OLS(U, X) results = model.fit() U = U.reshape( -1, ) final_U = U - results.fittedvalues.values final_U = pd.Series(U) return final_U def sensitivity_linear_partial_r2( data: pd.DataFrame, estimate: CausalEstimate, treatment_name: str, frac_strength_treatment: float = 1.0, frac_strength_outcome: float = 1.0, percent_change_estimate: float = 1.0, benchmark_common_causes: Optional[List[str]] = None, significance_level: Optional[float] = None, null_hypothesis_effect: Optional[float] = None, plot_estimate: bool = True, ) -> LinearSensitivityAnalyzer: """Add an unobserved confounder for refutation using Linear partial R2 methond (Sensitivity Analysis for linear models). :param data: pd.DataFrame: Data to run the refutation :param estimate: CausalEstimate: Estimate to run the refutation :param treatment_name: str: Name of the treatment :param frac_strength_treatment: float: This parameter decides the effect strength of the simulated confounder as a fraction of the effect strength of observed confounders on treatment. Defaults to 1. :param frac_strength_outcome: float: This parameter decides the effect strength of the simulated confounder as a fraction of the effect strength of observed confounders on outcome. Defaults to 1. :param percent_change_estimate: It is the percentage of reduction of treatment estimate that could alter the results (default = 1). if percent_change_estimate = 1, the robustness value describes the strength of association of confounders with treatment and outcome in order to reduce the estimate by 100% i.e bring it down to 0. (relevant only for Linear Sensitivity Analysis, ignore for rest) :param benchmark_common_causes: names of variables for bounding strength of confounders. (relevant only for partial-r2 based simulation methods) :param significance_level: confidence interval for statistical inference(default = 0.05). (relevant only for partial-r2 based simulation methods) :param null_hypothesis_effect: assumed effect under the null hypothesis. (relevant only for linear-partial-R2, ignore for rest) :param plot_estimate: Generate contour plot for estimate while performing sensitivity analysis. (default = True). (relevant only for partial-r2 based simulation methods) """ if not (isinstance(estimate.estimator, LinearRegressionEstimator)): raise NotImplementedError("Currently only LinearRegressionEstimator is supported for Sensitivity Analysis") if len(estimate.estimator._effect_modifier_names) > 0: raise NotImplementedError("The current implementation does not support effect modifiers") if frac_strength_outcome == 1: frac_strength_outcome = frac_strength_treatment analyzer = LinearSensitivityAnalyzer( estimator=estimate.estimator, data=data, treatment_name=treatment_name, percent_change_estimate=percent_change_estimate, significance_level=significance_level, benchmark_common_causes=benchmark_common_causes, null_hypothesis_effect=null_hypothesis_effect, frac_strength_treatment=frac_strength_treatment, frac_strength_outcome=frac_strength_outcome, common_causes_order=estimate.estimator._observed_common_causes.columns, ) analyzer.check_sensitivity(plot=plot_estimate) return analyzer def sensitivity_non_parametric_partial_r2( estimate: CausalEstimate, kappa_t: Optional[Union[float, np.ndarray]] = None, kappa_y: Optional[Union[float, np.ndarray]] = None, frac_strength_treatment: float = 1.0, frac_strength_outcome: float = 1.0, benchmark_common_causes: Optional[List[str]] = None, plot_estimate: bool = True, alpha_s_estimator_list: Optional[List] = None, alpha_s_estimator_param_list: Optional[List[Dict]] = None, g_s_estimator_list: Optional[List] = None, g_s_estimator_param_list: Optional[List[Dict]] = None, plugin_reisz: bool = False, ) -> Union[PartialLinearSensitivityAnalyzer, NonParametricSensitivityAnalyzer]: """Add an unobserved confounder for refutation using Non-parametric partial R2 methond (Sensitivity Analysis for non-parametric models). :param estimate: CausalEstimate: Estimate to run the refutation :param kappa_t: float, numpy.ndarray: Partial R2 of the unobserved confounder wrt the treatment conditioned on the observed confounders. Only in the case of general non-parametric-partial-R2, it is the fraction of variance in the reisz representer that is explained by the unobserved confounder; specifically (1-r), where r is the ratio of variance of reisz representer, alpha^2, based on observed confounders and that based on all confounders. :param kappa_y: float, numpy.ndarray: Partial R2 of the unobserved confounder wrt the outcome conditioned on the treatment and observed confounders. :param frac_strength_treatment: float: This parameter decides the effect strength of the simulated confounder as a fraction of the effect strength of observed confounders on treatment. Defaults to 1. :param frac_strength_outcome: float: This parameter decides the effect strength of the simulated confounder as a fraction of the effect strength of observed confounders on outcome. Defaults to 1. :param benchmark_common_causes: names of variables for bounding strength of confounders. (relevant only for partial-r2 based simulation methods) :param plot_estimate: Generate contour plot for estimate while performing sensitivity analysis. (default = True). (relevant only for partial-r2 based simulation methods) :param alpha_s_estimator_list: list of estimator objects for estimating alpha_s. These objects should have fit() and predict() methods (relevant only for non-parametric-partial-R2 method) :param alpha_s_estimator_param_list: list of dictionaries with parameters for finding alpha_s. (relevant only for non-parametric-partial-R2 simulation method) :param g_s_estimator_list: list of estimator objects for finding g_s. These objects should have fit() and predict() functions implemented. (relevant only for non-parametric-partial-R2 simulation method) :param g_s_estimator_param_list: list of dictionaries with parameters for tuning respective estimators in "g_s_estimator_list". The order of the dictionaries in the list should be consistent with the estimator objects order in "g_s_estimator_list". (relevant only for non-parametric-partial-R2 simulation method) :plugin_reisz: bool: Flag on whether to use the plugin estimator or the nonparametric estimator for reisz representer function (alpha_s). """ # If the estimator used is LinearDML, partially linear sensitivity analysis will be automatically chosen if isinstance(estimate.estimator, dowhy.causal_estimators.econml.Econml): if estimate.estimator._econml_methodname == "econml.dml.LinearDML": analyzer = PartialLinearSensitivityAnalyzer( estimator=estimate._estimator_object, observed_common_causes=estimate.estimator._observed_common_causes, treatment=estimate.estimator._treatment, outcome=estimate.estimator._outcome, alpha_s_estimator_param_list=alpha_s_estimator_param_list, g_s_estimator_list=g_s_estimator_list, g_s_estimator_param_list=g_s_estimator_param_list, effect_strength_treatment=kappa_t, effect_strength_outcome=kappa_y, benchmark_common_causes=benchmark_common_causes, frac_strength_treatment=frac_strength_treatment, frac_strength_outcome=frac_strength_outcome, ) analyzer.check_sensitivity(plot=plot_estimate) return analyzer analyzer = NonParametricSensitivityAnalyzer( estimator=estimate.estimator, observed_common_causes=estimate.estimator._observed_common_causes, treatment=estimate.estimator._treatment, outcome=estimate.estimator._outcome, alpha_s_estimator_list=alpha_s_estimator_list, alpha_s_estimator_param_list=alpha_s_estimator_param_list, g_s_estimator_list=g_s_estimator_list, g_s_estimator_param_list=g_s_estimator_param_list, effect_strength_treatment=kappa_t, effect_strength_outcome=kappa_y, benchmark_common_causes=benchmark_common_causes, frac_strength_treatment=frac_strength_treatment, frac_strength_outcome=frac_strength_outcome, theta_s=estimate.value, plugin_reisz=plugin_reisz, ) analyzer.check_sensitivity(plot=plot_estimate) return analyzer def sensitivity_e_value( data: pd.DataFrame, target_estimand: IdentifiedEstimand, estimate: CausalEstimate, treatment_name: List[str], outcome_name: List[str], plot_estimate: bool = True, ) -> EValueSensitivityAnalyzer: if not isinstance(estimate.estimator, RegressionEstimator): raise NotImplementedError("E-Value sensitivity analysis is currently only implemented RegressionEstimator.") if len(estimate.estimator._effect_modifier_names) > 0: raise NotImplementedError("The current implementation does not support effect modifiers") analyzer = EValueSensitivityAnalyzer( estimate=estimate, estimand=target_estimand, data=data, treatment_name=treatment_name[0], outcome_name=outcome_name[0], ) analyzer.check_sensitivity(plot=plot_estimate) return analyzer def sensitivity_simulation( data: pd.DataFrame, target_estimand: IdentifiedEstimand, estimate: CausalEstimate, treatment_name: str, outcome_name: str, kappa_t: Optional[Union[float, np.ndarray]] = None, kappa_y: Optional[Union[float, np.ndarray]] = None, confounders_effect_on_treatment: str = "binary_flip", confounders_effect_on_outcome: str = "linear", frac_strength_treatment: float = 1.0, frac_strength_outcome: float = 1.0, plotmethod: Optional[str] = None, show_progress_bar=False, **_, ) -> CausalRefutation: """ This function attempts to add an unobserved common cause to the outcome and the treatment. At present, we have implemented the behavior for one dimensional behaviors for continuous and binary variables. This function can either take single valued inputs or a range of inputs. The function then looks at the data type of the input and then decides on the course of action. :param data: pd.DataFrame: Data to run the refutation :param target_estimand: IdentifiedEstimand: Identified estimand to run the refutation :param estimate: CausalEstimate: Estimate to run the refutation :param treatment_name: str: Name of the treatment :param outcome_name: str: Name of the outcome :param kappa_t: float, numpy.ndarray: Strength of the confounder's effect on treatment. When confounders_effect_on_treatment is linear, it is the regression coefficient. When the confounders_effect_on_treatment is binary flip, it is the probability with which effect of unobserved confounder can invert the value of the treatment. :param kappa_y: float, numpy.ndarray: Strength of the confounder's effect on outcome. Its interpretation depends on confounders_effect_on_outcome and the simulation_method. When simulation_method is direct-simulation, for a linear effect it behaves like the regression coefficient and for a binary flip, it is the probability with which it can invert the value of the outcome. :param confounders_effect_on_treatment: str : The type of effect on the treatment due to the unobserved confounder. Possible values are ['binary_flip', 'linear'] :param confounders_effect_on_outcome: str : The type of effect on the outcome due to the unobserved confounder. Possible values are ['binary_flip', 'linear'] :param frac_strength_treatment: float: This parameter decides the effect strength of the simulated confounder as a fraction of the effect strength of observed confounders on treatment. Defaults to 1. :param frac_strength_outcome: float: This parameter decides the effect strength of the simulated confounder as a fraction of the effect strength of observed confounders on outcome. Defaults to 1. :param plotmethod: string: Type of plot to be shown. If None, no plot is generated. This parameter is used only only when more than one treatment confounder effect values or outcome confounder effect values are provided. Default is "colormesh". Supported values are "contour", "colormesh" when more than one value is provided for both confounder effect value parameters; "line" when provided for only one of them. :return: CausalRefuter: An object that contains the estimated effect and a new effect and the name of the refutation used. """ if kappa_t is None: kappa_t = _infer_default_kappa_t( data, target_estimand, treatment_name, confounders_effect_on_treatment, frac_strength_treatment ) if kappa_y is None: kappa_y = _infer_default_kappa_y( data, target_estimand, outcome_name, confounders_effect_on_outcome, frac_strength_outcome ) if not isinstance(kappa_t, (list, np.ndarray)) and not isinstance( kappa_y, (list, np.ndarray) ): # Deal with single value inputs new_data = copy.deepcopy(data) new_data = _include_confounders_effect( data, new_data, confounders_effect_on_treatment, treatment_name, kappa_t, confounders_effect_on_outcome, outcome_name, kappa_y, ) new_estimator = CausalEstimator.get_estimator_object(new_data, target_estimand, estimate) new_effect = new_estimator.estimate_effect() refute = CausalRefutation( estimate.value, new_effect.value, refutation_type="Refute: Add an Unobserved Common Cause" ) refute.new_effect_array = np.array(new_effect.value) refute.new_effect = new_effect.value return refute else: # Deal with multiple value inputs if isinstance(kappa_t, (list, np.ndarray)) and isinstance( kappa_y, (list, np.ndarray) ): # Deal with range inputs # Get a 2D matrix of values # x,y = np.meshgrid(self.kappa_t, self.kappa_y) # x,y are both MxN results_matrix = np.random.rand(len(kappa_t), len(kappa_y)) # Matrix to hold all the results of NxM orig_data = copy.deepcopy(data) for i in tqdm( range(len(kappa_t)), colour=CausalRefuter.PROGRESS_BAR_COLOR, disable=not show_progress_bar, desc="Refuting Estimates: ", ): for j in range(len(kappa_y)): new_data = _include_confounders_effect( data, orig_data, confounders_effect_on_treatment, treatment_name, kappa_t[i], confounders_effect_on_outcome, outcome_name, kappa_y[j], ) new_estimator = CausalEstimator.get_estimator_object(new_data, target_estimand, estimate) new_effect = new_estimator.estimate_effect() refute = CausalRefutation( estimate.value, new_effect.value, refutation_type="Refute: Add an Unobserved Common Cause", ) results_matrix[i][j] = refute.new_effect # Populate the results refute.new_effect_array = results_matrix refute.new_effect = (np.min(results_matrix), np.max(results_matrix)) # Store the values into the refute object if plotmethod is None: return refute import matplotlib import matplotlib.pyplot as plt fig = plt.figure(figsize=(6, 5)) left, bottom, width, height = 0.1, 0.1, 0.8, 0.8 ax = fig.add_axes([left, bottom, width, height]) oe = estimate.value contour_levels = [oe / 4.0, oe / 2.0, (3.0 / 4) * oe, oe] contour_levels.extend([0, np.min(results_matrix), np.max(results_matrix)]) if plotmethod == "contour": cp = plt.contourf(kappa_y, kappa_t, results_matrix, levels=sorted(contour_levels)) # Adding a label on the contour line for the original estimate fmt = {} trueeffect_index = np.where(cp.levels == oe)[0][0] fmt[cp.levels[trueeffect_index]] = "Estimated Effect" # Label every other level using strings plt.clabel(cp, [cp.levels[trueeffect_index]], inline=True, fmt=fmt) plt.colorbar(cp) elif plotmethod == "colormesh": cp = plt.pcolormesh(kappa_y, kappa_t, results_matrix, shading="nearest") plt.colorbar(cp, ticks=contour_levels) ax.yaxis.set_ticks(kappa_t) ax.xaxis.set_ticks(kappa_y) plt.xticks(rotation=45) ax.set_title("Effect of Unobserved Common Cause") ax.set_ylabel("Value of Linear Constant on Treatment") ax.set_xlabel("Value of Linear Constant on Outcome") plt.show() return refute elif isinstance(kappa_t, (list, np.ndarray)): outcomes = np.random.rand(len(kappa_t)) orig_data = copy.deepcopy(data) for i in tqdm( range(0, len(kappa_t)), colour=CausalRefuter.PROGRESS_BAR_COLOR, disable=not show_progress_bar, desc="Refuting Estimates: ", ): new_data = _include_confounders_effect( data, orig_data, confounders_effect_on_treatment, treatment_name, kappa_t[i], confounders_effect_on_outcome, outcome_name, kappa_y, ) new_estimator = CausalEstimator.get_estimator_object(new_data, target_estimand, estimate) new_effect = new_estimator.estimate_effect() refute = CausalRefutation( estimate.value, new_effect.value, refutation_type="Refute: Add an Unobserved Common Cause" ) logger.debug(refute) outcomes[i] = refute.new_effect # Populate the results refute.new_effect_array = outcomes refute.new_effect = (np.min(outcomes), np.max(outcomes)) if plotmethod is None: return refute import matplotlib import matplotlib.pyplot as plt fig = plt.figure(figsize=(6, 5)) left, bottom, width, height = 0.1, 0.1, 0.8, 0.8 ax = fig.add_axes([left, bottom, width, height]) plt.plot(kappa_t, outcomes) plt.axhline(estimate.value, linestyle="--", color="gray") ax.set_title("Effect of Unobserved Common Cause") ax.set_xlabel("Value of Linear Constant on Treatment") ax.set_ylabel("Estimated Effect after adding the common cause") plt.show() return refute elif isinstance(kappa_y, (list, np.ndarray)): outcomes = np.random.rand(len(kappa_y)) orig_data = copy.deepcopy(data) for i in tqdm( range(0, len(kappa_y)), colour=CausalRefuter.PROGRESS_BAR_COLOR, disable=not show_progress_bar, desc="Refuting Estimates: ", ): new_data = _include_confounders_effect( data, orig_data, confounders_effect_on_treatment, treatment_name, kappa_t, confounders_effect_on_outcome, outcome_name, kappa_y[i], ) new_estimator = CausalEstimator.get_estimator_object(new_data, target_estimand, estimate) new_effect = new_estimator.estimate_effect() refute = CausalRefutation( estimate.value, new_effect.value, refutation_type="Refute: Add an Unobserved Common Cause" ) logger.debug(refute) outcomes[i] = refute.new_effect # Populate the results refute.new_effect_array = outcomes refute.new_effect = (np.min(outcomes), np.max(outcomes)) if plotmethod is None: return refute import matplotlib import matplotlib.pyplot as plt fig = plt.figure(figsize=(6, 5)) left, bottom, width, height = 0.1, 0.1, 0.8, 0.8 ax = fig.add_axes([left, bottom, width, height]) plt.plot(kappa_y, outcomes) plt.axhline(estimate.value, linestyle="--", color="gray") ax.set_title("Effect of Unobserved Common Cause") ax.set_xlabel("Value of Linear Constant on Outcome") ax.set_ylabel("Estimated Effect after adding the common cause") plt.show() return refute

andresmor-ms

133e7b9a4ed32aae8ab5f39a01eb02b3a4d1c0ba

e1652ec3c6606b1bb2dfe91ef830e4b4b566712d

This sound good. We can follow this policy throughout.

amit-sharma

py-why/dowhy

Functional api/refute estimate

* Refactor refuters into functions * Rename functional_api notebook for clarity * Add return types to identify_estimate * Update `__init__.py` for imports * Add joblib for bootstrap refuter * Create `refute_estimate` function * Add types for refuter parameters & return types

2022-10-04 16:18:49+00:00

2022-10-07 04:30:22+00:00

dowhy/causal_refuters/add_unobserved_common_cause.py

import copy import logging import math import numpy as np import pandas as pd import scipy.stats import statsmodels.api as sm from sklearn.linear_model import LogisticRegression from sklearn.preprocessing import StandardScaler from tqdm.auto import tqdm import dowhy.causal_estimators.econml from dowhy.causal_estimator import CausalEstimator from dowhy.causal_estimators.linear_regression_estimator import LinearRegressionEstimator from dowhy.causal_estimators.regression_estimator import RegressionEstimator from dowhy.causal_refuter import CausalRefutation, CausalRefuter from dowhy.causal_refuters.evalue_sensitivity_analyzer import EValueSensitivityAnalyzer from dowhy.causal_refuters.linear_sensitivity_analyzer import LinearSensitivityAnalyzer from dowhy.causal_refuters.non_parametric_sensitivity_analyzer import NonParametricSensitivityAnalyzer from dowhy.causal_refuters.partial_linear_sensitivity_analyzer import PartialLinearSensitivityAnalyzer class AddUnobservedCommonCause(CausalRefuter): """Add an unobserved confounder for refutation. AddUnobservedCommonCause class supports three methods: 1) Simulation of an unobserved confounder 2) Linear partial R2 : Sensitivity Analysis for linear models. 3) Non-Parametric partial R2 based : Sensitivity Analyis for non-parametric models. Supports additional parameters that can be specified in the refute_estimate() method. """ def __init__(self, *args, **kwargs): """ Initialize the parameters required for the refuter. For direct_simulation, if effect_strength_on_treatment or effect_strength_on_outcome is not given, it is calculated automatically as a range between the minimum and maximum effect strength of observed confounders on treatment and outcome respectively. :param simulation_method: The method to use for simulating effect of unobserved confounder. Possible values are ["direct-simulation", "linear-partial-R2", "non-parametric-partial-R2", "e-value"]. :param confounders_effect_on_treatment: str : The type of effect on the treatment due to the unobserved confounder. Possible values are ['binary_flip', 'linear'] :param confounders_effect_on_outcome: str : The type of effect on the outcome due to the unobserved confounder. Possible values are ['binary_flip', 'linear'] :param effect_strength_on_treatment: float, numpy.ndarray: [Used when simulation_method="direct-simulation"] Strength of the confounder's effect on treatment. When confounders_effect_on_treatment is linear, it is the regression coefficient. When the confounders_effect_on_treatment is binary flip, it is the probability with which effect of unobserved confounder can invert the value of the treatment. :param effect_strength_on_outcome: float, numpy.ndarray: Strength of the confounder's effect on outcome. Its interpretation depends on confounders_effect_on_outcome and the simulation_method. When simulation_method is direct-simulation, for a linear effect it behaves like the regression coefficient and for a binary flip, it is the probability with which it can invert the value of the outcome. :param partial_r2_confounder_treatment: float, numpy.ndarray: [Used when simulation_method is linear-partial-R2 or non-parametric-partial-R2] Partial R2 of the unobserved confounder wrt the treatment conditioned on the observed confounders. Only in the case of general non-parametric-partial-R2, it is the fraction of variance in the reisz representer that is explained by the unobserved confounder; specifically (1-r), where r is the ratio of variance of reisz representer, alpha^2, based on observed confounders and that based on all confounders. :param partial_r2_confounder_outcome: float, numpy.ndarray: [Used when simulation_method is linear-partial-R2 or non-parametric-partial-R2] Partial R2 of the unobserved confounder wrt the outcome conditioned on the treatment and observed confounders. :param frac_strength_treatment: float: This parameter decides the effect strength of the simulated confounder as a fraction of the effect strength of observed confounders on treatment. Defaults to 1. :param frac_strength_outcome: float: This parameter decides the effect strength of the simulated confounder as a fraction of the effect strength of observed confounders on outcome. Defaults to 1. :param plotmethod: string: Type of plot to be shown. If None, no plot is generated. This parameter is used only only when more than one treatment confounder effect values or outcome confounder effect values are provided. Default is "colormesh". Supported values are "contour", "colormesh" when more than one value is provided for both confounder effect value parameters; "line" when provided for only one of them. :param percent_change_estimate: It is the percentage of reduction of treatment estimate that could alter the results (default = 1). if percent_change_estimate = 1, the robustness value describes the strength of association of confounders with treatment and outcome in order to reduce the estimate by 100% i.e bring it down to 0. (relevant only for Linear Sensitivity Analysis, ignore for rest) :param confounder_increases_estimate: True implies that confounder increases the absolute value of estimate and vice versa. (Default = False). (relevant only for Linear Sensitivity Analysis, ignore for rest) :param benchmark_common_causes: names of variables for bounding strength of confounders. (relevant only for partial-r2 based simulation methods) :param significance_level: confidence interval for statistical inference(default = 0.05). (relevant only for partial-r2 based simulation methods) :param null_hypothesis_effect: assumed effect under the null hypothesis. (relevant only for linear-partial-R2, ignore for rest) :param plot_estimate: Generate contour plot for estimate while performing sensitivity analysis. (default = True). (relevant only for partial-r2 based simulation methods) :param num_splits: number of splits for cross validation. (default = 5). (relevant only for non-parametric-partial-R2 simulation method) :param shuffle_data : shuffle data or not before splitting into folds (default = False). (relevant only for non-parametric-partial-R2 simulation method) :param shuffle_random_seed: seed for randomly shuffling data. (relevant only for non-parametric-partial-R2 simulation method) :param alpha_s_estimator_param_list: list of dictionaries with parameters for finding alpha_s. (relevant only for non-parametric-partial-R2 simulation method) :param g_s_estimator_list: list of estimator objects for finding g_s. These objects should have fit() and predict() functions implemented. (relevant only for non-parametric-partial-R2 simulation method) :param g_s_estimator_param_list: list of dictionaries with parameters for tuning respective estimators in "g_s_estimator_list". The order of the dictionaries in the list should be consistent with the estimator objects order in "g_s_estimator_list". (relevant only for non-parametric-partial-R2 simulation method) """ super().__init__(*args, **kwargs) self.simulation_method = kwargs["simulation_method"] if "simulation_method" in kwargs else "direct-simulation" self.effect_on_t = ( kwargs["confounders_effect_on_treatment"] if "confounders_effect_on_treatment" in kwargs else "binary_flip" ) self.effect_on_y = ( kwargs["confounders_effect_on_outcome"] if "confounders_effect_on_outcome" in kwargs else "linear" ) if self.simulation_method == "direct-simulation": self.kappa_t = kwargs["effect_strength_on_treatment"] if "effect_strength_on_treatment" in kwargs else None self.kappa_y = kwargs["effect_strength_on_outcome"] if "effect_strength_on_outcome" in kwargs else None elif self.simulation_method in ["linear-partial-R2", "non-parametric-partial-R2"]: self.kappa_t = ( kwargs["partial_r2_confounder_treatment"] if "partial_r2_confounder_treatment" in kwargs else None ) self.kappa_y = ( kwargs["partial_r2_confounder_outcome"] if "partial_r2_confounder_outcome" in kwargs else None ) elif self.simulation_method == "e-value": pass else: raise ValueError( "simulation method is not supported. Try direct-simulation, linear-partial-R2, non-parametric-partial-R2, or e-value" ) self.frac_strength_treatment = ( kwargs["effect_fraction_on_treatment"] if "effect_fraction_on_treatment" in kwargs else 1 ) self.frac_strength_outcome = ( kwargs["effect_fraction_on_outcome"] if "effect_fraction_on_outcome" in kwargs else 1 ) self.plotmethod = kwargs["plotmethod"] if "plotmethod" in kwargs else "colormesh" self.percent_change_estimate = kwargs["percent_change_estimate"] if "percent_change_estimate" in kwargs else 1.0 self.significance_level = kwargs["significance_level"] if "significance_level" in kwargs else 0.05 self.confounder_increases_estimate = ( kwargs["confounder_increases_estimate"] if "confounder_increases_estimate" in kwargs else False ) self.benchmark_common_causes = ( kwargs["benchmark_common_causes"] if "benchmark_common_causes" in kwargs else None ) self.null_hypothesis_effect = kwargs["null_hypothesis_effect"] if "null_hypothesis_effect" in kwargs else 0 self.plot_estimate = kwargs["plot_estimate"] if "plot_estimate" in kwargs else True self.num_splits = kwargs["num_splits"] if "num_splits" in kwargs else 5 self.shuffle_data = kwargs["shuffle_data"] if "shuffle_data" in kwargs else False self.shuffle_random_seed = kwargs["shuffle_random_seed"] if "shuffle_random_seed" in kwargs else None self.alpha_s_estimator_param_list = ( kwargs["alpha_s_estimator_param_list"] if "alpha_s_estimator_param_list" in kwargs else None ) self.alpha_s_estimator_list = kwargs["alpha_s_estimator_list"] if "alpha_s_estimator_list" in kwargs else None self.g_s_estimator_list = kwargs["g_s_estimator_list"] if "g_s_estimator_list" in kwargs else None self.g_s_estimator_param_list = ( kwargs["g_s_estimator_param_list"] if "g_s_estimator_param_list" in kwargs else None ) self.plugin_reisz = kwargs["plugin_reisz"] if "plugin_reisz" in kwargs else False self.logger = logging.getLogger(__name__) def infer_default_kappa_t(self, len_kappa_t=10): """Infer default effect strength of simulated confounder on treatment.""" observed_common_causes_names = self._target_estimand.get_backdoor_variables() if len(observed_common_causes_names) > 0: observed_common_causes = self._data[observed_common_causes_names] observed_common_causes = pd.get_dummies(observed_common_causes, drop_first=True) else: raise ValueError( "There needs to be at least one common cause to" + "automatically compute the default value of kappa_t." + " Provide a value for kappa_t" ) t = self._data[self._treatment_name] # Standardizing the data observed_common_causes = StandardScaler().fit_transform(observed_common_causes) if self.effect_on_t == "binary_flip": # Fit a model containing all confounders and compare predictions # using all features compared to all features except a given # confounder. tmodel = LogisticRegression().fit(observed_common_causes, t) tpred = tmodel.predict(observed_common_causes).astype(int) flips = [] for i in range(observed_common_causes.shape[1]): oldval = np.copy(observed_common_causes[:, i]) observed_common_causes[:, i] = 0 tcap = tmodel.predict(observed_common_causes).astype(int) observed_common_causes[:, i] = oldval flips.append(np.sum(abs(tcap - tpred)) / tpred.shape[0]) min_coeff, max_coeff = min(flips), max(flips) elif self.effect_on_t == "linear": # Estimating the regression coefficient from standardized features to t corrcoef_var_t = np.corrcoef(observed_common_causes, t, rowvar=False)[-1, :-1] std_dev_t = np.std(t)[0] max_coeff = max(corrcoef_var_t) * std_dev_t min_coeff = min(corrcoef_var_t) * std_dev_t else: raise NotImplementedError( "'" + self.effect_on_t + "' method not supported for confounders' effect on treatment" ) min_coeff, max_coeff = self._compute_min_max_coeff(min_coeff, max_coeff, self.frac_strength_treatment) # By default, return a plot with 10 points # consider 10 values of the effect of the unobserved confounder step = (max_coeff - min_coeff) / len_kappa_t self.logger.info("(Min, Max) kappa_t for observed common causes, ({0}, {1})".format(min_coeff, max_coeff)) if np.equal(max_coeff, min_coeff): return max_coeff else: return np.arange(min_coeff, max_coeff, step) def _compute_min_max_coeff(self, min_coeff, max_coeff, effect_strength_fraction): max_coeff = effect_strength_fraction * max_coeff min_coeff = effect_strength_fraction * min_coeff return min_coeff, max_coeff def infer_default_kappa_y(self, len_kappa_y=10): """Infer default effect strength of simulated confounder on treatment.""" observed_common_causes_names = self._target_estimand.get_backdoor_variables() if len(observed_common_causes_names) > 0: observed_common_causes = self._data[observed_common_causes_names] observed_common_causes = pd.get_dummies(observed_common_causes, drop_first=True) else: raise ValueError( "There needs to be at least one common cause to" + "automatically compute the default value of kappa_y." + " Provide a value for kappa_y" ) y = self._data[self._outcome_name] # Standardizing the data observed_common_causes = StandardScaler().fit_transform(observed_common_causes) if self.effect_on_y == "binary_flip": # Fit a model containing all confounders and compare predictions # using all features compared to all features except a given # confounder. ymodel = LogisticRegression().fit(observed_common_causes, y) ypred = ymodel.predict(observed_common_causes).astype(int) flips = [] for i in range(observed_common_causes.shape[1]): oldval = np.copy(observed_common_causes[:, i]) observed_common_causes[:, i] = 0 ycap = ymodel.predict(observed_common_causes).astype(int) observed_common_causes[:, i] = oldval flips.append(np.sum(abs(ycap - ypred)) / ypred.shape[0]) min_coeff, max_coeff = min(flips), max(flips) elif self.effect_on_y == "linear": corrcoef_var_y = np.corrcoef(observed_common_causes, y, rowvar=False)[-1, :-1] std_dev_y = np.std(y)[0] max_coeff = max(corrcoef_var_y) * std_dev_y min_coeff = min(corrcoef_var_y) * std_dev_y else: raise NotImplementedError( "'" + self.effect_on_y + "' method not supported for confounders' effect on outcome" ) min_coeff, max_coeff = self._compute_min_max_coeff(min_coeff, max_coeff, self.frac_strength_outcome) # By default, return a plot with 10 points # consider 10 values of the effect of the unobserved confounder step = (max_coeff - min_coeff) / len_kappa_y self.logger.info("(Min, Max) kappa_y for observed common causes, ({0}, {1})".format(min_coeff, max_coeff)) if np.equal(max_coeff, min_coeff): return max_coeff else: return np.arange(min_coeff, max_coeff, step) def refute_estimate(self, show_progress_bar=False): """ This function attempts to add an unobserved common cause to the outcome and the treatment. At present, we have implemented the behavior for one dimensional behaviors for continuous and binary variables. This function can either take single valued inputs or a range of inputs. The function then looks at the data type of the input and then decides on the course of action. :return: CausalRefuter: An object that contains the estimated effect and a new effect and the name of the refutation used. """ if self.simulation_method == "linear-partial-R2": if not (isinstance(self._estimate.estimator, LinearRegressionEstimator)): raise NotImplementedError( "Currently only LinearRegressionEstimator is supported for Sensitivity Analysis" ) if len(self._estimate.estimator._effect_modifier_names) > 0: raise NotImplementedError("The current implementation does not support effect modifiers") if self.frac_strength_outcome == 1: self.frac_strength_outcome = self.frac_strength_treatment analyzer = LinearSensitivityAnalyzer( estimator=self._estimate.estimator, data=self._data, treatment_name=self._treatment_name, percent_change_estimate=self.percent_change_estimate, significance_level=self.significance_level, benchmark_common_causes=self.benchmark_common_causes, null_hypothesis_effect=self.null_hypothesis_effect, frac_strength_treatment=self.frac_strength_treatment, frac_strength_outcome=self.frac_strength_outcome, common_causes_order=self._estimate.estimator._observed_common_causes.columns, ) analyzer.check_sensitivity(plot=self.plot_estimate) return analyzer if self.simulation_method == "non-parametric-partial-R2": # If the estimator used is LinearDML, partially linear sensitivity analysis will be automatically chosen if isinstance(self._estimate.estimator, dowhy.causal_estimators.econml.Econml): if self._estimate.estimator._econml_methodname == "econml.dml.LinearDML": analyzer = PartialLinearSensitivityAnalyzer( estimator=self._estimate._estimator_object, observed_common_causes=self._estimate.estimator._observed_common_causes, treatment=self._estimate.estimator._treatment, outcome=self._estimate.estimator._outcome, alpha_s_estimator_param_list=self.alpha_s_estimator_param_list, g_s_estimator_list=self.g_s_estimator_list, g_s_estimator_param_list=self.g_s_estimator_param_list, effect_strength_treatment=self.kappa_t, effect_strength_outcome=self.kappa_y, benchmark_common_causes=self.benchmark_common_causes, frac_strength_treatment=self.frac_strength_treatment, frac_strength_outcome=self.frac_strength_outcome, ) analyzer.check_sensitivity(plot=self.plot_estimate) return analyzer analyzer = NonParametricSensitivityAnalyzer( estimator=self._estimate.estimator, observed_common_causes=self._estimate.estimator._observed_common_causes, treatment=self._estimate.estimator._treatment, outcome=self._estimate.estimator._outcome, alpha_s_estimator_list=self.alpha_s_estimator_list, alpha_s_estimator_param_list=self.alpha_s_estimator_param_list, g_s_estimator_list=self.g_s_estimator_list, g_s_estimator_param_list=self.g_s_estimator_param_list, effect_strength_treatment=self.kappa_t, effect_strength_outcome=self.kappa_y, benchmark_common_causes=self.benchmark_common_causes, frac_strength_treatment=self.frac_strength_treatment, frac_strength_outcome=self.frac_strength_outcome, theta_s=self._estimate.value, plugin_reisz=self.plugin_reisz, ) analyzer.check_sensitivity(plot=self.plot_estimate) return analyzer if self.simulation_method == "e-value": if not isinstance(self._estimate.estimator, RegressionEstimator): raise NotImplementedError( "E-Value sensitivity analysis is currently only implemented RegressionEstimator." ) if len(self._estimate.estimator._effect_modifier_names) > 0: raise NotImplementedError("The current implementation does not support effect modifiers") analyzer = EValueSensitivityAnalyzer( estimate=self._estimate, estimand=self._target_estimand, data=self._data, treatment_name=self._treatment_name[0], outcome_name=self._outcome_name[0], ) analyzer.check_sensitivity(plot=self.plot_estimate) return analyzer if self.kappa_t is None: self.kappa_t = self.infer_default_kappa_t() if self.kappa_y is None: self.kappa_y = self.infer_default_kappa_y() if not isinstance(self.kappa_t, (list, np.ndarray)) and not isinstance( self.kappa_y, (list, np.ndarray) ): # Deal with single value inputs new_data = copy.deepcopy(self._data) new_data = self.include_confounders_effect(new_data, self.kappa_t, self.kappa_y) new_estimator = CausalEstimator.get_estimator_object(new_data, self._target_estimand, self._estimate) new_effect = new_estimator.estimate_effect() refute = CausalRefutation( self._estimate.value, new_effect.value, refutation_type="Refute: Add an Unobserved Common Cause" ) refute.new_effect_array = np.array(new_effect.value) refute.new_effect = new_effect.value refute.add_refuter(self) return refute else: # Deal with multiple value inputs if isinstance(self.kappa_t, (list, np.ndarray)) and isinstance( self.kappa_y, (list, np.ndarray) ): # Deal with range inputs # Get a 2D matrix of values # x,y = np.meshgrid(self.kappa_t, self.kappa_y) # x,y are both MxN results_matrix = np.random.rand( len(self.kappa_t), len(self.kappa_y) ) # Matrix to hold all the results of NxM orig_data = copy.deepcopy(self._data) for i in tqdm( range(len(self.kappa_t)), colour=CausalRefuter.PROGRESS_BAR_COLOR, disable=not show_progress_bar, desc="Refuting Estimates: ", ): for j in range(len(self.kappa_y)): new_data = self.include_confounders_effect(orig_data, self.kappa_t[i], self.kappa_y[j]) new_estimator = CausalEstimator.get_estimator_object( new_data, self._target_estimand, self._estimate ) new_effect = new_estimator.estimate_effect() refute = CausalRefutation( self._estimate.value, new_effect.value, refutation_type="Refute: Add an Unobserved Common Cause", ) results_matrix[i][j] = refute.new_effect # Populate the results refute.new_effect_array = results_matrix refute.new_effect = (np.min(results_matrix), np.max(results_matrix)) # Store the values into the refute object refute.add_refuter(self) if self.plotmethod is None: return refute import matplotlib import matplotlib.pyplot as plt fig = plt.figure(figsize=(6, 5)) left, bottom, width, height = 0.1, 0.1, 0.8, 0.8 ax = fig.add_axes([left, bottom, width, height]) oe = self._estimate.value contour_levels = [oe / 4.0, oe / 2.0, (3.0 / 4) * oe, oe] contour_levels.extend([0, np.min(results_matrix), np.max(results_matrix)]) if self.plotmethod == "contour": cp = plt.contourf(self.kappa_y, self.kappa_t, results_matrix, levels=sorted(contour_levels)) # Adding a label on the contour line for the original estimate fmt = {} trueeffect_index = np.where(cp.levels == oe)[0][0] fmt[cp.levels[trueeffect_index]] = "Estimated Effect" # Label every other level using strings plt.clabel(cp, [cp.levels[trueeffect_index]], inline=True, fmt=fmt) plt.colorbar(cp) elif self.plotmethod == "colormesh": cp = plt.pcolormesh(self.kappa_y, self.kappa_t, results_matrix, shading="nearest") plt.colorbar(cp, ticks=contour_levels) ax.yaxis.set_ticks(self.kappa_t) ax.xaxis.set_ticks(self.kappa_y) plt.xticks(rotation=45) ax.set_title("Effect of Unobserved Common Cause") ax.set_ylabel("Value of Linear Constant on Treatment") ax.set_xlabel("Value of Linear Constant on Outcome") plt.show() return refute elif isinstance(self.kappa_t, (list, np.ndarray)): outcomes = np.random.rand(len(self.kappa_t)) orig_data = copy.deepcopy(self._data) for i in tqdm( range(0, len(self.kappa_t)), colour=CausalRefuter.PROGRESS_BAR_COLOR, disable=not show_progress_bar, desc="Refuting Estimates: ", ): new_data = self.include_confounders_effect(orig_data, self.kappa_t[i], self.kappa_y) new_estimator = CausalEstimator.get_estimator_object( new_data, self._target_estimand, self._estimate ) new_effect = new_estimator.estimate_effect() refute = CausalRefutation( self._estimate.value, new_effect.value, refutation_type="Refute: Add an Unobserved Common Cause" ) self.logger.debug(refute) outcomes[i] = refute.new_effect # Populate the results refute.new_effect_array = outcomes refute.new_effect = (np.min(outcomes), np.max(outcomes)) refute.add_refuter(self) if self.plotmethod is None: return refute import matplotlib import matplotlib.pyplot as plt fig = plt.figure(figsize=(6, 5)) left, bottom, width, height = 0.1, 0.1, 0.8, 0.8 ax = fig.add_axes([left, bottom, width, height]) plt.plot(self.kappa_t, outcomes) plt.axhline(self._estimate.value, linestyle="--", color="gray") ax.set_title("Effect of Unobserved Common Cause") ax.set_xlabel("Value of Linear Constant on Treatment") ax.set_ylabel("Estimated Effect after adding the common cause") plt.show() return refute elif isinstance(self.kappa_y, (list, np.ndarray)): outcomes = np.random.rand(len(self.kappa_y)) orig_data = copy.deepcopy(self._data) for i in tqdm( range(0, len(self.kappa_y)), colour=CausalRefuter.PROGRESS_BAR_COLOR, disable=not show_progress_bar, desc="Refuting Estimates: ", ): new_data = self.include_confounders_effect(orig_data, self.kappa_t, self.kappa_y[i]) new_estimator = CausalEstimator.get_estimator_object( new_data, self._target_estimand, self._estimate ) new_effect = new_estimator.estimate_effect() refute = CausalRefutation( self._estimate.value, new_effect.value, refutation_type="Refute: Add an Unobserved Common Cause" ) self.logger.debug(refute) outcomes[i] = refute.new_effect # Populate the results refute.new_effect_array = outcomes refute.new_effect = (np.min(outcomes), np.max(outcomes)) refute.add_refuter(self) if self.plotmethod is None: return refute import matplotlib import matplotlib.pyplot as plt fig = plt.figure(figsize=(6, 5)) left, bottom, width, height = 0.1, 0.1, 0.8, 0.8 ax = fig.add_axes([left, bottom, width, height]) plt.plot(self.kappa_y, outcomes) plt.axhline(self._estimate.value, linestyle="--", color="gray") ax.set_title("Effect of Unobserved Common Cause") ax.set_xlabel("Value of Linear Constant on Outcome") ax.set_ylabel("Estimated Effect after adding the common cause") plt.show() return refute def include_confounders_effect(self, new_data, kappa_t, kappa_y): """ This function deals with the change in the value of the data due to the effect of the unobserved confounder. In the case of a binary flip, we flip only if the random number is greater than the threshold set. In the case of a linear effect, we use the variable as the linear regression constant. :param new_data: pandas.DataFrame: The data to be changed due to the effects of the unobserved confounder. :param kappa_t: numpy.float64: The value of the threshold for binary_flip or the value of the regression coefficient for linear effect. :param kappa_y: numpy.float64: The value of the threshold for binary_flip or the value of the regression coefficient for linear effect. :return: pandas.DataFrame: The DataFrame that includes the effects of the unobserved confounder. """ num_rows = self._data.shape[0] stdnorm = scipy.stats.norm() w_random = stdnorm.rvs(num_rows) if self.effect_on_t == "binary_flip": alpha = 2 * kappa_t - 1 if kappa_t >= 0.5 else 1 - 2 * kappa_t interval = stdnorm.interval(alpha) rel_interval = interval[0] if kappa_t >= 0.5 else interval[1] new_data.loc[rel_interval <= w_random, self._treatment_name] = ( 1 - new_data.loc[rel_interval <= w_random, self._treatment_name] ) for tname in self._treatment_name: if pd.api.types.is_bool_dtype(self._data[tname]): new_data = new_data.astype({tname: "bool"}, copy=False) elif self.effect_on_t == "linear": confounder_t_effect = kappa_t * w_random # By default, we add the effect of simulated confounder for treatment. # But subtract it from outcome to create a negative correlation # assuming that the original confounder's effect was positive on both. # This is to remove the effect of the original confounder. new_data[self._treatment_name] = new_data[self._treatment_name].values + np.ndarray( shape=(num_rows, 1), buffer=confounder_t_effect ) else: raise NotImplementedError( "'" + self.effect_on_t + "' method not supported for confounders' effect on treatment" ) if self.effect_on_y == "binary_flip": alpha = 2 * kappa_y - 1 if kappa_y >= 0.5 else 1 - 2 * kappa_y interval = stdnorm.interval(alpha) rel_interval = interval[0] if kappa_y >= 0.5 else interval[1] new_data.loc[rel_interval <= w_random, self._outcome_name] = ( 1 - new_data.loc[rel_interval <= w_random, self._outcome_name] ) for yname in self._outcome_name: if pd.api.types.is_bool_dtype(self._data[yname]): new_data = new_data.astype({yname: "bool"}, copy=False) elif self.effect_on_y == "linear": confounder_y_effect = (-1) * kappa_y * w_random # By default, we add the effect of simulated confounder for treatment. # But subtract it from outcome to create a negative correlation # assuming that the original confounder's effect was positive on both. # This is to remove the effect of the original confounder. new_data[self._outcome_name] = new_data[self._outcome_name].values + np.ndarray( shape=(num_rows, 1), buffer=confounder_y_effect ) else: raise NotImplementedError( "'" + self.effect_on_y + "' method not supported for confounders' effect on outcome" ) return new_data def include_simulated_confounder(self, convergence_threshold=0.1, c_star_max=1000): """ This function simulates an unobserved confounder based on the data using the following steps: 1. It calculates the "residuals" from the treatment and outcome model i.) The outcome model has outcome as the dependent variable and all the observed variables including treatment as independent variables ii.) The treatment model has treatment as the dependent variable and all the observed variables as independent variables. 2. U is an intermediate random variable drawn from the normal distribution with the weighted average of residuals as mean and a unit variance U ~ N(c1*d_y + c2*d_t, 1) where *d_y and d_t are residuals from the treatment and outcome model *c1 and c2 are coefficients to the residuals 3. The final U, which is the simulated unobserved confounder is obtained by debiasing the intermediate variable U by residualising it with X Choosing the coefficients c1 and c2: The coefficients are chosen based on these basic assumptions: 1. There is a hyperbolic relationship satisfying c1*c2 = c_star 2. c_star is chosen from a range of possible values based on the correlation of the obtained simulated variable with outcome and treatment. 3. The product of correlations with treatment and outcome should be at a minimum distance to the maximum correlations with treatment and outcome in any of the observed confounders 4. The ratio of the weights should be such that they maintain the ratio of the maximum possible observed coefficients within some confidence interval :param c_star_max: The maximum possible value for the hyperbolic curve on which the coefficients to the residuals lie. It defaults to 1000 in the code if not specified by the user. :type int :param convergence_threshold: The threshold to check the plateauing of the correlation while selecting a c_star. It defaults to 0.1 in the code if not specified by the user :type float :returns: The simulated values of the unobserved confounder based on the data :type pandas.core.series.Series """ # Obtaining the list of observed variables required_variables = True observed_variables = self.choose_variables(required_variables) observed_variables_with_treatment_and_outcome = observed_variables + self._treatment_name + self._outcome_name # Taking a subset of the dataframe that has only observed variables self._data = self._data[observed_variables_with_treatment_and_outcome] # Residuals from the outcome model obtained by fitting a linear model y = self._data[self._outcome_name[0]] observed_variables_with_treatment = observed_variables + self._treatment_name X = self._data[observed_variables_with_treatment] model = sm.OLS(y, X.astype("float")) results = model.fit() residuals_y = y - results.fittedvalues d_y = list(pd.Series(residuals_y)) # Residuals from the treatment model obtained by fitting a linear model t = self._data[self._treatment_name[0]].astype("int64") X = self._data[observed_variables] model = sm.OLS(t, X) results = model.fit() residuals_t = t - results.fittedvalues d_t = list(pd.Series(residuals_t)) # Initialising product_cor_metric_observed with a really low value as finding maximum product_cor_metric_observed = -10000000000 for i in observed_variables: current_obs_confounder = self._data[i] outcome_values = self._data[self._outcome_name[0]] correlation_y = current_obs_confounder.corr(outcome_values) treatment_values = t correlation_t = current_obs_confounder.corr(treatment_values) product_cor_metric_current = correlation_y * correlation_t if product_cor_metric_current >= product_cor_metric_observed: product_cor_metric_observed = product_cor_metric_current correlation_t_observed = correlation_t correlation_y_observed = correlation_y # The user has an option to give the the effect_strength_on_y and effect_strength_on_t which can be then used instead of maximum correlation with treatment and outcome in the observed variables as it specifies the desired effect. if self.kappa_t is not None: correlation_t_observed = self.kappa_t if self.kappa_y is not None: correlation_y_observed = self.kappa_y # Choosing a c_star based on the data. # The correlations stop increasing upon increasing c_star after a certain value, that is it plateaus and we choose the value of c_star to be the value it plateaus. correlation_y_list = [] correlation_t_list = [] product_cor_metric_simulated_list = [] x_list = [] step = int(c_star_max / 10) for i in range(0, int(c_star_max), step): c1 = math.sqrt(i) c2 = c1 final_U = self.generate_confounder_from_residuals(c1, c2, d_y, d_t, X) current_simulated_confounder = final_U outcome_values = self._data[self._outcome_name[0]] correlation_y = current_simulated_confounder.corr(outcome_values) correlation_y_list.append(correlation_y) treatment_values = t correlation_t = current_simulated_confounder.corr(treatment_values) correlation_t_list.append(correlation_t) product_cor_metric_simulated = correlation_y * correlation_t product_cor_metric_simulated_list.append(product_cor_metric_simulated) x_list.append(i) index = 1 while index < len(correlation_y_list): if (correlation_y_list[index] - correlation_y_list[index - 1]) <= convergence_threshold: c_star = x_list[index] break index = index + 1 # Choosing c1 and c2 based on the hyperbolic relationship once c_star is chosen by going over various combinations of c1 and c2 values and choosing the combination which # which maintains the minimum distance between the product of correlations of the simulated variable and the product of maximum correlations of one of the observed variables # and additionally checks if the ratio of the weights are such that they maintain the ratio of the maximum possible observed coefficients within some confidence interval # c1_final and c2_final are initialised to the values on the hyperbolic curve such that c1_final = c2_final and c1_final*c2_final = c_star c1_final = math.sqrt(c_star) c2_final = math.sqrt(c_star) # initialising min_distance_between_product_cor_metrics to be a value greater than 1 min_distance_between_product_cor_metrics = 1.5 i = 0.05 threshold = c_star / 0.05 while i <= threshold: c2 = i c1 = c_star / c2 final_U = self.generate_confounder_from_residuals(c1, c2, d_y, d_t, X) current_simulated_confounder = final_U outcome_values = self._data[self._outcome_name[0]] correlation_y = current_simulated_confounder.corr(outcome_values) treatment_values = t correlation_t = current_simulated_confounder.corr(treatment_values) product_cor_metric_simulated = correlation_y * correlation_t if min_distance_between_product_cor_metrics >= abs( product_cor_metric_simulated - product_cor_metric_observed ): min_distance_between_product_cor_metrics = abs( product_cor_metric_simulated - product_cor_metric_observed ) additional_condition = correlation_y_observed / correlation_t_observed if ((c1 / c2) <= (additional_condition + 0.3 * additional_condition)) and ( (c1 / c2) >= (additional_condition - 0.3 * additional_condition) ): # choose minimum positive value c1_final = c1 c2_final = c2 i = i * 1.5 """#closed form solution print("c_star_max before closed form", c_star_max) if max_correlation_with_t == -1000: c2 = 0 c1 = c_star_max else: additional_condition = abs(max_correlation_with_y/max_correlation_with_t) print("additional_condition", additional_condition) c2 = math.sqrt(c_star_max/additional_condition) c1 = c_star_max/c2""" final_U = self.generate_confounder_from_residuals(c1_final, c2_final, d_y, d_t, X) return final_U def generate_confounder_from_residuals(self, c1, c2, d_y, d_t, X): """ This function takes the residuals from the treatment and outcome model and their coefficients and simulates the intermediate random variable U by taking the row wise normal distribution corresponding to each residual value and then debiasing the intermediate variable to get the final variable. :param c1: coefficient to the residual from the outcome model :type float :param c2: coefficient to the residual from the treatment model :type float :param d_y: residuals from the outcome model :type list :param d_t: residuals from the treatment model :type list :returns: The simulated values of the unobserved confounder based on the data :type pandas.core.series.Series """ U = [] for j in range(len(d_t)): simulated_variable_mean = c1 * d_y[j] + c2 * d_t[j] simulated_variable_stddev = 1 U.append(np.random.normal(simulated_variable_mean, simulated_variable_stddev, 1)) U = np.array(U) model = sm.OLS(U, X) results = model.fit() U = U.reshape( -1, ) final_U = U - results.fittedvalues.values final_U = pd.Series(U) return final_U

import copy import logging import math from typing import Dict, List, Optional, Union import numpy as np import pandas as pd import scipy.stats import statsmodels.api as sm from sklearn.linear_model import LogisticRegression from sklearn.preprocessing import StandardScaler from tqdm.auto import tqdm import dowhy.causal_estimators.econml from dowhy.causal_estimator import CausalEstimate, CausalEstimator from dowhy.causal_estimators.linear_regression_estimator import LinearRegressionEstimator from dowhy.causal_estimators.regression_estimator import RegressionEstimator from dowhy.causal_identifier.identified_estimand import IdentifiedEstimand from dowhy.causal_refuter import CausalRefutation, CausalRefuter, choose_variables from dowhy.causal_refuters.evalue_sensitivity_analyzer import EValueSensitivityAnalyzer from dowhy.causal_refuters.linear_sensitivity_analyzer import LinearSensitivityAnalyzer from dowhy.causal_refuters.non_parametric_sensitivity_analyzer import NonParametricSensitivityAnalyzer from dowhy.causal_refuters.partial_linear_sensitivity_analyzer import PartialLinearSensitivityAnalyzer logger = logging.getLogger(__name__) class AddUnobservedCommonCause(CausalRefuter): """Add an unobserved confounder for refutation. AddUnobservedCommonCause class supports three methods: 1) Simulation of an unobserved confounder 2) Linear partial R2 : Sensitivity Analysis for linear models. 3) Non-Parametric partial R2 based : Sensitivity Analyis for non-parametric models. Supports additional parameters that can be specified in the refute_estimate() method. """ def __init__(self, *args, **kwargs): """ Initialize the parameters required for the refuter. For direct_simulation, if effect_strength_on_treatment or effect_strength_on_outcome is not given, it is calculated automatically as a range between the minimum and maximum effect strength of observed confounders on treatment and outcome respectively. :param simulation_method: The method to use for simulating effect of unobserved confounder. Possible values are ["direct-simulation", "linear-partial-R2", "non-parametric-partial-R2", "e-value"]. :param confounders_effect_on_treatment: str : The type of effect on the treatment due to the unobserved confounder. Possible values are ['binary_flip', 'linear'] :param confounders_effect_on_outcome: str : The type of effect on the outcome due to the unobserved confounder. Possible values are ['binary_flip', 'linear'] :param effect_strength_on_treatment: float, numpy.ndarray: [Used when simulation_method="direct-simulation"] Strength of the confounder's effect on treatment. When confounders_effect_on_treatment is linear, it is the regression coefficient. When the confounders_effect_on_treatment is binary flip, it is the probability with which effect of unobserved confounder can invert the value of the treatment. :param effect_strength_on_outcome: float, numpy.ndarray: Strength of the confounder's effect on outcome. Its interpretation depends on confounders_effect_on_outcome and the simulation_method. When simulation_method is direct-simulation, for a linear effect it behaves like the regression coefficient and for a binary flip, it is the probability with which it can invert the value of the outcome. :param partial_r2_confounder_treatment: float, numpy.ndarray: [Used when simulation_method is linear-partial-R2 or non-parametric-partial-R2] Partial R2 of the unobserved confounder wrt the treatment conditioned on the observed confounders. Only in the case of general non-parametric-partial-R2, it is the fraction of variance in the reisz representer that is explained by the unobserved confounder; specifically (1-r), where r is the ratio of variance of reisz representer, alpha^2, based on observed confounders and that based on all confounders. :param partial_r2_confounder_outcome: float, numpy.ndarray: [Used when simulation_method is linear-partial-R2 or non-parametric-partial-R2] Partial R2 of the unobserved confounder wrt the outcome conditioned on the treatment and observed confounders. :param frac_strength_treatment: float: This parameter decides the effect strength of the simulated confounder as a fraction of the effect strength of observed confounders on treatment. Defaults to 1. :param frac_strength_outcome: float: This parameter decides the effect strength of the simulated confounder as a fraction of the effect strength of observed confounders on outcome. Defaults to 1. :param plotmethod: string: Type of plot to be shown. If None, no plot is generated. This parameter is used only only when more than one treatment confounder effect values or outcome confounder effect values are provided. Default is "colormesh". Supported values are "contour", "colormesh" when more than one value is provided for both confounder effect value parameters; "line" when provided for only one of them. :param percent_change_estimate: It is the percentage of reduction of treatment estimate that could alter the results (default = 1). if percent_change_estimate = 1, the robustness value describes the strength of association of confounders with treatment and outcome in order to reduce the estimate by 100% i.e bring it down to 0. (relevant only for Linear Sensitivity Analysis, ignore for rest) :param confounder_increases_estimate: True implies that confounder increases the absolute value of estimate and vice versa. (Default = False). (relevant only for Linear Sensitivity Analysis, ignore for rest) :param benchmark_common_causes: names of variables for bounding strength of confounders. (relevant only for partial-r2 based simulation methods) :param significance_level: confidence interval for statistical inference(default = 0.05). (relevant only for partial-r2 based simulation methods) :param null_hypothesis_effect: assumed effect under the null hypothesis. (relevant only for linear-partial-R2, ignore for rest) :param plot_estimate: Generate contour plot for estimate while performing sensitivity analysis. (default = True). (relevant only for partial-r2 based simulation methods) :param num_splits: number of splits for cross validation. (default = 5). (relevant only for non-parametric-partial-R2 simulation method) :param shuffle_data : shuffle data or not before splitting into folds (default = False). (relevant only for non-parametric-partial-R2 simulation method) :param shuffle_random_seed: seed for randomly shuffling data. (relevant only for non-parametric-partial-R2 simulation method) :param alpha_s_estimator_param_list: list of dictionaries with parameters for finding alpha_s. (relevant only for non-parametric-partial-R2 simulation method) :param g_s_estimator_list: list of estimator objects for finding g_s. These objects should have fit() and predict() functions implemented. (relevant only for non-parametric-partial-R2 simulation method) :param g_s_estimator_param_list: list of dictionaries with parameters for tuning respective estimators in "g_s_estimator_list". The order of the dictionaries in the list should be consistent with the estimator objects order in "g_s_estimator_list". (relevant only for non-parametric-partial-R2 simulation method) """ super().__init__(*args, **kwargs) self.simulation_method = kwargs["simulation_method"] if "simulation_method" in kwargs else "direct-simulation" self.effect_on_t = ( kwargs["confounders_effect_on_treatment"] if "confounders_effect_on_treatment" in kwargs else "binary_flip" ) self.effect_on_y = ( kwargs["confounders_effect_on_outcome"] if "confounders_effect_on_outcome" in kwargs else "linear" ) if self.simulation_method == "direct-simulation": self.kappa_t = kwargs["effect_strength_on_treatment"] if "effect_strength_on_treatment" in kwargs else None self.kappa_y = kwargs["effect_strength_on_outcome"] if "effect_strength_on_outcome" in kwargs else None elif self.simulation_method in ["linear-partial-R2", "non-parametric-partial-R2"]: self.kappa_t = ( kwargs["partial_r2_confounder_treatment"] if "partial_r2_confounder_treatment" in kwargs else None ) self.kappa_y = ( kwargs["partial_r2_confounder_outcome"] if "partial_r2_confounder_outcome" in kwargs else None ) elif self.simulation_method == "e-value": pass else: raise ValueError( "simulation method is not supported. Try direct-simulation, linear-partial-R2, non-parametric-partial-R2, or e-value" ) self.frac_strength_treatment = ( kwargs["effect_fraction_on_treatment"] if "effect_fraction_on_treatment" in kwargs else 1 ) self.frac_strength_outcome = ( kwargs["effect_fraction_on_outcome"] if "effect_fraction_on_outcome" in kwargs else 1 ) self.plotmethod = kwargs["plotmethod"] if "plotmethod" in kwargs else "colormesh" self.percent_change_estimate = kwargs["percent_change_estimate"] if "percent_change_estimate" in kwargs else 1.0 self.significance_level = kwargs["significance_level"] if "significance_level" in kwargs else 0.05 self.confounder_increases_estimate = ( kwargs["confounder_increases_estimate"] if "confounder_increases_estimate" in kwargs else False ) self.benchmark_common_causes = ( kwargs["benchmark_common_causes"] if "benchmark_common_causes" in kwargs else None ) self.null_hypothesis_effect = kwargs["null_hypothesis_effect"] if "null_hypothesis_effect" in kwargs else 0 self.plot_estimate = kwargs["plot_estimate"] if "plot_estimate" in kwargs else True self.num_splits = kwargs["num_splits"] if "num_splits" in kwargs else 5 self.shuffle_data = kwargs["shuffle_data"] if "shuffle_data" in kwargs else False self.shuffle_random_seed = kwargs["shuffle_random_seed"] if "shuffle_random_seed" in kwargs else None self.alpha_s_estimator_param_list = ( kwargs["alpha_s_estimator_param_list"] if "alpha_s_estimator_param_list" in kwargs else None ) self.alpha_s_estimator_list = kwargs["alpha_s_estimator_list"] if "alpha_s_estimator_list" in kwargs else None self.g_s_estimator_list = kwargs["g_s_estimator_list"] if "g_s_estimator_list" in kwargs else None self.g_s_estimator_param_list = ( kwargs["g_s_estimator_param_list"] if "g_s_estimator_param_list" in kwargs else None ) self.plugin_reisz = kwargs["plugin_reisz"] if "plugin_reisz" in kwargs else False self.logger = logging.getLogger(__name__) def refute_estimate(self, show_progress_bar=False): if self.simulation_method == "linear-partial-R2": return sensitivity_linear_partial_r2( self._data, self._estimate, self._treatment_name, self.frac_strength_treatment, self.frac_strength_outcome, self.percent_change_estimate, self.benchmark_common_causes, self.significance_level, self.null_hypothesis_effect, self.plot_estimate, ) elif self.simulation_method == "non-parametric-partial-R2": return sensitivity_non_parametric_partial_r2( self._estimate, self.kappa_t, self.kappa_y, self.frac_strength_treatment, self.frac_strength_outcome, self.benchmark_common_causes, self.plot_estimate, self.alpha_s_estimator_list, self.alpha_s_estimator_param_list, self.g_s_estimator_list, self.g_s_estimator_param_list, self.plugin_reisz, ) elif self.simulation_method == "e-value": return sensitivity_e_value( self._data, self._target_estimand, self._estimate, self._treatment_name, self._outcome_name, self.plot_estimate, ) elif self.simulation_method == "direct-simulation": refute = sensitivity_simulation( self._data, self._target_estimand, self._estimate, self._treatment_name, self._outcome_name, self.kappa_t, self.kappa_y, self.effect_on_t, self.effect_on_y, self.frac_strength_treatment, self.frac_strength_outcome, self.plotmethod, show_progress_bar, ) refute.add_refuter(self) return refute def _infer_default_kappa_t( data: pd.DataFrame, target_estimand: IdentifiedEstimand, treatment_name: List[str], effect_on_t: str, frac_strength_treatment: float, len_kappa_t: int = 10, ): """Infer default effect strength of simulated confounder on treatment.""" observed_common_causes_names = target_estimand.get_backdoor_variables() if len(observed_common_causes_names) > 0: observed_common_causes = data[observed_common_causes_names] observed_common_causes = pd.get_dummies(observed_common_causes, drop_first=True) else: raise ValueError( "There needs to be at least one common cause to" + "automatically compute the default value of kappa_t." + " Provide a value for kappa_t" ) t = data[treatment_name] # Standardizing the data observed_common_causes = StandardScaler().fit_transform(observed_common_causes) if effect_on_t == "binary_flip": # Fit a model containing all confounders and compare predictions # using all features compared to all features except a given # confounder. tmodel = LogisticRegression().fit(observed_common_causes, t) tpred = tmodel.predict(observed_common_causes).astype(int) flips = [] for i in range(observed_common_causes.shape[1]): oldval = np.copy(observed_common_causes[:, i]) observed_common_causes[:, i] = 0 tcap = tmodel.predict(observed_common_causes).astype(int) observed_common_causes[:, i] = oldval flips.append(np.sum(abs(tcap - tpred)) / tpred.shape[0]) min_coeff, max_coeff = min(flips), max(flips) elif effect_on_t == "linear": # Estimating the regression coefficient from standardized features to t corrcoef_var_t = np.corrcoef(observed_common_causes, t, rowvar=False)[-1, :-1] std_dev_t = np.std(t)[0] max_coeff = max(corrcoef_var_t) * std_dev_t min_coeff = min(corrcoef_var_t) * std_dev_t else: raise NotImplementedError("'" + effect_on_t + "' method not supported for confounders' effect on treatment") min_coeff, max_coeff = _compute_min_max_coeff(min_coeff, max_coeff, frac_strength_treatment) # By default, return a plot with 10 points # consider 10 values of the effect of the unobserved confounder step = (max_coeff - min_coeff) / len_kappa_t logger.info("(Min, Max) kappa_t for observed common causes, ({0}, {1})".format(min_coeff, max_coeff)) if np.equal(max_coeff, min_coeff): return max_coeff else: return np.arange(min_coeff, max_coeff, step) def _compute_min_max_coeff(min_coeff: float, max_coeff: float, effect_strength_fraction: np.ndarray): max_coeff = effect_strength_fraction * max_coeff min_coeff = effect_strength_fraction * min_coeff return min_coeff, max_coeff def _infer_default_kappa_y( data: pd.DataFrame, target_estimand: IdentifiedEstimand, outcome_name: List[str], effect_on_y: str, frac_strength_outcome: float, len_kappa_y: int = 10, ): """Infer default effect strength of simulated confounder on treatment.""" observed_common_causes_names = target_estimand.get_backdoor_variables() if len(observed_common_causes_names) > 0: observed_common_causes = data[observed_common_causes_names] observed_common_causes = pd.get_dummies(observed_common_causes, drop_first=True) else: raise ValueError( "There needs to be at least one common cause to" + "automatically compute the default value of kappa_y." + " Provide a value for kappa_y" ) y = data[outcome_name] # Standardizing the data observed_common_causes = StandardScaler().fit_transform(observed_common_causes) if effect_on_y == "binary_flip": # Fit a model containing all confounders and compare predictions # using all features compared to all features except a given # confounder. ymodel = LogisticRegression().fit(observed_common_causes, y) ypred = ymodel.predict(observed_common_causes).astype(int) flips = [] for i in range(observed_common_causes.shape[1]): oldval = np.copy(observed_common_causes[:, i]) observed_common_causes[:, i] = 0 ycap = ymodel.predict(observed_common_causes).astype(int) observed_common_causes[:, i] = oldval flips.append(np.sum(abs(ycap - ypred)) / ypred.shape[0]) min_coeff, max_coeff = min(flips), max(flips) elif effect_on_y == "linear": corrcoef_var_y = np.corrcoef(observed_common_causes, y, rowvar=False)[-1, :-1] std_dev_y = np.std(y)[0] max_coeff = max(corrcoef_var_y) * std_dev_y min_coeff = min(corrcoef_var_y) * std_dev_y else: raise NotImplementedError("'" + effect_on_y + "' method not supported for confounders' effect on outcome") min_coeff, max_coeff = _compute_min_max_coeff(min_coeff, max_coeff, frac_strength_outcome) # By default, return a plot with 10 points # consider 10 values of the effect of the unobserved confounder step = (max_coeff - min_coeff) / len_kappa_y logger.info("(Min, Max) kappa_y for observed common causes, ({0}, {1})".format(min_coeff, max_coeff)) if np.equal(max_coeff, min_coeff): return max_coeff else: return np.arange(min_coeff, max_coeff, step) def _include_confounders_effect( data: pd.DataFrame, new_data: pd.DataFrame, effect_on_t: str, treatment_name: str, kappa_t: float, effect_on_y: str, outcome_name: str, kappa_y: float, ): """ This function deals with the change in the value of the data due to the effect of the unobserved confounder. In the case of a binary flip, we flip only if the random number is greater than the threshold set. In the case of a linear effect, we use the variable as the linear regression constant. :param new_data: pandas.DataFrame: The data to be changed due to the effects of the unobserved confounder. :param kappa_t: numpy.float64: The value of the threshold for binary_flip or the value of the regression coefficient for linear effect. :param kappa_y: numpy.float64: The value of the threshold for binary_flip or the value of the regression coefficient for linear effect. :return: pandas.DataFrame: The DataFrame that includes the effects of the unobserved confounder. """ num_rows = data.shape[0] stdnorm = scipy.stats.norm() w_random = stdnorm.rvs(num_rows) if effect_on_t == "binary_flip": alpha = 2 * kappa_t - 1 if kappa_t >= 0.5 else 1 - 2 * kappa_t interval = stdnorm.interval(alpha) rel_interval = interval[0] if kappa_t >= 0.5 else interval[1] new_data.loc[rel_interval <= w_random, treatment_name] = ( 1 - new_data.loc[rel_interval <= w_random, treatment_name] ) for tname in treatment_name: if pd.api.types.is_bool_dtype(data[tname]): new_data = new_data.astype({tname: "bool"}, copy=False) elif effect_on_t == "linear": confounder_t_effect = kappa_t * w_random # By default, we add the effect of simulated confounder for treatment. # But subtract it from outcome to create a negative correlation # assuming that the original confounder's effect was positive on both. # This is to remove the effect of the original confounder. new_data[treatment_name] = new_data[treatment_name].values + np.ndarray( shape=(num_rows, 1), buffer=confounder_t_effect ) else: raise NotImplementedError("'" + effect_on_t + "' method not supported for confounders' effect on treatment") if effect_on_y == "binary_flip": alpha = 2 * kappa_y - 1 if kappa_y >= 0.5 else 1 - 2 * kappa_y interval = stdnorm.interval(alpha) rel_interval = interval[0] if kappa_y >= 0.5 else interval[1] new_data.loc[rel_interval <= w_random, outcome_name] = 1 - new_data.loc[rel_interval <= w_random, outcome_name] for yname in outcome_name: if pd.api.types.is_bool_dtype(data[yname]): new_data = new_data.astype({yname: "bool"}, copy=False) elif effect_on_y == "linear": confounder_y_effect = (-1) * kappa_y * w_random # By default, we add the effect of simulated confounder for treatment. # But subtract it from outcome to create a negative correlation # assuming that the original confounder's effect was positive on both. # This is to remove the effect of the original confounder. new_data[outcome_name] = new_data[outcome_name].values + np.ndarray( shape=(num_rows, 1), buffer=confounder_y_effect ) else: raise NotImplementedError("'" + effect_on_y + "' method not supported for confounders' effect on outcome") return new_data def include_simulated_confounder( data: pd.DataFrame, treatment_name: str, outcome_name: str, kappa_t: float, kappa_y: float, convergence_threshold: float = 0.1, c_star_max: int = 1000, ): """ This function simulates an unobserved confounder based on the data using the following steps: 1. It calculates the "residuals" from the treatment and outcome model i.) The outcome model has outcome as the dependent variable and all the observed variables including treatment as independent variables ii.) The treatment model has treatment as the dependent variable and all the observed variables as independent variables. 2. U is an intermediate random variable drawn from the normal distribution with the weighted average of residuals as mean and a unit variance U ~ N(c1*d_y + c2*d_t, 1) where *d_y and d_t are residuals from the treatment and outcome model *c1 and c2 are coefficients to the residuals 3. The final U, which is the simulated unobserved confounder is obtained by debiasing the intermediate variable U by residualising it with X Choosing the coefficients c1 and c2: The coefficients are chosen based on these basic assumptions: 1. There is a hyperbolic relationship satisfying c1*c2 = c_star 2. c_star is chosen from a range of possible values based on the correlation of the obtained simulated variable with outcome and treatment. 3. The product of correlations with treatment and outcome should be at a minimum distance to the maximum correlations with treatment and outcome in any of the observed confounders 4. The ratio of the weights should be such that they maintain the ratio of the maximum possible observed coefficients within some confidence interval :param c_star_max: The maximum possible value for the hyperbolic curve on which the coefficients to the residuals lie. It defaults to 1000 in the code if not specified by the user. :type int :param convergence_threshold: The threshold to check the plateauing of the correlation while selecting a c_star. It defaults to 0.1 in the code if not specified by the user :type float :returns: The simulated values of the unobserved confounder based on the data :type pandas.core.series.Series """ # Obtaining the list of observed variables required_variables = True observed_variables = choose_variables(required_variables) observed_variables_with_treatment_and_outcome = observed_variables + treatment_name + outcome_name # Taking a subset of the dataframe that has only observed variables data = data[observed_variables_with_treatment_and_outcome] # Residuals from the outcome model obtained by fitting a linear model y = data[outcome_name[0]] observed_variables_with_treatment = observed_variables + treatment_name X = data[observed_variables_with_treatment] model = sm.OLS(y, X.astype("float")) results = model.fit() residuals_y = y - results.fittedvalues d_y = list(pd.Series(residuals_y)) # Residuals from the treatment model obtained by fitting a linear model t = data[treatment_name[0]].astype("int64") X = data[observed_variables] model = sm.OLS(t, X) results = model.fit() residuals_t = t - results.fittedvalues d_t = list(pd.Series(residuals_t)) # Initialising product_cor_metric_observed with a really low value as finding maximum product_cor_metric_observed = -10000000000 for i in observed_variables: current_obs_confounder = data[i] outcome_values = data[outcome_name[0]] correlation_y = current_obs_confounder.corr(outcome_values) treatment_values = t correlation_t = current_obs_confounder.corr(treatment_values) product_cor_metric_current = correlation_y * correlation_t if product_cor_metric_current >= product_cor_metric_observed: product_cor_metric_observed = product_cor_metric_current correlation_t_observed = correlation_t correlation_y_observed = correlation_y # The user has an option to give the the effect_strength_on_y and effect_strength_on_t which can be then used instead of maximum correlation with treatment and outcome in the observed variables as it specifies the desired effect. if kappa_t is not None: correlation_t_observed = kappa_t if kappa_y is not None: correlation_y_observed = kappa_y # Choosing a c_star based on the data. # The correlations stop increasing upon increasing c_star after a certain value, that is it plateaus and we choose the value of c_star to be the value it plateaus. correlation_y_list = [] correlation_t_list = [] product_cor_metric_simulated_list = [] x_list = [] step = int(c_star_max / 10) for i in range(0, int(c_star_max), step): c1 = math.sqrt(i) c2 = c1 final_U = _generate_confounder_from_residuals(c1, c2, d_y, d_t, X) current_simulated_confounder = final_U outcome_values = data[outcome_name[0]] correlation_y = current_simulated_confounder.corr(outcome_values) correlation_y_list.append(correlation_y) treatment_values = t correlation_t = current_simulated_confounder.corr(treatment_values) correlation_t_list.append(correlation_t) product_cor_metric_simulated = correlation_y * correlation_t product_cor_metric_simulated_list.append(product_cor_metric_simulated) x_list.append(i) index = 1 while index < len(correlation_y_list): if (correlation_y_list[index] - correlation_y_list[index - 1]) <= convergence_threshold: c_star = x_list[index] break index = index + 1 # Choosing c1 and c2 based on the hyperbolic relationship once c_star is chosen by going over various combinations of c1 and c2 values and choosing the combination which # which maintains the minimum distance between the product of correlations of the simulated variable and the product of maximum correlations of one of the observed variables # and additionally checks if the ratio of the weights are such that they maintain the ratio of the maximum possible observed coefficients within some confidence interval # c1_final and c2_final are initialised to the values on the hyperbolic curve such that c1_final = c2_final and c1_final*c2_final = c_star c1_final = math.sqrt(c_star) c2_final = math.sqrt(c_star) # initialising min_distance_between_product_cor_metrics to be a value greater than 1 min_distance_between_product_cor_metrics = 1.5 i = 0.05 threshold = c_star / 0.05 while i <= threshold: c2 = i c1 = c_star / c2 final_U = _generate_confounder_from_residuals(c1, c2, d_y, d_t, X) current_simulated_confounder = final_U outcome_values = data[outcome_name[0]] correlation_y = current_simulated_confounder.corr(outcome_values) treatment_values = t correlation_t = current_simulated_confounder.corr(treatment_values) product_cor_metric_simulated = correlation_y * correlation_t if min_distance_between_product_cor_metrics >= abs(product_cor_metric_simulated - product_cor_metric_observed): min_distance_between_product_cor_metrics = abs(product_cor_metric_simulated - product_cor_metric_observed) additional_condition = correlation_y_observed / correlation_t_observed if ((c1 / c2) <= (additional_condition + 0.3 * additional_condition)) and ( (c1 / c2) >= (additional_condition - 0.3 * additional_condition) ): # choose minimum positive value c1_final = c1 c2_final = c2 i = i * 1.5 """#closed form solution print("c_star_max before closed form", c_star_max) if max_correlation_with_t == -1000: c2 = 0 c1 = c_star_max else: additional_condition = abs(max_correlation_with_y/max_correlation_with_t) print("additional_condition", additional_condition) c2 = math.sqrt(c_star_max/additional_condition) c1 = c_star_max/c2""" final_U = _generate_confounder_from_residuals(c1_final, c2_final, d_y, d_t, X) return final_U def _generate_confounder_from_residuals(c1, c2, d_y, d_t, X): """ This function takes the residuals from the treatment and outcome model and their coefficients and simulates the intermediate random variable U by taking the row wise normal distribution corresponding to each residual value and then debiasing the intermediate variable to get the final variable. :param c1: coefficient to the residual from the outcome model :type float :param c2: coefficient to the residual from the treatment model :type float :param d_y: residuals from the outcome model :type list :param d_t: residuals from the treatment model :type list :returns: The simulated values of the unobserved confounder based on the data :type pandas.core.series.Series """ U = [] for j in range(len(d_t)): simulated_variable_mean = c1 * d_y[j] + c2 * d_t[j] simulated_variable_stddev = 1 U.append(np.random.normal(simulated_variable_mean, simulated_variable_stddev, 1)) U = np.array(U) model = sm.OLS(U, X) results = model.fit() U = U.reshape( -1, ) final_U = U - results.fittedvalues.values final_U = pd.Series(U) return final_U def sensitivity_linear_partial_r2( data: pd.DataFrame, estimate: CausalEstimate, treatment_name: str, frac_strength_treatment: float = 1.0, frac_strength_outcome: float = 1.0, percent_change_estimate: float = 1.0, benchmark_common_causes: Optional[List[str]] = None, significance_level: Optional[float] = None, null_hypothesis_effect: Optional[float] = None, plot_estimate: bool = True, ) -> LinearSensitivityAnalyzer: """Add an unobserved confounder for refutation using Linear partial R2 methond (Sensitivity Analysis for linear models). :param data: pd.DataFrame: Data to run the refutation :param estimate: CausalEstimate: Estimate to run the refutation :param treatment_name: str: Name of the treatment :param frac_strength_treatment: float: This parameter decides the effect strength of the simulated confounder as a fraction of the effect strength of observed confounders on treatment. Defaults to 1. :param frac_strength_outcome: float: This parameter decides the effect strength of the simulated confounder as a fraction of the effect strength of observed confounders on outcome. Defaults to 1. :param percent_change_estimate: It is the percentage of reduction of treatment estimate that could alter the results (default = 1). if percent_change_estimate = 1, the robustness value describes the strength of association of confounders with treatment and outcome in order to reduce the estimate by 100% i.e bring it down to 0. (relevant only for Linear Sensitivity Analysis, ignore for rest) :param benchmark_common_causes: names of variables for bounding strength of confounders. (relevant only for partial-r2 based simulation methods) :param significance_level: confidence interval for statistical inference(default = 0.05). (relevant only for partial-r2 based simulation methods) :param null_hypothesis_effect: assumed effect under the null hypothesis. (relevant only for linear-partial-R2, ignore for rest) :param plot_estimate: Generate contour plot for estimate while performing sensitivity analysis. (default = True). (relevant only for partial-r2 based simulation methods) """ if not (isinstance(estimate.estimator, LinearRegressionEstimator)): raise NotImplementedError("Currently only LinearRegressionEstimator is supported for Sensitivity Analysis") if len(estimate.estimator._effect_modifier_names) > 0: raise NotImplementedError("The current implementation does not support effect modifiers") if frac_strength_outcome == 1: frac_strength_outcome = frac_strength_treatment analyzer = LinearSensitivityAnalyzer( estimator=estimate.estimator, data=data, treatment_name=treatment_name, percent_change_estimate=percent_change_estimate, significance_level=significance_level, benchmark_common_causes=benchmark_common_causes, null_hypothesis_effect=null_hypothesis_effect, frac_strength_treatment=frac_strength_treatment, frac_strength_outcome=frac_strength_outcome, common_causes_order=estimate.estimator._observed_common_causes.columns, ) analyzer.check_sensitivity(plot=plot_estimate) return analyzer def sensitivity_non_parametric_partial_r2( estimate: CausalEstimate, kappa_t: Optional[Union[float, np.ndarray]] = None, kappa_y: Optional[Union[float, np.ndarray]] = None, frac_strength_treatment: float = 1.0, frac_strength_outcome: float = 1.0, benchmark_common_causes: Optional[List[str]] = None, plot_estimate: bool = True, alpha_s_estimator_list: Optional[List] = None, alpha_s_estimator_param_list: Optional[List[Dict]] = None, g_s_estimator_list: Optional[List] = None, g_s_estimator_param_list: Optional[List[Dict]] = None, plugin_reisz: bool = False, ) -> Union[PartialLinearSensitivityAnalyzer, NonParametricSensitivityAnalyzer]: """Add an unobserved confounder for refutation using Non-parametric partial R2 methond (Sensitivity Analysis for non-parametric models). :param estimate: CausalEstimate: Estimate to run the refutation :param kappa_t: float, numpy.ndarray: Partial R2 of the unobserved confounder wrt the treatment conditioned on the observed confounders. Only in the case of general non-parametric-partial-R2, it is the fraction of variance in the reisz representer that is explained by the unobserved confounder; specifically (1-r), where r is the ratio of variance of reisz representer, alpha^2, based on observed confounders and that based on all confounders. :param kappa_y: float, numpy.ndarray: Partial R2 of the unobserved confounder wrt the outcome conditioned on the treatment and observed confounders. :param frac_strength_treatment: float: This parameter decides the effect strength of the simulated confounder as a fraction of the effect strength of observed confounders on treatment. Defaults to 1. :param frac_strength_outcome: float: This parameter decides the effect strength of the simulated confounder as a fraction of the effect strength of observed confounders on outcome. Defaults to 1. :param benchmark_common_causes: names of variables for bounding strength of confounders. (relevant only for partial-r2 based simulation methods) :param plot_estimate: Generate contour plot for estimate while performing sensitivity analysis. (default = True). (relevant only for partial-r2 based simulation methods) :param alpha_s_estimator_list: list of estimator objects for estimating alpha_s. These objects should have fit() and predict() methods (relevant only for non-parametric-partial-R2 method) :param alpha_s_estimator_param_list: list of dictionaries with parameters for finding alpha_s. (relevant only for non-parametric-partial-R2 simulation method) :param g_s_estimator_list: list of estimator objects for finding g_s. These objects should have fit() and predict() functions implemented. (relevant only for non-parametric-partial-R2 simulation method) :param g_s_estimator_param_list: list of dictionaries with parameters for tuning respective estimators in "g_s_estimator_list". The order of the dictionaries in the list should be consistent with the estimator objects order in "g_s_estimator_list". (relevant only for non-parametric-partial-R2 simulation method) :plugin_reisz: bool: Flag on whether to use the plugin estimator or the nonparametric estimator for reisz representer function (alpha_s). """ # If the estimator used is LinearDML, partially linear sensitivity analysis will be automatically chosen if isinstance(estimate.estimator, dowhy.causal_estimators.econml.Econml): if estimate.estimator._econml_methodname == "econml.dml.LinearDML": analyzer = PartialLinearSensitivityAnalyzer( estimator=estimate._estimator_object, observed_common_causes=estimate.estimator._observed_common_causes, treatment=estimate.estimator._treatment, outcome=estimate.estimator._outcome, alpha_s_estimator_param_list=alpha_s_estimator_param_list, g_s_estimator_list=g_s_estimator_list, g_s_estimator_param_list=g_s_estimator_param_list, effect_strength_treatment=kappa_t, effect_strength_outcome=kappa_y, benchmark_common_causes=benchmark_common_causes, frac_strength_treatment=frac_strength_treatment, frac_strength_outcome=frac_strength_outcome, ) analyzer.check_sensitivity(plot=plot_estimate) return analyzer analyzer = NonParametricSensitivityAnalyzer( estimator=estimate.estimator, observed_common_causes=estimate.estimator._observed_common_causes, treatment=estimate.estimator._treatment, outcome=estimate.estimator._outcome, alpha_s_estimator_list=alpha_s_estimator_list, alpha_s_estimator_param_list=alpha_s_estimator_param_list, g_s_estimator_list=g_s_estimator_list, g_s_estimator_param_list=g_s_estimator_param_list, effect_strength_treatment=kappa_t, effect_strength_outcome=kappa_y, benchmark_common_causes=benchmark_common_causes, frac_strength_treatment=frac_strength_treatment, frac_strength_outcome=frac_strength_outcome, theta_s=estimate.value, plugin_reisz=plugin_reisz, ) analyzer.check_sensitivity(plot=plot_estimate) return analyzer def sensitivity_e_value( data: pd.DataFrame, target_estimand: IdentifiedEstimand, estimate: CausalEstimate, treatment_name: List[str], outcome_name: List[str], plot_estimate: bool = True, ) -> EValueSensitivityAnalyzer: if not isinstance(estimate.estimator, RegressionEstimator): raise NotImplementedError("E-Value sensitivity analysis is currently only implemented RegressionEstimator.") if len(estimate.estimator._effect_modifier_names) > 0: raise NotImplementedError("The current implementation does not support effect modifiers") analyzer = EValueSensitivityAnalyzer( estimate=estimate, estimand=target_estimand, data=data, treatment_name=treatment_name[0], outcome_name=outcome_name[0], ) analyzer.check_sensitivity(plot=plot_estimate) return analyzer def sensitivity_simulation( data: pd.DataFrame, target_estimand: IdentifiedEstimand, estimate: CausalEstimate, treatment_name: str, outcome_name: str, kappa_t: Optional[Union[float, np.ndarray]] = None, kappa_y: Optional[Union[float, np.ndarray]] = None, confounders_effect_on_treatment: str = "binary_flip", confounders_effect_on_outcome: str = "linear", frac_strength_treatment: float = 1.0, frac_strength_outcome: float = 1.0, plotmethod: Optional[str] = None, show_progress_bar=False, **_, ) -> CausalRefutation: """ This function attempts to add an unobserved common cause to the outcome and the treatment. At present, we have implemented the behavior for one dimensional behaviors for continuous and binary variables. This function can either take single valued inputs or a range of inputs. The function then looks at the data type of the input and then decides on the course of action. :param data: pd.DataFrame: Data to run the refutation :param target_estimand: IdentifiedEstimand: Identified estimand to run the refutation :param estimate: CausalEstimate: Estimate to run the refutation :param treatment_name: str: Name of the treatment :param outcome_name: str: Name of the outcome :param kappa_t: float, numpy.ndarray: Strength of the confounder's effect on treatment. When confounders_effect_on_treatment is linear, it is the regression coefficient. When the confounders_effect_on_treatment is binary flip, it is the probability with which effect of unobserved confounder can invert the value of the treatment. :param kappa_y: float, numpy.ndarray: Strength of the confounder's effect on outcome. Its interpretation depends on confounders_effect_on_outcome and the simulation_method. When simulation_method is direct-simulation, for a linear effect it behaves like the regression coefficient and for a binary flip, it is the probability with which it can invert the value of the outcome. :param confounders_effect_on_treatment: str : The type of effect on the treatment due to the unobserved confounder. Possible values are ['binary_flip', 'linear'] :param confounders_effect_on_outcome: str : The type of effect on the outcome due to the unobserved confounder. Possible values are ['binary_flip', 'linear'] :param frac_strength_treatment: float: This parameter decides the effect strength of the simulated confounder as a fraction of the effect strength of observed confounders on treatment. Defaults to 1. :param frac_strength_outcome: float: This parameter decides the effect strength of the simulated confounder as a fraction of the effect strength of observed confounders on outcome. Defaults to 1. :param plotmethod: string: Type of plot to be shown. If None, no plot is generated. This parameter is used only only when more than one treatment confounder effect values or outcome confounder effect values are provided. Default is "colormesh". Supported values are "contour", "colormesh" when more than one value is provided for both confounder effect value parameters; "line" when provided for only one of them. :return: CausalRefuter: An object that contains the estimated effect and a new effect and the name of the refutation used. """ if kappa_t is None: kappa_t = _infer_default_kappa_t( data, target_estimand, treatment_name, confounders_effect_on_treatment, frac_strength_treatment ) if kappa_y is None: kappa_y = _infer_default_kappa_y( data, target_estimand, outcome_name, confounders_effect_on_outcome, frac_strength_outcome ) if not isinstance(kappa_t, (list, np.ndarray)) and not isinstance( kappa_y, (list, np.ndarray) ): # Deal with single value inputs new_data = copy.deepcopy(data) new_data = _include_confounders_effect( data, new_data, confounders_effect_on_treatment, treatment_name, kappa_t, confounders_effect_on_outcome, outcome_name, kappa_y, ) new_estimator = CausalEstimator.get_estimator_object(new_data, target_estimand, estimate) new_effect = new_estimator.estimate_effect() refute = CausalRefutation( estimate.value, new_effect.value, refutation_type="Refute: Add an Unobserved Common Cause" ) refute.new_effect_array = np.array(new_effect.value) refute.new_effect = new_effect.value return refute else: # Deal with multiple value inputs if isinstance(kappa_t, (list, np.ndarray)) and isinstance( kappa_y, (list, np.ndarray) ): # Deal with range inputs # Get a 2D matrix of values # x,y = np.meshgrid(self.kappa_t, self.kappa_y) # x,y are both MxN results_matrix = np.random.rand(len(kappa_t), len(kappa_y)) # Matrix to hold all the results of NxM orig_data = copy.deepcopy(data) for i in tqdm( range(len(kappa_t)), colour=CausalRefuter.PROGRESS_BAR_COLOR, disable=not show_progress_bar, desc="Refuting Estimates: ", ): for j in range(len(kappa_y)): new_data = _include_confounders_effect( data, orig_data, confounders_effect_on_treatment, treatment_name, kappa_t[i], confounders_effect_on_outcome, outcome_name, kappa_y[j], ) new_estimator = CausalEstimator.get_estimator_object(new_data, target_estimand, estimate) new_effect = new_estimator.estimate_effect() refute = CausalRefutation( estimate.value, new_effect.value, refutation_type="Refute: Add an Unobserved Common Cause", ) results_matrix[i][j] = refute.new_effect # Populate the results refute.new_effect_array = results_matrix refute.new_effect = (np.min(results_matrix), np.max(results_matrix)) # Store the values into the refute object if plotmethod is None: return refute import matplotlib import matplotlib.pyplot as plt fig = plt.figure(figsize=(6, 5)) left, bottom, width, height = 0.1, 0.1, 0.8, 0.8 ax = fig.add_axes([left, bottom, width, height]) oe = estimate.value contour_levels = [oe / 4.0, oe / 2.0, (3.0 / 4) * oe, oe] contour_levels.extend([0, np.min(results_matrix), np.max(results_matrix)]) if plotmethod == "contour": cp = plt.contourf(kappa_y, kappa_t, results_matrix, levels=sorted(contour_levels)) # Adding a label on the contour line for the original estimate fmt = {} trueeffect_index = np.where(cp.levels == oe)[0][0] fmt[cp.levels[trueeffect_index]] = "Estimated Effect" # Label every other level using strings plt.clabel(cp, [cp.levels[trueeffect_index]], inline=True, fmt=fmt) plt.colorbar(cp) elif plotmethod == "colormesh": cp = plt.pcolormesh(kappa_y, kappa_t, results_matrix, shading="nearest") plt.colorbar(cp, ticks=contour_levels) ax.yaxis.set_ticks(kappa_t) ax.xaxis.set_ticks(kappa_y) plt.xticks(rotation=45) ax.set_title("Effect of Unobserved Common Cause") ax.set_ylabel("Value of Linear Constant on Treatment") ax.set_xlabel("Value of Linear Constant on Outcome") plt.show() return refute elif isinstance(kappa_t, (list, np.ndarray)): outcomes = np.random.rand(len(kappa_t)) orig_data = copy.deepcopy(data) for i in tqdm( range(0, len(kappa_t)), colour=CausalRefuter.PROGRESS_BAR_COLOR, disable=not show_progress_bar, desc="Refuting Estimates: ", ): new_data = _include_confounders_effect( data, orig_data, confounders_effect_on_treatment, treatment_name, kappa_t[i], confounders_effect_on_outcome, outcome_name, kappa_y, ) new_estimator = CausalEstimator.get_estimator_object(new_data, target_estimand, estimate) new_effect = new_estimator.estimate_effect() refute = CausalRefutation( estimate.value, new_effect.value, refutation_type="Refute: Add an Unobserved Common Cause" ) logger.debug(refute) outcomes[i] = refute.new_effect # Populate the results refute.new_effect_array = outcomes refute.new_effect = (np.min(outcomes), np.max(outcomes)) if plotmethod is None: return refute import matplotlib import matplotlib.pyplot as plt fig = plt.figure(figsize=(6, 5)) left, bottom, width, height = 0.1, 0.1, 0.8, 0.8 ax = fig.add_axes([left, bottom, width, height]) plt.plot(kappa_t, outcomes) plt.axhline(estimate.value, linestyle="--", color="gray") ax.set_title("Effect of Unobserved Common Cause") ax.set_xlabel("Value of Linear Constant on Treatment") ax.set_ylabel("Estimated Effect after adding the common cause") plt.show() return refute elif isinstance(kappa_y, (list, np.ndarray)): outcomes = np.random.rand(len(kappa_y)) orig_data = copy.deepcopy(data) for i in tqdm( range(0, len(kappa_y)), colour=CausalRefuter.PROGRESS_BAR_COLOR, disable=not show_progress_bar, desc="Refuting Estimates: ", ): new_data = _include_confounders_effect( data, orig_data, confounders_effect_on_treatment, treatment_name, kappa_t, confounders_effect_on_outcome, outcome_name, kappa_y[i], ) new_estimator = CausalEstimator.get_estimator_object(new_data, target_estimand, estimate) new_effect = new_estimator.estimate_effect() refute = CausalRefutation( estimate.value, new_effect.value, refutation_type="Refute: Add an Unobserved Common Cause" ) logger.debug(refute) outcomes[i] = refute.new_effect # Populate the results refute.new_effect_array = outcomes refute.new_effect = (np.min(outcomes), np.max(outcomes)) if plotmethod is None: return refute import matplotlib import matplotlib.pyplot as plt fig = plt.figure(figsize=(6, 5)) left, bottom, width, height = 0.1, 0.1, 0.8, 0.8 ax = fig.add_axes([left, bottom, width, height]) plt.plot(kappa_y, outcomes) plt.axhline(estimate.value, linestyle="--", color="gray") ax.set_title("Effect of Unobserved Common Cause") ax.set_xlabel("Value of Linear Constant on Outcome") ax.set_ylabel("Estimated Effect after adding the common cause") plt.show() return refute

andresmor-ms

133e7b9a4ed32aae8ab5f39a01eb02b3a4d1c0ba

e1652ec3c6606b1bb2dfe91ef830e4b4b566712d

Got, thanks for clarifying. I do agree that adding a class as protocol may not be needed. We can do it through PR reviews and docs to communicate the expected signature. Perhaps the flexibility will also be useful for any future method that may not require to take in the usual parameters.

amit-sharma

py-why/dowhy

Functional api/refute estimate

* Refactor refuters into functions * Rename functional_api notebook for clarity * Add return types to identify_estimate * Update `__init__.py` for imports * Add joblib for bootstrap refuter * Create `refute_estimate` function * Add types for refuter parameters & return types

2022-10-04 16:18:49+00:00

2022-10-07 04:30:22+00:00

dowhy/causal_refuters/add_unobserved_common_cause.py

import copy import logging import math import numpy as np import pandas as pd import scipy.stats import statsmodels.api as sm from sklearn.linear_model import LogisticRegression from sklearn.preprocessing import StandardScaler from tqdm.auto import tqdm import dowhy.causal_estimators.econml from dowhy.causal_estimator import CausalEstimator from dowhy.causal_estimators.linear_regression_estimator import LinearRegressionEstimator from dowhy.causal_estimators.regression_estimator import RegressionEstimator from dowhy.causal_refuter import CausalRefutation, CausalRefuter from dowhy.causal_refuters.evalue_sensitivity_analyzer import EValueSensitivityAnalyzer from dowhy.causal_refuters.linear_sensitivity_analyzer import LinearSensitivityAnalyzer from dowhy.causal_refuters.non_parametric_sensitivity_analyzer import NonParametricSensitivityAnalyzer from dowhy.causal_refuters.partial_linear_sensitivity_analyzer import PartialLinearSensitivityAnalyzer class AddUnobservedCommonCause(CausalRefuter): """Add an unobserved confounder for refutation. AddUnobservedCommonCause class supports three methods: 1) Simulation of an unobserved confounder 2) Linear partial R2 : Sensitivity Analysis for linear models. 3) Non-Parametric partial R2 based : Sensitivity Analyis for non-parametric models. Supports additional parameters that can be specified in the refute_estimate() method. """ def __init__(self, *args, **kwargs): """ Initialize the parameters required for the refuter. For direct_simulation, if effect_strength_on_treatment or effect_strength_on_outcome is not given, it is calculated automatically as a range between the minimum and maximum effect strength of observed confounders on treatment and outcome respectively. :param simulation_method: The method to use for simulating effect of unobserved confounder. Possible values are ["direct-simulation", "linear-partial-R2", "non-parametric-partial-R2", "e-value"]. :param confounders_effect_on_treatment: str : The type of effect on the treatment due to the unobserved confounder. Possible values are ['binary_flip', 'linear'] :param confounders_effect_on_outcome: str : The type of effect on the outcome due to the unobserved confounder. Possible values are ['binary_flip', 'linear'] :param effect_strength_on_treatment: float, numpy.ndarray: [Used when simulation_method="direct-simulation"] Strength of the confounder's effect on treatment. When confounders_effect_on_treatment is linear, it is the regression coefficient. When the confounders_effect_on_treatment is binary flip, it is the probability with which effect of unobserved confounder can invert the value of the treatment. :param effect_strength_on_outcome: float, numpy.ndarray: Strength of the confounder's effect on outcome. Its interpretation depends on confounders_effect_on_outcome and the simulation_method. When simulation_method is direct-simulation, for a linear effect it behaves like the regression coefficient and for a binary flip, it is the probability with which it can invert the value of the outcome. :param partial_r2_confounder_treatment: float, numpy.ndarray: [Used when simulation_method is linear-partial-R2 or non-parametric-partial-R2] Partial R2 of the unobserved confounder wrt the treatment conditioned on the observed confounders. Only in the case of general non-parametric-partial-R2, it is the fraction of variance in the reisz representer that is explained by the unobserved confounder; specifically (1-r), where r is the ratio of variance of reisz representer, alpha^2, based on observed confounders and that based on all confounders. :param partial_r2_confounder_outcome: float, numpy.ndarray: [Used when simulation_method is linear-partial-R2 or non-parametric-partial-R2] Partial R2 of the unobserved confounder wrt the outcome conditioned on the treatment and observed confounders. :param frac_strength_treatment: float: This parameter decides the effect strength of the simulated confounder as a fraction of the effect strength of observed confounders on treatment. Defaults to 1. :param frac_strength_outcome: float: This parameter decides the effect strength of the simulated confounder as a fraction of the effect strength of observed confounders on outcome. Defaults to 1. :param plotmethod: string: Type of plot to be shown. If None, no plot is generated. This parameter is used only only when more than one treatment confounder effect values or outcome confounder effect values are provided. Default is "colormesh". Supported values are "contour", "colormesh" when more than one value is provided for both confounder effect value parameters; "line" when provided for only one of them. :param percent_change_estimate: It is the percentage of reduction of treatment estimate that could alter the results (default = 1). if percent_change_estimate = 1, the robustness value describes the strength of association of confounders with treatment and outcome in order to reduce the estimate by 100% i.e bring it down to 0. (relevant only for Linear Sensitivity Analysis, ignore for rest) :param confounder_increases_estimate: True implies that confounder increases the absolute value of estimate and vice versa. (Default = False). (relevant only for Linear Sensitivity Analysis, ignore for rest) :param benchmark_common_causes: names of variables for bounding strength of confounders. (relevant only for partial-r2 based simulation methods) :param significance_level: confidence interval for statistical inference(default = 0.05). (relevant only for partial-r2 based simulation methods) :param null_hypothesis_effect: assumed effect under the null hypothesis. (relevant only for linear-partial-R2, ignore for rest) :param plot_estimate: Generate contour plot for estimate while performing sensitivity analysis. (default = True). (relevant only for partial-r2 based simulation methods) :param num_splits: number of splits for cross validation. (default = 5). (relevant only for non-parametric-partial-R2 simulation method) :param shuffle_data : shuffle data or not before splitting into folds (default = False). (relevant only for non-parametric-partial-R2 simulation method) :param shuffle_random_seed: seed for randomly shuffling data. (relevant only for non-parametric-partial-R2 simulation method) :param alpha_s_estimator_param_list: list of dictionaries with parameters for finding alpha_s. (relevant only for non-parametric-partial-R2 simulation method) :param g_s_estimator_list: list of estimator objects for finding g_s. These objects should have fit() and predict() functions implemented. (relevant only for non-parametric-partial-R2 simulation method) :param g_s_estimator_param_list: list of dictionaries with parameters for tuning respective estimators in "g_s_estimator_list". The order of the dictionaries in the list should be consistent with the estimator objects order in "g_s_estimator_list". (relevant only for non-parametric-partial-R2 simulation method) """ super().__init__(*args, **kwargs) self.simulation_method = kwargs["simulation_method"] if "simulation_method" in kwargs else "direct-simulation" self.effect_on_t = ( kwargs["confounders_effect_on_treatment"] if "confounders_effect_on_treatment" in kwargs else "binary_flip" ) self.effect_on_y = ( kwargs["confounders_effect_on_outcome"] if "confounders_effect_on_outcome" in kwargs else "linear" ) if self.simulation_method == "direct-simulation": self.kappa_t = kwargs["effect_strength_on_treatment"] if "effect_strength_on_treatment" in kwargs else None self.kappa_y = kwargs["effect_strength_on_outcome"] if "effect_strength_on_outcome" in kwargs else None elif self.simulation_method in ["linear-partial-R2", "non-parametric-partial-R2"]: self.kappa_t = ( kwargs["partial_r2_confounder_treatment"] if "partial_r2_confounder_treatment" in kwargs else None ) self.kappa_y = ( kwargs["partial_r2_confounder_outcome"] if "partial_r2_confounder_outcome" in kwargs else None ) elif self.simulation_method == "e-value": pass else: raise ValueError( "simulation method is not supported. Try direct-simulation, linear-partial-R2, non-parametric-partial-R2, or e-value" ) self.frac_strength_treatment = ( kwargs["effect_fraction_on_treatment"] if "effect_fraction_on_treatment" in kwargs else 1 ) self.frac_strength_outcome = ( kwargs["effect_fraction_on_outcome"] if "effect_fraction_on_outcome" in kwargs else 1 ) self.plotmethod = kwargs["plotmethod"] if "plotmethod" in kwargs else "colormesh" self.percent_change_estimate = kwargs["percent_change_estimate"] if "percent_change_estimate" in kwargs else 1.0 self.significance_level = kwargs["significance_level"] if "significance_level" in kwargs else 0.05 self.confounder_increases_estimate = ( kwargs["confounder_increases_estimate"] if "confounder_increases_estimate" in kwargs else False ) self.benchmark_common_causes = ( kwargs["benchmark_common_causes"] if "benchmark_common_causes" in kwargs else None ) self.null_hypothesis_effect = kwargs["null_hypothesis_effect"] if "null_hypothesis_effect" in kwargs else 0 self.plot_estimate = kwargs["plot_estimate"] if "plot_estimate" in kwargs else True self.num_splits = kwargs["num_splits"] if "num_splits" in kwargs else 5 self.shuffle_data = kwargs["shuffle_data"] if "shuffle_data" in kwargs else False self.shuffle_random_seed = kwargs["shuffle_random_seed"] if "shuffle_random_seed" in kwargs else None self.alpha_s_estimator_param_list = ( kwargs["alpha_s_estimator_param_list"] if "alpha_s_estimator_param_list" in kwargs else None ) self.alpha_s_estimator_list = kwargs["alpha_s_estimator_list"] if "alpha_s_estimator_list" in kwargs else None self.g_s_estimator_list = kwargs["g_s_estimator_list"] if "g_s_estimator_list" in kwargs else None self.g_s_estimator_param_list = ( kwargs["g_s_estimator_param_list"] if "g_s_estimator_param_list" in kwargs else None ) self.plugin_reisz = kwargs["plugin_reisz"] if "plugin_reisz" in kwargs else False self.logger = logging.getLogger(__name__) def infer_default_kappa_t(self, len_kappa_t=10): """Infer default effect strength of simulated confounder on treatment.""" observed_common_causes_names = self._target_estimand.get_backdoor_variables() if len(observed_common_causes_names) > 0: observed_common_causes = self._data[observed_common_causes_names] observed_common_causes = pd.get_dummies(observed_common_causes, drop_first=True) else: raise ValueError( "There needs to be at least one common cause to" + "automatically compute the default value of kappa_t." + " Provide a value for kappa_t" ) t = self._data[self._treatment_name] # Standardizing the data observed_common_causes = StandardScaler().fit_transform(observed_common_causes) if self.effect_on_t == "binary_flip": # Fit a model containing all confounders and compare predictions # using all features compared to all features except a given # confounder. tmodel = LogisticRegression().fit(observed_common_causes, t) tpred = tmodel.predict(observed_common_causes).astype(int) flips = [] for i in range(observed_common_causes.shape[1]): oldval = np.copy(observed_common_causes[:, i]) observed_common_causes[:, i] = 0 tcap = tmodel.predict(observed_common_causes).astype(int) observed_common_causes[:, i] = oldval flips.append(np.sum(abs(tcap - tpred)) / tpred.shape[0]) min_coeff, max_coeff = min(flips), max(flips) elif self.effect_on_t == "linear": # Estimating the regression coefficient from standardized features to t corrcoef_var_t = np.corrcoef(observed_common_causes, t, rowvar=False)[-1, :-1] std_dev_t = np.std(t)[0] max_coeff = max(corrcoef_var_t) * std_dev_t min_coeff = min(corrcoef_var_t) * std_dev_t else: raise NotImplementedError( "'" + self.effect_on_t + "' method not supported for confounders' effect on treatment" ) min_coeff, max_coeff = self._compute_min_max_coeff(min_coeff, max_coeff, self.frac_strength_treatment) # By default, return a plot with 10 points # consider 10 values of the effect of the unobserved confounder step = (max_coeff - min_coeff) / len_kappa_t self.logger.info("(Min, Max) kappa_t for observed common causes, ({0}, {1})".format(min_coeff, max_coeff)) if np.equal(max_coeff, min_coeff): return max_coeff else: return np.arange(min_coeff, max_coeff, step) def _compute_min_max_coeff(self, min_coeff, max_coeff, effect_strength_fraction): max_coeff = effect_strength_fraction * max_coeff min_coeff = effect_strength_fraction * min_coeff return min_coeff, max_coeff def infer_default_kappa_y(self, len_kappa_y=10): """Infer default effect strength of simulated confounder on treatment.""" observed_common_causes_names = self._target_estimand.get_backdoor_variables() if len(observed_common_causes_names) > 0: observed_common_causes = self._data[observed_common_causes_names] observed_common_causes = pd.get_dummies(observed_common_causes, drop_first=True) else: raise ValueError( "There needs to be at least one common cause to" + "automatically compute the default value of kappa_y." + " Provide a value for kappa_y" ) y = self._data[self._outcome_name] # Standardizing the data observed_common_causes = StandardScaler().fit_transform(observed_common_causes) if self.effect_on_y == "binary_flip": # Fit a model containing all confounders and compare predictions # using all features compared to all features except a given # confounder. ymodel = LogisticRegression().fit(observed_common_causes, y) ypred = ymodel.predict(observed_common_causes).astype(int) flips = [] for i in range(observed_common_causes.shape[1]): oldval = np.copy(observed_common_causes[:, i]) observed_common_causes[:, i] = 0 ycap = ymodel.predict(observed_common_causes).astype(int) observed_common_causes[:, i] = oldval flips.append(np.sum(abs(ycap - ypred)) / ypred.shape[0]) min_coeff, max_coeff = min(flips), max(flips) elif self.effect_on_y == "linear": corrcoef_var_y = np.corrcoef(observed_common_causes, y, rowvar=False)[-1, :-1] std_dev_y = np.std(y)[0] max_coeff = max(corrcoef_var_y) * std_dev_y min_coeff = min(corrcoef_var_y) * std_dev_y else: raise NotImplementedError( "'" + self.effect_on_y + "' method not supported for confounders' effect on outcome" ) min_coeff, max_coeff = self._compute_min_max_coeff(min_coeff, max_coeff, self.frac_strength_outcome) # By default, return a plot with 10 points # consider 10 values of the effect of the unobserved confounder step = (max_coeff - min_coeff) / len_kappa_y self.logger.info("(Min, Max) kappa_y for observed common causes, ({0}, {1})".format(min_coeff, max_coeff)) if np.equal(max_coeff, min_coeff): return max_coeff else: return np.arange(min_coeff, max_coeff, step) def refute_estimate(self, show_progress_bar=False): """ This function attempts to add an unobserved common cause to the outcome and the treatment. At present, we have implemented the behavior for one dimensional behaviors for continuous and binary variables. This function can either take single valued inputs or a range of inputs. The function then looks at the data type of the input and then decides on the course of action. :return: CausalRefuter: An object that contains the estimated effect and a new effect and the name of the refutation used. """ if self.simulation_method == "linear-partial-R2": if not (isinstance(self._estimate.estimator, LinearRegressionEstimator)): raise NotImplementedError( "Currently only LinearRegressionEstimator is supported for Sensitivity Analysis" ) if len(self._estimate.estimator._effect_modifier_names) > 0: raise NotImplementedError("The current implementation does not support effect modifiers") if self.frac_strength_outcome == 1: self.frac_strength_outcome = self.frac_strength_treatment analyzer = LinearSensitivityAnalyzer( estimator=self._estimate.estimator, data=self._data, treatment_name=self._treatment_name, percent_change_estimate=self.percent_change_estimate, significance_level=self.significance_level, benchmark_common_causes=self.benchmark_common_causes, null_hypothesis_effect=self.null_hypothesis_effect, frac_strength_treatment=self.frac_strength_treatment, frac_strength_outcome=self.frac_strength_outcome, common_causes_order=self._estimate.estimator._observed_common_causes.columns, ) analyzer.check_sensitivity(plot=self.plot_estimate) return analyzer if self.simulation_method == "non-parametric-partial-R2": # If the estimator used is LinearDML, partially linear sensitivity analysis will be automatically chosen if isinstance(self._estimate.estimator, dowhy.causal_estimators.econml.Econml): if self._estimate.estimator._econml_methodname == "econml.dml.LinearDML": analyzer = PartialLinearSensitivityAnalyzer( estimator=self._estimate._estimator_object, observed_common_causes=self._estimate.estimator._observed_common_causes, treatment=self._estimate.estimator._treatment, outcome=self._estimate.estimator._outcome, alpha_s_estimator_param_list=self.alpha_s_estimator_param_list, g_s_estimator_list=self.g_s_estimator_list, g_s_estimator_param_list=self.g_s_estimator_param_list, effect_strength_treatment=self.kappa_t, effect_strength_outcome=self.kappa_y, benchmark_common_causes=self.benchmark_common_causes, frac_strength_treatment=self.frac_strength_treatment, frac_strength_outcome=self.frac_strength_outcome, ) analyzer.check_sensitivity(plot=self.plot_estimate) return analyzer analyzer = NonParametricSensitivityAnalyzer( estimator=self._estimate.estimator, observed_common_causes=self._estimate.estimator._observed_common_causes, treatment=self._estimate.estimator._treatment, outcome=self._estimate.estimator._outcome, alpha_s_estimator_list=self.alpha_s_estimator_list, alpha_s_estimator_param_list=self.alpha_s_estimator_param_list, g_s_estimator_list=self.g_s_estimator_list, g_s_estimator_param_list=self.g_s_estimator_param_list, effect_strength_treatment=self.kappa_t, effect_strength_outcome=self.kappa_y, benchmark_common_causes=self.benchmark_common_causes, frac_strength_treatment=self.frac_strength_treatment, frac_strength_outcome=self.frac_strength_outcome, theta_s=self._estimate.value, plugin_reisz=self.plugin_reisz, ) analyzer.check_sensitivity(plot=self.plot_estimate) return analyzer if self.simulation_method == "e-value": if not isinstance(self._estimate.estimator, RegressionEstimator): raise NotImplementedError( "E-Value sensitivity analysis is currently only implemented RegressionEstimator." ) if len(self._estimate.estimator._effect_modifier_names) > 0: raise NotImplementedError("The current implementation does not support effect modifiers") analyzer = EValueSensitivityAnalyzer( estimate=self._estimate, estimand=self._target_estimand, data=self._data, treatment_name=self._treatment_name[0], outcome_name=self._outcome_name[0], ) analyzer.check_sensitivity(plot=self.plot_estimate) return analyzer if self.kappa_t is None: self.kappa_t = self.infer_default_kappa_t() if self.kappa_y is None: self.kappa_y = self.infer_default_kappa_y() if not isinstance(self.kappa_t, (list, np.ndarray)) and not isinstance( self.kappa_y, (list, np.ndarray) ): # Deal with single value inputs new_data = copy.deepcopy(self._data) new_data = self.include_confounders_effect(new_data, self.kappa_t, self.kappa_y) new_estimator = CausalEstimator.get_estimator_object(new_data, self._target_estimand, self._estimate) new_effect = new_estimator.estimate_effect() refute = CausalRefutation( self._estimate.value, new_effect.value, refutation_type="Refute: Add an Unobserved Common Cause" ) refute.new_effect_array = np.array(new_effect.value) refute.new_effect = new_effect.value refute.add_refuter(self) return refute else: # Deal with multiple value inputs if isinstance(self.kappa_t, (list, np.ndarray)) and isinstance( self.kappa_y, (list, np.ndarray) ): # Deal with range inputs # Get a 2D matrix of values # x,y = np.meshgrid(self.kappa_t, self.kappa_y) # x,y are both MxN results_matrix = np.random.rand( len(self.kappa_t), len(self.kappa_y) ) # Matrix to hold all the results of NxM orig_data = copy.deepcopy(self._data) for i in tqdm( range(len(self.kappa_t)), colour=CausalRefuter.PROGRESS_BAR_COLOR, disable=not show_progress_bar, desc="Refuting Estimates: ", ): for j in range(len(self.kappa_y)): new_data = self.include_confounders_effect(orig_data, self.kappa_t[i], self.kappa_y[j]) new_estimator = CausalEstimator.get_estimator_object( new_data, self._target_estimand, self._estimate ) new_effect = new_estimator.estimate_effect() refute = CausalRefutation( self._estimate.value, new_effect.value, refutation_type="Refute: Add an Unobserved Common Cause", ) results_matrix[i][j] = refute.new_effect # Populate the results refute.new_effect_array = results_matrix refute.new_effect = (np.min(results_matrix), np.max(results_matrix)) # Store the values into the refute object refute.add_refuter(self) if self.plotmethod is None: return refute import matplotlib import matplotlib.pyplot as plt fig = plt.figure(figsize=(6, 5)) left, bottom, width, height = 0.1, 0.1, 0.8, 0.8 ax = fig.add_axes([left, bottom, width, height]) oe = self._estimate.value contour_levels = [oe / 4.0, oe / 2.0, (3.0 / 4) * oe, oe] contour_levels.extend([0, np.min(results_matrix), np.max(results_matrix)]) if self.plotmethod == "contour": cp = plt.contourf(self.kappa_y, self.kappa_t, results_matrix, levels=sorted(contour_levels)) # Adding a label on the contour line for the original estimate fmt = {} trueeffect_index = np.where(cp.levels == oe)[0][0] fmt[cp.levels[trueeffect_index]] = "Estimated Effect" # Label every other level using strings plt.clabel(cp, [cp.levels[trueeffect_index]], inline=True, fmt=fmt) plt.colorbar(cp) elif self.plotmethod == "colormesh": cp = plt.pcolormesh(self.kappa_y, self.kappa_t, results_matrix, shading="nearest") plt.colorbar(cp, ticks=contour_levels) ax.yaxis.set_ticks(self.kappa_t) ax.xaxis.set_ticks(self.kappa_y) plt.xticks(rotation=45) ax.set_title("Effect of Unobserved Common Cause") ax.set_ylabel("Value of Linear Constant on Treatment") ax.set_xlabel("Value of Linear Constant on Outcome") plt.show() return refute elif isinstance(self.kappa_t, (list, np.ndarray)): outcomes = np.random.rand(len(self.kappa_t)) orig_data = copy.deepcopy(self._data) for i in tqdm( range(0, len(self.kappa_t)), colour=CausalRefuter.PROGRESS_BAR_COLOR, disable=not show_progress_bar, desc="Refuting Estimates: ", ): new_data = self.include_confounders_effect(orig_data, self.kappa_t[i], self.kappa_y) new_estimator = CausalEstimator.get_estimator_object( new_data, self._target_estimand, self._estimate ) new_effect = new_estimator.estimate_effect() refute = CausalRefutation( self._estimate.value, new_effect.value, refutation_type="Refute: Add an Unobserved Common Cause" ) self.logger.debug(refute) outcomes[i] = refute.new_effect # Populate the results refute.new_effect_array = outcomes refute.new_effect = (np.min(outcomes), np.max(outcomes)) refute.add_refuter(self) if self.plotmethod is None: return refute import matplotlib import matplotlib.pyplot as plt fig = plt.figure(figsize=(6, 5)) left, bottom, width, height = 0.1, 0.1, 0.8, 0.8 ax = fig.add_axes([left, bottom, width, height]) plt.plot(self.kappa_t, outcomes) plt.axhline(self._estimate.value, linestyle="--", color="gray") ax.set_title("Effect of Unobserved Common Cause") ax.set_xlabel("Value of Linear Constant on Treatment") ax.set_ylabel("Estimated Effect after adding the common cause") plt.show() return refute elif isinstance(self.kappa_y, (list, np.ndarray)): outcomes = np.random.rand(len(self.kappa_y)) orig_data = copy.deepcopy(self._data) for i in tqdm( range(0, len(self.kappa_y)), colour=CausalRefuter.PROGRESS_BAR_COLOR, disable=not show_progress_bar, desc="Refuting Estimates: ", ): new_data = self.include_confounders_effect(orig_data, self.kappa_t, self.kappa_y[i]) new_estimator = CausalEstimator.get_estimator_object( new_data, self._target_estimand, self._estimate ) new_effect = new_estimator.estimate_effect() refute = CausalRefutation( self._estimate.value, new_effect.value, refutation_type="Refute: Add an Unobserved Common Cause" ) self.logger.debug(refute) outcomes[i] = refute.new_effect # Populate the results refute.new_effect_array = outcomes refute.new_effect = (np.min(outcomes), np.max(outcomes)) refute.add_refuter(self) if self.plotmethod is None: return refute import matplotlib import matplotlib.pyplot as plt fig = plt.figure(figsize=(6, 5)) left, bottom, width, height = 0.1, 0.1, 0.8, 0.8 ax = fig.add_axes([left, bottom, width, height]) plt.plot(self.kappa_y, outcomes) plt.axhline(self._estimate.value, linestyle="--", color="gray") ax.set_title("Effect of Unobserved Common Cause") ax.set_xlabel("Value of Linear Constant on Outcome") ax.set_ylabel("Estimated Effect after adding the common cause") plt.show() return refute def include_confounders_effect(self, new_data, kappa_t, kappa_y): """ This function deals with the change in the value of the data due to the effect of the unobserved confounder. In the case of a binary flip, we flip only if the random number is greater than the threshold set. In the case of a linear effect, we use the variable as the linear regression constant. :param new_data: pandas.DataFrame: The data to be changed due to the effects of the unobserved confounder. :param kappa_t: numpy.float64: The value of the threshold for binary_flip or the value of the regression coefficient for linear effect. :param kappa_y: numpy.float64: The value of the threshold for binary_flip or the value of the regression coefficient for linear effect. :return: pandas.DataFrame: The DataFrame that includes the effects of the unobserved confounder. """ num_rows = self._data.shape[0] stdnorm = scipy.stats.norm() w_random = stdnorm.rvs(num_rows) if self.effect_on_t == "binary_flip": alpha = 2 * kappa_t - 1 if kappa_t >= 0.5 else 1 - 2 * kappa_t interval = stdnorm.interval(alpha) rel_interval = interval[0] if kappa_t >= 0.5 else interval[1] new_data.loc[rel_interval <= w_random, self._treatment_name] = ( 1 - new_data.loc[rel_interval <= w_random, self._treatment_name] ) for tname in self._treatment_name: if pd.api.types.is_bool_dtype(self._data[tname]): new_data = new_data.astype({tname: "bool"}, copy=False) elif self.effect_on_t == "linear": confounder_t_effect = kappa_t * w_random # By default, we add the effect of simulated confounder for treatment. # But subtract it from outcome to create a negative correlation # assuming that the original confounder's effect was positive on both. # This is to remove the effect of the original confounder. new_data[self._treatment_name] = new_data[self._treatment_name].values + np.ndarray( shape=(num_rows, 1), buffer=confounder_t_effect ) else: raise NotImplementedError( "'" + self.effect_on_t + "' method not supported for confounders' effect on treatment" ) if self.effect_on_y == "binary_flip": alpha = 2 * kappa_y - 1 if kappa_y >= 0.5 else 1 - 2 * kappa_y interval = stdnorm.interval(alpha) rel_interval = interval[0] if kappa_y >= 0.5 else interval[1] new_data.loc[rel_interval <= w_random, self._outcome_name] = ( 1 - new_data.loc[rel_interval <= w_random, self._outcome_name] ) for yname in self._outcome_name: if pd.api.types.is_bool_dtype(self._data[yname]): new_data = new_data.astype({yname: "bool"}, copy=False) elif self.effect_on_y == "linear": confounder_y_effect = (-1) * kappa_y * w_random # By default, we add the effect of simulated confounder for treatment. # But subtract it from outcome to create a negative correlation # assuming that the original confounder's effect was positive on both. # This is to remove the effect of the original confounder. new_data[self._outcome_name] = new_data[self._outcome_name].values + np.ndarray( shape=(num_rows, 1), buffer=confounder_y_effect ) else: raise NotImplementedError( "'" + self.effect_on_y + "' method not supported for confounders' effect on outcome" ) return new_data def include_simulated_confounder(self, convergence_threshold=0.1, c_star_max=1000): """ This function simulates an unobserved confounder based on the data using the following steps: 1. It calculates the "residuals" from the treatment and outcome model i.) The outcome model has outcome as the dependent variable and all the observed variables including treatment as independent variables ii.) The treatment model has treatment as the dependent variable and all the observed variables as independent variables. 2. U is an intermediate random variable drawn from the normal distribution with the weighted average of residuals as mean and a unit variance U ~ N(c1*d_y + c2*d_t, 1) where *d_y and d_t are residuals from the treatment and outcome model *c1 and c2 are coefficients to the residuals 3. The final U, which is the simulated unobserved confounder is obtained by debiasing the intermediate variable U by residualising it with X Choosing the coefficients c1 and c2: The coefficients are chosen based on these basic assumptions: 1. There is a hyperbolic relationship satisfying c1*c2 = c_star 2. c_star is chosen from a range of possible values based on the correlation of the obtained simulated variable with outcome and treatment. 3. The product of correlations with treatment and outcome should be at a minimum distance to the maximum correlations with treatment and outcome in any of the observed confounders 4. The ratio of the weights should be such that they maintain the ratio of the maximum possible observed coefficients within some confidence interval :param c_star_max: The maximum possible value for the hyperbolic curve on which the coefficients to the residuals lie. It defaults to 1000 in the code if not specified by the user. :type int :param convergence_threshold: The threshold to check the plateauing of the correlation while selecting a c_star. It defaults to 0.1 in the code if not specified by the user :type float :returns: The simulated values of the unobserved confounder based on the data :type pandas.core.series.Series """ # Obtaining the list of observed variables required_variables = True observed_variables = self.choose_variables(required_variables) observed_variables_with_treatment_and_outcome = observed_variables + self._treatment_name + self._outcome_name # Taking a subset of the dataframe that has only observed variables self._data = self._data[observed_variables_with_treatment_and_outcome] # Residuals from the outcome model obtained by fitting a linear model y = self._data[self._outcome_name[0]] observed_variables_with_treatment = observed_variables + self._treatment_name X = self._data[observed_variables_with_treatment] model = sm.OLS(y, X.astype("float")) results = model.fit() residuals_y = y - results.fittedvalues d_y = list(pd.Series(residuals_y)) # Residuals from the treatment model obtained by fitting a linear model t = self._data[self._treatment_name[0]].astype("int64") X = self._data[observed_variables] model = sm.OLS(t, X) results = model.fit() residuals_t = t - results.fittedvalues d_t = list(pd.Series(residuals_t)) # Initialising product_cor_metric_observed with a really low value as finding maximum product_cor_metric_observed = -10000000000 for i in observed_variables: current_obs_confounder = self._data[i] outcome_values = self._data[self._outcome_name[0]] correlation_y = current_obs_confounder.corr(outcome_values) treatment_values = t correlation_t = current_obs_confounder.corr(treatment_values) product_cor_metric_current = correlation_y * correlation_t if product_cor_metric_current >= product_cor_metric_observed: product_cor_metric_observed = product_cor_metric_current correlation_t_observed = correlation_t correlation_y_observed = correlation_y # The user has an option to give the the effect_strength_on_y and effect_strength_on_t which can be then used instead of maximum correlation with treatment and outcome in the observed variables as it specifies the desired effect. if self.kappa_t is not None: correlation_t_observed = self.kappa_t if self.kappa_y is not None: correlation_y_observed = self.kappa_y # Choosing a c_star based on the data. # The correlations stop increasing upon increasing c_star after a certain value, that is it plateaus and we choose the value of c_star to be the value it plateaus. correlation_y_list = [] correlation_t_list = [] product_cor_metric_simulated_list = [] x_list = [] step = int(c_star_max / 10) for i in range(0, int(c_star_max), step): c1 = math.sqrt(i) c2 = c1 final_U = self.generate_confounder_from_residuals(c1, c2, d_y, d_t, X) current_simulated_confounder = final_U outcome_values = self._data[self._outcome_name[0]] correlation_y = current_simulated_confounder.corr(outcome_values) correlation_y_list.append(correlation_y) treatment_values = t correlation_t = current_simulated_confounder.corr(treatment_values) correlation_t_list.append(correlation_t) product_cor_metric_simulated = correlation_y * correlation_t product_cor_metric_simulated_list.append(product_cor_metric_simulated) x_list.append(i) index = 1 while index < len(correlation_y_list): if (correlation_y_list[index] - correlation_y_list[index - 1]) <= convergence_threshold: c_star = x_list[index] break index = index + 1 # Choosing c1 and c2 based on the hyperbolic relationship once c_star is chosen by going over various combinations of c1 and c2 values and choosing the combination which # which maintains the minimum distance between the product of correlations of the simulated variable and the product of maximum correlations of one of the observed variables # and additionally checks if the ratio of the weights are such that they maintain the ratio of the maximum possible observed coefficients within some confidence interval # c1_final and c2_final are initialised to the values on the hyperbolic curve such that c1_final = c2_final and c1_final*c2_final = c_star c1_final = math.sqrt(c_star) c2_final = math.sqrt(c_star) # initialising min_distance_between_product_cor_metrics to be a value greater than 1 min_distance_between_product_cor_metrics = 1.5 i = 0.05 threshold = c_star / 0.05 while i <= threshold: c2 = i c1 = c_star / c2 final_U = self.generate_confounder_from_residuals(c1, c2, d_y, d_t, X) current_simulated_confounder = final_U outcome_values = self._data[self._outcome_name[0]] correlation_y = current_simulated_confounder.corr(outcome_values) treatment_values = t correlation_t = current_simulated_confounder.corr(treatment_values) product_cor_metric_simulated = correlation_y * correlation_t if min_distance_between_product_cor_metrics >= abs( product_cor_metric_simulated - product_cor_metric_observed ): min_distance_between_product_cor_metrics = abs( product_cor_metric_simulated - product_cor_metric_observed ) additional_condition = correlation_y_observed / correlation_t_observed if ((c1 / c2) <= (additional_condition + 0.3 * additional_condition)) and ( (c1 / c2) >= (additional_condition - 0.3 * additional_condition) ): # choose minimum positive value c1_final = c1 c2_final = c2 i = i * 1.5 """#closed form solution print("c_star_max before closed form", c_star_max) if max_correlation_with_t == -1000: c2 = 0 c1 = c_star_max else: additional_condition = abs(max_correlation_with_y/max_correlation_with_t) print("additional_condition", additional_condition) c2 = math.sqrt(c_star_max/additional_condition) c1 = c_star_max/c2""" final_U = self.generate_confounder_from_residuals(c1_final, c2_final, d_y, d_t, X) return final_U def generate_confounder_from_residuals(self, c1, c2, d_y, d_t, X): """ This function takes the residuals from the treatment and outcome model and their coefficients and simulates the intermediate random variable U by taking the row wise normal distribution corresponding to each residual value and then debiasing the intermediate variable to get the final variable. :param c1: coefficient to the residual from the outcome model :type float :param c2: coefficient to the residual from the treatment model :type float :param d_y: residuals from the outcome model :type list :param d_t: residuals from the treatment model :type list :returns: The simulated values of the unobserved confounder based on the data :type pandas.core.series.Series """ U = [] for j in range(len(d_t)): simulated_variable_mean = c1 * d_y[j] + c2 * d_t[j] simulated_variable_stddev = 1 U.append(np.random.normal(simulated_variable_mean, simulated_variable_stddev, 1)) U = np.array(U) model = sm.OLS(U, X) results = model.fit() U = U.reshape( -1, ) final_U = U - results.fittedvalues.values final_U = pd.Series(U) return final_U

import copy import logging import math from typing import Dict, List, Optional, Union import numpy as np import pandas as pd import scipy.stats import statsmodels.api as sm from sklearn.linear_model import LogisticRegression from sklearn.preprocessing import StandardScaler from tqdm.auto import tqdm import dowhy.causal_estimators.econml from dowhy.causal_estimator import CausalEstimate, CausalEstimator from dowhy.causal_estimators.linear_regression_estimator import LinearRegressionEstimator from dowhy.causal_estimators.regression_estimator import RegressionEstimator from dowhy.causal_identifier.identified_estimand import IdentifiedEstimand from dowhy.causal_refuter import CausalRefutation, CausalRefuter, choose_variables from dowhy.causal_refuters.evalue_sensitivity_analyzer import EValueSensitivityAnalyzer from dowhy.causal_refuters.linear_sensitivity_analyzer import LinearSensitivityAnalyzer from dowhy.causal_refuters.non_parametric_sensitivity_analyzer import NonParametricSensitivityAnalyzer from dowhy.causal_refuters.partial_linear_sensitivity_analyzer import PartialLinearSensitivityAnalyzer logger = logging.getLogger(__name__) class AddUnobservedCommonCause(CausalRefuter): """Add an unobserved confounder for refutation. AddUnobservedCommonCause class supports three methods: 1) Simulation of an unobserved confounder 2) Linear partial R2 : Sensitivity Analysis for linear models. 3) Non-Parametric partial R2 based : Sensitivity Analyis for non-parametric models. Supports additional parameters that can be specified in the refute_estimate() method. """ def __init__(self, *args, **kwargs): """ Initialize the parameters required for the refuter. For direct_simulation, if effect_strength_on_treatment or effect_strength_on_outcome is not given, it is calculated automatically as a range between the minimum and maximum effect strength of observed confounders on treatment and outcome respectively. :param simulation_method: The method to use for simulating effect of unobserved confounder. Possible values are ["direct-simulation", "linear-partial-R2", "non-parametric-partial-R2", "e-value"]. :param confounders_effect_on_treatment: str : The type of effect on the treatment due to the unobserved confounder. Possible values are ['binary_flip', 'linear'] :param confounders_effect_on_outcome: str : The type of effect on the outcome due to the unobserved confounder. Possible values are ['binary_flip', 'linear'] :param effect_strength_on_treatment: float, numpy.ndarray: [Used when simulation_method="direct-simulation"] Strength of the confounder's effect on treatment. When confounders_effect_on_treatment is linear, it is the regression coefficient. When the confounders_effect_on_treatment is binary flip, it is the probability with which effect of unobserved confounder can invert the value of the treatment. :param effect_strength_on_outcome: float, numpy.ndarray: Strength of the confounder's effect on outcome. Its interpretation depends on confounders_effect_on_outcome and the simulation_method. When simulation_method is direct-simulation, for a linear effect it behaves like the regression coefficient and for a binary flip, it is the probability with which it can invert the value of the outcome. :param partial_r2_confounder_treatment: float, numpy.ndarray: [Used when simulation_method is linear-partial-R2 or non-parametric-partial-R2] Partial R2 of the unobserved confounder wrt the treatment conditioned on the observed confounders. Only in the case of general non-parametric-partial-R2, it is the fraction of variance in the reisz representer that is explained by the unobserved confounder; specifically (1-r), where r is the ratio of variance of reisz representer, alpha^2, based on observed confounders and that based on all confounders. :param partial_r2_confounder_outcome: float, numpy.ndarray: [Used when simulation_method is linear-partial-R2 or non-parametric-partial-R2] Partial R2 of the unobserved confounder wrt the outcome conditioned on the treatment and observed confounders. :param frac_strength_treatment: float: This parameter decides the effect strength of the simulated confounder as a fraction of the effect strength of observed confounders on treatment. Defaults to 1. :param frac_strength_outcome: float: This parameter decides the effect strength of the simulated confounder as a fraction of the effect strength of observed confounders on outcome. Defaults to 1. :param plotmethod: string: Type of plot to be shown. If None, no plot is generated. This parameter is used only only when more than one treatment confounder effect values or outcome confounder effect values are provided. Default is "colormesh". Supported values are "contour", "colormesh" when more than one value is provided for both confounder effect value parameters; "line" when provided for only one of them. :param percent_change_estimate: It is the percentage of reduction of treatment estimate that could alter the results (default = 1). if percent_change_estimate = 1, the robustness value describes the strength of association of confounders with treatment and outcome in order to reduce the estimate by 100% i.e bring it down to 0. (relevant only for Linear Sensitivity Analysis, ignore for rest) :param confounder_increases_estimate: True implies that confounder increases the absolute value of estimate and vice versa. (Default = False). (relevant only for Linear Sensitivity Analysis, ignore for rest) :param benchmark_common_causes: names of variables for bounding strength of confounders. (relevant only for partial-r2 based simulation methods) :param significance_level: confidence interval for statistical inference(default = 0.05). (relevant only for partial-r2 based simulation methods) :param null_hypothesis_effect: assumed effect under the null hypothesis. (relevant only for linear-partial-R2, ignore for rest) :param plot_estimate: Generate contour plot for estimate while performing sensitivity analysis. (default = True). (relevant only for partial-r2 based simulation methods) :param num_splits: number of splits for cross validation. (default = 5). (relevant only for non-parametric-partial-R2 simulation method) :param shuffle_data : shuffle data or not before splitting into folds (default = False). (relevant only for non-parametric-partial-R2 simulation method) :param shuffle_random_seed: seed for randomly shuffling data. (relevant only for non-parametric-partial-R2 simulation method) :param alpha_s_estimator_param_list: list of dictionaries with parameters for finding alpha_s. (relevant only for non-parametric-partial-R2 simulation method) :param g_s_estimator_list: list of estimator objects for finding g_s. These objects should have fit() and predict() functions implemented. (relevant only for non-parametric-partial-R2 simulation method) :param g_s_estimator_param_list: list of dictionaries with parameters for tuning respective estimators in "g_s_estimator_list". The order of the dictionaries in the list should be consistent with the estimator objects order in "g_s_estimator_list". (relevant only for non-parametric-partial-R2 simulation method) """ super().__init__(*args, **kwargs) self.simulation_method = kwargs["simulation_method"] if "simulation_method" in kwargs else "direct-simulation" self.effect_on_t = ( kwargs["confounders_effect_on_treatment"] if "confounders_effect_on_treatment" in kwargs else "binary_flip" ) self.effect_on_y = ( kwargs["confounders_effect_on_outcome"] if "confounders_effect_on_outcome" in kwargs else "linear" ) if self.simulation_method == "direct-simulation": self.kappa_t = kwargs["effect_strength_on_treatment"] if "effect_strength_on_treatment" in kwargs else None self.kappa_y = kwargs["effect_strength_on_outcome"] if "effect_strength_on_outcome" in kwargs else None elif self.simulation_method in ["linear-partial-R2", "non-parametric-partial-R2"]: self.kappa_t = ( kwargs["partial_r2_confounder_treatment"] if "partial_r2_confounder_treatment" in kwargs else None ) self.kappa_y = ( kwargs["partial_r2_confounder_outcome"] if "partial_r2_confounder_outcome" in kwargs else None ) elif self.simulation_method == "e-value": pass else: raise ValueError( "simulation method is not supported. Try direct-simulation, linear-partial-R2, non-parametric-partial-R2, or e-value" ) self.frac_strength_treatment = ( kwargs["effect_fraction_on_treatment"] if "effect_fraction_on_treatment" in kwargs else 1 ) self.frac_strength_outcome = ( kwargs["effect_fraction_on_outcome"] if "effect_fraction_on_outcome" in kwargs else 1 ) self.plotmethod = kwargs["plotmethod"] if "plotmethod" in kwargs else "colormesh" self.percent_change_estimate = kwargs["percent_change_estimate"] if "percent_change_estimate" in kwargs else 1.0 self.significance_level = kwargs["significance_level"] if "significance_level" in kwargs else 0.05 self.confounder_increases_estimate = ( kwargs["confounder_increases_estimate"] if "confounder_increases_estimate" in kwargs else False ) self.benchmark_common_causes = ( kwargs["benchmark_common_causes"] if "benchmark_common_causes" in kwargs else None ) self.null_hypothesis_effect = kwargs["null_hypothesis_effect"] if "null_hypothesis_effect" in kwargs else 0 self.plot_estimate = kwargs["plot_estimate"] if "plot_estimate" in kwargs else True self.num_splits = kwargs["num_splits"] if "num_splits" in kwargs else 5 self.shuffle_data = kwargs["shuffle_data"] if "shuffle_data" in kwargs else False self.shuffle_random_seed = kwargs["shuffle_random_seed"] if "shuffle_random_seed" in kwargs else None self.alpha_s_estimator_param_list = ( kwargs["alpha_s_estimator_param_list"] if "alpha_s_estimator_param_list" in kwargs else None ) self.alpha_s_estimator_list = kwargs["alpha_s_estimator_list"] if "alpha_s_estimator_list" in kwargs else None self.g_s_estimator_list = kwargs["g_s_estimator_list"] if "g_s_estimator_list" in kwargs else None self.g_s_estimator_param_list = ( kwargs["g_s_estimator_param_list"] if "g_s_estimator_param_list" in kwargs else None ) self.plugin_reisz = kwargs["plugin_reisz"] if "plugin_reisz" in kwargs else False self.logger = logging.getLogger(__name__) def refute_estimate(self, show_progress_bar=False): if self.simulation_method == "linear-partial-R2": return sensitivity_linear_partial_r2( self._data, self._estimate, self._treatment_name, self.frac_strength_treatment, self.frac_strength_outcome, self.percent_change_estimate, self.benchmark_common_causes, self.significance_level, self.null_hypothesis_effect, self.plot_estimate, ) elif self.simulation_method == "non-parametric-partial-R2": return sensitivity_non_parametric_partial_r2( self._estimate, self.kappa_t, self.kappa_y, self.frac_strength_treatment, self.frac_strength_outcome, self.benchmark_common_causes, self.plot_estimate, self.alpha_s_estimator_list, self.alpha_s_estimator_param_list, self.g_s_estimator_list, self.g_s_estimator_param_list, self.plugin_reisz, ) elif self.simulation_method == "e-value": return sensitivity_e_value( self._data, self._target_estimand, self._estimate, self._treatment_name, self._outcome_name, self.plot_estimate, ) elif self.simulation_method == "direct-simulation": refute = sensitivity_simulation( self._data, self._target_estimand, self._estimate, self._treatment_name, self._outcome_name, self.kappa_t, self.kappa_y, self.effect_on_t, self.effect_on_y, self.frac_strength_treatment, self.frac_strength_outcome, self.plotmethod, show_progress_bar, ) refute.add_refuter(self) return refute def _infer_default_kappa_t( data: pd.DataFrame, target_estimand: IdentifiedEstimand, treatment_name: List[str], effect_on_t: str, frac_strength_treatment: float, len_kappa_t: int = 10, ): """Infer default effect strength of simulated confounder on treatment.""" observed_common_causes_names = target_estimand.get_backdoor_variables() if len(observed_common_causes_names) > 0: observed_common_causes = data[observed_common_causes_names] observed_common_causes = pd.get_dummies(observed_common_causes, drop_first=True) else: raise ValueError( "There needs to be at least one common cause to" + "automatically compute the default value of kappa_t." + " Provide a value for kappa_t" ) t = data[treatment_name] # Standardizing the data observed_common_causes = StandardScaler().fit_transform(observed_common_causes) if effect_on_t == "binary_flip": # Fit a model containing all confounders and compare predictions # using all features compared to all features except a given # confounder. tmodel = LogisticRegression().fit(observed_common_causes, t) tpred = tmodel.predict(observed_common_causes).astype(int) flips = [] for i in range(observed_common_causes.shape[1]): oldval = np.copy(observed_common_causes[:, i]) observed_common_causes[:, i] = 0 tcap = tmodel.predict(observed_common_causes).astype(int) observed_common_causes[:, i] = oldval flips.append(np.sum(abs(tcap - tpred)) / tpred.shape[0]) min_coeff, max_coeff = min(flips), max(flips) elif effect_on_t == "linear": # Estimating the regression coefficient from standardized features to t corrcoef_var_t = np.corrcoef(observed_common_causes, t, rowvar=False)[-1, :-1] std_dev_t = np.std(t)[0] max_coeff = max(corrcoef_var_t) * std_dev_t min_coeff = min(corrcoef_var_t) * std_dev_t else: raise NotImplementedError("'" + effect_on_t + "' method not supported for confounders' effect on treatment") min_coeff, max_coeff = _compute_min_max_coeff(min_coeff, max_coeff, frac_strength_treatment) # By default, return a plot with 10 points # consider 10 values of the effect of the unobserved confounder step = (max_coeff - min_coeff) / len_kappa_t logger.info("(Min, Max) kappa_t for observed common causes, ({0}, {1})".format(min_coeff, max_coeff)) if np.equal(max_coeff, min_coeff): return max_coeff else: return np.arange(min_coeff, max_coeff, step) def _compute_min_max_coeff(min_coeff: float, max_coeff: float, effect_strength_fraction: np.ndarray): max_coeff = effect_strength_fraction * max_coeff min_coeff = effect_strength_fraction * min_coeff return min_coeff, max_coeff def _infer_default_kappa_y( data: pd.DataFrame, target_estimand: IdentifiedEstimand, outcome_name: List[str], effect_on_y: str, frac_strength_outcome: float, len_kappa_y: int = 10, ): """Infer default effect strength of simulated confounder on treatment.""" observed_common_causes_names = target_estimand.get_backdoor_variables() if len(observed_common_causes_names) > 0: observed_common_causes = data[observed_common_causes_names] observed_common_causes = pd.get_dummies(observed_common_causes, drop_first=True) else: raise ValueError( "There needs to be at least one common cause to" + "automatically compute the default value of kappa_y." + " Provide a value for kappa_y" ) y = data[outcome_name] # Standardizing the data observed_common_causes = StandardScaler().fit_transform(observed_common_causes) if effect_on_y == "binary_flip": # Fit a model containing all confounders and compare predictions # using all features compared to all features except a given # confounder. ymodel = LogisticRegression().fit(observed_common_causes, y) ypred = ymodel.predict(observed_common_causes).astype(int) flips = [] for i in range(observed_common_causes.shape[1]): oldval = np.copy(observed_common_causes[:, i]) observed_common_causes[:, i] = 0 ycap = ymodel.predict(observed_common_causes).astype(int) observed_common_causes[:, i] = oldval flips.append(np.sum(abs(ycap - ypred)) / ypred.shape[0]) min_coeff, max_coeff = min(flips), max(flips) elif effect_on_y == "linear": corrcoef_var_y = np.corrcoef(observed_common_causes, y, rowvar=False)[-1, :-1] std_dev_y = np.std(y)[0] max_coeff = max(corrcoef_var_y) * std_dev_y min_coeff = min(corrcoef_var_y) * std_dev_y else: raise NotImplementedError("'" + effect_on_y + "' method not supported for confounders' effect on outcome") min_coeff, max_coeff = _compute_min_max_coeff(min_coeff, max_coeff, frac_strength_outcome) # By default, return a plot with 10 points # consider 10 values of the effect of the unobserved confounder step = (max_coeff - min_coeff) / len_kappa_y logger.info("(Min, Max) kappa_y for observed common causes, ({0}, {1})".format(min_coeff, max_coeff)) if np.equal(max_coeff, min_coeff): return max_coeff else: return np.arange(min_coeff, max_coeff, step) def _include_confounders_effect( data: pd.DataFrame, new_data: pd.DataFrame, effect_on_t: str, treatment_name: str, kappa_t: float, effect_on_y: str, outcome_name: str, kappa_y: float, ): """ This function deals with the change in the value of the data due to the effect of the unobserved confounder. In the case of a binary flip, we flip only if the random number is greater than the threshold set. In the case of a linear effect, we use the variable as the linear regression constant. :param new_data: pandas.DataFrame: The data to be changed due to the effects of the unobserved confounder. :param kappa_t: numpy.float64: The value of the threshold for binary_flip or the value of the regression coefficient for linear effect. :param kappa_y: numpy.float64: The value of the threshold for binary_flip or the value of the regression coefficient for linear effect. :return: pandas.DataFrame: The DataFrame that includes the effects of the unobserved confounder. """ num_rows = data.shape[0] stdnorm = scipy.stats.norm() w_random = stdnorm.rvs(num_rows) if effect_on_t == "binary_flip": alpha = 2 * kappa_t - 1 if kappa_t >= 0.5 else 1 - 2 * kappa_t interval = stdnorm.interval(alpha) rel_interval = interval[0] if kappa_t >= 0.5 else interval[1] new_data.loc[rel_interval <= w_random, treatment_name] = ( 1 - new_data.loc[rel_interval <= w_random, treatment_name] ) for tname in treatment_name: if pd.api.types.is_bool_dtype(data[tname]): new_data = new_data.astype({tname: "bool"}, copy=False) elif effect_on_t == "linear": confounder_t_effect = kappa_t * w_random # By default, we add the effect of simulated confounder for treatment. # But subtract it from outcome to create a negative correlation # assuming that the original confounder's effect was positive on both. # This is to remove the effect of the original confounder. new_data[treatment_name] = new_data[treatment_name].values + np.ndarray( shape=(num_rows, 1), buffer=confounder_t_effect ) else: raise NotImplementedError("'" + effect_on_t + "' method not supported for confounders' effect on treatment") if effect_on_y == "binary_flip": alpha = 2 * kappa_y - 1 if kappa_y >= 0.5 else 1 - 2 * kappa_y interval = stdnorm.interval(alpha) rel_interval = interval[0] if kappa_y >= 0.5 else interval[1] new_data.loc[rel_interval <= w_random, outcome_name] = 1 - new_data.loc[rel_interval <= w_random, outcome_name] for yname in outcome_name: if pd.api.types.is_bool_dtype(data[yname]): new_data = new_data.astype({yname: "bool"}, copy=False) elif effect_on_y == "linear": confounder_y_effect = (-1) * kappa_y * w_random # By default, we add the effect of simulated confounder for treatment. # But subtract it from outcome to create a negative correlation # assuming that the original confounder's effect was positive on both. # This is to remove the effect of the original confounder. new_data[outcome_name] = new_data[outcome_name].values + np.ndarray( shape=(num_rows, 1), buffer=confounder_y_effect ) else: raise NotImplementedError("'" + effect_on_y + "' method not supported for confounders' effect on outcome") return new_data def include_simulated_confounder( data: pd.DataFrame, treatment_name: str, outcome_name: str, kappa_t: float, kappa_y: float, convergence_threshold: float = 0.1, c_star_max: int = 1000, ): """ This function simulates an unobserved confounder based on the data using the following steps: 1. It calculates the "residuals" from the treatment and outcome model i.) The outcome model has outcome as the dependent variable and all the observed variables including treatment as independent variables ii.) The treatment model has treatment as the dependent variable and all the observed variables as independent variables. 2. U is an intermediate random variable drawn from the normal distribution with the weighted average of residuals as mean and a unit variance U ~ N(c1*d_y + c2*d_t, 1) where *d_y and d_t are residuals from the treatment and outcome model *c1 and c2 are coefficients to the residuals 3. The final U, which is the simulated unobserved confounder is obtained by debiasing the intermediate variable U by residualising it with X Choosing the coefficients c1 and c2: The coefficients are chosen based on these basic assumptions: 1. There is a hyperbolic relationship satisfying c1*c2 = c_star 2. c_star is chosen from a range of possible values based on the correlation of the obtained simulated variable with outcome and treatment. 3. The product of correlations with treatment and outcome should be at a minimum distance to the maximum correlations with treatment and outcome in any of the observed confounders 4. The ratio of the weights should be such that they maintain the ratio of the maximum possible observed coefficients within some confidence interval :param c_star_max: The maximum possible value for the hyperbolic curve on which the coefficients to the residuals lie. It defaults to 1000 in the code if not specified by the user. :type int :param convergence_threshold: The threshold to check the plateauing of the correlation while selecting a c_star. It defaults to 0.1 in the code if not specified by the user :type float :returns: The simulated values of the unobserved confounder based on the data :type pandas.core.series.Series """ # Obtaining the list of observed variables required_variables = True observed_variables = choose_variables(required_variables) observed_variables_with_treatment_and_outcome = observed_variables + treatment_name + outcome_name # Taking a subset of the dataframe that has only observed variables data = data[observed_variables_with_treatment_and_outcome] # Residuals from the outcome model obtained by fitting a linear model y = data[outcome_name[0]] observed_variables_with_treatment = observed_variables + treatment_name X = data[observed_variables_with_treatment] model = sm.OLS(y, X.astype("float")) results = model.fit() residuals_y = y - results.fittedvalues d_y = list(pd.Series(residuals_y)) # Residuals from the treatment model obtained by fitting a linear model t = data[treatment_name[0]].astype("int64") X = data[observed_variables] model = sm.OLS(t, X) results = model.fit() residuals_t = t - results.fittedvalues d_t = list(pd.Series(residuals_t)) # Initialising product_cor_metric_observed with a really low value as finding maximum product_cor_metric_observed = -10000000000 for i in observed_variables: current_obs_confounder = data[i] outcome_values = data[outcome_name[0]] correlation_y = current_obs_confounder.corr(outcome_values) treatment_values = t correlation_t = current_obs_confounder.corr(treatment_values) product_cor_metric_current = correlation_y * correlation_t if product_cor_metric_current >= product_cor_metric_observed: product_cor_metric_observed = product_cor_metric_current correlation_t_observed = correlation_t correlation_y_observed = correlation_y # The user has an option to give the the effect_strength_on_y and effect_strength_on_t which can be then used instead of maximum correlation with treatment and outcome in the observed variables as it specifies the desired effect. if kappa_t is not None: correlation_t_observed = kappa_t if kappa_y is not None: correlation_y_observed = kappa_y # Choosing a c_star based on the data. # The correlations stop increasing upon increasing c_star after a certain value, that is it plateaus and we choose the value of c_star to be the value it plateaus. correlation_y_list = [] correlation_t_list = [] product_cor_metric_simulated_list = [] x_list = [] step = int(c_star_max / 10) for i in range(0, int(c_star_max), step): c1 = math.sqrt(i) c2 = c1 final_U = _generate_confounder_from_residuals(c1, c2, d_y, d_t, X) current_simulated_confounder = final_U outcome_values = data[outcome_name[0]] correlation_y = current_simulated_confounder.corr(outcome_values) correlation_y_list.append(correlation_y) treatment_values = t correlation_t = current_simulated_confounder.corr(treatment_values) correlation_t_list.append(correlation_t) product_cor_metric_simulated = correlation_y * correlation_t product_cor_metric_simulated_list.append(product_cor_metric_simulated) x_list.append(i) index = 1 while index < len(correlation_y_list): if (correlation_y_list[index] - correlation_y_list[index - 1]) <= convergence_threshold: c_star = x_list[index] break index = index + 1 # Choosing c1 and c2 based on the hyperbolic relationship once c_star is chosen by going over various combinations of c1 and c2 values and choosing the combination which # which maintains the minimum distance between the product of correlations of the simulated variable and the product of maximum correlations of one of the observed variables # and additionally checks if the ratio of the weights are such that they maintain the ratio of the maximum possible observed coefficients within some confidence interval # c1_final and c2_final are initialised to the values on the hyperbolic curve such that c1_final = c2_final and c1_final*c2_final = c_star c1_final = math.sqrt(c_star) c2_final = math.sqrt(c_star) # initialising min_distance_between_product_cor_metrics to be a value greater than 1 min_distance_between_product_cor_metrics = 1.5 i = 0.05 threshold = c_star / 0.05 while i <= threshold: c2 = i c1 = c_star / c2 final_U = _generate_confounder_from_residuals(c1, c2, d_y, d_t, X) current_simulated_confounder = final_U outcome_values = data[outcome_name[0]] correlation_y = current_simulated_confounder.corr(outcome_values) treatment_values = t correlation_t = current_simulated_confounder.corr(treatment_values) product_cor_metric_simulated = correlation_y * correlation_t if min_distance_between_product_cor_metrics >= abs(product_cor_metric_simulated - product_cor_metric_observed): min_distance_between_product_cor_metrics = abs(product_cor_metric_simulated - product_cor_metric_observed) additional_condition = correlation_y_observed / correlation_t_observed if ((c1 / c2) <= (additional_condition + 0.3 * additional_condition)) and ( (c1 / c2) >= (additional_condition - 0.3 * additional_condition) ): # choose minimum positive value c1_final = c1 c2_final = c2 i = i * 1.5 """#closed form solution print("c_star_max before closed form", c_star_max) if max_correlation_with_t == -1000: c2 = 0 c1 = c_star_max else: additional_condition = abs(max_correlation_with_y/max_correlation_with_t) print("additional_condition", additional_condition) c2 = math.sqrt(c_star_max/additional_condition) c1 = c_star_max/c2""" final_U = _generate_confounder_from_residuals(c1_final, c2_final, d_y, d_t, X) return final_U def _generate_confounder_from_residuals(c1, c2, d_y, d_t, X): """ This function takes the residuals from the treatment and outcome model and their coefficients and simulates the intermediate random variable U by taking the row wise normal distribution corresponding to each residual value and then debiasing the intermediate variable to get the final variable. :param c1: coefficient to the residual from the outcome model :type float :param c2: coefficient to the residual from the treatment model :type float :param d_y: residuals from the outcome model :type list :param d_t: residuals from the treatment model :type list :returns: The simulated values of the unobserved confounder based on the data :type pandas.core.series.Series """ U = [] for j in range(len(d_t)): simulated_variable_mean = c1 * d_y[j] + c2 * d_t[j] simulated_variable_stddev = 1 U.append(np.random.normal(simulated_variable_mean, simulated_variable_stddev, 1)) U = np.array(U) model = sm.OLS(U, X) results = model.fit() U = U.reshape( -1, ) final_U = U - results.fittedvalues.values final_U = pd.Series(U) return final_U def sensitivity_linear_partial_r2( data: pd.DataFrame, estimate: CausalEstimate, treatment_name: str, frac_strength_treatment: float = 1.0, frac_strength_outcome: float = 1.0, percent_change_estimate: float = 1.0, benchmark_common_causes: Optional[List[str]] = None, significance_level: Optional[float] = None, null_hypothesis_effect: Optional[float] = None, plot_estimate: bool = True, ) -> LinearSensitivityAnalyzer: """Add an unobserved confounder for refutation using Linear partial R2 methond (Sensitivity Analysis for linear models). :param data: pd.DataFrame: Data to run the refutation :param estimate: CausalEstimate: Estimate to run the refutation :param treatment_name: str: Name of the treatment :param frac_strength_treatment: float: This parameter decides the effect strength of the simulated confounder as a fraction of the effect strength of observed confounders on treatment. Defaults to 1. :param frac_strength_outcome: float: This parameter decides the effect strength of the simulated confounder as a fraction of the effect strength of observed confounders on outcome. Defaults to 1. :param percent_change_estimate: It is the percentage of reduction of treatment estimate that could alter the results (default = 1). if percent_change_estimate = 1, the robustness value describes the strength of association of confounders with treatment and outcome in order to reduce the estimate by 100% i.e bring it down to 0. (relevant only for Linear Sensitivity Analysis, ignore for rest) :param benchmark_common_causes: names of variables for bounding strength of confounders. (relevant only for partial-r2 based simulation methods) :param significance_level: confidence interval for statistical inference(default = 0.05). (relevant only for partial-r2 based simulation methods) :param null_hypothesis_effect: assumed effect under the null hypothesis. (relevant only for linear-partial-R2, ignore for rest) :param plot_estimate: Generate contour plot for estimate while performing sensitivity analysis. (default = True). (relevant only for partial-r2 based simulation methods) """ if not (isinstance(estimate.estimator, LinearRegressionEstimator)): raise NotImplementedError("Currently only LinearRegressionEstimator is supported for Sensitivity Analysis") if len(estimate.estimator._effect_modifier_names) > 0: raise NotImplementedError("The current implementation does not support effect modifiers") if frac_strength_outcome == 1: frac_strength_outcome = frac_strength_treatment analyzer = LinearSensitivityAnalyzer( estimator=estimate.estimator, data=data, treatment_name=treatment_name, percent_change_estimate=percent_change_estimate, significance_level=significance_level, benchmark_common_causes=benchmark_common_causes, null_hypothesis_effect=null_hypothesis_effect, frac_strength_treatment=frac_strength_treatment, frac_strength_outcome=frac_strength_outcome, common_causes_order=estimate.estimator._observed_common_causes.columns, ) analyzer.check_sensitivity(plot=plot_estimate) return analyzer def sensitivity_non_parametric_partial_r2( estimate: CausalEstimate, kappa_t: Optional[Union[float, np.ndarray]] = None, kappa_y: Optional[Union[float, np.ndarray]] = None, frac_strength_treatment: float = 1.0, frac_strength_outcome: float = 1.0, benchmark_common_causes: Optional[List[str]] = None, plot_estimate: bool = True, alpha_s_estimator_list: Optional[List] = None, alpha_s_estimator_param_list: Optional[List[Dict]] = None, g_s_estimator_list: Optional[List] = None, g_s_estimator_param_list: Optional[List[Dict]] = None, plugin_reisz: bool = False, ) -> Union[PartialLinearSensitivityAnalyzer, NonParametricSensitivityAnalyzer]: """Add an unobserved confounder for refutation using Non-parametric partial R2 methond (Sensitivity Analysis for non-parametric models). :param estimate: CausalEstimate: Estimate to run the refutation :param kappa_t: float, numpy.ndarray: Partial R2 of the unobserved confounder wrt the treatment conditioned on the observed confounders. Only in the case of general non-parametric-partial-R2, it is the fraction of variance in the reisz representer that is explained by the unobserved confounder; specifically (1-r), where r is the ratio of variance of reisz representer, alpha^2, based on observed confounders and that based on all confounders. :param kappa_y: float, numpy.ndarray: Partial R2 of the unobserved confounder wrt the outcome conditioned on the treatment and observed confounders. :param frac_strength_treatment: float: This parameter decides the effect strength of the simulated confounder as a fraction of the effect strength of observed confounders on treatment. Defaults to 1. :param frac_strength_outcome: float: This parameter decides the effect strength of the simulated confounder as a fraction of the effect strength of observed confounders on outcome. Defaults to 1. :param benchmark_common_causes: names of variables for bounding strength of confounders. (relevant only for partial-r2 based simulation methods) :param plot_estimate: Generate contour plot for estimate while performing sensitivity analysis. (default = True). (relevant only for partial-r2 based simulation methods) :param alpha_s_estimator_list: list of estimator objects for estimating alpha_s. These objects should have fit() and predict() methods (relevant only for non-parametric-partial-R2 method) :param alpha_s_estimator_param_list: list of dictionaries with parameters for finding alpha_s. (relevant only for non-parametric-partial-R2 simulation method) :param g_s_estimator_list: list of estimator objects for finding g_s. These objects should have fit() and predict() functions implemented. (relevant only for non-parametric-partial-R2 simulation method) :param g_s_estimator_param_list: list of dictionaries with parameters for tuning respective estimators in "g_s_estimator_list". The order of the dictionaries in the list should be consistent with the estimator objects order in "g_s_estimator_list". (relevant only for non-parametric-partial-R2 simulation method) :plugin_reisz: bool: Flag on whether to use the plugin estimator or the nonparametric estimator for reisz representer function (alpha_s). """ # If the estimator used is LinearDML, partially linear sensitivity analysis will be automatically chosen if isinstance(estimate.estimator, dowhy.causal_estimators.econml.Econml): if estimate.estimator._econml_methodname == "econml.dml.LinearDML": analyzer = PartialLinearSensitivityAnalyzer( estimator=estimate._estimator_object, observed_common_causes=estimate.estimator._observed_common_causes, treatment=estimate.estimator._treatment, outcome=estimate.estimator._outcome, alpha_s_estimator_param_list=alpha_s_estimator_param_list, g_s_estimator_list=g_s_estimator_list, g_s_estimator_param_list=g_s_estimator_param_list, effect_strength_treatment=kappa_t, effect_strength_outcome=kappa_y, benchmark_common_causes=benchmark_common_causes, frac_strength_treatment=frac_strength_treatment, frac_strength_outcome=frac_strength_outcome, ) analyzer.check_sensitivity(plot=plot_estimate) return analyzer analyzer = NonParametricSensitivityAnalyzer( estimator=estimate.estimator, observed_common_causes=estimate.estimator._observed_common_causes, treatment=estimate.estimator._treatment, outcome=estimate.estimator._outcome, alpha_s_estimator_list=alpha_s_estimator_list, alpha_s_estimator_param_list=alpha_s_estimator_param_list, g_s_estimator_list=g_s_estimator_list, g_s_estimator_param_list=g_s_estimator_param_list, effect_strength_treatment=kappa_t, effect_strength_outcome=kappa_y, benchmark_common_causes=benchmark_common_causes, frac_strength_treatment=frac_strength_treatment, frac_strength_outcome=frac_strength_outcome, theta_s=estimate.value, plugin_reisz=plugin_reisz, ) analyzer.check_sensitivity(plot=plot_estimate) return analyzer def sensitivity_e_value( data: pd.DataFrame, target_estimand: IdentifiedEstimand, estimate: CausalEstimate, treatment_name: List[str], outcome_name: List[str], plot_estimate: bool = True, ) -> EValueSensitivityAnalyzer: if not isinstance(estimate.estimator, RegressionEstimator): raise NotImplementedError("E-Value sensitivity analysis is currently only implemented RegressionEstimator.") if len(estimate.estimator._effect_modifier_names) > 0: raise NotImplementedError("The current implementation does not support effect modifiers") analyzer = EValueSensitivityAnalyzer( estimate=estimate, estimand=target_estimand, data=data, treatment_name=treatment_name[0], outcome_name=outcome_name[0], ) analyzer.check_sensitivity(plot=plot_estimate) return analyzer def sensitivity_simulation( data: pd.DataFrame, target_estimand: IdentifiedEstimand, estimate: CausalEstimate, treatment_name: str, outcome_name: str, kappa_t: Optional[Union[float, np.ndarray]] = None, kappa_y: Optional[Union[float, np.ndarray]] = None, confounders_effect_on_treatment: str = "binary_flip", confounders_effect_on_outcome: str = "linear", frac_strength_treatment: float = 1.0, frac_strength_outcome: float = 1.0, plotmethod: Optional[str] = None, show_progress_bar=False, **_, ) -> CausalRefutation: """ This function attempts to add an unobserved common cause to the outcome and the treatment. At present, we have implemented the behavior for one dimensional behaviors for continuous and binary variables. This function can either take single valued inputs or a range of inputs. The function then looks at the data type of the input and then decides on the course of action. :param data: pd.DataFrame: Data to run the refutation :param target_estimand: IdentifiedEstimand: Identified estimand to run the refutation :param estimate: CausalEstimate: Estimate to run the refutation :param treatment_name: str: Name of the treatment :param outcome_name: str: Name of the outcome :param kappa_t: float, numpy.ndarray: Strength of the confounder's effect on treatment. When confounders_effect_on_treatment is linear, it is the regression coefficient. When the confounders_effect_on_treatment is binary flip, it is the probability with which effect of unobserved confounder can invert the value of the treatment. :param kappa_y: float, numpy.ndarray: Strength of the confounder's effect on outcome. Its interpretation depends on confounders_effect_on_outcome and the simulation_method. When simulation_method is direct-simulation, for a linear effect it behaves like the regression coefficient and for a binary flip, it is the probability with which it can invert the value of the outcome. :param confounders_effect_on_treatment: str : The type of effect on the treatment due to the unobserved confounder. Possible values are ['binary_flip', 'linear'] :param confounders_effect_on_outcome: str : The type of effect on the outcome due to the unobserved confounder. Possible values are ['binary_flip', 'linear'] :param frac_strength_treatment: float: This parameter decides the effect strength of the simulated confounder as a fraction of the effect strength of observed confounders on treatment. Defaults to 1. :param frac_strength_outcome: float: This parameter decides the effect strength of the simulated confounder as a fraction of the effect strength of observed confounders on outcome. Defaults to 1. :param plotmethod: string: Type of plot to be shown. If None, no plot is generated. This parameter is used only only when more than one treatment confounder effect values or outcome confounder effect values are provided. Default is "colormesh". Supported values are "contour", "colormesh" when more than one value is provided for both confounder effect value parameters; "line" when provided for only one of them. :return: CausalRefuter: An object that contains the estimated effect and a new effect and the name of the refutation used. """ if kappa_t is None: kappa_t = _infer_default_kappa_t( data, target_estimand, treatment_name, confounders_effect_on_treatment, frac_strength_treatment ) if kappa_y is None: kappa_y = _infer_default_kappa_y( data, target_estimand, outcome_name, confounders_effect_on_outcome, frac_strength_outcome ) if not isinstance(kappa_t, (list, np.ndarray)) and not isinstance( kappa_y, (list, np.ndarray) ): # Deal with single value inputs new_data = copy.deepcopy(data) new_data = _include_confounders_effect( data, new_data, confounders_effect_on_treatment, treatment_name, kappa_t, confounders_effect_on_outcome, outcome_name, kappa_y, ) new_estimator = CausalEstimator.get_estimator_object(new_data, target_estimand, estimate) new_effect = new_estimator.estimate_effect() refute = CausalRefutation( estimate.value, new_effect.value, refutation_type="Refute: Add an Unobserved Common Cause" ) refute.new_effect_array = np.array(new_effect.value) refute.new_effect = new_effect.value return refute else: # Deal with multiple value inputs if isinstance(kappa_t, (list, np.ndarray)) and isinstance( kappa_y, (list, np.ndarray) ): # Deal with range inputs # Get a 2D matrix of values # x,y = np.meshgrid(self.kappa_t, self.kappa_y) # x,y are both MxN results_matrix = np.random.rand(len(kappa_t), len(kappa_y)) # Matrix to hold all the results of NxM orig_data = copy.deepcopy(data) for i in tqdm( range(len(kappa_t)), colour=CausalRefuter.PROGRESS_BAR_COLOR, disable=not show_progress_bar, desc="Refuting Estimates: ", ): for j in range(len(kappa_y)): new_data = _include_confounders_effect( data, orig_data, confounders_effect_on_treatment, treatment_name, kappa_t[i], confounders_effect_on_outcome, outcome_name, kappa_y[j], ) new_estimator = CausalEstimator.get_estimator_object(new_data, target_estimand, estimate) new_effect = new_estimator.estimate_effect() refute = CausalRefutation( estimate.value, new_effect.value, refutation_type="Refute: Add an Unobserved Common Cause", ) results_matrix[i][j] = refute.new_effect # Populate the results refute.new_effect_array = results_matrix refute.new_effect = (np.min(results_matrix), np.max(results_matrix)) # Store the values into the refute object if plotmethod is None: return refute import matplotlib import matplotlib.pyplot as plt fig = plt.figure(figsize=(6, 5)) left, bottom, width, height = 0.1, 0.1, 0.8, 0.8 ax = fig.add_axes([left, bottom, width, height]) oe = estimate.value contour_levels = [oe / 4.0, oe / 2.0, (3.0 / 4) * oe, oe] contour_levels.extend([0, np.min(results_matrix), np.max(results_matrix)]) if plotmethod == "contour": cp = plt.contourf(kappa_y, kappa_t, results_matrix, levels=sorted(contour_levels)) # Adding a label on the contour line for the original estimate fmt = {} trueeffect_index = np.where(cp.levels == oe)[0][0] fmt[cp.levels[trueeffect_index]] = "Estimated Effect" # Label every other level using strings plt.clabel(cp, [cp.levels[trueeffect_index]], inline=True, fmt=fmt) plt.colorbar(cp) elif plotmethod == "colormesh": cp = plt.pcolormesh(kappa_y, kappa_t, results_matrix, shading="nearest") plt.colorbar(cp, ticks=contour_levels) ax.yaxis.set_ticks(kappa_t) ax.xaxis.set_ticks(kappa_y) plt.xticks(rotation=45) ax.set_title("Effect of Unobserved Common Cause") ax.set_ylabel("Value of Linear Constant on Treatment") ax.set_xlabel("Value of Linear Constant on Outcome") plt.show() return refute elif isinstance(kappa_t, (list, np.ndarray)): outcomes = np.random.rand(len(kappa_t)) orig_data = copy.deepcopy(data) for i in tqdm( range(0, len(kappa_t)), colour=CausalRefuter.PROGRESS_BAR_COLOR, disable=not show_progress_bar, desc="Refuting Estimates: ", ): new_data = _include_confounders_effect( data, orig_data, confounders_effect_on_treatment, treatment_name, kappa_t[i], confounders_effect_on_outcome, outcome_name, kappa_y, ) new_estimator = CausalEstimator.get_estimator_object(new_data, target_estimand, estimate) new_effect = new_estimator.estimate_effect() refute = CausalRefutation( estimate.value, new_effect.value, refutation_type="Refute: Add an Unobserved Common Cause" ) logger.debug(refute) outcomes[i] = refute.new_effect # Populate the results refute.new_effect_array = outcomes refute.new_effect = (np.min(outcomes), np.max(outcomes)) if plotmethod is None: return refute import matplotlib import matplotlib.pyplot as plt fig = plt.figure(figsize=(6, 5)) left, bottom, width, height = 0.1, 0.1, 0.8, 0.8 ax = fig.add_axes([left, bottom, width, height]) plt.plot(kappa_t, outcomes) plt.axhline(estimate.value, linestyle="--", color="gray") ax.set_title("Effect of Unobserved Common Cause") ax.set_xlabel("Value of Linear Constant on Treatment") ax.set_ylabel("Estimated Effect after adding the common cause") plt.show() return refute elif isinstance(kappa_y, (list, np.ndarray)): outcomes = np.random.rand(len(kappa_y)) orig_data = copy.deepcopy(data) for i in tqdm( range(0, len(kappa_y)), colour=CausalRefuter.PROGRESS_BAR_COLOR, disable=not show_progress_bar, desc="Refuting Estimates: ", ): new_data = _include_confounders_effect( data, orig_data, confounders_effect_on_treatment, treatment_name, kappa_t, confounders_effect_on_outcome, outcome_name, kappa_y[i], ) new_estimator = CausalEstimator.get_estimator_object(new_data, target_estimand, estimate) new_effect = new_estimator.estimate_effect() refute = CausalRefutation( estimate.value, new_effect.value, refutation_type="Refute: Add an Unobserved Common Cause" ) logger.debug(refute) outcomes[i] = refute.new_effect # Populate the results refute.new_effect_array = outcomes refute.new_effect = (np.min(outcomes), np.max(outcomes)) if plotmethod is None: return refute import matplotlib import matplotlib.pyplot as plt fig = plt.figure(figsize=(6, 5)) left, bottom, width, height = 0.1, 0.1, 0.8, 0.8 ax = fig.add_axes([left, bottom, width, height]) plt.plot(kappa_y, outcomes) plt.axhline(estimate.value, linestyle="--", color="gray") ax.set_title("Effect of Unobserved Common Cause") ax.set_xlabel("Value of Linear Constant on Outcome") ax.set_ylabel("Estimated Effect after adding the common cause") plt.show() return refute

andresmor-ms

133e7b9a4ed32aae8ab5f39a01eb02b3a4d1c0ba

e1652ec3c6606b1bb2dfe91ef830e4b4b566712d

This removal is introducing a non-backwards-compatible change. Will create an issue to address this.

petergtz

py-why/dowhy

Update README.rst

Added direct link to https://github.com/py-why/dowhy/blob/main/docs/source/contributing/contributing-code.rst that has detailed instructions for code contribution steps Signed-off-by: emrekiciman <emrek@microsoft.com>

2022-09-17 01:02:37+00:00

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README.rst

|BuildStatus|_ |PyPiVersion|_ |PythonSupport|_ |Downloads|_ .. |PyPiVersion| image:: https://img.shields.io/pypi/v/dowhy.svg .. _PyPiVersion: https://pypi.org/project/dowhy/ .. |PythonSupport| image:: https://img.shields.io/pypi/pyversions/dowhy.svg .. _PythonSupport: https://pypi.org/project/dowhy/ .. |BuildStatus| image:: https://github.com/microsoft/dowhy/workflows/Python%20package/badge.svg .. _BuildStatus: https://github.com/microsoft/dowhy/actions .. |Downloads| image:: https://pepy.tech/badge/dowhy .. _Downloads: https://pepy.tech/project/dowhy DoWhy | An end-to-end library for causal inference =================================================== Introducing DoWhy and the 4 steps of causal inference | `Microsoft Research Blog <https://www.microsoft.com/en-us/research/blog/dowhy-a-library-for-causal-inference/>`_ | `Video Tutorial <https://note.microsoft.com/MSR-Webinar-DoWhy-Library-Registration-On-Demand.html>`_ | `Arxiv Paper <https://arxiv.org/abs/2011.04216>`_ | `Arxiv Paper (GCM-extension) <https://arxiv.org/abs/2206.06821>`_ | `Slides <https://www2.slideshare.net/AmitSharma315/dowhy-an-endtoend-library-for-causal-inference>`_ Read the `docs <https://py-why.github.io/dowhy/>`_ | Try it online! |Binder|_ .. |Binder| image:: https://mybinder.org/badge_logo.svg .. _Binder: https://mybinder.org/v2/gh/microsoft/dowhy/main?filepath=docs%2Fsource%2F **Case Studies using DoWhy**: `Hotel booking cancellations <https://towardsdatascience.com/beyond-predictive-models-the-causal-story-behind-hotel-booking-cancellations-d29e8558cbaf>`_ | `Effect of customer loyalty programs <https://github.com/microsoft/dowhy/blob/main/docs/source/example_notebooks/dowhy_example_effect_of_memberrewards_program.ipynb>`_ | `Optimizing article headlines <https://medium.com/@akelleh/introducing-the-do-sampler-for-causal-inference-a3296ea9e78d>`_ | `Effect of home visits on infant health (IHDP) <https://towardsdatascience.com/implementing-causal-inference-a-key-step-towards-agi-de2cde8ea599>`_ | `Causes of customer churn/attrition <https://medium.com/geekculture/a-quickstart-for-causal-analysis-decision-making-with-dowhy-2ce2d4d1efa9>`_ .. image:: https://raw.githubusercontent.com/microsoft/dowhy/main/docs/images/dowhy-schematic.png As computing systems are more frequently and more actively intervening in societally critical domains such as healthcare, education, and governance, it is critical to correctly predict and understand the causal effects of these interventions. Without an A/B test, conventional machine learning methods, built on pattern recognition and correlational analyses, are insufficient for decision-making. Much like machine learning libraries have done for prediction, **"DoWhy" is a Python library that aims to spark causal thinking and analysis**. DoWhy provides a principled four-step interface for causal inference that focuses on explicitly modeling causal assumptions and validating them as much as possible. The key feature of DoWhy is its state-of-the-art refutation API that can automatically test causal assumptions for any estimation method, thus making inference more robust and accessible to non-experts. DoWhy supports estimation of the average causal effect for backdoor, frontdoor, instrumental variable and other identification methods, and estimation of the conditional effect (CATE) through an integration with the EconML library. For a quick introduction to causal inference, check out `amit-sharma/causal-inference-tutorial <https://github.com/amit-sharma/causal-inference-tutorial/>`_. We also gave a more comprehensive tutorial at the ACM Knowledge Discovery and Data Mining (`KDD 2018 <http://www.kdd.org/kdd2018/>`_) conference: `causalinference.gitlab.io/kdd-tutorial <http://causalinference.gitlab.io/kdd-tutorial/>`_. For an introduction to the four steps of causal inference and its implications for machine learning, you can access this video tutorial from Microsoft Research: `DoWhy Webinar <https://note.microsoft.com/MSR-Webinar-DoWhy-Library-Registration-On-Demand.html>`_. Documentation for DoWhy is available at `py-why.github.io/dowhy <https://py-why.github.io/dowhy/>`_. .. i here comment toctree:: .. i here comment :maxdepth: 4 .. i here comment :caption: Contents: .. contents:: **Contents** News ----- **2022.05.27**: * **DoWhy now part of PyWhy** We have moved DoWhy from microsoft/dowhy to py-why/dowhy. While GitHub will automatically redirect your git command for cloning, pulling, etc., we recommend updating git remotes and bookmarks. Please note that the **documentation** has now moved to https://py-why.github.io/dowhy with **no** redirect from the old URL. * **Experimental support for GCM-based inference** We have started adding support for graphical causal model-based inference (or in short GCM-based). At the moment, this includes support for interventions, counterfactuals, and attributing distribution changes. As part of this, we also added features for Shapley value estimation and independence tests. We're still in the process of fleshing everything out, including `documentation <https://py-why.github.io/dowhy/main/user_guide/gcm_based_inference/index.html>`_. Some of it is already on `main <https://py-why.github.io/dowhy/main/user_guide/gcm_based_inference/index.html>`_, other parts are on feature branches (prefixed with ``gcm-``) with open pull-requests, other parts will appear as new pull-requests in the next couple of weeks. Be sure to watch this space here as we quickly expand functionality and documentation. The need for causal inference ---------------------------------- Predictive models uncover patterns that connect the inputs and outcome in observed data. To intervene, however, we need to estimate the effect of changing an input from its current value, for which no data exists. Such questions, involving estimating a *counterfactual*, are common in decision-making scenarios. * Will it work? * Does a proposed change to a system improve people's outcomes? * Why did it work? * What led to a change in a system's outcome? * What should we do? * What changes to a system are likely to improve outcomes for people? * What are the overall effects? * How does the system interact with human behavior? * What is the effect of a system's recommendations on people's activity? Answering these questions requires causal reasoning. While many methods exist for causal inference, it is hard to compare their assumptions and robustness of results. DoWhy makes three contributions, 1. Provides a principled way of modeling a given problem as a causal graph so that all assumptions are explicit. 2. Provides a unified interface for many popular causal inference methods, combining the two major frameworks of graphical models and potential outcomes. 3. Automatically tests for the validity of assumptions if possible and assesses the robustness of the estimate to violations. To see DoWhy in action, check out how it can be applied to estimate the effect of a subscription or rewards program for customers [`Rewards notebook <https://github.com/microsoft/dowhy/blob/main/docs/source/example_notebooks/dowhy_example_effect_of_memberrewards_program.ipynb>`_] and for implementing and evaluating causal inference methods on benchmark datasets like the `Infant Health and Development Program (IHDP) <https://github.com/microsoft/dowhy/blob/main/docs/source/example_notebooks/dowhy_ihdp_data_example.ipynb>`_ dataset, `Infant Mortality (Twins) <https://github.com/microsoft/dowhy/blob/main/docs/source/example_notebooks/dowhy_twins_example.ipynb>`_ dataset, and the `Lalonde Jobs <https://github.com/microsoft/dowhy/blob/main/docs/source/example_notebooks/dowhy_lalonde_example.ipynb>`_ dataset. Installation ------------- DoWhy support Python 3.6+. To install, you can use pip or conda. **Latest Release** Install the latest `release <https://pypi.org/project/dowhy/>`__ using pip. .. code:: shell pip install dowhy Install the latest `release <https://anaconda.org/conda-forge/dowhy>`__ using conda. .. code:: shell conda install -c conda-forge dowhy If you face "Solving environment" problems with conda, then try :code:`conda update --all` and then install dowhy. If that does not work, then use :code:`conda config --set channel_priority false` and try to install again. If the problem persists, please add your issue `here <https://github.com/microsoft/dowhy/issues/197>`_. **Development Version** If you prefer the latest dev version, clone this repository and run the following command from the top-most folder of the repository. .. code:: shell pip install -e . **Requirements** DoWhy requires the following packages: * numpy * scipy * scikit-learn * pandas * networkx (for analyzing causal graphs) * matplotlib (for general plotting) * sympy (for rendering symbolic expressions) If you face any problems, try installing dependencies manually. .. code:: shell pip install -r requirements.txt Optionally, if you wish to input graphs in the dot format, then install pydot (or pygraphviz). For better-looking graphs, you can optionally install pygraphviz. To proceed, first install graphviz and then pygraphviz (on Ubuntu and Ubuntu WSL). .. code:: shell sudo apt install graphviz libgraphviz-dev graphviz-dev pkg-config ## from https://github.com/pygraphviz/pygraphviz/issues/71 pip install pygraphviz --install-option="--include-path=/usr/include/graphviz" \ --install-option="--library-path=/usr/lib/graphviz/" Sample causal inference analysis in DoWhy ------------------------------------------- Most DoWhy analyses for causal inference take 4 lines to write, assuming a pandas dataframe df that contains the data: .. code:: python from dowhy import CausalModel import dowhy.datasets # Load some sample data data = dowhy.datasets.linear_dataset( beta=10, num_common_causes=5, num_instruments=2, num_samples=10000, treatment_is_binary=True) DoWhy supports two formats for providing the causal graph: `gml <https://github.com/GunterMueller/UNI_PASSAU_FMI_Graph_Drawing>`_ (preferred) and `dot <http://www.graphviz.org/documentation/>`_. After loading in the data, we use the four main operations in DoWhy: *model*, *estimate*, *identify* and *refute*: .. code:: python # I. Create a causal model from the data and given graph. model = CausalModel( data=data["df"], treatment=data["treatment_name"], outcome=data["outcome_name"], graph=data["gml_graph"]) # II. Identify causal effect and return target estimands identified_estimand = model.identify_effect() # III. Estimate the target estimand using a statistical method. estimate = model.estimate_effect(identified_estimand, method_name="backdoor.propensity_score_matching") # IV. Refute the obtained estimate using multiple robustness checks. refute_results = model.refute_estimate(identified_estimand, estimate, method_name="random_common_cause") DoWhy stresses on the interpretability of its output. At any point in the analysis, you can inspect the untested assumptions, identified estimands (if any) and the estimate (if any). Here's a sample output of the linear regression estimator. .. image:: https://raw.githubusercontent.com/microsoft/dowhy/main/docs/images/regression_output.png For a full code example, check out the `Getting Started with DoWhy <https://github.com/microsoft/dowhy/blob/main/docs/source/example_notebooks/dowhy_simple_example.ipynb>`_ notebook. You can also use Conditional Average Treatment Effect (CATE) estimation methods from other libraries such as EconML and CausalML, as shown in the `Conditional Treatment Effects <https://github.com/microsoft/dowhy/blob/main/docs/source/example_notebooks/dowhy-conditional-treatment-effects.ipynb>`_ notebook. For more examples of using DoWhy, check out the Jupyter notebooks in `docs/source/example_notebooks <https://github.com/microsoft/dowhy/tree/main/docs/source/example_notebooks/>`_ or try them online at `Binder <https://mybinder.org/v2/gh/microsoft/dowhy/main?filepath=docs%2Fsource%2F>`_. GCM-based inference (experimental) ---------------------------------- Graphical causal model-based inference, or GCM-based inference for short, is an experimental addition to DoWhy. For details, check out the `documentation for the gcm sub-package <https://py-why.github.io/dowhy/main/user_guide/gcm_based_inference/index.html>`_. The basic recipe for this API works as follows: .. code:: python # 1. Modeling cause-effect relationships as a structural causal model # (causal graph + functional causal models): scm = gcm.StructuralCausalModel(nx.DiGraph([('X', 'Y'), ('Y', 'Z')])) # X -> Y -> Z scm.set_causal_mechanism('X', gcm.EmpiricalDistribution()) scm.set_causal_mechanism('Y', gcm.AdditiveNoiseModel(gcm.ml.create_linear_regressor())) scm.set_causal_mechanism('Z', gcm.AdditiveNoiseModel(gcm.ml.create_linear_regressor())) # 2. Fitting the SCM to the data: gcm.fit(scm, data) # 3. Answering a causal query based on the SCM: results = gcm.<causal_query>(scm, ...) Where <causal_query> can be one of multiple functions explained in `Answering Causal Questions <https://py-why.github.io/dowhy/main/user_guide/gcm_based_inference/answering_causal_questions/index.html>`_. A high-level Pandas API ----------------------- We've made an even simpler API for dowhy which is a light layer on top of the standard one. The goal is to make causal analysis much more like regular exploratory analysis. To use this API, simply import :code:`dowhy.api`. This will magically add the :code:`causal` namespace to your :code:`pandas.DataFrame` s. Then, you can use the namespace as follows. .. code:: python import dowhy.api import dowhy.datasets data = dowhy.datasets.linear_dataset(beta=5, num_common_causes=1, num_instruments = 0, num_samples=1000, treatment_is_binary=True) # data['df'] is just a regular pandas.DataFrame data['df'].causal.do(x='v0', # name of treatment variable variable_types={'v0': 'b', 'y': 'c', 'W0': 'c'}, outcome='y', common_causes=['W0']).groupby('v0').mean().plot(y='y', kind='bar') .. image:: https://raw.githubusercontent.com/microsoft/dowhy/main/docs/images/do_barplot.png For some methods, the :code:`variable_types` field must be specified. It should be a :code:`dict`, where the keys are variable names, and values are 'o' for ordered discrete, 'u' for un-ordered discrete, 'd' for discrete, or 'c' for continuous. **Note:If the** :code:`variable_types` **is not specified we make use of the following implicit conversions:** :: int -> 'c' float -> 'c' binary -> 'b' category -> 'd' **Currently we have not added support for timestamps.** The :code:`do` method in the causal namespace generates a random sample from $P(outcome|do(X=x))$ of the same length as your data set, and returns this outcome as a new :code:`DataFrame`. You can continue to perform the usual :code:`DataFrame` operations with this sample, and so you can compute statistics and create plots for causal outcomes! The :code:`do` method is built on top of the lower-level :code:`dowhy` objects, so can still take a graph and perform identification automatically when you provide a graph instead of :code:`common_causes`. For more details, check out the `Pandas API <https://github.com/microsoft/dowhy/blob/main/docs/source/example_notebooks/dowhy_causal_api.ipynb>`_ notebook or the `Do Sampler <https://github.com/microsoft/dowhy/blob/main/docs/source/example_notebooks/do_sampler_demo.ipynb>`_ notebook. Graphical Models and Potential Outcomes: Best of both worlds ============================================================ DoWhy builds on two of the most powerful frameworks for causal inference: graphical models and potential outcomes. It uses graph-based criteria and do-calculus for modeling assumptions and identifying a non-parametric causal effect. For estimation, it switches to methods based primarily on potential outcomes. A unifying language for causal inference ---------------------------------------- DoWhy is based on a simple unifying language for causal inference. Causal inference may seem tricky, but almost all methods follow four key steps: 1. Model a causal inference problem using assumptions. 2. Identify an expression for the causal effect under these assumptions ("causal estimand"). 3. Estimate the expression using statistical methods such as matching or instrumental variables. 4. Finally, verify the validity of the estimate using a variety of robustness checks. This workflow can be captured by four key verbs in DoWhy: - model - identify - estimate - refute Using these verbs, DoWhy implements a causal inference engine that can support a variety of methods. *model* encodes prior knowledge as a formal causal graph, *identify* uses graph-based methods to identify the causal effect, *estimate* uses statistical methods for estimating the identified estimand, and finally *refute* tries to refute the obtained estimate by testing robustness to assumptions. Key differences compared to available causal inference software ---------------------------------------------------------------- DoWhy brings three key differences compared to available software for causal inference: **Explicit identifying assumptions** Assumptions are first-class citizens in DoWhy. Each analysis starts with a building a causal model. The assumptions can be viewed graphically or in terms of conditional independence statements. Wherever possible, DoWhy can also automatically test for stated assumptions using observed data. **Separation between identification and estimation** Identification is the causal problem. Estimation is simply a statistical problem. DoWhy respects this boundary and treats them separately. This focuses the causal inference effort on identification, and frees up estimation using any available statistical estimator for a target estimand. In addition, multiple estimation methods can be used for a single identified_estimand and vice-versa. **Automated robustness checks** What happens when key identifying assumptions may not be satisfied? The most critical, and often skipped, part of causal analysis is checking the robustness of an estimate to unverified assumptions. DoWhy makes it easy to automatically run sensitivity and robustness checks on the obtained estimate. Finally, DoWhy is easily extensible, allowing other implementations of the four verbs to co-exist (e.g., we support implementations of the *estimation* verb from EconML and CausalML libraries). The four verbs are mutually independent, so their implementations can be combined in any way. Below are more details about the current implementation of each of these verbs. Four steps of causal inference =============================== I. Model a causal problem ----------------------------- DoWhy creates an underlying causal graphical model for each problem. This serves to make each causal assumption explicit. This graph need not be complete---you can provide a partial graph, representing prior knowledge about some of the variables. DoWhy automatically considers the rest of the variables as potential confounders. Currently, DoWhy supports two formats for graph input: `gml <https://github.com/GunterMueller/UNI_PASSAU_FMI_Graph_Drawing>`_ (preferred) and `dot <http://www.graphviz.org/documentation/>`_. We strongly suggest to use gml as the input format, as it works well with networkx. You can provide the graph either as a .gml file or as a string. If you prefer to use dot format, you will need to install additional packages (pydot or pygraphviz, see the installation section above). Both .dot files and string format are supported. While not recommended, you can also specify common causes and/or instruments directly instead of providing a graph. Supported formats for specifying causal assumptions ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ * **Graph**: Provide a causal graph in either gml or dot format. Can be a text file or a string. * **Named variable sets**: Instead of the graph, provide variable names that correspond to relevant categories, such as common causes, instrumental variables, effect modifiers, frontdoor variables, etc. Examples of how to instantiate a causal model are in the `Getting Started <https://github.com/microsoft/dowhy/blob/main/docs/source/example_notebooks/dowhy_simple_example.ipynb>`_ notebook. .. i comment image:: causal_model.png II. Identify a target estimand under the model ---------------------------------------------- Based on the causal graph, DoWhy finds all possible ways of identifying a desired causal effect based on the graphical model. It uses graph-based criteria and do-calculus to find potential ways find expressions that can identify the causal effect. Supported identification criteria ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ * Back-door criterion * Front-door criterion * Instrumental Variables * Mediation (Direct and indirect effect identification) Different notebooks illustrate how to use these identification criteria. Check out the `Simple Backdoor <https://github.com/microsoft/dowhy/blob/main/docs/source/example_notebooks/dowhy_confounder_example.ipynb>`_ notebook for the back-door criterion, and the `Simple IV <https://github.com/microsoft/dowhy/blob/main/docs/source/example_notebooks/dowhy-simple-iv-example.ipynb>`_ notebook for the instrumental variable criterion. III. Estimate causal effect based on the identified estimand ------------------------------------------------------------ DoWhy supports methods based on both back-door criterion and instrumental variables. It also provides a non-parametric confidence intervals and a permutation test for testing the statistical significance of obtained estimate. Supported estimation methods ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ * Methods based on estimating the treatment assignment * Propensity-based Stratification * Propensity Score Matching * Inverse Propensity Weighting * Methods based on estimating the outcome model * Linear Regression * Generalized Linear Models * Methods based on the instrumental variable equation * Binary Instrument/Wald Estimator * Two-stage least squares * Regression discontinuity * Methods for front-door criterion and general mediation * Two-stage linear regression Examples of using these methods are in the `Estimation methods <https://github.com/microsoft/dowhy/blob/main/docs/source/example_notebooks/dowhy_estimation_methods.ipynb>`_ notebook. Using EconML and CausalML estimation methods in DoWhy ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ It is easy to call external estimation methods using DoWhy. Currently we support integrations with the `EconML <https://github.com/microsoft/econml>`_ and `CausalML <https://github.com/uber/causalml>`_ packages. Here's an example of estimating conditional treatment effects using EconML's double machine learning estimator. .. code:: python from sklearn.preprocessing import PolynomialFeatures from sklearn.linear_model import LassoCV from sklearn.ensemble import GradientBoostingRegressor dml_estimate = model.estimate_effect(identified_estimand, method_name="backdoor.econml.dml.DML", control_value = 0, treatment_value = 1, target_units = lambda df: df["X0"]>1, confidence_intervals=False, method_params={ "init_params":{'model_y':GradientBoostingRegressor(), 'model_t': GradientBoostingRegressor(), 'model_final':LassoCV(), 'featurizer':PolynomialFeatures(degree=1, include_bias=True)}, "fit_params":{}} ) More examples are in the `Conditional Treatment Effects with DoWhy <https://github.com/microsoft/dowhy/blob/main/docs/source/example_notebooks/dowhy-conditional-treatment-effects.ipynb>`_ notebook. IV. Refute the obtained estimate ------------------------------------- Having access to multiple refutation methods to validate an effect estimate from a causal estimator is a key benefit of using DoWhy. Supported refutation methods ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ * **Add Random Common Cause**: Does the estimation method change its estimate after we add an independent random variable as a common cause to the dataset? (*Hint: It should not*) * **Placebo Treatment**: What happens to the estimated causal effect when we replace the true treatment variable with an independent random variable? (*Hint: the effect should go to zero*) * **Dummy Outcome**: What happens to the estimated causal effect when we replace the true outcome variable with an independent random variable? (*Hint: The effect should go to zero*) * **Simulated Outcome**: What happens to the estimated causal effect when we replace the dataset with a simulated dataset based on a known data-generating process closest to the given dataset? (*Hint: It should match the effect parameter from the data-generating process*) * **Add Unobserved Common Causes**: How sensitive is the effect estimate when we add an additional common cause (confounder) to the dataset that is correlated with the treatment and the outcome? (*Hint: It should not be too sensitive*) * **Data Subsets Validation**: Does the estimated effect change significantly when we replace the given dataset with a randomly selected subset? (*Hint: It should not*) * **Bootstrap Validation**: Does the estimated effect change significantly when we replace the given dataset with bootstrapped samples from the same dataset? (*Hint: It should not*) Examples of using refutation methods are in the `Refutations <https://github.com/microsoft/dowhy/blob/main/docs/source/example_notebooks/dowhy_refuter_notebook.ipynb>`_ notebook. For an advanced refutation that uses a simulated dataset based on user-provided or learnt data-generating processes, check out the `Dummy Outcome Refuter <https://github.com/microsoft/dowhy/blob/main/docs/source/example_notebooks/dowhy_demo_dummy_outcome_refuter.ipynb>`_ notebook. As a practical example, `this notebook <https://github.com/microsoft/dowhy/blob/main/docs/source/example_notebooks/dowhy_refutation_testing.ipynb>`_ shows an application of refutation methods on evaluating effect estimators for the Infant Health and Development Program (IHDP) and Lalonde datasets. Citing this package ==================== If you find DoWhy useful for your research work, please cite us as follows: Amit Sharma, Emre Kiciman, et al. DoWhy: A Python package for causal inference. 2019. https://github.com/microsoft/dowhy Bibtex:: @misc{dowhy, author={Sharma, Amit and Kiciman, Emre and others}, title={Do{W}hy: {A Python package for causal inference}}, howpublished={https://github.com/microsoft/dowhy}, year={2019} } Alternatively, you can cite our Arxiv paper on DoWhy. Amit Sharma, Emre Kiciman. DoWhy: An End-to-End Library for Causal Inference. 2020. https://arxiv.org/abs/2011.04216 Bibtex:: @article{dowhypaper, title={DoWhy: An End-to-End Library for Causal Inference}, author={Sharma, Amit and Kiciman, Emre}, journal={arXiv preprint arXiv:2011.04216}, year={2020} } And if you find the gcm package useful for your work, please also cite us as: Patrick Blöbaum, Peter Götz, Kailash Budhathoki, Atalanti A. Mastakouri, Dominik Janzing. DoWhy-GCM: An extension of DoWhy for causal inference in graphical causal models. 2022. https://arxiv.org/abs/2206.06821 Bibtex:: @article{dowhy_gcm, author = {Bl{\"o}baum, Patrick and G{\"o}tz, Peter and Budhathoki, Kailash and Mastakouri, Atalanti A. and Janzing, Dominik}, title = {DoWhy-GCM: An extension of DoWhy for causal inference in graphical causal models}, journal={arXiv preprint arXiv:2206.06821}, year={2022} } Roadmap ======= The `projects <https://github.com/microsoft/dowhy/projects>`_ page lists the next steps for DoWhy. If you would like to contribute, have a look at the current projects. If you have a specific request for DoWhy, please `raise an issue <https://github.com/microsoft/dowhy/issues>`_. Contributing ============ This project welcomes contributions and suggestions. For a guide to contributing and a list of all contributors, check out `CONTRIBUTING.md <https://github.com/microsoft/dowhy/blob/main/CONTRIBUTING.md>`_. Our contributor code of conduct is available [here](https://github.com/py-why/governance/blob/main/CODE-OF-CONDUCT.md). You can also join the DoWhy development channel on Discord: |discord|_ .. |discord| image:: https://img.shields.io/discord/818456847551168542 .. _discord: https://discord.gg/cSBGb3vsZb

|BuildStatus|_ |PyPiVersion|_ |PythonSupport|_ |Downloads|_ .. |PyPiVersion| image:: https://img.shields.io/pypi/v/dowhy.svg .. _PyPiVersion: https://pypi.org/project/dowhy/ .. |PythonSupport| image:: https://img.shields.io/pypi/pyversions/dowhy.svg .. _PythonSupport: https://pypi.org/project/dowhy/ .. |BuildStatus| image:: https://github.com/microsoft/dowhy/workflows/Python%20package/badge.svg .. _BuildStatus: https://github.com/microsoft/dowhy/actions .. |Downloads| image:: https://pepy.tech/badge/dowhy .. _Downloads: https://pepy.tech/project/dowhy DoWhy | An end-to-end library for causal inference =================================================== Introducing DoWhy and the 4 steps of causal inference | `Microsoft Research Blog <https://www.microsoft.com/en-us/research/blog/dowhy-a-library-for-causal-inference/>`_ | `Video Tutorial <https://note.microsoft.com/MSR-Webinar-DoWhy-Library-Registration-On-Demand.html>`_ | `Arxiv Paper <https://arxiv.org/abs/2011.04216>`_ | `Arxiv Paper (GCM-extension) <https://arxiv.org/abs/2206.06821>`_ | `Slides <https://www2.slideshare.net/AmitSharma315/dowhy-an-endtoend-library-for-causal-inference>`_ Read the `docs <https://py-why.github.io/dowhy/>`_ | Try it online! |Binder|_ .. |Binder| image:: https://mybinder.org/badge_logo.svg .. _Binder: https://mybinder.org/v2/gh/microsoft/dowhy/main?filepath=docs%2Fsource%2F **Case Studies using DoWhy**: `Hotel booking cancellations <https://towardsdatascience.com/beyond-predictive-models-the-causal-story-behind-hotel-booking-cancellations-d29e8558cbaf>`_ | `Effect of customer loyalty programs <https://github.com/microsoft/dowhy/blob/main/docs/source/example_notebooks/dowhy_example_effect_of_memberrewards_program.ipynb>`_ | `Optimizing article headlines <https://medium.com/@akelleh/introducing-the-do-sampler-for-causal-inference-a3296ea9e78d>`_ | `Effect of home visits on infant health (IHDP) <https://towardsdatascience.com/implementing-causal-inference-a-key-step-towards-agi-de2cde8ea599>`_ | `Causes of customer churn/attrition <https://medium.com/geekculture/a-quickstart-for-causal-analysis-decision-making-with-dowhy-2ce2d4d1efa9>`_ .. image:: https://raw.githubusercontent.com/microsoft/dowhy/main/docs/images/dowhy-schematic.png As computing systems are more frequently and more actively intervening in societally critical domains such as healthcare, education, and governance, it is critical to correctly predict and understand the causal effects of these interventions. Without an A/B test, conventional machine learning methods, built on pattern recognition and correlational analyses, are insufficient for decision-making. Much like machine learning libraries have done for prediction, **"DoWhy" is a Python library that aims to spark causal thinking and analysis**. DoWhy provides a principled four-step interface for causal inference that focuses on explicitly modeling causal assumptions and validating them as much as possible. The key feature of DoWhy is its state-of-the-art refutation API that can automatically test causal assumptions for any estimation method, thus making inference more robust and accessible to non-experts. DoWhy supports estimation of the average causal effect for backdoor, frontdoor, instrumental variable and other identification methods, and estimation of the conditional effect (CATE) through an integration with the EconML library. For a quick introduction to causal inference, check out `amit-sharma/causal-inference-tutorial <https://github.com/amit-sharma/causal-inference-tutorial/>`_. We also gave a more comprehensive tutorial at the ACM Knowledge Discovery and Data Mining (`KDD 2018 <http://www.kdd.org/kdd2018/>`_) conference: `causalinference.gitlab.io/kdd-tutorial <http://causalinference.gitlab.io/kdd-tutorial/>`_. For an introduction to the four steps of causal inference and its implications for machine learning, you can access this video tutorial from Microsoft Research: `DoWhy Webinar <https://note.microsoft.com/MSR-Webinar-DoWhy-Library-Registration-On-Demand.html>`_. Documentation for DoWhy is available at `py-why.github.io/dowhy <https://py-why.github.io/dowhy/>`_. .. i here comment toctree:: .. i here comment :maxdepth: 4 .. i here comment :caption: Contents: .. contents:: **Contents** News ----- **2022.05.27**: * **DoWhy now part of PyWhy** We have moved DoWhy from microsoft/dowhy to py-why/dowhy. While GitHub will automatically redirect your git command for cloning, pulling, etc., we recommend updating git remotes and bookmarks. Please note that the **documentation** has now moved to https://py-why.github.io/dowhy with **no** redirect from the old URL. * **Experimental support for GCM-based inference** We have started adding support for graphical causal model-based inference (or in short GCM-based). At the moment, this includes support for interventions, counterfactuals, and attributing distribution changes. As part of this, we also added features for Shapley value estimation and independence tests. We're still in the process of fleshing everything out, including `documentation <https://py-why.github.io/dowhy/main/user_guide/gcm_based_inference/index.html>`_. Some of it is already on `main <https://py-why.github.io/dowhy/main/user_guide/gcm_based_inference/index.html>`_, other parts are on feature branches (prefixed with ``gcm-``) with open pull-requests, other parts will appear as new pull-requests in the next couple of weeks. Be sure to watch this space here as we quickly expand functionality and documentation. The need for causal inference ---------------------------------- Predictive models uncover patterns that connect the inputs and outcome in observed data. To intervene, however, we need to estimate the effect of changing an input from its current value, for which no data exists. Such questions, involving estimating a *counterfactual*, are common in decision-making scenarios. * Will it work? * Does a proposed change to a system improve people's outcomes? * Why did it work? * What led to a change in a system's outcome? * What should we do? * What changes to a system are likely to improve outcomes for people? * What are the overall effects? * How does the system interact with human behavior? * What is the effect of a system's recommendations on people's activity? Answering these questions requires causal reasoning. While many methods exist for causal inference, it is hard to compare their assumptions and robustness of results. DoWhy makes three contributions, 1. Provides a principled way of modeling a given problem as a causal graph so that all assumptions are explicit. 2. Provides a unified interface for many popular causal inference methods, combining the two major frameworks of graphical models and potential outcomes. 3. Automatically tests for the validity of assumptions if possible and assesses the robustness of the estimate to violations. To see DoWhy in action, check out how it can be applied to estimate the effect of a subscription or rewards program for customers [`Rewards notebook <https://github.com/microsoft/dowhy/blob/main/docs/source/example_notebooks/dowhy_example_effect_of_memberrewards_program.ipynb>`_] and for implementing and evaluating causal inference methods on benchmark datasets like the `Infant Health and Development Program (IHDP) <https://github.com/microsoft/dowhy/blob/main/docs/source/example_notebooks/dowhy_ihdp_data_example.ipynb>`_ dataset, `Infant Mortality (Twins) <https://github.com/microsoft/dowhy/blob/main/docs/source/example_notebooks/dowhy_twins_example.ipynb>`_ dataset, and the `Lalonde Jobs <https://github.com/microsoft/dowhy/blob/main/docs/source/example_notebooks/dowhy_lalonde_example.ipynb>`_ dataset. Installation ------------- DoWhy support Python 3.6+. To install, you can use pip or conda. **Latest Release** Install the latest `release <https://pypi.org/project/dowhy/>`__ using pip. .. code:: shell pip install dowhy Install the latest `release <https://anaconda.org/conda-forge/dowhy>`__ using conda. .. code:: shell conda install -c conda-forge dowhy If you face "Solving environment" problems with conda, then try :code:`conda update --all` and then install dowhy. If that does not work, then use :code:`conda config --set channel_priority false` and try to install again. If the problem persists, please `add your issue here <https://github.com/microsoft/dowhy/issues/197>`_. **Development Version** If you prefer the latest dev version, clone this repository and run the following command from the top-most folder of the repository. .. code:: shell pip install -e . **Requirements** DoWhy requires the following packages: * numpy * scipy * scikit-learn * pandas * networkx (for analyzing causal graphs) * matplotlib (for general plotting) * sympy (for rendering symbolic expressions) If you face any problems, try installing dependencies manually. .. code:: shell pip install -r requirements.txt Optionally, if you wish to input graphs in the dot format, then install pydot (or pygraphviz). For better-looking graphs, you can optionally install pygraphviz. To proceed, first install graphviz and then pygraphviz (on Ubuntu and Ubuntu WSL). .. code:: shell sudo apt install graphviz libgraphviz-dev graphviz-dev pkg-config ## from https://github.com/pygraphviz/pygraphviz/issues/71 pip install pygraphviz --install-option="--include-path=/usr/include/graphviz" \ --install-option="--library-path=/usr/lib/graphviz/" Sample causal inference analysis in DoWhy ------------------------------------------- Most DoWhy analyses for causal inference take 4 lines to write, assuming a pandas dataframe df that contains the data: .. code:: python from dowhy import CausalModel import dowhy.datasets # Load some sample data data = dowhy.datasets.linear_dataset( beta=10, num_common_causes=5, num_instruments=2, num_samples=10000, treatment_is_binary=True) DoWhy supports two formats for providing the causal graph: `gml <https://github.com/GunterMueller/UNI_PASSAU_FMI_Graph_Drawing>`_ (preferred) and `dot <http://www.graphviz.org/documentation/>`_. After loading in the data, we use the four main operations in DoWhy: *model*, *estimate*, *identify* and *refute*: .. code:: python # I. Create a causal model from the data and given graph. model = CausalModel( data=data["df"], treatment=data["treatment_name"], outcome=data["outcome_name"], graph=data["gml_graph"]) # II. Identify causal effect and return target estimands identified_estimand = model.identify_effect() # III. Estimate the target estimand using a statistical method. estimate = model.estimate_effect(identified_estimand, method_name="backdoor.propensity_score_matching") # IV. Refute the obtained estimate using multiple robustness checks. refute_results = model.refute_estimate(identified_estimand, estimate, method_name="random_common_cause") DoWhy stresses on the interpretability of its output. At any point in the analysis, you can inspect the untested assumptions, identified estimands (if any) and the estimate (if any). Here's a sample output of the linear regression estimator. .. image:: https://raw.githubusercontent.com/microsoft/dowhy/main/docs/images/regression_output.png For a full code example, check out the `Getting Started with DoWhy <https://github.com/microsoft/dowhy/blob/main/docs/source/example_notebooks/dowhy_simple_example.ipynb>`_ notebook. You can also use Conditional Average Treatment Effect (CATE) estimation methods from other libraries such as EconML and CausalML, as shown in the `Conditional Treatment Effects <https://github.com/microsoft/dowhy/blob/main/docs/source/example_notebooks/dowhy-conditional-treatment-effects.ipynb>`_ notebook. For more examples of using DoWhy, check out the Jupyter notebooks in `docs/source/example_notebooks <https://github.com/microsoft/dowhy/tree/main/docs/source/example_notebooks/>`_ or try them online at `Binder <https://mybinder.org/v2/gh/microsoft/dowhy/main?filepath=docs%2Fsource%2F>`_. GCM-based inference (experimental) ---------------------------------- Graphical causal model-based inference, or GCM-based inference for short, is an experimental addition to DoWhy. For details, check out the `documentation for the gcm sub-package <https://py-why.github.io/dowhy/main/user_guide/gcm_based_inference/index.html>`_. The basic recipe for this API works as follows: .. code:: python # 1. Modeling cause-effect relationships as a structural causal model # (causal graph + functional causal models): scm = gcm.StructuralCausalModel(nx.DiGraph([('X', 'Y'), ('Y', 'Z')])) # X -> Y -> Z scm.set_causal_mechanism('X', gcm.EmpiricalDistribution()) scm.set_causal_mechanism('Y', gcm.AdditiveNoiseModel(gcm.ml.create_linear_regressor())) scm.set_causal_mechanism('Z', gcm.AdditiveNoiseModel(gcm.ml.create_linear_regressor())) # 2. Fitting the SCM to the data: gcm.fit(scm, data) # 3. Answering a causal query based on the SCM: results = gcm.<causal_query>(scm, ...) Where <causal_query> can be one of multiple functions explained in `Answering Causal Questions <https://py-why.github.io/dowhy/main/user_guide/gcm_based_inference/answering_causal_questions/index.html>`_. A high-level Pandas API ----------------------- We've made an even simpler API for dowhy which is a light layer on top of the standard one. The goal is to make causal analysis much more like regular exploratory analysis. To use this API, simply import :code:`dowhy.api`. This will magically add the :code:`causal` namespace to your :code:`pandas.DataFrame` s. Then, you can use the namespace as follows. .. code:: python import dowhy.api import dowhy.datasets data = dowhy.datasets.linear_dataset(beta=5, num_common_causes=1, num_instruments = 0, num_samples=1000, treatment_is_binary=True) # data['df'] is just a regular pandas.DataFrame data['df'].causal.do(x='v0', # name of treatment variable variable_types={'v0': 'b', 'y': 'c', 'W0': 'c'}, outcome='y', common_causes=['W0']).groupby('v0').mean().plot(y='y', kind='bar') .. image:: https://raw.githubusercontent.com/microsoft/dowhy/main/docs/images/do_barplot.png For some methods, the :code:`variable_types` field must be specified. It should be a :code:`dict`, where the keys are variable names, and values are 'o' for ordered discrete, 'u' for un-ordered discrete, 'd' for discrete, or 'c' for continuous. **Note:If the** :code:`variable_types` **is not specified we make use of the following implicit conversions:** :: int -> 'c' float -> 'c' binary -> 'b' category -> 'd' **Currently we have not added support for timestamps.** The :code:`do` method in the causal namespace generates a random sample from $P(outcome|do(X=x))$ of the same length as your data set, and returns this outcome as a new :code:`DataFrame`. You can continue to perform the usual :code:`DataFrame` operations with this sample, and so you can compute statistics and create plots for causal outcomes! The :code:`do` method is built on top of the lower-level :code:`dowhy` objects, so can still take a graph and perform identification automatically when you provide a graph instead of :code:`common_causes`. For more details, check out the `Pandas API <https://github.com/microsoft/dowhy/blob/main/docs/source/example_notebooks/dowhy_causal_api.ipynb>`_ notebook or the `Do Sampler <https://github.com/microsoft/dowhy/blob/main/docs/source/example_notebooks/do_sampler_demo.ipynb>`_ notebook. Graphical Models and Potential Outcomes: Best of both worlds ============================================================ DoWhy builds on two of the most powerful frameworks for causal inference: graphical models and potential outcomes. It uses graph-based criteria and do-calculus for modeling assumptions and identifying a non-parametric causal effect. For estimation, it switches to methods based primarily on potential outcomes. A unifying language for causal inference ---------------------------------------- DoWhy is based on a simple unifying language for causal inference. Causal inference may seem tricky, but almost all methods follow four key steps: 1. Model a causal inference problem using assumptions. 2. Identify an expression for the causal effect under these assumptions ("causal estimand"). 3. Estimate the expression using statistical methods such as matching or instrumental variables. 4. Finally, verify the validity of the estimate using a variety of robustness checks. This workflow can be captured by four key verbs in DoWhy: - model - identify - estimate - refute Using these verbs, DoWhy implements a causal inference engine that can support a variety of methods. *model* encodes prior knowledge as a formal causal graph, *identify* uses graph-based methods to identify the causal effect, *estimate* uses statistical methods for estimating the identified estimand, and finally *refute* tries to refute the obtained estimate by testing robustness to assumptions. Key differences compared to available causal inference software ---------------------------------------------------------------- DoWhy brings three key differences compared to available software for causal inference: **Explicit identifying assumptions** Assumptions are first-class citizens in DoWhy. Each analysis starts with a building a causal model. The assumptions can be viewed graphically or in terms of conditional independence statements. Wherever possible, DoWhy can also automatically test for stated assumptions using observed data. **Separation between identification and estimation** Identification is the causal problem. Estimation is simply a statistical problem. DoWhy respects this boundary and treats them separately. This focuses the causal inference effort on identification, and frees up estimation using any available statistical estimator for a target estimand. In addition, multiple estimation methods can be used for a single identified_estimand and vice-versa. **Automated robustness checks** What happens when key identifying assumptions may not be satisfied? The most critical, and often skipped, part of causal analysis is checking the robustness of an estimate to unverified assumptions. DoWhy makes it easy to automatically run sensitivity and robustness checks on the obtained estimate. Finally, DoWhy is easily extensible, allowing other implementations of the four verbs to co-exist (e.g., we support implementations of the *estimation* verb from EconML and CausalML libraries). The four verbs are mutually independent, so their implementations can be combined in any way. Below are more details about the current implementation of each of these verbs. Four steps of causal inference =============================== I. Model a causal problem ----------------------------- DoWhy creates an underlying causal graphical model for each problem. This serves to make each causal assumption explicit. This graph need not be complete---you can provide a partial graph, representing prior knowledge about some of the variables. DoWhy automatically considers the rest of the variables as potential confounders. Currently, DoWhy supports two formats for graph input: `gml <https://github.com/GunterMueller/UNI_PASSAU_FMI_Graph_Drawing>`_ (preferred) and `dot <http://www.graphviz.org/documentation/>`_. We strongly suggest to use gml as the input format, as it works well with networkx. You can provide the graph either as a .gml file or as a string. If you prefer to use dot format, you will need to install additional packages (pydot or pygraphviz, see the installation section above). Both .dot files and string format are supported. While not recommended, you can also specify common causes and/or instruments directly instead of providing a graph. Supported formats for specifying causal assumptions ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ * **Graph**: Provide a causal graph in either gml or dot format. Can be a text file or a string. * **Named variable sets**: Instead of the graph, provide variable names that correspond to relevant categories, such as common causes, instrumental variables, effect modifiers, frontdoor variables, etc. Examples of how to instantiate a causal model are in the `Getting Started <https://github.com/microsoft/dowhy/blob/main/docs/source/example_notebooks/dowhy_simple_example.ipynb>`_ notebook. .. i comment image:: causal_model.png II. Identify a target estimand under the model ---------------------------------------------- Based on the causal graph, DoWhy finds all possible ways of identifying a desired causal effect based on the graphical model. It uses graph-based criteria and do-calculus to find potential ways find expressions that can identify the causal effect. Supported identification criteria ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ * Back-door criterion * Front-door criterion * Instrumental Variables * Mediation (Direct and indirect effect identification) Different notebooks illustrate how to use these identification criteria. Check out the `Simple Backdoor <https://github.com/microsoft/dowhy/blob/main/docs/source/example_notebooks/dowhy_confounder_example.ipynb>`_ notebook for the back-door criterion, and the `Simple IV <https://github.com/microsoft/dowhy/blob/main/docs/source/example_notebooks/dowhy-simple-iv-example.ipynb>`_ notebook for the instrumental variable criterion. III. Estimate causal effect based on the identified estimand ------------------------------------------------------------ DoWhy supports methods based on both back-door criterion and instrumental variables. It also provides a non-parametric confidence intervals and a permutation test for testing the statistical significance of obtained estimate. Supported estimation methods ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ * Methods based on estimating the treatment assignment * Propensity-based Stratification * Propensity Score Matching * Inverse Propensity Weighting * Methods based on estimating the outcome model * Linear Regression * Generalized Linear Models * Methods based on the instrumental variable equation * Binary Instrument/Wald Estimator * Two-stage least squares * Regression discontinuity * Methods for front-door criterion and general mediation * Two-stage linear regression Examples of using these methods are in the `Estimation methods <https://github.com/microsoft/dowhy/blob/main/docs/source/example_notebooks/dowhy_estimation_methods.ipynb>`_ notebook. Using EconML and CausalML estimation methods in DoWhy ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ It is easy to call external estimation methods using DoWhy. Currently we support integrations with the `EconML <https://github.com/microsoft/econml>`_ and `CausalML <https://github.com/uber/causalml>`_ packages. Here's an example of estimating conditional treatment effects using EconML's double machine learning estimator. .. code:: python from sklearn.preprocessing import PolynomialFeatures from sklearn.linear_model import LassoCV from sklearn.ensemble import GradientBoostingRegressor dml_estimate = model.estimate_effect(identified_estimand, method_name="backdoor.econml.dml.DML", control_value = 0, treatment_value = 1, target_units = lambda df: df["X0"]>1, confidence_intervals=False, method_params={ "init_params":{'model_y':GradientBoostingRegressor(), 'model_t': GradientBoostingRegressor(), 'model_final':LassoCV(), 'featurizer':PolynomialFeatures(degree=1, include_bias=True)}, "fit_params":{}} ) More examples are in the `Conditional Treatment Effects with DoWhy <https://github.com/microsoft/dowhy/blob/main/docs/source/example_notebooks/dowhy-conditional-treatment-effects.ipynb>`_ notebook. IV. Refute the obtained estimate ------------------------------------- Having access to multiple refutation methods to validate an effect estimate from a causal estimator is a key benefit of using DoWhy. Supported refutation methods ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ * **Add Random Common Cause**: Does the estimation method change its estimate after we add an independent random variable as a common cause to the dataset? (*Hint: It should not*) * **Placebo Treatment**: What happens to the estimated causal effect when we replace the true treatment variable with an independent random variable? (*Hint: the effect should go to zero*) * **Dummy Outcome**: What happens to the estimated causal effect when we replace the true outcome variable with an independent random variable? (*Hint: The effect should go to zero*) * **Simulated Outcome**: What happens to the estimated causal effect when we replace the dataset with a simulated dataset based on a known data-generating process closest to the given dataset? (*Hint: It should match the effect parameter from the data-generating process*) * **Add Unobserved Common Causes**: How sensitive is the effect estimate when we add an additional common cause (confounder) to the dataset that is correlated with the treatment and the outcome? (*Hint: It should not be too sensitive*) * **Data Subsets Validation**: Does the estimated effect change significantly when we replace the given dataset with a randomly selected subset? (*Hint: It should not*) * **Bootstrap Validation**: Does the estimated effect change significantly when we replace the given dataset with bootstrapped samples from the same dataset? (*Hint: It should not*) Examples of using refutation methods are in the `Refutations <https://github.com/microsoft/dowhy/blob/main/docs/source/example_notebooks/dowhy_refuter_notebook.ipynb>`_ notebook. For an advanced refutation that uses a simulated dataset based on user-provided or learnt data-generating processes, check out the `Dummy Outcome Refuter <https://github.com/microsoft/dowhy/blob/main/docs/source/example_notebooks/dowhy_demo_dummy_outcome_refuter.ipynb>`_ notebook. As a practical example, `this notebook <https://github.com/microsoft/dowhy/blob/main/docs/source/example_notebooks/dowhy_refutation_testing.ipynb>`_ shows an application of refutation methods on evaluating effect estimators for the Infant Health and Development Program (IHDP) and Lalonde datasets. Citing this package ==================== If you find DoWhy useful for your research work, please cite us as follows: Amit Sharma, Emre Kiciman, et al. DoWhy: A Python package for causal inference. 2019. https://github.com/microsoft/dowhy Bibtex:: @misc{dowhy, author={Sharma, Amit and Kiciman, Emre and others}, title={Do{W}hy: {A Python package for causal inference}}, howpublished={https://github.com/microsoft/dowhy}, year={2019} } Alternatively, you can cite our Arxiv paper on DoWhy. Amit Sharma, Emre Kiciman. DoWhy: An End-to-End Library for Causal Inference. 2020. https://arxiv.org/abs/2011.04216 Bibtex:: @article{dowhypaper, title={DoWhy: An End-to-End Library for Causal Inference}, author={Sharma, Amit and Kiciman, Emre}, journal={arXiv preprint arXiv:2011.04216}, year={2020} } And if you find the gcm package useful for your work, please also cite us as: Patrick Blöbaum, Peter Götz, Kailash Budhathoki, Atalanti A. Mastakouri, Dominik Janzing. DoWhy-GCM: An extension of DoWhy for causal inference in graphical causal models. 2022. https://arxiv.org/abs/2206.06821 Bibtex:: @article{dowhy_gcm, author = {Bl{\"o}baum, Patrick and G{\"o}tz, Peter and Budhathoki, Kailash and Mastakouri, Atalanti A. and Janzing, Dominik}, title = {DoWhy-GCM: An extension of DoWhy for causal inference in graphical causal models}, journal={arXiv preprint arXiv:2206.06821}, year={2022} } Roadmap ======= The `projects <https://github.com/microsoft/dowhy/projects>`_ page lists the next steps for DoWhy. If you would like to contribute, have a look at the current projects. If you have a specific request for DoWhy, please `raise an issue <https://github.com/microsoft/dowhy/issues>`_. Contributing ============ This project welcomes contributions and suggestions. For a guide to contributing and a list of all contributors, check out `CONTRIBUTING.md <https://github.com/microsoft/dowhy/blob/main/CONTRIBUTING.md>`_ and our `docs for contributing code <https://github.com/py-why/dowhy/blob/main/docs/source/contributing/contributing-code.rst>`_. Our `contributor code of conduct is available here <https://github.com/py-why/governance/blob/main/CODE-OF-CONDUCT.md>`_. You can also join the DoWhy development channel on Discord: |discord|_ .. |discord| image:: https://img.shields.io/discord/818456847551168542 .. _discord: https://discord.gg/cSBGb3vsZb

emrekiciman

c74b024a16ef0634422ffdda2c715031f46309bb

81fe5d9cbd998796f02d0d9f5b1d923ba0e85383

@emrekiciman There are `_`s missing after the ``>` ``s. rst syntax is a bit of a pain...

petergtz

py-why/dowhy

Update README.rst

Added direct link to https://github.com/py-why/dowhy/blob/main/docs/source/contributing/contributing-code.rst that has detailed instructions for code contribution steps Signed-off-by: emrekiciman <emrek@microsoft.com>

2022-09-17 01:02:37+00:00

2022-09-22 18:33:00+00:00

README.rst

|BuildStatus|_ |PyPiVersion|_ |PythonSupport|_ |Downloads|_ .. |PyPiVersion| image:: https://img.shields.io/pypi/v/dowhy.svg .. _PyPiVersion: https://pypi.org/project/dowhy/ .. |PythonSupport| image:: https://img.shields.io/pypi/pyversions/dowhy.svg .. _PythonSupport: https://pypi.org/project/dowhy/ .. |BuildStatus| image:: https://github.com/microsoft/dowhy/workflows/Python%20package/badge.svg .. _BuildStatus: https://github.com/microsoft/dowhy/actions .. |Downloads| image:: https://pepy.tech/badge/dowhy .. _Downloads: https://pepy.tech/project/dowhy DoWhy | An end-to-end library for causal inference =================================================== Introducing DoWhy and the 4 steps of causal inference | `Microsoft Research Blog <https://www.microsoft.com/en-us/research/blog/dowhy-a-library-for-causal-inference/>`_ | `Video Tutorial <https://note.microsoft.com/MSR-Webinar-DoWhy-Library-Registration-On-Demand.html>`_ | `Arxiv Paper <https://arxiv.org/abs/2011.04216>`_ | `Arxiv Paper (GCM-extension) <https://arxiv.org/abs/2206.06821>`_ | `Slides <https://www2.slideshare.net/AmitSharma315/dowhy-an-endtoend-library-for-causal-inference>`_ Read the `docs <https://py-why.github.io/dowhy/>`_ | Try it online! |Binder|_ .. |Binder| image:: https://mybinder.org/badge_logo.svg .. _Binder: https://mybinder.org/v2/gh/microsoft/dowhy/main?filepath=docs%2Fsource%2F **Case Studies using DoWhy**: `Hotel booking cancellations <https://towardsdatascience.com/beyond-predictive-models-the-causal-story-behind-hotel-booking-cancellations-d29e8558cbaf>`_ | `Effect of customer loyalty programs <https://github.com/microsoft/dowhy/blob/main/docs/source/example_notebooks/dowhy_example_effect_of_memberrewards_program.ipynb>`_ | `Optimizing article headlines <https://medium.com/@akelleh/introducing-the-do-sampler-for-causal-inference-a3296ea9e78d>`_ | `Effect of home visits on infant health (IHDP) <https://towardsdatascience.com/implementing-causal-inference-a-key-step-towards-agi-de2cde8ea599>`_ | `Causes of customer churn/attrition <https://medium.com/geekculture/a-quickstart-for-causal-analysis-decision-making-with-dowhy-2ce2d4d1efa9>`_ .. image:: https://raw.githubusercontent.com/microsoft/dowhy/main/docs/images/dowhy-schematic.png As computing systems are more frequently and more actively intervening in societally critical domains such as healthcare, education, and governance, it is critical to correctly predict and understand the causal effects of these interventions. Without an A/B test, conventional machine learning methods, built on pattern recognition and correlational analyses, are insufficient for decision-making. Much like machine learning libraries have done for prediction, **"DoWhy" is a Python library that aims to spark causal thinking and analysis**. DoWhy provides a principled four-step interface for causal inference that focuses on explicitly modeling causal assumptions and validating them as much as possible. The key feature of DoWhy is its state-of-the-art refutation API that can automatically test causal assumptions for any estimation method, thus making inference more robust and accessible to non-experts. DoWhy supports estimation of the average causal effect for backdoor, frontdoor, instrumental variable and other identification methods, and estimation of the conditional effect (CATE) through an integration with the EconML library. For a quick introduction to causal inference, check out `amit-sharma/causal-inference-tutorial <https://github.com/amit-sharma/causal-inference-tutorial/>`_. We also gave a more comprehensive tutorial at the ACM Knowledge Discovery and Data Mining (`KDD 2018 <http://www.kdd.org/kdd2018/>`_) conference: `causalinference.gitlab.io/kdd-tutorial <http://causalinference.gitlab.io/kdd-tutorial/>`_. For an introduction to the four steps of causal inference and its implications for machine learning, you can access this video tutorial from Microsoft Research: `DoWhy Webinar <https://note.microsoft.com/MSR-Webinar-DoWhy-Library-Registration-On-Demand.html>`_. Documentation for DoWhy is available at `py-why.github.io/dowhy <https://py-why.github.io/dowhy/>`_. .. i here comment toctree:: .. i here comment :maxdepth: 4 .. i here comment :caption: Contents: .. contents:: **Contents** News ----- **2022.05.27**: * **DoWhy now part of PyWhy** We have moved DoWhy from microsoft/dowhy to py-why/dowhy. While GitHub will automatically redirect your git command for cloning, pulling, etc., we recommend updating git remotes and bookmarks. Please note that the **documentation** has now moved to https://py-why.github.io/dowhy with **no** redirect from the old URL. * **Experimental support for GCM-based inference** We have started adding support for graphical causal model-based inference (or in short GCM-based). At the moment, this includes support for interventions, counterfactuals, and attributing distribution changes. As part of this, we also added features for Shapley value estimation and independence tests. We're still in the process of fleshing everything out, including `documentation <https://py-why.github.io/dowhy/main/user_guide/gcm_based_inference/index.html>`_. Some of it is already on `main <https://py-why.github.io/dowhy/main/user_guide/gcm_based_inference/index.html>`_, other parts are on feature branches (prefixed with ``gcm-``) with open pull-requests, other parts will appear as new pull-requests in the next couple of weeks. Be sure to watch this space here as we quickly expand functionality and documentation. The need for causal inference ---------------------------------- Predictive models uncover patterns that connect the inputs and outcome in observed data. To intervene, however, we need to estimate the effect of changing an input from its current value, for which no data exists. Such questions, involving estimating a *counterfactual*, are common in decision-making scenarios. * Will it work? * Does a proposed change to a system improve people's outcomes? * Why did it work? * What led to a change in a system's outcome? * What should we do? * What changes to a system are likely to improve outcomes for people? * What are the overall effects? * How does the system interact with human behavior? * What is the effect of a system's recommendations on people's activity? Answering these questions requires causal reasoning. While many methods exist for causal inference, it is hard to compare their assumptions and robustness of results. DoWhy makes three contributions, 1. Provides a principled way of modeling a given problem as a causal graph so that all assumptions are explicit. 2. Provides a unified interface for many popular causal inference methods, combining the two major frameworks of graphical models and potential outcomes. 3. Automatically tests for the validity of assumptions if possible and assesses the robustness of the estimate to violations. To see DoWhy in action, check out how it can be applied to estimate the effect of a subscription or rewards program for customers [`Rewards notebook <https://github.com/microsoft/dowhy/blob/main/docs/source/example_notebooks/dowhy_example_effect_of_memberrewards_program.ipynb>`_] and for implementing and evaluating causal inference methods on benchmark datasets like the `Infant Health and Development Program (IHDP) <https://github.com/microsoft/dowhy/blob/main/docs/source/example_notebooks/dowhy_ihdp_data_example.ipynb>`_ dataset, `Infant Mortality (Twins) <https://github.com/microsoft/dowhy/blob/main/docs/source/example_notebooks/dowhy_twins_example.ipynb>`_ dataset, and the `Lalonde Jobs <https://github.com/microsoft/dowhy/blob/main/docs/source/example_notebooks/dowhy_lalonde_example.ipynb>`_ dataset. Installation ------------- DoWhy support Python 3.6+. To install, you can use pip or conda. **Latest Release** Install the latest `release <https://pypi.org/project/dowhy/>`__ using pip. .. code:: shell pip install dowhy Install the latest `release <https://anaconda.org/conda-forge/dowhy>`__ using conda. .. code:: shell conda install -c conda-forge dowhy If you face "Solving environment" problems with conda, then try :code:`conda update --all` and then install dowhy. If that does not work, then use :code:`conda config --set channel_priority false` and try to install again. If the problem persists, please add your issue `here <https://github.com/microsoft/dowhy/issues/197>`_. **Development Version** If you prefer the latest dev version, clone this repository and run the following command from the top-most folder of the repository. .. code:: shell pip install -e . **Requirements** DoWhy requires the following packages: * numpy * scipy * scikit-learn * pandas * networkx (for analyzing causal graphs) * matplotlib (for general plotting) * sympy (for rendering symbolic expressions) If you face any problems, try installing dependencies manually. .. code:: shell pip install -r requirements.txt Optionally, if you wish to input graphs in the dot format, then install pydot (or pygraphviz). For better-looking graphs, you can optionally install pygraphviz. To proceed, first install graphviz and then pygraphviz (on Ubuntu and Ubuntu WSL). .. code:: shell sudo apt install graphviz libgraphviz-dev graphviz-dev pkg-config ## from https://github.com/pygraphviz/pygraphviz/issues/71 pip install pygraphviz --install-option="--include-path=/usr/include/graphviz" \ --install-option="--library-path=/usr/lib/graphviz/" Sample causal inference analysis in DoWhy ------------------------------------------- Most DoWhy analyses for causal inference take 4 lines to write, assuming a pandas dataframe df that contains the data: .. code:: python from dowhy import CausalModel import dowhy.datasets # Load some sample data data = dowhy.datasets.linear_dataset( beta=10, num_common_causes=5, num_instruments=2, num_samples=10000, treatment_is_binary=True) DoWhy supports two formats for providing the causal graph: `gml <https://github.com/GunterMueller/UNI_PASSAU_FMI_Graph_Drawing>`_ (preferred) and `dot <http://www.graphviz.org/documentation/>`_. After loading in the data, we use the four main operations in DoWhy: *model*, *estimate*, *identify* and *refute*: .. code:: python # I. Create a causal model from the data and given graph. model = CausalModel( data=data["df"], treatment=data["treatment_name"], outcome=data["outcome_name"], graph=data["gml_graph"]) # II. Identify causal effect and return target estimands identified_estimand = model.identify_effect() # III. Estimate the target estimand using a statistical method. estimate = model.estimate_effect(identified_estimand, method_name="backdoor.propensity_score_matching") # IV. Refute the obtained estimate using multiple robustness checks. refute_results = model.refute_estimate(identified_estimand, estimate, method_name="random_common_cause") DoWhy stresses on the interpretability of its output. At any point in the analysis, you can inspect the untested assumptions, identified estimands (if any) and the estimate (if any). Here's a sample output of the linear regression estimator. .. image:: https://raw.githubusercontent.com/microsoft/dowhy/main/docs/images/regression_output.png For a full code example, check out the `Getting Started with DoWhy <https://github.com/microsoft/dowhy/blob/main/docs/source/example_notebooks/dowhy_simple_example.ipynb>`_ notebook. You can also use Conditional Average Treatment Effect (CATE) estimation methods from other libraries such as EconML and CausalML, as shown in the `Conditional Treatment Effects <https://github.com/microsoft/dowhy/blob/main/docs/source/example_notebooks/dowhy-conditional-treatment-effects.ipynb>`_ notebook. For more examples of using DoWhy, check out the Jupyter notebooks in `docs/source/example_notebooks <https://github.com/microsoft/dowhy/tree/main/docs/source/example_notebooks/>`_ or try them online at `Binder <https://mybinder.org/v2/gh/microsoft/dowhy/main?filepath=docs%2Fsource%2F>`_. GCM-based inference (experimental) ---------------------------------- Graphical causal model-based inference, or GCM-based inference for short, is an experimental addition to DoWhy. For details, check out the `documentation for the gcm sub-package <https://py-why.github.io/dowhy/main/user_guide/gcm_based_inference/index.html>`_. The basic recipe for this API works as follows: .. code:: python # 1. Modeling cause-effect relationships as a structural causal model # (causal graph + functional causal models): scm = gcm.StructuralCausalModel(nx.DiGraph([('X', 'Y'), ('Y', 'Z')])) # X -> Y -> Z scm.set_causal_mechanism('X', gcm.EmpiricalDistribution()) scm.set_causal_mechanism('Y', gcm.AdditiveNoiseModel(gcm.ml.create_linear_regressor())) scm.set_causal_mechanism('Z', gcm.AdditiveNoiseModel(gcm.ml.create_linear_regressor())) # 2. Fitting the SCM to the data: gcm.fit(scm, data) # 3. Answering a causal query based on the SCM: results = gcm.<causal_query>(scm, ...) Where <causal_query> can be one of multiple functions explained in `Answering Causal Questions <https://py-why.github.io/dowhy/main/user_guide/gcm_based_inference/answering_causal_questions/index.html>`_. A high-level Pandas API ----------------------- We've made an even simpler API for dowhy which is a light layer on top of the standard one. The goal is to make causal analysis much more like regular exploratory analysis. To use this API, simply import :code:`dowhy.api`. This will magically add the :code:`causal` namespace to your :code:`pandas.DataFrame` s. Then, you can use the namespace as follows. .. code:: python import dowhy.api import dowhy.datasets data = dowhy.datasets.linear_dataset(beta=5, num_common_causes=1, num_instruments = 0, num_samples=1000, treatment_is_binary=True) # data['df'] is just a regular pandas.DataFrame data['df'].causal.do(x='v0', # name of treatment variable variable_types={'v0': 'b', 'y': 'c', 'W0': 'c'}, outcome='y', common_causes=['W0']).groupby('v0').mean().plot(y='y', kind='bar') .. image:: https://raw.githubusercontent.com/microsoft/dowhy/main/docs/images/do_barplot.png For some methods, the :code:`variable_types` field must be specified. It should be a :code:`dict`, where the keys are variable names, and values are 'o' for ordered discrete, 'u' for un-ordered discrete, 'd' for discrete, or 'c' for continuous. **Note:If the** :code:`variable_types` **is not specified we make use of the following implicit conversions:** :: int -> 'c' float -> 'c' binary -> 'b' category -> 'd' **Currently we have not added support for timestamps.** The :code:`do` method in the causal namespace generates a random sample from $P(outcome|do(X=x))$ of the same length as your data set, and returns this outcome as a new :code:`DataFrame`. You can continue to perform the usual :code:`DataFrame` operations with this sample, and so you can compute statistics and create plots for causal outcomes! The :code:`do` method is built on top of the lower-level :code:`dowhy` objects, so can still take a graph and perform identification automatically when you provide a graph instead of :code:`common_causes`. For more details, check out the `Pandas API <https://github.com/microsoft/dowhy/blob/main/docs/source/example_notebooks/dowhy_causal_api.ipynb>`_ notebook or the `Do Sampler <https://github.com/microsoft/dowhy/blob/main/docs/source/example_notebooks/do_sampler_demo.ipynb>`_ notebook. Graphical Models and Potential Outcomes: Best of both worlds ============================================================ DoWhy builds on two of the most powerful frameworks for causal inference: graphical models and potential outcomes. It uses graph-based criteria and do-calculus for modeling assumptions and identifying a non-parametric causal effect. For estimation, it switches to methods based primarily on potential outcomes. A unifying language for causal inference ---------------------------------------- DoWhy is based on a simple unifying language for causal inference. Causal inference may seem tricky, but almost all methods follow four key steps: 1. Model a causal inference problem using assumptions. 2. Identify an expression for the causal effect under these assumptions ("causal estimand"). 3. Estimate the expression using statistical methods such as matching or instrumental variables. 4. Finally, verify the validity of the estimate using a variety of robustness checks. This workflow can be captured by four key verbs in DoWhy: - model - identify - estimate - refute Using these verbs, DoWhy implements a causal inference engine that can support a variety of methods. *model* encodes prior knowledge as a formal causal graph, *identify* uses graph-based methods to identify the causal effect, *estimate* uses statistical methods for estimating the identified estimand, and finally *refute* tries to refute the obtained estimate by testing robustness to assumptions. Key differences compared to available causal inference software ---------------------------------------------------------------- DoWhy brings three key differences compared to available software for causal inference: **Explicit identifying assumptions** Assumptions are first-class citizens in DoWhy. Each analysis starts with a building a causal model. The assumptions can be viewed graphically or in terms of conditional independence statements. Wherever possible, DoWhy can also automatically test for stated assumptions using observed data. **Separation between identification and estimation** Identification is the causal problem. Estimation is simply a statistical problem. DoWhy respects this boundary and treats them separately. This focuses the causal inference effort on identification, and frees up estimation using any available statistical estimator for a target estimand. In addition, multiple estimation methods can be used for a single identified_estimand and vice-versa. **Automated robustness checks** What happens when key identifying assumptions may not be satisfied? The most critical, and often skipped, part of causal analysis is checking the robustness of an estimate to unverified assumptions. DoWhy makes it easy to automatically run sensitivity and robustness checks on the obtained estimate. Finally, DoWhy is easily extensible, allowing other implementations of the four verbs to co-exist (e.g., we support implementations of the *estimation* verb from EconML and CausalML libraries). The four verbs are mutually independent, so their implementations can be combined in any way. Below are more details about the current implementation of each of these verbs. Four steps of causal inference =============================== I. Model a causal problem ----------------------------- DoWhy creates an underlying causal graphical model for each problem. This serves to make each causal assumption explicit. This graph need not be complete---you can provide a partial graph, representing prior knowledge about some of the variables. DoWhy automatically considers the rest of the variables as potential confounders. Currently, DoWhy supports two formats for graph input: `gml <https://github.com/GunterMueller/UNI_PASSAU_FMI_Graph_Drawing>`_ (preferred) and `dot <http://www.graphviz.org/documentation/>`_. We strongly suggest to use gml as the input format, as it works well with networkx. You can provide the graph either as a .gml file or as a string. If you prefer to use dot format, you will need to install additional packages (pydot or pygraphviz, see the installation section above). Both .dot files and string format are supported. While not recommended, you can also specify common causes and/or instruments directly instead of providing a graph. Supported formats for specifying causal assumptions ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ * **Graph**: Provide a causal graph in either gml or dot format. Can be a text file or a string. * **Named variable sets**: Instead of the graph, provide variable names that correspond to relevant categories, such as common causes, instrumental variables, effect modifiers, frontdoor variables, etc. Examples of how to instantiate a causal model are in the `Getting Started <https://github.com/microsoft/dowhy/blob/main/docs/source/example_notebooks/dowhy_simple_example.ipynb>`_ notebook. .. i comment image:: causal_model.png II. Identify a target estimand under the model ---------------------------------------------- Based on the causal graph, DoWhy finds all possible ways of identifying a desired causal effect based on the graphical model. It uses graph-based criteria and do-calculus to find potential ways find expressions that can identify the causal effect. Supported identification criteria ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ * Back-door criterion * Front-door criterion * Instrumental Variables * Mediation (Direct and indirect effect identification) Different notebooks illustrate how to use these identification criteria. Check out the `Simple Backdoor <https://github.com/microsoft/dowhy/blob/main/docs/source/example_notebooks/dowhy_confounder_example.ipynb>`_ notebook for the back-door criterion, and the `Simple IV <https://github.com/microsoft/dowhy/blob/main/docs/source/example_notebooks/dowhy-simple-iv-example.ipynb>`_ notebook for the instrumental variable criterion. III. Estimate causal effect based on the identified estimand ------------------------------------------------------------ DoWhy supports methods based on both back-door criterion and instrumental variables. It also provides a non-parametric confidence intervals and a permutation test for testing the statistical significance of obtained estimate. Supported estimation methods ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ * Methods based on estimating the treatment assignment * Propensity-based Stratification * Propensity Score Matching * Inverse Propensity Weighting * Methods based on estimating the outcome model * Linear Regression * Generalized Linear Models * Methods based on the instrumental variable equation * Binary Instrument/Wald Estimator * Two-stage least squares * Regression discontinuity * Methods for front-door criterion and general mediation * Two-stage linear regression Examples of using these methods are in the `Estimation methods <https://github.com/microsoft/dowhy/blob/main/docs/source/example_notebooks/dowhy_estimation_methods.ipynb>`_ notebook. Using EconML and CausalML estimation methods in DoWhy ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ It is easy to call external estimation methods using DoWhy. Currently we support integrations with the `EconML <https://github.com/microsoft/econml>`_ and `CausalML <https://github.com/uber/causalml>`_ packages. Here's an example of estimating conditional treatment effects using EconML's double machine learning estimator. .. code:: python from sklearn.preprocessing import PolynomialFeatures from sklearn.linear_model import LassoCV from sklearn.ensemble import GradientBoostingRegressor dml_estimate = model.estimate_effect(identified_estimand, method_name="backdoor.econml.dml.DML", control_value = 0, treatment_value = 1, target_units = lambda df: df["X0"]>1, confidence_intervals=False, method_params={ "init_params":{'model_y':GradientBoostingRegressor(), 'model_t': GradientBoostingRegressor(), 'model_final':LassoCV(), 'featurizer':PolynomialFeatures(degree=1, include_bias=True)}, "fit_params":{}} ) More examples are in the `Conditional Treatment Effects with DoWhy <https://github.com/microsoft/dowhy/blob/main/docs/source/example_notebooks/dowhy-conditional-treatment-effects.ipynb>`_ notebook. IV. Refute the obtained estimate ------------------------------------- Having access to multiple refutation methods to validate an effect estimate from a causal estimator is a key benefit of using DoWhy. Supported refutation methods ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ * **Add Random Common Cause**: Does the estimation method change its estimate after we add an independent random variable as a common cause to the dataset? (*Hint: It should not*) * **Placebo Treatment**: What happens to the estimated causal effect when we replace the true treatment variable with an independent random variable? (*Hint: the effect should go to zero*) * **Dummy Outcome**: What happens to the estimated causal effect when we replace the true outcome variable with an independent random variable? (*Hint: The effect should go to zero*) * **Simulated Outcome**: What happens to the estimated causal effect when we replace the dataset with a simulated dataset based on a known data-generating process closest to the given dataset? (*Hint: It should match the effect parameter from the data-generating process*) * **Add Unobserved Common Causes**: How sensitive is the effect estimate when we add an additional common cause (confounder) to the dataset that is correlated with the treatment and the outcome? (*Hint: It should not be too sensitive*) * **Data Subsets Validation**: Does the estimated effect change significantly when we replace the given dataset with a randomly selected subset? (*Hint: It should not*) * **Bootstrap Validation**: Does the estimated effect change significantly when we replace the given dataset with bootstrapped samples from the same dataset? (*Hint: It should not*) Examples of using refutation methods are in the `Refutations <https://github.com/microsoft/dowhy/blob/main/docs/source/example_notebooks/dowhy_refuter_notebook.ipynb>`_ notebook. For an advanced refutation that uses a simulated dataset based on user-provided or learnt data-generating processes, check out the `Dummy Outcome Refuter <https://github.com/microsoft/dowhy/blob/main/docs/source/example_notebooks/dowhy_demo_dummy_outcome_refuter.ipynb>`_ notebook. As a practical example, `this notebook <https://github.com/microsoft/dowhy/blob/main/docs/source/example_notebooks/dowhy_refutation_testing.ipynb>`_ shows an application of refutation methods on evaluating effect estimators for the Infant Health and Development Program (IHDP) and Lalonde datasets. Citing this package ==================== If you find DoWhy useful for your research work, please cite us as follows: Amit Sharma, Emre Kiciman, et al. DoWhy: A Python package for causal inference. 2019. https://github.com/microsoft/dowhy Bibtex:: @misc{dowhy, author={Sharma, Amit and Kiciman, Emre and others}, title={Do{W}hy: {A Python package for causal inference}}, howpublished={https://github.com/microsoft/dowhy}, year={2019} } Alternatively, you can cite our Arxiv paper on DoWhy. Amit Sharma, Emre Kiciman. DoWhy: An End-to-End Library for Causal Inference. 2020. https://arxiv.org/abs/2011.04216 Bibtex:: @article{dowhypaper, title={DoWhy: An End-to-End Library for Causal Inference}, author={Sharma, Amit and Kiciman, Emre}, journal={arXiv preprint arXiv:2011.04216}, year={2020} } And if you find the gcm package useful for your work, please also cite us as: Patrick Blöbaum, Peter Götz, Kailash Budhathoki, Atalanti A. Mastakouri, Dominik Janzing. DoWhy-GCM: An extension of DoWhy for causal inference in graphical causal models. 2022. https://arxiv.org/abs/2206.06821 Bibtex:: @article{dowhy_gcm, author = {Bl{\"o}baum, Patrick and G{\"o}tz, Peter and Budhathoki, Kailash and Mastakouri, Atalanti A. and Janzing, Dominik}, title = {DoWhy-GCM: An extension of DoWhy for causal inference in graphical causal models}, journal={arXiv preprint arXiv:2206.06821}, year={2022} } Roadmap ======= The `projects <https://github.com/microsoft/dowhy/projects>`_ page lists the next steps for DoWhy. If you would like to contribute, have a look at the current projects. If you have a specific request for DoWhy, please `raise an issue <https://github.com/microsoft/dowhy/issues>`_. Contributing ============ This project welcomes contributions and suggestions. For a guide to contributing and a list of all contributors, check out `CONTRIBUTING.md <https://github.com/microsoft/dowhy/blob/main/CONTRIBUTING.md>`_. Our contributor code of conduct is available [here](https://github.com/py-why/governance/blob/main/CODE-OF-CONDUCT.md). You can also join the DoWhy development channel on Discord: |discord|_ .. |discord| image:: https://img.shields.io/discord/818456847551168542 .. _discord: https://discord.gg/cSBGb3vsZb

|BuildStatus|_ |PyPiVersion|_ |PythonSupport|_ |Downloads|_ .. |PyPiVersion| image:: https://img.shields.io/pypi/v/dowhy.svg .. _PyPiVersion: https://pypi.org/project/dowhy/ .. |PythonSupport| image:: https://img.shields.io/pypi/pyversions/dowhy.svg .. _PythonSupport: https://pypi.org/project/dowhy/ .. |BuildStatus| image:: https://github.com/microsoft/dowhy/workflows/Python%20package/badge.svg .. _BuildStatus: https://github.com/microsoft/dowhy/actions .. |Downloads| image:: https://pepy.tech/badge/dowhy .. _Downloads: https://pepy.tech/project/dowhy DoWhy | An end-to-end library for causal inference =================================================== Introducing DoWhy and the 4 steps of causal inference | `Microsoft Research Blog <https://www.microsoft.com/en-us/research/blog/dowhy-a-library-for-causal-inference/>`_ | `Video Tutorial <https://note.microsoft.com/MSR-Webinar-DoWhy-Library-Registration-On-Demand.html>`_ | `Arxiv Paper <https://arxiv.org/abs/2011.04216>`_ | `Arxiv Paper (GCM-extension) <https://arxiv.org/abs/2206.06821>`_ | `Slides <https://www2.slideshare.net/AmitSharma315/dowhy-an-endtoend-library-for-causal-inference>`_ Read the `docs <https://py-why.github.io/dowhy/>`_ | Try it online! |Binder|_ .. |Binder| image:: https://mybinder.org/badge_logo.svg .. _Binder: https://mybinder.org/v2/gh/microsoft/dowhy/main?filepath=docs%2Fsource%2F **Case Studies using DoWhy**: `Hotel booking cancellations <https://towardsdatascience.com/beyond-predictive-models-the-causal-story-behind-hotel-booking-cancellations-d29e8558cbaf>`_ | `Effect of customer loyalty programs <https://github.com/microsoft/dowhy/blob/main/docs/source/example_notebooks/dowhy_example_effect_of_memberrewards_program.ipynb>`_ | `Optimizing article headlines <https://medium.com/@akelleh/introducing-the-do-sampler-for-causal-inference-a3296ea9e78d>`_ | `Effect of home visits on infant health (IHDP) <https://towardsdatascience.com/implementing-causal-inference-a-key-step-towards-agi-de2cde8ea599>`_ | `Causes of customer churn/attrition <https://medium.com/geekculture/a-quickstart-for-causal-analysis-decision-making-with-dowhy-2ce2d4d1efa9>`_ .. image:: https://raw.githubusercontent.com/microsoft/dowhy/main/docs/images/dowhy-schematic.png As computing systems are more frequently and more actively intervening in societally critical domains such as healthcare, education, and governance, it is critical to correctly predict and understand the causal effects of these interventions. Without an A/B test, conventional machine learning methods, built on pattern recognition and correlational analyses, are insufficient for decision-making. Much like machine learning libraries have done for prediction, **"DoWhy" is a Python library that aims to spark causal thinking and analysis**. DoWhy provides a principled four-step interface for causal inference that focuses on explicitly modeling causal assumptions and validating them as much as possible. The key feature of DoWhy is its state-of-the-art refutation API that can automatically test causal assumptions for any estimation method, thus making inference more robust and accessible to non-experts. DoWhy supports estimation of the average causal effect for backdoor, frontdoor, instrumental variable and other identification methods, and estimation of the conditional effect (CATE) through an integration with the EconML library. For a quick introduction to causal inference, check out `amit-sharma/causal-inference-tutorial <https://github.com/amit-sharma/causal-inference-tutorial/>`_. We also gave a more comprehensive tutorial at the ACM Knowledge Discovery and Data Mining (`KDD 2018 <http://www.kdd.org/kdd2018/>`_) conference: `causalinference.gitlab.io/kdd-tutorial <http://causalinference.gitlab.io/kdd-tutorial/>`_. For an introduction to the four steps of causal inference and its implications for machine learning, you can access this video tutorial from Microsoft Research: `DoWhy Webinar <https://note.microsoft.com/MSR-Webinar-DoWhy-Library-Registration-On-Demand.html>`_. Documentation for DoWhy is available at `py-why.github.io/dowhy <https://py-why.github.io/dowhy/>`_. .. i here comment toctree:: .. i here comment :maxdepth: 4 .. i here comment :caption: Contents: .. contents:: **Contents** News ----- **2022.05.27**: * **DoWhy now part of PyWhy** We have moved DoWhy from microsoft/dowhy to py-why/dowhy. While GitHub will automatically redirect your git command for cloning, pulling, etc., we recommend updating git remotes and bookmarks. Please note that the **documentation** has now moved to https://py-why.github.io/dowhy with **no** redirect from the old URL. * **Experimental support for GCM-based inference** We have started adding support for graphical causal model-based inference (or in short GCM-based). At the moment, this includes support for interventions, counterfactuals, and attributing distribution changes. As part of this, we also added features for Shapley value estimation and independence tests. We're still in the process of fleshing everything out, including `documentation <https://py-why.github.io/dowhy/main/user_guide/gcm_based_inference/index.html>`_. Some of it is already on `main <https://py-why.github.io/dowhy/main/user_guide/gcm_based_inference/index.html>`_, other parts are on feature branches (prefixed with ``gcm-``) with open pull-requests, other parts will appear as new pull-requests in the next couple of weeks. Be sure to watch this space here as we quickly expand functionality and documentation. The need for causal inference ---------------------------------- Predictive models uncover patterns that connect the inputs and outcome in observed data. To intervene, however, we need to estimate the effect of changing an input from its current value, for which no data exists. Such questions, involving estimating a *counterfactual*, are common in decision-making scenarios. * Will it work? * Does a proposed change to a system improve people's outcomes? * Why did it work? * What led to a change in a system's outcome? * What should we do? * What changes to a system are likely to improve outcomes for people? * What are the overall effects? * How does the system interact with human behavior? * What is the effect of a system's recommendations on people's activity? Answering these questions requires causal reasoning. While many methods exist for causal inference, it is hard to compare their assumptions and robustness of results. DoWhy makes three contributions, 1. Provides a principled way of modeling a given problem as a causal graph so that all assumptions are explicit. 2. Provides a unified interface for many popular causal inference methods, combining the two major frameworks of graphical models and potential outcomes. 3. Automatically tests for the validity of assumptions if possible and assesses the robustness of the estimate to violations. To see DoWhy in action, check out how it can be applied to estimate the effect of a subscription or rewards program for customers [`Rewards notebook <https://github.com/microsoft/dowhy/blob/main/docs/source/example_notebooks/dowhy_example_effect_of_memberrewards_program.ipynb>`_] and for implementing and evaluating causal inference methods on benchmark datasets like the `Infant Health and Development Program (IHDP) <https://github.com/microsoft/dowhy/blob/main/docs/source/example_notebooks/dowhy_ihdp_data_example.ipynb>`_ dataset, `Infant Mortality (Twins) <https://github.com/microsoft/dowhy/blob/main/docs/source/example_notebooks/dowhy_twins_example.ipynb>`_ dataset, and the `Lalonde Jobs <https://github.com/microsoft/dowhy/blob/main/docs/source/example_notebooks/dowhy_lalonde_example.ipynb>`_ dataset. Installation ------------- DoWhy support Python 3.6+. To install, you can use pip or conda. **Latest Release** Install the latest `release <https://pypi.org/project/dowhy/>`__ using pip. .. code:: shell pip install dowhy Install the latest `release <https://anaconda.org/conda-forge/dowhy>`__ using conda. .. code:: shell conda install -c conda-forge dowhy If you face "Solving environment" problems with conda, then try :code:`conda update --all` and then install dowhy. If that does not work, then use :code:`conda config --set channel_priority false` and try to install again. If the problem persists, please `add your issue here <https://github.com/microsoft/dowhy/issues/197>`_. **Development Version** If you prefer the latest dev version, clone this repository and run the following command from the top-most folder of the repository. .. code:: shell pip install -e . **Requirements** DoWhy requires the following packages: * numpy * scipy * scikit-learn * pandas * networkx (for analyzing causal graphs) * matplotlib (for general plotting) * sympy (for rendering symbolic expressions) If you face any problems, try installing dependencies manually. .. code:: shell pip install -r requirements.txt Optionally, if you wish to input graphs in the dot format, then install pydot (or pygraphviz). For better-looking graphs, you can optionally install pygraphviz. To proceed, first install graphviz and then pygraphviz (on Ubuntu and Ubuntu WSL). .. code:: shell sudo apt install graphviz libgraphviz-dev graphviz-dev pkg-config ## from https://github.com/pygraphviz/pygraphviz/issues/71 pip install pygraphviz --install-option="--include-path=/usr/include/graphviz" \ --install-option="--library-path=/usr/lib/graphviz/" Sample causal inference analysis in DoWhy ------------------------------------------- Most DoWhy analyses for causal inference take 4 lines to write, assuming a pandas dataframe df that contains the data: .. code:: python from dowhy import CausalModel import dowhy.datasets # Load some sample data data = dowhy.datasets.linear_dataset( beta=10, num_common_causes=5, num_instruments=2, num_samples=10000, treatment_is_binary=True) DoWhy supports two formats for providing the causal graph: `gml <https://github.com/GunterMueller/UNI_PASSAU_FMI_Graph_Drawing>`_ (preferred) and `dot <http://www.graphviz.org/documentation/>`_. After loading in the data, we use the four main operations in DoWhy: *model*, *estimate*, *identify* and *refute*: .. code:: python # I. Create a causal model from the data and given graph. model = CausalModel( data=data["df"], treatment=data["treatment_name"], outcome=data["outcome_name"], graph=data["gml_graph"]) # II. Identify causal effect and return target estimands identified_estimand = model.identify_effect() # III. Estimate the target estimand using a statistical method. estimate = model.estimate_effect(identified_estimand, method_name="backdoor.propensity_score_matching") # IV. Refute the obtained estimate using multiple robustness checks. refute_results = model.refute_estimate(identified_estimand, estimate, method_name="random_common_cause") DoWhy stresses on the interpretability of its output. At any point in the analysis, you can inspect the untested assumptions, identified estimands (if any) and the estimate (if any). Here's a sample output of the linear regression estimator. .. image:: https://raw.githubusercontent.com/microsoft/dowhy/main/docs/images/regression_output.png For a full code example, check out the `Getting Started with DoWhy <https://github.com/microsoft/dowhy/blob/main/docs/source/example_notebooks/dowhy_simple_example.ipynb>`_ notebook. You can also use Conditional Average Treatment Effect (CATE) estimation methods from other libraries such as EconML and CausalML, as shown in the `Conditional Treatment Effects <https://github.com/microsoft/dowhy/blob/main/docs/source/example_notebooks/dowhy-conditional-treatment-effects.ipynb>`_ notebook. For more examples of using DoWhy, check out the Jupyter notebooks in `docs/source/example_notebooks <https://github.com/microsoft/dowhy/tree/main/docs/source/example_notebooks/>`_ or try them online at `Binder <https://mybinder.org/v2/gh/microsoft/dowhy/main?filepath=docs%2Fsource%2F>`_. GCM-based inference (experimental) ---------------------------------- Graphical causal model-based inference, or GCM-based inference for short, is an experimental addition to DoWhy. For details, check out the `documentation for the gcm sub-package <https://py-why.github.io/dowhy/main/user_guide/gcm_based_inference/index.html>`_. The basic recipe for this API works as follows: .. code:: python # 1. Modeling cause-effect relationships as a structural causal model # (causal graph + functional causal models): scm = gcm.StructuralCausalModel(nx.DiGraph([('X', 'Y'), ('Y', 'Z')])) # X -> Y -> Z scm.set_causal_mechanism('X', gcm.EmpiricalDistribution()) scm.set_causal_mechanism('Y', gcm.AdditiveNoiseModel(gcm.ml.create_linear_regressor())) scm.set_causal_mechanism('Z', gcm.AdditiveNoiseModel(gcm.ml.create_linear_regressor())) # 2. Fitting the SCM to the data: gcm.fit(scm, data) # 3. Answering a causal query based on the SCM: results = gcm.<causal_query>(scm, ...) Where <causal_query> can be one of multiple functions explained in `Answering Causal Questions <https://py-why.github.io/dowhy/main/user_guide/gcm_based_inference/answering_causal_questions/index.html>`_. A high-level Pandas API ----------------------- We've made an even simpler API for dowhy which is a light layer on top of the standard one. The goal is to make causal analysis much more like regular exploratory analysis. To use this API, simply import :code:`dowhy.api`. This will magically add the :code:`causal` namespace to your :code:`pandas.DataFrame` s. Then, you can use the namespace as follows. .. code:: python import dowhy.api import dowhy.datasets data = dowhy.datasets.linear_dataset(beta=5, num_common_causes=1, num_instruments = 0, num_samples=1000, treatment_is_binary=True) # data['df'] is just a regular pandas.DataFrame data['df'].causal.do(x='v0', # name of treatment variable variable_types={'v0': 'b', 'y': 'c', 'W0': 'c'}, outcome='y', common_causes=['W0']).groupby('v0').mean().plot(y='y', kind='bar') .. image:: https://raw.githubusercontent.com/microsoft/dowhy/main/docs/images/do_barplot.png For some methods, the :code:`variable_types` field must be specified. It should be a :code:`dict`, where the keys are variable names, and values are 'o' for ordered discrete, 'u' for un-ordered discrete, 'd' for discrete, or 'c' for continuous. **Note:If the** :code:`variable_types` **is not specified we make use of the following implicit conversions:** :: int -> 'c' float -> 'c' binary -> 'b' category -> 'd' **Currently we have not added support for timestamps.** The :code:`do` method in the causal namespace generates a random sample from $P(outcome|do(X=x))$ of the same length as your data set, and returns this outcome as a new :code:`DataFrame`. You can continue to perform the usual :code:`DataFrame` operations with this sample, and so you can compute statistics and create plots for causal outcomes! The :code:`do` method is built on top of the lower-level :code:`dowhy` objects, so can still take a graph and perform identification automatically when you provide a graph instead of :code:`common_causes`. For more details, check out the `Pandas API <https://github.com/microsoft/dowhy/blob/main/docs/source/example_notebooks/dowhy_causal_api.ipynb>`_ notebook or the `Do Sampler <https://github.com/microsoft/dowhy/blob/main/docs/source/example_notebooks/do_sampler_demo.ipynb>`_ notebook. Graphical Models and Potential Outcomes: Best of both worlds ============================================================ DoWhy builds on two of the most powerful frameworks for causal inference: graphical models and potential outcomes. It uses graph-based criteria and do-calculus for modeling assumptions and identifying a non-parametric causal effect. For estimation, it switches to methods based primarily on potential outcomes. A unifying language for causal inference ---------------------------------------- DoWhy is based on a simple unifying language for causal inference. Causal inference may seem tricky, but almost all methods follow four key steps: 1. Model a causal inference problem using assumptions. 2. Identify an expression for the causal effect under these assumptions ("causal estimand"). 3. Estimate the expression using statistical methods such as matching or instrumental variables. 4. Finally, verify the validity of the estimate using a variety of robustness checks. This workflow can be captured by four key verbs in DoWhy: - model - identify - estimate - refute Using these verbs, DoWhy implements a causal inference engine that can support a variety of methods. *model* encodes prior knowledge as a formal causal graph, *identify* uses graph-based methods to identify the causal effect, *estimate* uses statistical methods for estimating the identified estimand, and finally *refute* tries to refute the obtained estimate by testing robustness to assumptions. Key differences compared to available causal inference software ---------------------------------------------------------------- DoWhy brings three key differences compared to available software for causal inference: **Explicit identifying assumptions** Assumptions are first-class citizens in DoWhy. Each analysis starts with a building a causal model. The assumptions can be viewed graphically or in terms of conditional independence statements. Wherever possible, DoWhy can also automatically test for stated assumptions using observed data. **Separation between identification and estimation** Identification is the causal problem. Estimation is simply a statistical problem. DoWhy respects this boundary and treats them separately. This focuses the causal inference effort on identification, and frees up estimation using any available statistical estimator for a target estimand. In addition, multiple estimation methods can be used for a single identified_estimand and vice-versa. **Automated robustness checks** What happens when key identifying assumptions may not be satisfied? The most critical, and often skipped, part of causal analysis is checking the robustness of an estimate to unverified assumptions. DoWhy makes it easy to automatically run sensitivity and robustness checks on the obtained estimate. Finally, DoWhy is easily extensible, allowing other implementations of the four verbs to co-exist (e.g., we support implementations of the *estimation* verb from EconML and CausalML libraries). The four verbs are mutually independent, so their implementations can be combined in any way. Below are more details about the current implementation of each of these verbs. Four steps of causal inference =============================== I. Model a causal problem ----------------------------- DoWhy creates an underlying causal graphical model for each problem. This serves to make each causal assumption explicit. This graph need not be complete---you can provide a partial graph, representing prior knowledge about some of the variables. DoWhy automatically considers the rest of the variables as potential confounders. Currently, DoWhy supports two formats for graph input: `gml <https://github.com/GunterMueller/UNI_PASSAU_FMI_Graph_Drawing>`_ (preferred) and `dot <http://www.graphviz.org/documentation/>`_. We strongly suggest to use gml as the input format, as it works well with networkx. You can provide the graph either as a .gml file or as a string. If you prefer to use dot format, you will need to install additional packages (pydot or pygraphviz, see the installation section above). Both .dot files and string format are supported. While not recommended, you can also specify common causes and/or instruments directly instead of providing a graph. Supported formats for specifying causal assumptions ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ * **Graph**: Provide a causal graph in either gml or dot format. Can be a text file or a string. * **Named variable sets**: Instead of the graph, provide variable names that correspond to relevant categories, such as common causes, instrumental variables, effect modifiers, frontdoor variables, etc. Examples of how to instantiate a causal model are in the `Getting Started <https://github.com/microsoft/dowhy/blob/main/docs/source/example_notebooks/dowhy_simple_example.ipynb>`_ notebook. .. i comment image:: causal_model.png II. Identify a target estimand under the model ---------------------------------------------- Based on the causal graph, DoWhy finds all possible ways of identifying a desired causal effect based on the graphical model. It uses graph-based criteria and do-calculus to find potential ways find expressions that can identify the causal effect. Supported identification criteria ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ * Back-door criterion * Front-door criterion * Instrumental Variables * Mediation (Direct and indirect effect identification) Different notebooks illustrate how to use these identification criteria. Check out the `Simple Backdoor <https://github.com/microsoft/dowhy/blob/main/docs/source/example_notebooks/dowhy_confounder_example.ipynb>`_ notebook for the back-door criterion, and the `Simple IV <https://github.com/microsoft/dowhy/blob/main/docs/source/example_notebooks/dowhy-simple-iv-example.ipynb>`_ notebook for the instrumental variable criterion. III. Estimate causal effect based on the identified estimand ------------------------------------------------------------ DoWhy supports methods based on both back-door criterion and instrumental variables. It also provides a non-parametric confidence intervals and a permutation test for testing the statistical significance of obtained estimate. Supported estimation methods ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ * Methods based on estimating the treatment assignment * Propensity-based Stratification * Propensity Score Matching * Inverse Propensity Weighting * Methods based on estimating the outcome model * Linear Regression * Generalized Linear Models * Methods based on the instrumental variable equation * Binary Instrument/Wald Estimator * Two-stage least squares * Regression discontinuity * Methods for front-door criterion and general mediation * Two-stage linear regression Examples of using these methods are in the `Estimation methods <https://github.com/microsoft/dowhy/blob/main/docs/source/example_notebooks/dowhy_estimation_methods.ipynb>`_ notebook. Using EconML and CausalML estimation methods in DoWhy ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ It is easy to call external estimation methods using DoWhy. Currently we support integrations with the `EconML <https://github.com/microsoft/econml>`_ and `CausalML <https://github.com/uber/causalml>`_ packages. Here's an example of estimating conditional treatment effects using EconML's double machine learning estimator. .. code:: python from sklearn.preprocessing import PolynomialFeatures from sklearn.linear_model import LassoCV from sklearn.ensemble import GradientBoostingRegressor dml_estimate = model.estimate_effect(identified_estimand, method_name="backdoor.econml.dml.DML", control_value = 0, treatment_value = 1, target_units = lambda df: df["X0"]>1, confidence_intervals=False, method_params={ "init_params":{'model_y':GradientBoostingRegressor(), 'model_t': GradientBoostingRegressor(), 'model_final':LassoCV(), 'featurizer':PolynomialFeatures(degree=1, include_bias=True)}, "fit_params":{}} ) More examples are in the `Conditional Treatment Effects with DoWhy <https://github.com/microsoft/dowhy/blob/main/docs/source/example_notebooks/dowhy-conditional-treatment-effects.ipynb>`_ notebook. IV. Refute the obtained estimate ------------------------------------- Having access to multiple refutation methods to validate an effect estimate from a causal estimator is a key benefit of using DoWhy. Supported refutation methods ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ * **Add Random Common Cause**: Does the estimation method change its estimate after we add an independent random variable as a common cause to the dataset? (*Hint: It should not*) * **Placebo Treatment**: What happens to the estimated causal effect when we replace the true treatment variable with an independent random variable? (*Hint: the effect should go to zero*) * **Dummy Outcome**: What happens to the estimated causal effect when we replace the true outcome variable with an independent random variable? (*Hint: The effect should go to zero*) * **Simulated Outcome**: What happens to the estimated causal effect when we replace the dataset with a simulated dataset based on a known data-generating process closest to the given dataset? (*Hint: It should match the effect parameter from the data-generating process*) * **Add Unobserved Common Causes**: How sensitive is the effect estimate when we add an additional common cause (confounder) to the dataset that is correlated with the treatment and the outcome? (*Hint: It should not be too sensitive*) * **Data Subsets Validation**: Does the estimated effect change significantly when we replace the given dataset with a randomly selected subset? (*Hint: It should not*) * **Bootstrap Validation**: Does the estimated effect change significantly when we replace the given dataset with bootstrapped samples from the same dataset? (*Hint: It should not*) Examples of using refutation methods are in the `Refutations <https://github.com/microsoft/dowhy/blob/main/docs/source/example_notebooks/dowhy_refuter_notebook.ipynb>`_ notebook. For an advanced refutation that uses a simulated dataset based on user-provided or learnt data-generating processes, check out the `Dummy Outcome Refuter <https://github.com/microsoft/dowhy/blob/main/docs/source/example_notebooks/dowhy_demo_dummy_outcome_refuter.ipynb>`_ notebook. As a practical example, `this notebook <https://github.com/microsoft/dowhy/blob/main/docs/source/example_notebooks/dowhy_refutation_testing.ipynb>`_ shows an application of refutation methods on evaluating effect estimators for the Infant Health and Development Program (IHDP) and Lalonde datasets. Citing this package ==================== If you find DoWhy useful for your research work, please cite us as follows: Amit Sharma, Emre Kiciman, et al. DoWhy: A Python package for causal inference. 2019. https://github.com/microsoft/dowhy Bibtex:: @misc{dowhy, author={Sharma, Amit and Kiciman, Emre and others}, title={Do{W}hy: {A Python package for causal inference}}, howpublished={https://github.com/microsoft/dowhy}, year={2019} } Alternatively, you can cite our Arxiv paper on DoWhy. Amit Sharma, Emre Kiciman. DoWhy: An End-to-End Library for Causal Inference. 2020. https://arxiv.org/abs/2011.04216 Bibtex:: @article{dowhypaper, title={DoWhy: An End-to-End Library for Causal Inference}, author={Sharma, Amit and Kiciman, Emre}, journal={arXiv preprint arXiv:2011.04216}, year={2020} } And if you find the gcm package useful for your work, please also cite us as: Patrick Blöbaum, Peter Götz, Kailash Budhathoki, Atalanti A. Mastakouri, Dominik Janzing. DoWhy-GCM: An extension of DoWhy for causal inference in graphical causal models. 2022. https://arxiv.org/abs/2206.06821 Bibtex:: @article{dowhy_gcm, author = {Bl{\"o}baum, Patrick and G{\"o}tz, Peter and Budhathoki, Kailash and Mastakouri, Atalanti A. and Janzing, Dominik}, title = {DoWhy-GCM: An extension of DoWhy for causal inference in graphical causal models}, journal={arXiv preprint arXiv:2206.06821}, year={2022} } Roadmap ======= The `projects <https://github.com/microsoft/dowhy/projects>`_ page lists the next steps for DoWhy. If you would like to contribute, have a look at the current projects. If you have a specific request for DoWhy, please `raise an issue <https://github.com/microsoft/dowhy/issues>`_. Contributing ============ This project welcomes contributions and suggestions. For a guide to contributing and a list of all contributors, check out `CONTRIBUTING.md <https://github.com/microsoft/dowhy/blob/main/CONTRIBUTING.md>`_ and our `docs for contributing code <https://github.com/py-why/dowhy/blob/main/docs/source/contributing/contributing-code.rst>`_. Our `contributor code of conduct is available here <https://github.com/py-why/governance/blob/main/CODE-OF-CONDUCT.md>`_. You can also join the DoWhy development channel on Discord: |discord|_ .. |discord| image:: https://img.shields.io/discord/818456847551168542 .. _discord: https://discord.gg/cSBGb3vsZb

emrekiciman

c74b024a16ef0634422ffdda2c715031f46309bb

81fe5d9cbd998796f02d0d9f5b1d923ba0e85383

Those spaces should be there now.

emrekiciman

py-why/dowhy

Functional api/identify effect

First of a series of PR to add a functional API according to: https://github.com/py-why/dowhy/wiki/API-proposal-for-v1 * Refactor `identify_effect` to have a functional API * Created `BackdoorIdentifier` class and extracted the logic from `CausalIdentifier` to be just a Protocol * Refactor the `identify_effect` method of `BackdoorIdentifier` and `IDIdentifier` to take the graph as parameter * Moved constants into `enums` for easier type checking * Backwards compatible with previous CausalModel API * Added notebook as demo that CausalModel API and new API behaves the same way

2022-09-16 21:35:24+00:00

2022-09-27 01:38:27+00:00

docs/source/example_notebooks/dowhy_efficient_backdoor_example.ipynb

{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Finding optimal adjustment sets" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Preliminaries" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This notebook illustrates the use of the algorithms developed in [Smucler, Sapienza and Rotnitzky (Biometrika, 2022)](https://arxiv.org/abs/1912.00306) and [Smucler and Rotnitzky (Journal of Causal Inference, 2022)](https://www.degruyter.com/document/doi/10.1515/jci-2022-0015/html) to compute backdoor sets that yield efficient estimators of interventional means and their contrasts (such as the ATE), under various constraints. We begin by recalling some definitions from these papers. We ommit most technical details, and point the reader to the original papers for them." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The **optimal backdoor set** is a backdoor set comprised of observable variables that yields non-parametric\n", "estimators of the interventional mean with the smallest asymptotic variance\n", "among those that are based on observable backdoor sets. This optimal backdoor\n", "set always exists when no variables are latent, and the algorithm is guaranteed to compute\n", "it in this case. Under a non-parametric graphical model with latent variables,\n", "such a backdoor set can fail to exist. \n", "\n", "The **optimal minimal backdoor set** is a minimal backdoor set comprised of observable variables that yields non-parametric\n", "estimators of the interventional mean with the smallest asymptotic variance\n", "among those that are based on observable minimal backdoor sets.\n", "\n", "The **optimal minimum cost backdoor set** is a minimum cost backdoor set comprised of observable variables that yields non-parametric estimators of the interventional mean with the smallest asymptotic variance\n", "among those that are based on observable minimum cost backdoor sets. The cost\n", "of a backdoor set is defined as the sum of the costs of the variables that comprise it. Note that \n", "when all costs are equal, the optimal minimum cost backdoor set is the optimal backdoor set among those that \n", "have minimum cardinality.\n", "\n", "These various optimal backdoor sets are not only optimal under\n", "non-parametric graphical models and non-parametric estimators of interventional mean,\n", "but also under linear graphical models and OLS estimators, per results in [Henckel, Perkovic\n", "and Maathuis (JRSS B, 2022)](https://arxiv.org/abs/1907.02435)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### The design of an observational study" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "from dowhy.causal_graph import CausalGraph\n", "from dowhy.causal_identifier import CausalIdentifier" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Consider the design of the following hypothetical observational study discussed in [Shrier & Platt (2008)](https://doi.org/10.1186/1471-2288-8-70). The aim of the study is to assess the\n", "effect of warm-up exercises on injury after playing sports. Suppose that a researcher postulates\n", "that the graph below represents a causal graphical model. The node warm-up is the treatment variable, which stands for the type of exercise an athlete performs prior to playing sports,\n", "and the node injury stands for the outcome variable. \n", "\n", "Suppose that the goal of the study is to estimate and\n", "compare the interventional means corresponding to different individualised treatment rules. Each\n", "rule prescribes the type of warm-up exercise as a function of previous injury and team motivation. For example, one such rule could be to allocate a patient to perform soft warm-up excercises when she has previous injury = 1 and team motivation > 6, but any other (possibly randomised) function of previous injury and team motivation to set the treatment variable could be of interest. More formally, the goal of the study is, for some set of policies such as the aforementioned one, to estimate the mean of the outcome, in a world in which all patients are allocated to a treatment variant according to one of these policies. We will suppose moreover that due to practical limitations, the variables genetics, pre-grame proprioception,\n", "intra-game proprioception and tissue weakness cannot be measured. Proprioception is an individual's ability to sense the movement, action, and location of their own bodies.\n", "\n", "To build the graph, we first create a string declaring the graph's nodes and edges. We then create a list of all observable variables, in this case, all variables in the graph except genetics, pre-game proprioception, intra-game proprioception and tissue weakness. We then pass all this information to the ```CausalGraph``` class, to create an instance of it." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "graph_str=\"\"\"graph[directed 1 node[id \"coach\" label \"coach\"]\n", " node[id \"team motivation\" label \"team motivation\"]\n", " node[id \"fitness\" label \"fitness\"]\n", " node[id \"pre-game prop\" label \"pre-game prop\"]\n", " node[id \"intra-game prop\" label \"intra-game prop\"] \n", " node[id \"neuromusc fatigue\" label \"neuromusc fatigue\"]\n", " node[id \"warm-up\" label \"warm-up\"]\n", " node[id \"previous injury\" label \"previous injury\"]\n", " node[id \"contact sport\" label \"contact sport\"]\n", " node[id \"genetics\" label \"genetics\"]\n", " node[id \"injury\" label \"injury\"]\n", " node[id \"tissue disorder\" label \"tissue disorder\"]\n", " node[id \"tissue weakness\" label \"tissue weakness\"]\n", " edge[source \"coach\" target \"team motivation\"]\n", " edge[source \"coach\" target \"fitness\"]\n", " edge[source \"fitness\" target \"pre-game prop\"]\n", " edge[source \"fitness\" target \"neuromusc fatigue\"]\n", " edge[source \"team motivation\" target \"warm-up\"]\n", " edge[source \"team motivation\" target \"previous injury\"]\n", " edge[source \"pre-game prop\" target \"warm-up\"]\n", " edge[source \"warm-up\" target \"intra-game prop\"]\n", " edge[source \"contact sport\" target \"previous injury\"]\n", " edge[source \"contact sport\" target \"intra-game prop\"]\n", " edge[source \"intra-game prop\" target \"injury\"]\n", " edge[source \"genetics\" target \"fitness\"]\n", " edge[source \"genetics\" target \"neuromusc fatigue\"]\n", " edge[source \"genetics\" target \"tissue disorder\"]\n", " edge[source \"tissue disorder\" target \"neuromusc fatigue\"]\n", " edge[source \"tissue disorder\" target \"tissue weakness\"]\n", " edge[source \"neuromusc fatigue\" target \"intra-game prop\"]\n", " edge[source \"neuromusc fatigue\" target \"injury\"]\n", " edge[source \"tissue weakness\" target \"injury\"]\n", " ]\n", "\"\"\"\n", "observed_node_names=[\"coach\", \"team motivation\", \"fitness\", \"neuromusc fatigue\",\n", " \"warm-up\", \"previous injury\", \"contact sport\", \"tissue disorder\", \"injury\"]\n", "treatment_name = \"warm-up\"\n", "outcome_name = \"injury\"\n", "G = CausalGraph(graph=graph_str, treatment_name=treatment_name, outcome_name=outcome_name,\n", " observed_node_names=observed_node_names)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can easily create a plot of the graph using the ```view_graph``` method." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "G.view_graph()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Next, we illustrate how to compute the backdoor sets defined in the preliminaries section for the example graph above, using the ```CausalIdentifier``` class. To compute the optimal backdoor set, optimal minimal backdoor set and optimal minimum cost backdoor set, we need to instantiate objects of the ```CausalIdentifier``` class, passing as ```method_name``` the values \"efficient-adjustment\", \"efficient-minimal-adjustment\" and \"efficient-mincost-adjustment\" respectively. Then, we need to call the ```identify_effect``` method, passing as an argument a list of conditional nodes, that is, the nodes that would be used to decide how to allocate treatment. As discussed above, in this example these nodes are previous injury and team motivation. For settings in which we are not interested in individualized interventions, we can just pass an empty list as conditional nodes." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "conditional_node_names=[\"previous injury\", \"team motivation\"]" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "ident_eff = CausalIdentifier(\n", " graph=G,\n", " estimand_type=\"nonparametric-ate\",\n", " method_name=\"efficient-adjustment\",\n", " )\n", "print(ident_eff.identify_effect(conditional_node_names=conditional_node_names))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Thus, the optimal backdoor set is formed by previous injury, neuromusc fatigue, team motivation, tissue disorder and contact sport." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Similarly, we can compute the optimal minimal backdoor set." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "ident_minimal_eff = CausalIdentifier(\n", " graph=G,\n", " estimand_type=\"nonparametric-ate\",\n", " method_name=\"efficient-minimal-adjustment\",\n", " )\n", "print(ident_minimal_eff.identify_effect(conditional_node_names=conditional_node_names))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Finally, we can compute the optimal minimum cost backdoor set. Since this graph does not have any costs associated with its nodes, we will not pass any costs to ```identify_effect```. The method will raise a warning, set the costs to one, and compute the optimal minimum cost backdoor set, which as stated above, in this case coincides with the optimal backdoor set of minimum cardinality." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "ident_mincost_eff = CausalIdentifier(\n", " graph=G,\n", " estimand_type=\"nonparametric-ate\",\n", " method_name=\"efficient-mincost-adjustment\",\n", " )\n", "print(ident_mincost_eff.identify_effect(conditional_node_names=conditional_node_names))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Later, we will compute the optimal minimum cost backdoor set for a graph with costs associated with its nodes." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### An example in which sufficient conditions to guarantee the existence of an optimal backdoor set do not hold" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "[Smucler, Sapienza and Rotnitzky (Biometrika, 2022)](https://arxiv.org/abs/1912.00306) proved that when all variables are observable, or when all observable variables are ancestors of either the treatment, outcome or conditional nodes, then an optimal backdoor set can be found solely based on the graph, and provided an algorithm to compute it. This is the algorithm implemented in the examples above. \n", "\n", "However, there exist cases in which an observable optimal backdoor sets cannot be found solely using graphical criteria. For the graph below, [Rotnitzky and Smucler (JMLR, 2021)](https://jmlr.csail.mit.edu/papers/volume21/19-1026/19-1026.pdf) in their Example 5 showed that depending on the law generating the data, the optimal backdoor set could be formed by Z1 and Z2, or be the empty set. More precisely, they showed that there exist probability laws compatible with the graph under which {Z1, Z2} is the most efficient adjustment set, and other probability laws under which the empty set is the most efficient adjustment set; unfortunately one cannot tell from the graph alone which of the two will be better. \n", "\n", "Notice that in this graph, the aforementioned sufficient condition for the existence of an optimal backdoor set does not hold, since Z2 is observable but not an ancestor of treatment outcome or the conditional nodes (the empty set in this case). \n", "\n", "On the other hand, [Smucler, Sapienza and Rotnitzky (Biometrika, 2022)](https://arxiv.org/abs/1912.00306) showed that optimal minimal and optimal minimum cost (cardinality) observable backdoor sets always exist, as long as there exists at least one backdoor set comprised of observable variables. That is, when the search is restricted to minimal or minimum cost (cardinality) backdoor sets, a situation such as the one described above cannot happen, and the most efficient backdoor set can always be detected based solely on graphical criteria.\n", "\n", "For this example, calling the ```identify_effect``` method of an instance of ```CausalIdentifier``` with attribute ```method_name``` equal to \"efficient-adjustment\" will raise an error. For this graph, the optimal minimal and the optimal minimum cardinality backdoor sets are equal to the empty set." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "graph_str=\"\"\"graph[directed 1 node[id \"X\" label \"X\"]\n", " node[id \"Y\" label \"Y\"]\n", " node[id \"Z1\" label \"Z1\"]\n", " node[id \"Z2\" label \"Z2\"]\n", " node[id \"U\" label \"U\"] \n", " edge[source \"X\" target \"Y\"]\n", " edge[source \"Z1\" target \"X\"]\n", " edge[source \"Z1\" target \"Z2\"]\n", " edge[source \"U\" target \"Z2\"]\n", " edge[source \"U\" target \"Y\"]\n", " ]\n", "\"\"\"\n", "observed_node_names = ['X', 'Y', 'Z1', 'Z2']\n", "treatment_name = 'X'\n", "outcome_name = 'Y'\n", "G = CausalGraph(graph=graph_str, treatment_name=treatment_name, outcome_name=outcome_name,\n", " observed_node_names=observed_node_names)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In this example, the treatment intervention is static, thus there are no conditional nodes." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "ident_eff = CausalIdentifier(\n", " graph=G,\n", " estimand_type=\"nonparametric-ate\",\n", " method_name=\"efficient-adjustment\",\n", " )\n", "try:\n", " results_eff=ident_eff.identify_effect()\n", "except ValueError as e:\n", " print(e)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "ident_minimal_eff = CausalIdentifier(\n", " graph=G,\n", " estimand_type=\"nonparametric-ate\",\n", " method_name=\"efficient-minimal-adjustment\",\n", " )\n", "print(ident_minimal_eff.identify_effect())" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "ident_mincost_eff = CausalIdentifier(\n", " graph=G,\n", " estimand_type=\"nonparametric-ate\",\n", " method_name=\"efficient-mincost-adjustment\",\n", " )\n", "print(ident_mincost_eff.identify_effect())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### An example in which there are no observable adjustment sets" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In the graph below there are no adjustment sets comprised of only observable variables. In this setting, using any of the above methods will raise an error." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "graph_str=\"\"\"graph[directed 1 node[id \"X\" label \"X\"]\n", " node[id \"Y\" label \"Y\"]\n", " node[id \"U\" label \"U\"] \n", " edge[source \"X\" target \"Y\"]\n", " edge[source \"U\" target \"X\"]\n", " edge[source \"U\" target \"Y\"]\n", " ]\n", "\"\"\"\n", "observed_node_names = ['X', 'Y']\n", "treatment_name = 'X'\n", "outcome_name = 'Y'\n", "G = CausalGraph(graph=graph_str, treatment_name=treatment_name, outcome_name=outcome_name,\n", " observed_node_names=observed_node_names)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "ident_eff = CausalIdentifier(\n", " graph=G,\n", " estimand_type=\"nonparametric-ate\",\n", " method_name=\"efficient-adjustment\",\n", " )\n", "try:\n", " results_eff=ident_eff.identify_effect()\n", "except ValueError as e:\n", " print(e)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### An example with costs" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This is the graph in Figures 1 and 2 of [Smucler and Rotnitzky (Journal of Causal Inference, 2022)](https://www.degruyter.com/document/doi/10.1515/jci-2022-0015/html). Here we assume that there are positive costs associated to observable variables." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "pycharm": { "name": "#%%\n" } }, "outputs": [], "source": [ "graph_str=\"\"\"graph[directed 1 node[id \"L\" label \"L\"]\n", " node[id \"X\" label \"X\"]\n", " node[id \"K\" label \"K\"]\n", " node[id \"B\" label \"B\"]\n", " node[id \"Q\" label \"Q\"]\n", " node[id \"R\" label \"R\"]\n", " node[id \"T\" label \"T\"]\n", " node[id \"M\" label \"M\"]\n", " node[id \"Y\" label \"Y\"]\n", " node[id \"U\" label \"U\"]\n", " node[id \"F\" label \"F\"]\n", " edge[source \"L\" target \"X\"]\n", " edge[source \"X\" target \"M\"]\n", " edge[source \"K\" target \"X\"]\n", " edge[source \"B\" target \"K\"]\n", " edge[source \"B\" target \"R\"]\n", " edge[source \"Q\" target \"K\"]\n", " edge[source \"Q\" target \"T\"]\n", " edge[source \"R\" target \"Y\"]\n", " edge[source \"T\" target \"Y\"]\n", " edge[source \"M\" target \"Y\"]\n", " edge[source \"U\" target \"Y\"]\n", " edge[source \"U\" target \"F\"]\n", " ]\n", " \"\"\"\n", "observed_node_names=[\"L\", \"X\", \"B\", \"K\", \"Q\", \"R\", \"M\", \"T\", \"Y\", \"F\"]\n", "conditional_node_names=[\"L\"]\n", "costs=[\n", " (\"L\", {\"cost\": 1}),\n", " (\"B\", {\"cost\": 1}),\n", " (\"K\", {\"cost\": 4}),\n", " (\"Q\", {\"cost\": 1}),\n", " (\"R\", {\"cost\": 2}),\n", " (\"T\", {\"cost\": 1}),\n", "]\n", "G = CausalGraph(graph=graph_str, treatment_name=treatment_name, outcome_name=outcome_name,\n", " observed_node_names=observed_node_names)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Notice how in this case we pass both the ```conditional_node_names``` list and the ```costs``` list to the ```identify_effect``` method." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "pycharm": { "name": "#%%\n" } }, "outputs": [], "source": [ "ident_mincost_eff = CausalIdentifier(\n", " graph=G,\n", " estimand_type=\"nonparametric-ate\",\n", " method_name=\"efficient-mincost-adjustment\",\n", " )\n", "print(ident_mincost_eff.identify_effect(conditional_node_names=conditional_node_names, costs=costs))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We also compute the optimal minimal backdoor set, which in this case is different from the optimal minimum cost backdoor set." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "ident_minimal_eff = CausalIdentifier(\n", " graph=G,\n", " estimand_type=\"nonparametric-ate\",\n", " method_name=\"efficient-minimal-adjustment\",\n", " )\n", "print(ident_minimal_eff.identify_effect(conditional_node_names=conditional_node_names))" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.9.7" }, "varInspector": { "cols": { "lenName": 16, "lenType": 16, "lenVar": 40 }, "kernels_config": { "python": { "delete_cmd_postfix": "", "delete_cmd_prefix": "del ", "library": "var_list.py", "varRefreshCmd": "print(var_dic_list())" }, "r": { "delete_cmd_postfix": ") ", "delete_cmd_prefix": "rm(", "library": "var_list.r", "varRefreshCmd": "cat(var_dic_list()) " } }, "types_to_exclude": [ "module", "function", "builtin_function_or_method", "instance", "_Feature" ], "window_display": false } }, "nbformat": 4, "nbformat_minor": 4 }

{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Finding optimal adjustment sets" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Preliminaries" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This notebook illustrates the use of the algorithms developed in [Smucler, Sapienza and Rotnitzky (Biometrika, 2022)](https://arxiv.org/abs/1912.00306) and [Smucler and Rotnitzky (Journal of Causal Inference, 2022)](https://www.degruyter.com/document/doi/10.1515/jci-2022-0015/html) to compute backdoor sets that yield efficient estimators of interventional means and their contrasts (such as the ATE), under various constraints. We begin by recalling some definitions from these papers. We ommit most technical details, and point the reader to the original papers for them." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The **optimal backdoor set** is a backdoor set comprised of observable variables that yields non-parametric\n", "estimators of the interventional mean with the smallest asymptotic variance\n", "among those that are based on observable backdoor sets. This optimal backdoor\n", "set always exists when no variables are latent, and the algorithm is guaranteed to compute\n", "it in this case. Under a non-parametric graphical model with latent variables,\n", "such a backdoor set can fail to exist. \n", "\n", "The **optimal minimal backdoor set** is a minimal backdoor set comprised of observable variables that yields non-parametric\n", "estimators of the interventional mean with the smallest asymptotic variance\n", "among those that are based on observable minimal backdoor sets.\n", "\n", "The **optimal minimum cost backdoor set** is a minimum cost backdoor set comprised of observable variables that yields non-parametric estimators of the interventional mean with the smallest asymptotic variance\n", "among those that are based on observable minimum cost backdoor sets. The cost\n", "of a backdoor set is defined as the sum of the costs of the variables that comprise it. Note that \n", "when all costs are equal, the optimal minimum cost backdoor set is the optimal backdoor set among those that \n", "have minimum cardinality.\n", "\n", "These various optimal backdoor sets are not only optimal under\n", "non-parametric graphical models and non-parametric estimators of interventional mean,\n", "but also under linear graphical models and OLS estimators, per results in [Henckel, Perkovic\n", "and Maathuis (JRSS B, 2022)](https://arxiv.org/abs/1907.02435)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### The design of an observational study" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "from dowhy.causal_graph import CausalGraph\n", "from dowhy.causal_identifier import AutoIdentifier, BackdoorAdjustment, EstimandType" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Consider the design of the following hypothetical observational study discussed in [Shrier & Platt (2008)](https://doi.org/10.1186/1471-2288-8-70). The aim of the study is to assess the\n", "effect of warm-up exercises on injury after playing sports. Suppose that a researcher postulates\n", "that the graph below represents a causal graphical model. The node warm-up is the treatment variable, which stands for the type of exercise an athlete performs prior to playing sports,\n", "and the node injury stands for the outcome variable. \n", "\n", "Suppose that the goal of the study is to estimate and\n", "compare the interventional means corresponding to different individualised treatment rules. Each\n", "rule prescribes the type of warm-up exercise as a function of previous injury and team motivation. For example, one such rule could be to allocate a patient to perform soft warm-up excercises when she has previous injury = 1 and team motivation > 6, but any other (possibly randomised) function of previous injury and team motivation to set the treatment variable could be of interest. More formally, the goal of the study is, for some set of policies such as the aforementioned one, to estimate the mean of the outcome, in a world in which all patients are allocated to a treatment variant according to one of these policies. We will suppose moreover that due to practical limitations, the variables genetics, pre-grame proprioception,\n", "intra-game proprioception and tissue weakness cannot be measured. Proprioception is an individual's ability to sense the movement, action, and location of their own bodies.\n", "\n", "To build the graph, we first create a string declaring the graph's nodes and edges. We then create a list of all observable variables, in this case, all variables in the graph except genetics, pre-game proprioception, intra-game proprioception and tissue weakness. We then pass all this information to the ```CausalGraph``` class, to create an instance of it." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "graph_str = \"\"\"graph[directed 1 node[id \"coach\" label \"coach\"]\n", " node[id \"team motivation\" label \"team motivation\"]\n", " node[id \"fitness\" label \"fitness\"]\n", " node[id \"pre-game prop\" label \"pre-game prop\"]\n", " node[id \"intra-game prop\" label \"intra-game prop\"] \n", " node[id \"neuromusc fatigue\" label \"neuromusc fatigue\"]\n", " node[id \"warm-up\" label \"warm-up\"]\n", " node[id \"previous injury\" label \"previous injury\"]\n", " node[id \"contact sport\" label \"contact sport\"]\n", " node[id \"genetics\" label \"genetics\"]\n", " node[id \"injury\" label \"injury\"]\n", " node[id \"tissue disorder\" label \"tissue disorder\"]\n", " node[id \"tissue weakness\" label \"tissue weakness\"]\n", " edge[source \"coach\" target \"team motivation\"]\n", " edge[source \"coach\" target \"fitness\"]\n", " edge[source \"fitness\" target \"pre-game prop\"]\n", " edge[source \"fitness\" target \"neuromusc fatigue\"]\n", " edge[source \"team motivation\" target \"warm-up\"]\n", " edge[source \"team motivation\" target \"previous injury\"]\n", " edge[source \"pre-game prop\" target \"warm-up\"]\n", " edge[source \"warm-up\" target \"intra-game prop\"]\n", " edge[source \"contact sport\" target \"previous injury\"]\n", " edge[source \"contact sport\" target \"intra-game prop\"]\n", " edge[source \"intra-game prop\" target \"injury\"]\n", " edge[source \"genetics\" target \"fitness\"]\n", " edge[source \"genetics\" target \"neuromusc fatigue\"]\n", " edge[source \"genetics\" target \"tissue disorder\"]\n", " edge[source \"tissue disorder\" target \"neuromusc fatigue\"]\n", " edge[source \"tissue disorder\" target \"tissue weakness\"]\n", " edge[source \"neuromusc fatigue\" target \"intra-game prop\"]\n", " edge[source \"neuromusc fatigue\" target \"injury\"]\n", " edge[source \"tissue weakness\" target \"injury\"]\n", " ]\n", "\"\"\"\n", "observed_node_names = [\n", " \"coach\",\n", " \"team motivation\",\n", " \"fitness\",\n", " \"neuromusc fatigue\",\n", " \"warm-up\",\n", " \"previous injury\",\n", " \"contact sport\",\n", " \"tissue disorder\",\n", " \"injury\",\n", "]\n", "treatment_name = \"warm-up\"\n", "outcome_name = \"injury\"\n", "G = CausalGraph(\n", " graph=graph_str, treatment_name=treatment_name, outcome_name=outcome_name, observed_node_names=observed_node_names\n", ")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can easily create a plot of the graph using the ```view_graph``` method." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "G.view_graph()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Next, we illustrate how to compute the backdoor sets defined in the preliminaries section for the example graph above, using the ```CausalIdentifier``` class. To compute the optimal backdoor set, optimal minimal backdoor set and optimal minimum cost backdoor set, we need to instantiate objects of the ```CausalIdentifier``` class, passing as ```method_name``` the values \"efficient-adjustment\", \"efficient-minimal-adjustment\" and \"efficient-mincost-adjustment\" respectively. Then, we need to call the ```identify_effect``` method, passing as an argument a list of conditional nodes, that is, the nodes that would be used to decide how to allocate treatment. As discussed above, in this example these nodes are previous injury and team motivation. For settings in which we are not interested in individualized interventions, we can just pass an empty list as conditional nodes." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "conditional_node_names = [\"previous injury\", \"team motivation\"]" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "ident_eff = AutoIdentifier(\n", " estimand_type=EstimandType.NONPARAMETRIC_ATE,\n", " backdoor_adjustment=BackdoorAdjustment.BACKDOOR_EFFICIENT,\n", ")\n", "print(\n", " ident_eff.identify_effect(\n", " graph=G, treatment_name=treatment_name, outcome_name=outcome_name, conditional_node_names=conditional_node_names\n", " )\n", ")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Thus, the optimal backdoor set is formed by previous injury, neuromusc fatigue, team motivation, tissue disorder and contact sport." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Similarly, we can compute the optimal minimal backdoor set." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "ident_minimal_eff = AutoIdentifier(\n", " estimand_type=EstimandType.NONPARAMETRIC_ATE,\n", " backdoor_adjustment=BackdoorAdjustment.BACKDOOR_MIN_EFFICIENT,\n", ")\n", "print(\n", " ident_minimal_eff.identify_effect(\n", " graph=G, treatment_name=treatment_name, outcome_name=outcome_name, conditional_node_names=conditional_node_names\n", " )\n", ")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Finally, we can compute the optimal minimum cost backdoor set. Since this graph does not have any costs associated with its nodes, we will not pass any costs to ```identify_effect```. The method will raise a warning, set the costs to one, and compute the optimal minimum cost backdoor set, which as stated above, in this case coincides with the optimal backdoor set of minimum cardinality." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "ident_mincost_eff = AutoIdentifier(\n", " estimand_type=EstimandType.NONPARAMETRIC_ATE,\n", " backdoor_adjustment=BackdoorAdjustment.BACKDOOR_MINCOST_EFFICIENT,\n", ")\n", "print(\n", " ident_mincost_eff.identify_effect(\n", " graph=G, treatment_name=treatment_name, outcome_name=outcome_name, conditional_node_names=conditional_node_names\n", " )\n", ")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Later, we will compute the optimal minimum cost backdoor set for a graph with costs associated with its nodes." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### An example in which sufficient conditions to guarantee the existence of an optimal backdoor set do not hold" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "[Smucler, Sapienza and Rotnitzky (Biometrika, 2022)](https://arxiv.org/abs/1912.00306) proved that when all variables are observable, or when all observable variables are ancestors of either the treatment, outcome or conditional nodes, then an optimal backdoor set can be found solely based on the graph, and provided an algorithm to compute it. This is the algorithm implemented in the examples above. \n", "\n", "However, there exist cases in which an observable optimal backdoor sets cannot be found solely using graphical criteria. For the graph below, [Rotnitzky and Smucler (JMLR, 2021)](https://jmlr.csail.mit.edu/papers/volume21/19-1026/19-1026.pdf) in their Example 5 showed that depending on the law generating the data, the optimal backdoor set could be formed by Z1 and Z2, or be the empty set. More precisely, they showed that there exist probability laws compatible with the graph under which {Z1, Z2} is the most efficient adjustment set, and other probability laws under which the empty set is the most efficient adjustment set; unfortunately one cannot tell from the graph alone which of the two will be better. \n", "\n", "Notice that in this graph, the aforementioned sufficient condition for the existence of an optimal backdoor set does not hold, since Z2 is observable but not an ancestor of treatment outcome or the conditional nodes (the empty set in this case). \n", "\n", "On the other hand, [Smucler, Sapienza and Rotnitzky (Biometrika, 2022)](https://arxiv.org/abs/1912.00306) showed that optimal minimal and optimal minimum cost (cardinality) observable backdoor sets always exist, as long as there exists at least one backdoor set comprised of observable variables. That is, when the search is restricted to minimal or minimum cost (cardinality) backdoor sets, a situation such as the one described above cannot happen, and the most efficient backdoor set can always be detected based solely on graphical criteria.\n", "\n", "For this example, calling the ```identify_effect``` method of an instance of ```CausalIdentifier``` with attribute ```method_name``` equal to \"efficient-adjustment\" will raise an error. For this graph, the optimal minimal and the optimal minimum cardinality backdoor sets are equal to the empty set." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "graph_str = \"\"\"graph[directed 1 node[id \"X\" label \"X\"]\n", " node[id \"Y\" label \"Y\"]\n", " node[id \"Z1\" label \"Z1\"]\n", " node[id \"Z2\" label \"Z2\"]\n", " node[id \"U\" label \"U\"] \n", " edge[source \"X\" target \"Y\"]\n", " edge[source \"Z1\" target \"X\"]\n", " edge[source \"Z1\" target \"Z2\"]\n", " edge[source \"U\" target \"Z2\"]\n", " edge[source \"U\" target \"Y\"]\n", " ]\n", "\"\"\"\n", "observed_node_names = [\"X\", \"Y\", \"Z1\", \"Z2\"]\n", "treatment_name = \"X\"\n", "outcome_name = \"Y\"\n", "G = CausalGraph(\n", " graph=graph_str, treatment_name=treatment_name, outcome_name=outcome_name, observed_node_names=observed_node_names\n", ")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In this example, the treatment intervention is static, thus there are no conditional nodes." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "ident_eff = AutoIdentifier(\n", " estimand_type=EstimandType.NONPARAMETRIC_ATE,\n", " backdoor_adjustment=BackdoorAdjustment.BACKDOOR_EFFICIENT,\n", ")\n", "try:\n", " results_eff = ident_eff.identify_effect(graph=G, treatment_name=treatment_name, outcome_name=outcome_name)\n", "except ValueError as e:\n", " print(e)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "ident_eff = AutoIdentifier(\n", " estimand_type=EstimandType.NONPARAMETRIC_ATE,\n", " backdoor_adjustment=BackdoorAdjustment.BACKDOOR_MIN_EFFICIENT,\n", ")\n", "print(\n", " ident_minimal_eff.identify_effect(\n", " graph=G,\n", " treatment_name=treatment_name,\n", " outcome_name=outcome_name,\n", " )\n", ")" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "ident_eff = AutoIdentifier(\n", " estimand_type=EstimandType.NONPARAMETRIC_ATE,\n", " backdoor_adjustment=BackdoorAdjustment.BACKDOOR_MINCOST_EFFICIENT,\n", ")\n", "print(\n", " ident_mincost_eff.identify_effect(\n", " graph=G,\n", " treatment_name=treatment_name,\n", " outcome_name=outcome_name,\n", " )\n", ")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### An example in which there are no observable adjustment sets" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In the graph below there are no adjustment sets comprised of only observable variables. In this setting, using any of the above methods will raise an error." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "graph_str = \"\"\"graph[directed 1 node[id \"X\" label \"X\"]\n", " node[id \"Y\" label \"Y\"]\n", " node[id \"U\" label \"U\"] \n", " edge[source \"X\" target \"Y\"]\n", " edge[source \"U\" target \"X\"]\n", " edge[source \"U\" target \"Y\"]\n", " ]\n", "\"\"\"\n", "observed_node_names = [\"X\", \"Y\"]\n", "treatment_name = \"X\"\n", "outcome_name = \"Y\"\n", "G = CausalGraph(\n", " graph=graph_str, treatment_name=treatment_name, outcome_name=outcome_name, observed_node_names=observed_node_names\n", ")" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "ident_eff = AutoIdentifier(\n", " estimand_type=EstimandType.NONPARAMETRIC_ATE,\n", " backdoor_adjustment=BackdoorAdjustment.BACKDOOR_EFFICIENT,\n", ")\n", "try:\n", " results_eff = ident_eff.identify_effect(\n", " graph=G,\n", " treatment_name=treatment_name,\n", " outcome_name=outcome_name,\n", " )\n", "except ValueError as e:\n", " print(e)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### An example with costs" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This is the graph in Figures 1 and 2 of [Smucler and Rotnitzky (Journal of Causal Inference, 2022)](https://www.degruyter.com/document/doi/10.1515/jci-2022-0015/html). Here we assume that there are positive costs associated to observable variables." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "pycharm": { "name": "#%%\n" } }, "outputs": [], "source": [ "graph_str = \"\"\"graph[directed 1 node[id \"L\" label \"L\"]\n", " node[id \"X\" label \"X\"]\n", " node[id \"K\" label \"K\"]\n", " node[id \"B\" label \"B\"]\n", " node[id \"Q\" label \"Q\"]\n", " node[id \"R\" label \"R\"]\n", " node[id \"T\" label \"T\"]\n", " node[id \"M\" label \"M\"]\n", " node[id \"Y\" label \"Y\"]\n", " node[id \"U\" label \"U\"]\n", " node[id \"F\" label \"F\"]\n", " edge[source \"L\" target \"X\"]\n", " edge[source \"X\" target \"M\"]\n", " edge[source \"K\" target \"X\"]\n", " edge[source \"B\" target \"K\"]\n", " edge[source \"B\" target \"R\"]\n", " edge[source \"Q\" target \"K\"]\n", " edge[source \"Q\" target \"T\"]\n", " edge[source \"R\" target \"Y\"]\n", " edge[source \"T\" target \"Y\"]\n", " edge[source \"M\" target \"Y\"]\n", " edge[source \"U\" target \"Y\"]\n", " edge[source \"U\" target \"F\"]\n", " ]\n", " \"\"\"\n", "observed_node_names = [\"L\", \"X\", \"B\", \"K\", \"Q\", \"R\", \"M\", \"T\", \"Y\", \"F\"]\n", "conditional_node_names = [\"L\"]\n", "costs = [\n", " (\"L\", {\"cost\": 1}),\n", " (\"B\", {\"cost\": 1}),\n", " (\"K\", {\"cost\": 4}),\n", " (\"Q\", {\"cost\": 1}),\n", " (\"R\", {\"cost\": 2}),\n", " (\"T\", {\"cost\": 1}),\n", "]\n", "G = CausalGraph(\n", " graph=graph_str, treatment_name=treatment_name, outcome_name=outcome_name, observed_node_names=observed_node_names\n", ")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Notice how in this case we pass both the ```conditional_node_names``` list and the ```costs``` list to the ```identify_effect``` method." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "pycharm": { "name": "#%%\n" } }, "outputs": [], "source": [ "ident_eff = AutoIdentifier(\n", " estimand_type=EstimandType.NONPARAMETRIC_ATE,\n", " backdoor_adjustment=BackdoorAdjustment.BACKDOOR_MINCOST_EFFICIENT,\n", " costs=costs,\n", ")\n", "print(\n", " ident_mincost_eff.identify_effect(\n", " graph=G, treatment_name=treatment_name, outcome_name=outcome_name, conditional_node_names=conditional_node_names\n", " )\n", ")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We also compute the optimal minimal backdoor set, which in this case is different from the optimal minimum cost backdoor set." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "ident_eff = AutoIdentifier(\n", " estimand_type=EstimandType.NONPARAMETRIC_ATE,\n", " backdoor_adjustment=BackdoorAdjustment.BACKDOOR_MIN_EFFICIENT,\n", ")\n", "print(\n", " ident_minimal_eff.identify_effect(\n", " graph=G, treatment_name=treatment_name, outcome_name=outcome_name, conditional_node_names=conditional_node_names\n", " )\n", ")" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3.8.10 ('dowhy-_zBapv7Q-py3.8')", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.8.10" }, "varInspector": { "cols": { "lenName": 16, "lenType": 16, "lenVar": 40 }, "kernels_config": { "python": { "delete_cmd_postfix": "", "delete_cmd_prefix": "del ", "library": "var_list.py", "varRefreshCmd": "print(var_dic_list())" }, "r": { "delete_cmd_postfix": ") ", "delete_cmd_prefix": "rm(", "library": "var_list.r", "varRefreshCmd": "cat(var_dic_list()) " } }, "types_to_exclude": [ "module", "function", "builtin_function_or_method", "instance", "_Feature" ], "window_display": false }, "vscode": { "interpreter": { "hash": "dcb481ad5d98e2afacd650b2c07afac80a299b7b701b553e333fc82865502500" } } }, "nbformat": 4, "nbformat_minor": 4 }

andresmor-ms

4d4df7a4637a5f5e9cd9c5362499b1fb38debeab

db953a63aae205951f028c1050f141e3cdc0c97a

need to remove outputs from this notebook. That's why it is showing a big diff.

amit-sharma

py-why/dowhy

Functional api/identify effect

First of a series of PR to add a functional API according to: https://github.com/py-why/dowhy/wiki/API-proposal-for-v1 * Refactor `identify_effect` to have a functional API * Created `BackdoorIdentifier` class and extracted the logic from `CausalIdentifier` to be just a Protocol * Refactor the `identify_effect` method of `BackdoorIdentifier` and `IDIdentifier` to take the graph as parameter * Moved constants into `enums` for easier type checking * Backwards compatible with previous CausalModel API * Added notebook as demo that CausalModel API and new API behaves the same way

2022-09-16 21:35:24+00:00

2022-09-27 01:38:27+00:00

dowhy/causal_estimators/two_stage_regression_estimator.py

import copy import itertools import numpy as np import pandas as pd from dowhy.causal_estimator import CausalEstimate, CausalEstimator from dowhy.causal_estimators.linear_regression_estimator import LinearRegressionEstimator from dowhy.causal_identifier import CausalIdentifier from dowhy.utils.api import parse_state class TwoStageRegressionEstimator(CausalEstimator): """Compute treatment effect whenever the effect is fully mediated by another variable (front-door) or when there is an instrument available. Currently only supports a linear model for the effects. For a list of standard args and kwargs, see documentation for :class:`~dowhy.causal_estimator.CausalEstimator`. Supports additional parameters as listed below. """ # First stage statistical model DEFAULT_FIRST_STAGE_MODEL = LinearRegressionEstimator # Second stage statistical model DEFAULT_SECOND_STAGE_MODEL = LinearRegressionEstimator def __init__(self, *args, first_stage_model=None, second_stage_model=None, **kwargs): """ :param first_stage_model: First stage estimator to be used. Default is linear regression. :param second_stage_model: Second stage estimator to be used. Default is linear regression. """ # Required to ensure that self.method_params contains all the # parameters needed to create an object of this class args_dict = {k: v for k, v in locals().items() if k not in type(self)._STD_INIT_ARGS} args_dict.update(kwargs) super().__init__(*args, **args_dict) self.logger.info("INFO: Using Two Stage Regression Estimator") # Check if the treatment is one-dimensional if len(self._treatment_name) > 1: error_msg = str(self.__class__) + "cannot handle more than one treatment variable" raise Exception(error_msg) if self._target_estimand.identifier_method == "frontdoor": self.logger.debug("Front-door variable used:" + ",".join(self._target_estimand.get_frontdoor_variables())) self._frontdoor_variables_names = self._target_estimand.get_frontdoor_variables() if self._frontdoor_variables_names: self._frontdoor_variables = self._data[self._frontdoor_variables_names] else: self._frontdoor_variables = None error_msg = "No front-door variable present. Two stage regression is not applicable" self.logger.error(error_msg) elif self._target_estimand.identifier_method == "mediation": self.logger.debug("Mediators used:" + ",".join(self._target_estimand.get_mediator_variables())) self._mediators_names = self._target_estimand.get_mediator_variables() if self._mediators_names: self._mediators = self._data[self._mediators_names] else: self._mediators = None error_msg = "No mediator variable present. Two stage regression is not applicable" self.logger.error(error_msg) elif self._target_estimand.identifier_method == "iv": self.logger.debug( "Instrumental variables used:" + ",".join(self._target_estimand.get_instrumental_variables()) ) self._instrumental_variables_names = self._target_estimand.get_instrumental_variables() if self._instrumental_variables_names: self._instrumental_variables = self._data[self._instrumental_variables_names] else: self._instrumental_variables = None error_msg = "No instrumental variable present. Two stage regression is not applicable" self.logger.error(error_msg) if first_stage_model is not None: self.first_stage_model = first_stage_model else: self.first_stage_model = self.__class__.DEFAULT_FIRST_STAGE_MODEL self.logger.warning("First stage model not provided. Defaulting to sklearn.linear_model.LinearRegression.") if second_stage_model is not None: self.second_stage_model = second_stage_model else: self.second_stage_model = self.__class__.DEFAULT_SECOND_STAGE_MODEL self.logger.warning("Second stage model not provided. Defaulting to backdoor.linear_regression.") def _estimate_effect(self): estimate_value = None # First stage modified_target_estimand = copy.deepcopy(self._target_estimand) modified_target_estimand.identifier_method = "backdoor" modified_target_estimand.backdoor_variables = self._target_estimand.mediation_first_stage_confounders if self._target_estimand.identifier_method == "frontdoor": modified_target_estimand.outcome_variable = parse_state(self._frontdoor_variables_names) elif self._target_estimand.identifier_method == "mediation": modified_target_estimand.outcome_variable = parse_state(self._mediators_names) first_stage_estimate = self.first_stage_model( self._data, modified_target_estimand, self._treatment_name, parse_state(modified_target_estimand.outcome_variable), control_value=self._control_value, treatment_value=self._treatment_value, test_significance=self._significance_test, evaluate_effect_strength=self._effect_strength_eval, confidence_intervals=self._confidence_intervals, target_units=self._target_units, effect_modifiers=self._effect_modifier_names, **self.method_params, )._estimate_effect() # Second Stage modified_target_estimand = copy.deepcopy(self._target_estimand) modified_target_estimand.identifier_method = "backdoor" modified_target_estimand.backdoor_variables = self._target_estimand.mediation_second_stage_confounders if self._target_estimand.identifier_method == "frontdoor": modified_target_estimand.treatment_variable = parse_state(self._frontdoor_variables_names) elif self._target_estimand.identifier_method == "mediation": modified_target_estimand.treatment_variable = parse_state(self._mediators_names) second_stage_estimate = self.second_stage_model( self._data, modified_target_estimand, parse_state(modified_target_estimand.treatment_variable), parse_state(self._outcome_name), # to convert it to array before passing to causal estimator control_value=self._control_value, treatment_value=self._treatment_value, test_significance=self._significance_test, evaluate_effect_strength=self._effect_strength_eval, confidence_intervals=self._confidence_intervals, target_units=self._target_units, effect_modifiers=self._effect_modifier_names, **self.method_params, )._estimate_effect() # Combining the two estimates natural_indirect_effect = first_stage_estimate.value * second_stage_estimate.value # This same estimate is valid for frontdoor as well as mediation (NIE) estimate_value = natural_indirect_effect self.symbolic_estimator = self.construct_symbolic_estimator( first_stage_estimate.realized_estimand_expr, second_stage_estimate.realized_estimand_expr, estimand_type=CausalIdentifier.NONPARAMETRIC_NIE, ) if self._target_estimand.estimand_type == CausalIdentifier.NONPARAMETRIC_NDE: # Total effect of treatment modified_target_estimand = copy.deepcopy(self._target_estimand) modified_target_estimand.identifier_method = "backdoor" total_effect_estimate = self.second_stage_model( self._data, modified_target_estimand, self._treatment_name, parse_state(self._outcome_name), control_value=self._control_value, treatment_value=self._treatment_value, test_significance=self._significance_test, evaluate_effect_strength=self._effect_strength_eval, confidence_intervals=self._confidence_intervals, target_units=self._target_units, effect_modifiers=self._effect_modifier_names, **self.method_params, )._estimate_effect() natural_direct_effect = total_effect_estimate.value - natural_indirect_effect estimate_value = natural_direct_effect self.symbolic_estimator = self.construct_symbolic_estimator( first_stage_estimate.realized_estimand_expr, second_stage_estimate.realized_estimand_expr, total_effect_estimate.realized_estimand_expr, estimand_type=self._target_estimand.estimand_type, ) return CausalEstimate( estimate=estimate_value, control_value=self._control_value, treatment_value=self._treatment_value, target_estimand=self._target_estimand, realized_estimand_expr=self.symbolic_estimator, ) def build_first_stage_features(self): data_df = self._data treatment_vals = data_df[self._treatment_name] if len(self._observed_common_causes_names) > 0: observed_common_causes_vals = data_df[self._observed_common_causes_names] observed_common_causes_vals = pd.get_dummies(observed_common_causes_vals, drop_first=True) if self._effect_modifier_names: effect_modifiers_vals = data_df[self._effect_modifier_names] effect_modifiers_vals = pd.get_dummies(effect_modifiers_vals, drop_first=True) if type(treatment_vals) is not np.ndarray: treatment_vals = treatment_vals.to_numpy() if treatment_vals.shape[0] != data_df.shape[0]: raise ValueError("Provided treatment values and dataframe should have the same length.") # Bulding the feature matrix n_samples = treatment_vals.shape[0] self.logger.debug("Number of samples" + str(n_samples) + str(len(self._treatment_name))) treatment_2d = treatment_vals.reshape((n_samples, len(self._treatment_name))) if len(self._observed_common_causes_names) > 0: features = np.concatenate((treatment_2d, observed_common_causes_vals), axis=1) else: features = treatment_2d if self._effect_modifier_names: for i in range(treatment_2d.shape[1]): curr_treatment = treatment_2d[:, i] new_features = curr_treatment[:, np.newaxis] * effect_modifiers_vals.to_numpy() features = np.concatenate((features, new_features), axis=1) features = features.astype( float, copy=False ) # converting to float in case of binary treatment and no other variables # features = sm.add_constant(features, has_constant='add') # to add an intercept term return features def construct_symbolic_estimator( self, first_stage_symbolic, second_stage_symbolic, total_effect_symbolic=None, estimand_type=None ): nie_symbolic = "(" + first_stage_symbolic + ")*(" + second_stage_symbolic + ")" if estimand_type == CausalIdentifier.NONPARAMETRIC_NIE: return nie_symbolic elif estimand_type == CausalIdentifier.NONPARAMETRIC_NDE: return "(" + total_effect_symbolic + ") - (" + nie_symbolic + ")"

import copy import itertools import numpy as np import pandas as pd from dowhy.causal_estimator import CausalEstimate, CausalEstimator from dowhy.causal_estimators.linear_regression_estimator import LinearRegressionEstimator from dowhy.causal_identifier.identify_effect import EstimandType from dowhy.utils.api import parse_state class TwoStageRegressionEstimator(CausalEstimator): """Compute treatment effect whenever the effect is fully mediated by another variable (front-door) or when there is an instrument available. Currently only supports a linear model for the effects. For a list of standard args and kwargs, see documentation for :class:`~dowhy.causal_estimator.CausalEstimator`. Supports additional parameters as listed below. """ # First stage statistical model DEFAULT_FIRST_STAGE_MODEL = LinearRegressionEstimator # Second stage statistical model DEFAULT_SECOND_STAGE_MODEL = LinearRegressionEstimator def __init__(self, *args, first_stage_model=None, second_stage_model=None, **kwargs): """ :param first_stage_model: First stage estimator to be used. Default is linear regression. :param second_stage_model: Second stage estimator to be used. Default is linear regression. """ # Required to ensure that self.method_params contains all the # parameters needed to create an object of this class args_dict = {k: v for k, v in locals().items() if k not in type(self)._STD_INIT_ARGS} args_dict.update(kwargs) super().__init__(*args, **args_dict) self.logger.info("INFO: Using Two Stage Regression Estimator") # Check if the treatment is one-dimensional if len(self._treatment_name) > 1: error_msg = str(self.__class__) + "cannot handle more than one treatment variable" raise Exception(error_msg) if self._target_estimand.identifier_method == "frontdoor": self.logger.debug("Front-door variable used:" + ",".join(self._target_estimand.get_frontdoor_variables())) self._frontdoor_variables_names = self._target_estimand.get_frontdoor_variables() if self._frontdoor_variables_names: self._frontdoor_variables = self._data[self._frontdoor_variables_names] else: self._frontdoor_variables = None error_msg = "No front-door variable present. Two stage regression is not applicable" self.logger.error(error_msg) elif self._target_estimand.identifier_method == "mediation": self.logger.debug("Mediators used:" + ",".join(self._target_estimand.get_mediator_variables())) self._mediators_names = self._target_estimand.get_mediator_variables() if self._mediators_names: self._mediators = self._data[self._mediators_names] else: self._mediators = None error_msg = "No mediator variable present. Two stage regression is not applicable" self.logger.error(error_msg) elif self._target_estimand.identifier_method == "iv": self.logger.debug( "Instrumental variables used:" + ",".join(self._target_estimand.get_instrumental_variables()) ) self._instrumental_variables_names = self._target_estimand.get_instrumental_variables() if self._instrumental_variables_names: self._instrumental_variables = self._data[self._instrumental_variables_names] else: self._instrumental_variables = None error_msg = "No instrumental variable present. Two stage regression is not applicable" self.logger.error(error_msg) if first_stage_model is not None: self.first_stage_model = first_stage_model else: self.first_stage_model = self.__class__.DEFAULT_FIRST_STAGE_MODEL self.logger.warning("First stage model not provided. Defaulting to sklearn.linear_model.LinearRegression.") if second_stage_model is not None: self.second_stage_model = second_stage_model else: self.second_stage_model = self.__class__.DEFAULT_SECOND_STAGE_MODEL self.logger.warning("Second stage model not provided. Defaulting to backdoor.linear_regression.") def _estimate_effect(self): estimate_value = None # First stage modified_target_estimand = copy.deepcopy(self._target_estimand) modified_target_estimand.identifier_method = "backdoor" modified_target_estimand.backdoor_variables = self._target_estimand.mediation_first_stage_confounders if self._target_estimand.identifier_method == "frontdoor": modified_target_estimand.outcome_variable = parse_state(self._frontdoor_variables_names) elif self._target_estimand.identifier_method == "mediation": modified_target_estimand.outcome_variable = parse_state(self._mediators_names) first_stage_estimate = self.first_stage_model( self._data, modified_target_estimand, self._treatment_name, parse_state(modified_target_estimand.outcome_variable), control_value=self._control_value, treatment_value=self._treatment_value, test_significance=self._significance_test, evaluate_effect_strength=self._effect_strength_eval, confidence_intervals=self._confidence_intervals, target_units=self._target_units, effect_modifiers=self._effect_modifier_names, **self.method_params, )._estimate_effect() # Second Stage modified_target_estimand = copy.deepcopy(self._target_estimand) modified_target_estimand.identifier_method = "backdoor" modified_target_estimand.backdoor_variables = self._target_estimand.mediation_second_stage_confounders if self._target_estimand.identifier_method == "frontdoor": modified_target_estimand.treatment_variable = parse_state(self._frontdoor_variables_names) elif self._target_estimand.identifier_method == "mediation": modified_target_estimand.treatment_variable = parse_state(self._mediators_names) second_stage_estimate = self.second_stage_model( self._data, modified_target_estimand, parse_state(modified_target_estimand.treatment_variable), parse_state(self._outcome_name), # to convert it to array before passing to causal estimator control_value=self._control_value, treatment_value=self._treatment_value, test_significance=self._significance_test, evaluate_effect_strength=self._effect_strength_eval, confidence_intervals=self._confidence_intervals, target_units=self._target_units, effect_modifiers=self._effect_modifier_names, **self.method_params, )._estimate_effect() # Combining the two estimates natural_indirect_effect = first_stage_estimate.value * second_stage_estimate.value # This same estimate is valid for frontdoor as well as mediation (NIE) estimate_value = natural_indirect_effect self.symbolic_estimator = self.construct_symbolic_estimator( first_stage_estimate.realized_estimand_expr, second_stage_estimate.realized_estimand_expr, estimand_type=EstimandType.NONPARAMETRIC_NIE, ) if self._target_estimand.estimand_type == EstimandType.NONPARAMETRIC_NDE: # Total effect of treatment modified_target_estimand = copy.deepcopy(self._target_estimand) modified_target_estimand.identifier_method = "backdoor" total_effect_estimate = self.second_stage_model( self._data, modified_target_estimand, self._treatment_name, parse_state(self._outcome_name), control_value=self._control_value, treatment_value=self._treatment_value, test_significance=self._significance_test, evaluate_effect_strength=self._effect_strength_eval, confidence_intervals=self._confidence_intervals, target_units=self._target_units, effect_modifiers=self._effect_modifier_names, **self.method_params, )._estimate_effect() natural_direct_effect = total_effect_estimate.value - natural_indirect_effect estimate_value = natural_direct_effect self.symbolic_estimator = self.construct_symbolic_estimator( first_stage_estimate.realized_estimand_expr, second_stage_estimate.realized_estimand_expr, total_effect_estimate.realized_estimand_expr, estimand_type=self._target_estimand.estimand_type, ) return CausalEstimate( estimate=estimate_value, control_value=self._control_value, treatment_value=self._treatment_value, target_estimand=self._target_estimand, realized_estimand_expr=self.symbolic_estimator, ) def build_first_stage_features(self): data_df = self._data treatment_vals = data_df[self._treatment_name] if len(self._observed_common_causes_names) > 0: observed_common_causes_vals = data_df[self._observed_common_causes_names] observed_common_causes_vals = pd.get_dummies(observed_common_causes_vals, drop_first=True) if self._effect_modifier_names: effect_modifiers_vals = data_df[self._effect_modifier_names] effect_modifiers_vals = pd.get_dummies(effect_modifiers_vals, drop_first=True) if type(treatment_vals) is not np.ndarray: treatment_vals = treatment_vals.to_numpy() if treatment_vals.shape[0] != data_df.shape[0]: raise ValueError("Provided treatment values and dataframe should have the same length.") # Bulding the feature matrix n_samples = treatment_vals.shape[0] self.logger.debug("Number of samples" + str(n_samples) + str(len(self._treatment_name))) treatment_2d = treatment_vals.reshape((n_samples, len(self._treatment_name))) if len(self._observed_common_causes_names) > 0: features = np.concatenate((treatment_2d, observed_common_causes_vals), axis=1) else: features = treatment_2d if self._effect_modifier_names: for i in range(treatment_2d.shape[1]): curr_treatment = treatment_2d[:, i] new_features = curr_treatment[:, np.newaxis] * effect_modifiers_vals.to_numpy() features = np.concatenate((features, new_features), axis=1) features = features.astype( float, copy=False ) # converting to float in case of binary treatment and no other variables # features = sm.add_constant(features, has_constant='add') # to add an intercept term return features def construct_symbolic_estimator( self, first_stage_symbolic, second_stage_symbolic, total_effect_symbolic=None, estimand_type=None ): nie_symbolic = "(" + first_stage_symbolic + ")*(" + second_stage_symbolic + ")" if estimand_type == EstimandType.NONPARAMETRIC_NIE: return nie_symbolic elif estimand_type == EstimandType.NONPARAMETRIC_NDE: return "(" + total_effect_symbolic + ") - (" + nie_symbolic + ")"

andresmor-ms

4d4df7a4637a5f5e9cd9c5362499b1fb38debeab

db953a63aae205951f028c1050f141e3cdc0c97a

we can simply call it CausalEstimandType. We do not need Identifier. In fact, since dowhy is about causality, EstimandType would also work.

amit-sharma

py-why/dowhy

Functional api/identify effect

First of a series of PR to add a functional API according to: https://github.com/py-why/dowhy/wiki/API-proposal-for-v1 * Refactor `identify_effect` to have a functional API * Created `BackdoorIdentifier` class and extracted the logic from `CausalIdentifier` to be just a Protocol * Refactor the `identify_effect` method of `BackdoorIdentifier` and `IDIdentifier` to take the graph as parameter * Moved constants into `enums` for easier type checking * Backwards compatible with previous CausalModel API * Added notebook as demo that CausalModel API and new API behaves the same way

2022-09-16 21:35:24+00:00

2022-09-27 01:38:27+00:00

dowhy/causal_estimators/two_stage_regression_estimator.py

import copy import itertools import numpy as np import pandas as pd from dowhy.causal_estimator import CausalEstimate, CausalEstimator from dowhy.causal_estimators.linear_regression_estimator import LinearRegressionEstimator from dowhy.causal_identifier import CausalIdentifier from dowhy.utils.api import parse_state class TwoStageRegressionEstimator(CausalEstimator): """Compute treatment effect whenever the effect is fully mediated by another variable (front-door) or when there is an instrument available. Currently only supports a linear model for the effects. For a list of standard args and kwargs, see documentation for :class:`~dowhy.causal_estimator.CausalEstimator`. Supports additional parameters as listed below. """ # First stage statistical model DEFAULT_FIRST_STAGE_MODEL = LinearRegressionEstimator # Second stage statistical model DEFAULT_SECOND_STAGE_MODEL = LinearRegressionEstimator def __init__(self, *args, first_stage_model=None, second_stage_model=None, **kwargs): """ :param first_stage_model: First stage estimator to be used. Default is linear regression. :param second_stage_model: Second stage estimator to be used. Default is linear regression. """ # Required to ensure that self.method_params contains all the # parameters needed to create an object of this class args_dict = {k: v for k, v in locals().items() if k not in type(self)._STD_INIT_ARGS} args_dict.update(kwargs) super().__init__(*args, **args_dict) self.logger.info("INFO: Using Two Stage Regression Estimator") # Check if the treatment is one-dimensional if len(self._treatment_name) > 1: error_msg = str(self.__class__) + "cannot handle more than one treatment variable" raise Exception(error_msg) if self._target_estimand.identifier_method == "frontdoor": self.logger.debug("Front-door variable used:" + ",".join(self._target_estimand.get_frontdoor_variables())) self._frontdoor_variables_names = self._target_estimand.get_frontdoor_variables() if self._frontdoor_variables_names: self._frontdoor_variables = self._data[self._frontdoor_variables_names] else: self._frontdoor_variables = None error_msg = "No front-door variable present. Two stage regression is not applicable" self.logger.error(error_msg) elif self._target_estimand.identifier_method == "mediation": self.logger.debug("Mediators used:" + ",".join(self._target_estimand.get_mediator_variables())) self._mediators_names = self._target_estimand.get_mediator_variables() if self._mediators_names: self._mediators = self._data[self._mediators_names] else: self._mediators = None error_msg = "No mediator variable present. Two stage regression is not applicable" self.logger.error(error_msg) elif self._target_estimand.identifier_method == "iv": self.logger.debug( "Instrumental variables used:" + ",".join(self._target_estimand.get_instrumental_variables()) ) self._instrumental_variables_names = self._target_estimand.get_instrumental_variables() if self._instrumental_variables_names: self._instrumental_variables = self._data[self._instrumental_variables_names] else: self._instrumental_variables = None error_msg = "No instrumental variable present. Two stage regression is not applicable" self.logger.error(error_msg) if first_stage_model is not None: self.first_stage_model = first_stage_model else: self.first_stage_model = self.__class__.DEFAULT_FIRST_STAGE_MODEL self.logger.warning("First stage model not provided. Defaulting to sklearn.linear_model.LinearRegression.") if second_stage_model is not None: self.second_stage_model = second_stage_model else: self.second_stage_model = self.__class__.DEFAULT_SECOND_STAGE_MODEL self.logger.warning("Second stage model not provided. Defaulting to backdoor.linear_regression.") def _estimate_effect(self): estimate_value = None # First stage modified_target_estimand = copy.deepcopy(self._target_estimand) modified_target_estimand.identifier_method = "backdoor" modified_target_estimand.backdoor_variables = self._target_estimand.mediation_first_stage_confounders if self._target_estimand.identifier_method == "frontdoor": modified_target_estimand.outcome_variable = parse_state(self._frontdoor_variables_names) elif self._target_estimand.identifier_method == "mediation": modified_target_estimand.outcome_variable = parse_state(self._mediators_names) first_stage_estimate = self.first_stage_model( self._data, modified_target_estimand, self._treatment_name, parse_state(modified_target_estimand.outcome_variable), control_value=self._control_value, treatment_value=self._treatment_value, test_significance=self._significance_test, evaluate_effect_strength=self._effect_strength_eval, confidence_intervals=self._confidence_intervals, target_units=self._target_units, effect_modifiers=self._effect_modifier_names, **self.method_params, )._estimate_effect() # Second Stage modified_target_estimand = copy.deepcopy(self._target_estimand) modified_target_estimand.identifier_method = "backdoor" modified_target_estimand.backdoor_variables = self._target_estimand.mediation_second_stage_confounders if self._target_estimand.identifier_method == "frontdoor": modified_target_estimand.treatment_variable = parse_state(self._frontdoor_variables_names) elif self._target_estimand.identifier_method == "mediation": modified_target_estimand.treatment_variable = parse_state(self._mediators_names) second_stage_estimate = self.second_stage_model( self._data, modified_target_estimand, parse_state(modified_target_estimand.treatment_variable), parse_state(self._outcome_name), # to convert it to array before passing to causal estimator control_value=self._control_value, treatment_value=self._treatment_value, test_significance=self._significance_test, evaluate_effect_strength=self._effect_strength_eval, confidence_intervals=self._confidence_intervals, target_units=self._target_units, effect_modifiers=self._effect_modifier_names, **self.method_params, )._estimate_effect() # Combining the two estimates natural_indirect_effect = first_stage_estimate.value * second_stage_estimate.value # This same estimate is valid for frontdoor as well as mediation (NIE) estimate_value = natural_indirect_effect self.symbolic_estimator = self.construct_symbolic_estimator( first_stage_estimate.realized_estimand_expr, second_stage_estimate.realized_estimand_expr, estimand_type=CausalIdentifier.NONPARAMETRIC_NIE, ) if self._target_estimand.estimand_type == CausalIdentifier.NONPARAMETRIC_NDE: # Total effect of treatment modified_target_estimand = copy.deepcopy(self._target_estimand) modified_target_estimand.identifier_method = "backdoor" total_effect_estimate = self.second_stage_model( self._data, modified_target_estimand, self._treatment_name, parse_state(self._outcome_name), control_value=self._control_value, treatment_value=self._treatment_value, test_significance=self._significance_test, evaluate_effect_strength=self._effect_strength_eval, confidence_intervals=self._confidence_intervals, target_units=self._target_units, effect_modifiers=self._effect_modifier_names, **self.method_params, )._estimate_effect() natural_direct_effect = total_effect_estimate.value - natural_indirect_effect estimate_value = natural_direct_effect self.symbolic_estimator = self.construct_symbolic_estimator( first_stage_estimate.realized_estimand_expr, second_stage_estimate.realized_estimand_expr, total_effect_estimate.realized_estimand_expr, estimand_type=self._target_estimand.estimand_type, ) return CausalEstimate( estimate=estimate_value, control_value=self._control_value, treatment_value=self._treatment_value, target_estimand=self._target_estimand, realized_estimand_expr=self.symbolic_estimator, ) def build_first_stage_features(self): data_df = self._data treatment_vals = data_df[self._treatment_name] if len(self._observed_common_causes_names) > 0: observed_common_causes_vals = data_df[self._observed_common_causes_names] observed_common_causes_vals = pd.get_dummies(observed_common_causes_vals, drop_first=True) if self._effect_modifier_names: effect_modifiers_vals = data_df[self._effect_modifier_names] effect_modifiers_vals = pd.get_dummies(effect_modifiers_vals, drop_first=True) if type(treatment_vals) is not np.ndarray: treatment_vals = treatment_vals.to_numpy() if treatment_vals.shape[0] != data_df.shape[0]: raise ValueError("Provided treatment values and dataframe should have the same length.") # Bulding the feature matrix n_samples = treatment_vals.shape[0] self.logger.debug("Number of samples" + str(n_samples) + str(len(self._treatment_name))) treatment_2d = treatment_vals.reshape((n_samples, len(self._treatment_name))) if len(self._observed_common_causes_names) > 0: features = np.concatenate((treatment_2d, observed_common_causes_vals), axis=1) else: features = treatment_2d if self._effect_modifier_names: for i in range(treatment_2d.shape[1]): curr_treatment = treatment_2d[:, i] new_features = curr_treatment[:, np.newaxis] * effect_modifiers_vals.to_numpy() features = np.concatenate((features, new_features), axis=1) features = features.astype( float, copy=False ) # converting to float in case of binary treatment and no other variables # features = sm.add_constant(features, has_constant='add') # to add an intercept term return features def construct_symbolic_estimator( self, first_stage_symbolic, second_stage_symbolic, total_effect_symbolic=None, estimand_type=None ): nie_symbolic = "(" + first_stage_symbolic + ")*(" + second_stage_symbolic + ")" if estimand_type == CausalIdentifier.NONPARAMETRIC_NIE: return nie_symbolic elif estimand_type == CausalIdentifier.NONPARAMETRIC_NDE: return "(" + total_effect_symbolic + ") - (" + nie_symbolic + ")"

import copy import itertools import numpy as np import pandas as pd from dowhy.causal_estimator import CausalEstimate, CausalEstimator from dowhy.causal_estimators.linear_regression_estimator import LinearRegressionEstimator from dowhy.causal_identifier.identify_effect import EstimandType from dowhy.utils.api import parse_state class TwoStageRegressionEstimator(CausalEstimator): """Compute treatment effect whenever the effect is fully mediated by another variable (front-door) or when there is an instrument available. Currently only supports a linear model for the effects. For a list of standard args and kwargs, see documentation for :class:`~dowhy.causal_estimator.CausalEstimator`. Supports additional parameters as listed below. """ # First stage statistical model DEFAULT_FIRST_STAGE_MODEL = LinearRegressionEstimator # Second stage statistical model DEFAULT_SECOND_STAGE_MODEL = LinearRegressionEstimator def __init__(self, *args, first_stage_model=None, second_stage_model=None, **kwargs): """ :param first_stage_model: First stage estimator to be used. Default is linear regression. :param second_stage_model: Second stage estimator to be used. Default is linear regression. """ # Required to ensure that self.method_params contains all the # parameters needed to create an object of this class args_dict = {k: v for k, v in locals().items() if k not in type(self)._STD_INIT_ARGS} args_dict.update(kwargs) super().__init__(*args, **args_dict) self.logger.info("INFO: Using Two Stage Regression Estimator") # Check if the treatment is one-dimensional if len(self._treatment_name) > 1: error_msg = str(self.__class__) + "cannot handle more than one treatment variable" raise Exception(error_msg) if self._target_estimand.identifier_method == "frontdoor": self.logger.debug("Front-door variable used:" + ",".join(self._target_estimand.get_frontdoor_variables())) self._frontdoor_variables_names = self._target_estimand.get_frontdoor_variables() if self._frontdoor_variables_names: self._frontdoor_variables = self._data[self._frontdoor_variables_names] else: self._frontdoor_variables = None error_msg = "No front-door variable present. Two stage regression is not applicable" self.logger.error(error_msg) elif self._target_estimand.identifier_method == "mediation": self.logger.debug("Mediators used:" + ",".join(self._target_estimand.get_mediator_variables())) self._mediators_names = self._target_estimand.get_mediator_variables() if self._mediators_names: self._mediators = self._data[self._mediators_names] else: self._mediators = None error_msg = "No mediator variable present. Two stage regression is not applicable" self.logger.error(error_msg) elif self._target_estimand.identifier_method == "iv": self.logger.debug( "Instrumental variables used:" + ",".join(self._target_estimand.get_instrumental_variables()) ) self._instrumental_variables_names = self._target_estimand.get_instrumental_variables() if self._instrumental_variables_names: self._instrumental_variables = self._data[self._instrumental_variables_names] else: self._instrumental_variables = None error_msg = "No instrumental variable present. Two stage regression is not applicable" self.logger.error(error_msg) if first_stage_model is not None: self.first_stage_model = first_stage_model else: self.first_stage_model = self.__class__.DEFAULT_FIRST_STAGE_MODEL self.logger.warning("First stage model not provided. Defaulting to sklearn.linear_model.LinearRegression.") if second_stage_model is not None: self.second_stage_model = second_stage_model else: self.second_stage_model = self.__class__.DEFAULT_SECOND_STAGE_MODEL self.logger.warning("Second stage model not provided. Defaulting to backdoor.linear_regression.") def _estimate_effect(self): estimate_value = None # First stage modified_target_estimand = copy.deepcopy(self._target_estimand) modified_target_estimand.identifier_method = "backdoor" modified_target_estimand.backdoor_variables = self._target_estimand.mediation_first_stage_confounders if self._target_estimand.identifier_method == "frontdoor": modified_target_estimand.outcome_variable = parse_state(self._frontdoor_variables_names) elif self._target_estimand.identifier_method == "mediation": modified_target_estimand.outcome_variable = parse_state(self._mediators_names) first_stage_estimate = self.first_stage_model( self._data, modified_target_estimand, self._treatment_name, parse_state(modified_target_estimand.outcome_variable), control_value=self._control_value, treatment_value=self._treatment_value, test_significance=self._significance_test, evaluate_effect_strength=self._effect_strength_eval, confidence_intervals=self._confidence_intervals, target_units=self._target_units, effect_modifiers=self._effect_modifier_names, **self.method_params, )._estimate_effect() # Second Stage modified_target_estimand = copy.deepcopy(self._target_estimand) modified_target_estimand.identifier_method = "backdoor" modified_target_estimand.backdoor_variables = self._target_estimand.mediation_second_stage_confounders if self._target_estimand.identifier_method == "frontdoor": modified_target_estimand.treatment_variable = parse_state(self._frontdoor_variables_names) elif self._target_estimand.identifier_method == "mediation": modified_target_estimand.treatment_variable = parse_state(self._mediators_names) second_stage_estimate = self.second_stage_model( self._data, modified_target_estimand, parse_state(modified_target_estimand.treatment_variable), parse_state(self._outcome_name), # to convert it to array before passing to causal estimator control_value=self._control_value, treatment_value=self._treatment_value, test_significance=self._significance_test, evaluate_effect_strength=self._effect_strength_eval, confidence_intervals=self._confidence_intervals, target_units=self._target_units, effect_modifiers=self._effect_modifier_names, **self.method_params, )._estimate_effect() # Combining the two estimates natural_indirect_effect = first_stage_estimate.value * second_stage_estimate.value # This same estimate is valid for frontdoor as well as mediation (NIE) estimate_value = natural_indirect_effect self.symbolic_estimator = self.construct_symbolic_estimator( first_stage_estimate.realized_estimand_expr, second_stage_estimate.realized_estimand_expr, estimand_type=EstimandType.NONPARAMETRIC_NIE, ) if self._target_estimand.estimand_type == EstimandType.NONPARAMETRIC_NDE: # Total effect of treatment modified_target_estimand = copy.deepcopy(self._target_estimand) modified_target_estimand.identifier_method = "backdoor" total_effect_estimate = self.second_stage_model( self._data, modified_target_estimand, self._treatment_name, parse_state(self._outcome_name), control_value=self._control_value, treatment_value=self._treatment_value, test_significance=self._significance_test, evaluate_effect_strength=self._effect_strength_eval, confidence_intervals=self._confidence_intervals, target_units=self._target_units, effect_modifiers=self._effect_modifier_names, **self.method_params, )._estimate_effect() natural_direct_effect = total_effect_estimate.value - natural_indirect_effect estimate_value = natural_direct_effect self.symbolic_estimator = self.construct_symbolic_estimator( first_stage_estimate.realized_estimand_expr, second_stage_estimate.realized_estimand_expr, total_effect_estimate.realized_estimand_expr, estimand_type=self._target_estimand.estimand_type, ) return CausalEstimate( estimate=estimate_value, control_value=self._control_value, treatment_value=self._treatment_value, target_estimand=self._target_estimand, realized_estimand_expr=self.symbolic_estimator, ) def build_first_stage_features(self): data_df = self._data treatment_vals = data_df[self._treatment_name] if len(self._observed_common_causes_names) > 0: observed_common_causes_vals = data_df[self._observed_common_causes_names] observed_common_causes_vals = pd.get_dummies(observed_common_causes_vals, drop_first=True) if self._effect_modifier_names: effect_modifiers_vals = data_df[self._effect_modifier_names] effect_modifiers_vals = pd.get_dummies(effect_modifiers_vals, drop_first=True) if type(treatment_vals) is not np.ndarray: treatment_vals = treatment_vals.to_numpy() if treatment_vals.shape[0] != data_df.shape[0]: raise ValueError("Provided treatment values and dataframe should have the same length.") # Bulding the feature matrix n_samples = treatment_vals.shape[0] self.logger.debug("Number of samples" + str(n_samples) + str(len(self._treatment_name))) treatment_2d = treatment_vals.reshape((n_samples, len(self._treatment_name))) if len(self._observed_common_causes_names) > 0: features = np.concatenate((treatment_2d, observed_common_causes_vals), axis=1) else: features = treatment_2d if self._effect_modifier_names: for i in range(treatment_2d.shape[1]): curr_treatment = treatment_2d[:, i] new_features = curr_treatment[:, np.newaxis] * effect_modifiers_vals.to_numpy() features = np.concatenate((features, new_features), axis=1) features = features.astype( float, copy=False ) # converting to float in case of binary treatment and no other variables # features = sm.add_constant(features, has_constant='add') # to add an intercept term return features def construct_symbolic_estimator( self, first_stage_symbolic, second_stage_symbolic, total_effect_symbolic=None, estimand_type=None ): nie_symbolic = "(" + first_stage_symbolic + ")*(" + second_stage_symbolic + ")" if estimand_type == EstimandType.NONPARAMETRIC_NIE: return nie_symbolic elif estimand_type == EstimandType.NONPARAMETRIC_NDE: return "(" + total_effect_symbolic + ") - (" + nie_symbolic + ")"

andresmor-ms

4d4df7a4637a5f5e9cd9c5362499b1fb38debeab

db953a63aae205951f028c1050f141e3cdc0c97a

Would you say this should be defined in a more generic package instead of causal_identifier so that it can be reused in a more general way across all of dowhy?

andresmor-ms

py-why/dowhy

Functional api/identify effect

First of a series of PR to add a functional API according to: https://github.com/py-why/dowhy/wiki/API-proposal-for-v1 * Refactor `identify_effect` to have a functional API * Created `BackdoorIdentifier` class and extracted the logic from `CausalIdentifier` to be just a Protocol * Refactor the `identify_effect` method of `BackdoorIdentifier` and `IDIdentifier` to take the graph as parameter * Moved constants into `enums` for easier type checking * Backwards compatible with previous CausalModel API * Added notebook as demo that CausalModel API and new API behaves the same way

2022-09-16 21:35:24+00:00

2022-09-27 01:38:27+00:00

dowhy/causal_estimators/two_stage_regression_estimator.py

import copy import itertools import numpy as np import pandas as pd from dowhy.causal_estimator import CausalEstimate, CausalEstimator from dowhy.causal_estimators.linear_regression_estimator import LinearRegressionEstimator from dowhy.causal_identifier import CausalIdentifier from dowhy.utils.api import parse_state class TwoStageRegressionEstimator(CausalEstimator): """Compute treatment effect whenever the effect is fully mediated by another variable (front-door) or when there is an instrument available. Currently only supports a linear model for the effects. For a list of standard args and kwargs, see documentation for :class:`~dowhy.causal_estimator.CausalEstimator`. Supports additional parameters as listed below. """ # First stage statistical model DEFAULT_FIRST_STAGE_MODEL = LinearRegressionEstimator # Second stage statistical model DEFAULT_SECOND_STAGE_MODEL = LinearRegressionEstimator def __init__(self, *args, first_stage_model=None, second_stage_model=None, **kwargs): """ :param first_stage_model: First stage estimator to be used. Default is linear regression. :param second_stage_model: Second stage estimator to be used. Default is linear regression. """ # Required to ensure that self.method_params contains all the # parameters needed to create an object of this class args_dict = {k: v for k, v in locals().items() if k not in type(self)._STD_INIT_ARGS} args_dict.update(kwargs) super().__init__(*args, **args_dict) self.logger.info("INFO: Using Two Stage Regression Estimator") # Check if the treatment is one-dimensional if len(self._treatment_name) > 1: error_msg = str(self.__class__) + "cannot handle more than one treatment variable" raise Exception(error_msg) if self._target_estimand.identifier_method == "frontdoor": self.logger.debug("Front-door variable used:" + ",".join(self._target_estimand.get_frontdoor_variables())) self._frontdoor_variables_names = self._target_estimand.get_frontdoor_variables() if self._frontdoor_variables_names: self._frontdoor_variables = self._data[self._frontdoor_variables_names] else: self._frontdoor_variables = None error_msg = "No front-door variable present. Two stage regression is not applicable" self.logger.error(error_msg) elif self._target_estimand.identifier_method == "mediation": self.logger.debug("Mediators used:" + ",".join(self._target_estimand.get_mediator_variables())) self._mediators_names = self._target_estimand.get_mediator_variables() if self._mediators_names: self._mediators = self._data[self._mediators_names] else: self._mediators = None error_msg = "No mediator variable present. Two stage regression is not applicable" self.logger.error(error_msg) elif self._target_estimand.identifier_method == "iv": self.logger.debug( "Instrumental variables used:" + ",".join(self._target_estimand.get_instrumental_variables()) ) self._instrumental_variables_names = self._target_estimand.get_instrumental_variables() if self._instrumental_variables_names: self._instrumental_variables = self._data[self._instrumental_variables_names] else: self._instrumental_variables = None error_msg = "No instrumental variable present. Two stage regression is not applicable" self.logger.error(error_msg) if first_stage_model is not None: self.first_stage_model = first_stage_model else: self.first_stage_model = self.__class__.DEFAULT_FIRST_STAGE_MODEL self.logger.warning("First stage model not provided. Defaulting to sklearn.linear_model.LinearRegression.") if second_stage_model is not None: self.second_stage_model = second_stage_model else: self.second_stage_model = self.__class__.DEFAULT_SECOND_STAGE_MODEL self.logger.warning("Second stage model not provided. Defaulting to backdoor.linear_regression.") def _estimate_effect(self): estimate_value = None # First stage modified_target_estimand = copy.deepcopy(self._target_estimand) modified_target_estimand.identifier_method = "backdoor" modified_target_estimand.backdoor_variables = self._target_estimand.mediation_first_stage_confounders if self._target_estimand.identifier_method == "frontdoor": modified_target_estimand.outcome_variable = parse_state(self._frontdoor_variables_names) elif self._target_estimand.identifier_method == "mediation": modified_target_estimand.outcome_variable = parse_state(self._mediators_names) first_stage_estimate = self.first_stage_model( self._data, modified_target_estimand, self._treatment_name, parse_state(modified_target_estimand.outcome_variable), control_value=self._control_value, treatment_value=self._treatment_value, test_significance=self._significance_test, evaluate_effect_strength=self._effect_strength_eval, confidence_intervals=self._confidence_intervals, target_units=self._target_units, effect_modifiers=self._effect_modifier_names, **self.method_params, )._estimate_effect() # Second Stage modified_target_estimand = copy.deepcopy(self._target_estimand) modified_target_estimand.identifier_method = "backdoor" modified_target_estimand.backdoor_variables = self._target_estimand.mediation_second_stage_confounders if self._target_estimand.identifier_method == "frontdoor": modified_target_estimand.treatment_variable = parse_state(self._frontdoor_variables_names) elif self._target_estimand.identifier_method == "mediation": modified_target_estimand.treatment_variable = parse_state(self._mediators_names) second_stage_estimate = self.second_stage_model( self._data, modified_target_estimand, parse_state(modified_target_estimand.treatment_variable), parse_state(self._outcome_name), # to convert it to array before passing to causal estimator control_value=self._control_value, treatment_value=self._treatment_value, test_significance=self._significance_test, evaluate_effect_strength=self._effect_strength_eval, confidence_intervals=self._confidence_intervals, target_units=self._target_units, effect_modifiers=self._effect_modifier_names, **self.method_params, )._estimate_effect() # Combining the two estimates natural_indirect_effect = first_stage_estimate.value * second_stage_estimate.value # This same estimate is valid for frontdoor as well as mediation (NIE) estimate_value = natural_indirect_effect self.symbolic_estimator = self.construct_symbolic_estimator( first_stage_estimate.realized_estimand_expr, second_stage_estimate.realized_estimand_expr, estimand_type=CausalIdentifier.NONPARAMETRIC_NIE, ) if self._target_estimand.estimand_type == CausalIdentifier.NONPARAMETRIC_NDE: # Total effect of treatment modified_target_estimand = copy.deepcopy(self._target_estimand) modified_target_estimand.identifier_method = "backdoor" total_effect_estimate = self.second_stage_model( self._data, modified_target_estimand, self._treatment_name, parse_state(self._outcome_name), control_value=self._control_value, treatment_value=self._treatment_value, test_significance=self._significance_test, evaluate_effect_strength=self._effect_strength_eval, confidence_intervals=self._confidence_intervals, target_units=self._target_units, effect_modifiers=self._effect_modifier_names, **self.method_params, )._estimate_effect() natural_direct_effect = total_effect_estimate.value - natural_indirect_effect estimate_value = natural_direct_effect self.symbolic_estimator = self.construct_symbolic_estimator( first_stage_estimate.realized_estimand_expr, second_stage_estimate.realized_estimand_expr, total_effect_estimate.realized_estimand_expr, estimand_type=self._target_estimand.estimand_type, ) return CausalEstimate( estimate=estimate_value, control_value=self._control_value, treatment_value=self._treatment_value, target_estimand=self._target_estimand, realized_estimand_expr=self.symbolic_estimator, ) def build_first_stage_features(self): data_df = self._data treatment_vals = data_df[self._treatment_name] if len(self._observed_common_causes_names) > 0: observed_common_causes_vals = data_df[self._observed_common_causes_names] observed_common_causes_vals = pd.get_dummies(observed_common_causes_vals, drop_first=True) if self._effect_modifier_names: effect_modifiers_vals = data_df[self._effect_modifier_names] effect_modifiers_vals = pd.get_dummies(effect_modifiers_vals, drop_first=True) if type(treatment_vals) is not np.ndarray: treatment_vals = treatment_vals.to_numpy() if treatment_vals.shape[0] != data_df.shape[0]: raise ValueError("Provided treatment values and dataframe should have the same length.") # Bulding the feature matrix n_samples = treatment_vals.shape[0] self.logger.debug("Number of samples" + str(n_samples) + str(len(self._treatment_name))) treatment_2d = treatment_vals.reshape((n_samples, len(self._treatment_name))) if len(self._observed_common_causes_names) > 0: features = np.concatenate((treatment_2d, observed_common_causes_vals), axis=1) else: features = treatment_2d if self._effect_modifier_names: for i in range(treatment_2d.shape[1]): curr_treatment = treatment_2d[:, i] new_features = curr_treatment[:, np.newaxis] * effect_modifiers_vals.to_numpy() features = np.concatenate((features, new_features), axis=1) features = features.astype( float, copy=False ) # converting to float in case of binary treatment and no other variables # features = sm.add_constant(features, has_constant='add') # to add an intercept term return features def construct_symbolic_estimator( self, first_stage_symbolic, second_stage_symbolic, total_effect_symbolic=None, estimand_type=None ): nie_symbolic = "(" + first_stage_symbolic + ")*(" + second_stage_symbolic + ")" if estimand_type == CausalIdentifier.NONPARAMETRIC_NIE: return nie_symbolic elif estimand_type == CausalIdentifier.NONPARAMETRIC_NDE: return "(" + total_effect_symbolic + ") - (" + nie_symbolic + ")"

import copy import itertools import numpy as np import pandas as pd from dowhy.causal_estimator import CausalEstimate, CausalEstimator from dowhy.causal_estimators.linear_regression_estimator import LinearRegressionEstimator from dowhy.causal_identifier.identify_effect import EstimandType from dowhy.utils.api import parse_state class TwoStageRegressionEstimator(CausalEstimator): """Compute treatment effect whenever the effect is fully mediated by another variable (front-door) or when there is an instrument available. Currently only supports a linear model for the effects. For a list of standard args and kwargs, see documentation for :class:`~dowhy.causal_estimator.CausalEstimator`. Supports additional parameters as listed below. """ # First stage statistical model DEFAULT_FIRST_STAGE_MODEL = LinearRegressionEstimator # Second stage statistical model DEFAULT_SECOND_STAGE_MODEL = LinearRegressionEstimator def __init__(self, *args, first_stage_model=None, second_stage_model=None, **kwargs): """ :param first_stage_model: First stage estimator to be used. Default is linear regression. :param second_stage_model: Second stage estimator to be used. Default is linear regression. """ # Required to ensure that self.method_params contains all the # parameters needed to create an object of this class args_dict = {k: v for k, v in locals().items() if k not in type(self)._STD_INIT_ARGS} args_dict.update(kwargs) super().__init__(*args, **args_dict) self.logger.info("INFO: Using Two Stage Regression Estimator") # Check if the treatment is one-dimensional if len(self._treatment_name) > 1: error_msg = str(self.__class__) + "cannot handle more than one treatment variable" raise Exception(error_msg) if self._target_estimand.identifier_method == "frontdoor": self.logger.debug("Front-door variable used:" + ",".join(self._target_estimand.get_frontdoor_variables())) self._frontdoor_variables_names = self._target_estimand.get_frontdoor_variables() if self._frontdoor_variables_names: self._frontdoor_variables = self._data[self._frontdoor_variables_names] else: self._frontdoor_variables = None error_msg = "No front-door variable present. Two stage regression is not applicable" self.logger.error(error_msg) elif self._target_estimand.identifier_method == "mediation": self.logger.debug("Mediators used:" + ",".join(self._target_estimand.get_mediator_variables())) self._mediators_names = self._target_estimand.get_mediator_variables() if self._mediators_names: self._mediators = self._data[self._mediators_names] else: self._mediators = None error_msg = "No mediator variable present. Two stage regression is not applicable" self.logger.error(error_msg) elif self._target_estimand.identifier_method == "iv": self.logger.debug( "Instrumental variables used:" + ",".join(self._target_estimand.get_instrumental_variables()) ) self._instrumental_variables_names = self._target_estimand.get_instrumental_variables() if self._instrumental_variables_names: self._instrumental_variables = self._data[self._instrumental_variables_names] else: self._instrumental_variables = None error_msg = "No instrumental variable present. Two stage regression is not applicable" self.logger.error(error_msg) if first_stage_model is not None: self.first_stage_model = first_stage_model else: self.first_stage_model = self.__class__.DEFAULT_FIRST_STAGE_MODEL self.logger.warning("First stage model not provided. Defaulting to sklearn.linear_model.LinearRegression.") if second_stage_model is not None: self.second_stage_model = second_stage_model else: self.second_stage_model = self.__class__.DEFAULT_SECOND_STAGE_MODEL self.logger.warning("Second stage model not provided. Defaulting to backdoor.linear_regression.") def _estimate_effect(self): estimate_value = None # First stage modified_target_estimand = copy.deepcopy(self._target_estimand) modified_target_estimand.identifier_method = "backdoor" modified_target_estimand.backdoor_variables = self._target_estimand.mediation_first_stage_confounders if self._target_estimand.identifier_method == "frontdoor": modified_target_estimand.outcome_variable = parse_state(self._frontdoor_variables_names) elif self._target_estimand.identifier_method == "mediation": modified_target_estimand.outcome_variable = parse_state(self._mediators_names) first_stage_estimate = self.first_stage_model( self._data, modified_target_estimand, self._treatment_name, parse_state(modified_target_estimand.outcome_variable), control_value=self._control_value, treatment_value=self._treatment_value, test_significance=self._significance_test, evaluate_effect_strength=self._effect_strength_eval, confidence_intervals=self._confidence_intervals, target_units=self._target_units, effect_modifiers=self._effect_modifier_names, **self.method_params, )._estimate_effect() # Second Stage modified_target_estimand = copy.deepcopy(self._target_estimand) modified_target_estimand.identifier_method = "backdoor" modified_target_estimand.backdoor_variables = self._target_estimand.mediation_second_stage_confounders if self._target_estimand.identifier_method == "frontdoor": modified_target_estimand.treatment_variable = parse_state(self._frontdoor_variables_names) elif self._target_estimand.identifier_method == "mediation": modified_target_estimand.treatment_variable = parse_state(self._mediators_names) second_stage_estimate = self.second_stage_model( self._data, modified_target_estimand, parse_state(modified_target_estimand.treatment_variable), parse_state(self._outcome_name), # to convert it to array before passing to causal estimator control_value=self._control_value, treatment_value=self._treatment_value, test_significance=self._significance_test, evaluate_effect_strength=self._effect_strength_eval, confidence_intervals=self._confidence_intervals, target_units=self._target_units, effect_modifiers=self._effect_modifier_names, **self.method_params, )._estimate_effect() # Combining the two estimates natural_indirect_effect = first_stage_estimate.value * second_stage_estimate.value # This same estimate is valid for frontdoor as well as mediation (NIE) estimate_value = natural_indirect_effect self.symbolic_estimator = self.construct_symbolic_estimator( first_stage_estimate.realized_estimand_expr, second_stage_estimate.realized_estimand_expr, estimand_type=EstimandType.NONPARAMETRIC_NIE, ) if self._target_estimand.estimand_type == EstimandType.NONPARAMETRIC_NDE: # Total effect of treatment modified_target_estimand = copy.deepcopy(self._target_estimand) modified_target_estimand.identifier_method = "backdoor" total_effect_estimate = self.second_stage_model( self._data, modified_target_estimand, self._treatment_name, parse_state(self._outcome_name), control_value=self._control_value, treatment_value=self._treatment_value, test_significance=self._significance_test, evaluate_effect_strength=self._effect_strength_eval, confidence_intervals=self._confidence_intervals, target_units=self._target_units, effect_modifiers=self._effect_modifier_names, **self.method_params, )._estimate_effect() natural_direct_effect = total_effect_estimate.value - natural_indirect_effect estimate_value = natural_direct_effect self.symbolic_estimator = self.construct_symbolic_estimator( first_stage_estimate.realized_estimand_expr, second_stage_estimate.realized_estimand_expr, total_effect_estimate.realized_estimand_expr, estimand_type=self._target_estimand.estimand_type, ) return CausalEstimate( estimate=estimate_value, control_value=self._control_value, treatment_value=self._treatment_value, target_estimand=self._target_estimand, realized_estimand_expr=self.symbolic_estimator, ) def build_first_stage_features(self): data_df = self._data treatment_vals = data_df[self._treatment_name] if len(self._observed_common_causes_names) > 0: observed_common_causes_vals = data_df[self._observed_common_causes_names] observed_common_causes_vals = pd.get_dummies(observed_common_causes_vals, drop_first=True) if self._effect_modifier_names: effect_modifiers_vals = data_df[self._effect_modifier_names] effect_modifiers_vals = pd.get_dummies(effect_modifiers_vals, drop_first=True) if type(treatment_vals) is not np.ndarray: treatment_vals = treatment_vals.to_numpy() if treatment_vals.shape[0] != data_df.shape[0]: raise ValueError("Provided treatment values and dataframe should have the same length.") # Bulding the feature matrix n_samples = treatment_vals.shape[0] self.logger.debug("Number of samples" + str(n_samples) + str(len(self._treatment_name))) treatment_2d = treatment_vals.reshape((n_samples, len(self._treatment_name))) if len(self._observed_common_causes_names) > 0: features = np.concatenate((treatment_2d, observed_common_causes_vals), axis=1) else: features = treatment_2d if self._effect_modifier_names: for i in range(treatment_2d.shape[1]): curr_treatment = treatment_2d[:, i] new_features = curr_treatment[:, np.newaxis] * effect_modifiers_vals.to_numpy() features = np.concatenate((features, new_features), axis=1) features = features.astype( float, copy=False ) # converting to float in case of binary treatment and no other variables # features = sm.add_constant(features, has_constant='add') # to add an intercept term return features def construct_symbolic_estimator( self, first_stage_symbolic, second_stage_symbolic, total_effect_symbolic=None, estimand_type=None ): nie_symbolic = "(" + first_stage_symbolic + ")*(" + second_stage_symbolic + ")" if estimand_type == EstimandType.NONPARAMETRIC_NIE: return nie_symbolic elif estimand_type == EstimandType.NONPARAMETRIC_NDE: return "(" + total_effect_symbolic + ") - (" + nie_symbolic + ")"

andresmor-ms

4d4df7a4637a5f5e9cd9c5362499b1fb38debeab

db953a63aae205951f028c1050f141e3cdc0c97a

Let's keep it where it is right now. The current EstimandType is specific to the effect inference pipeline and the interface between identification and estimation.

emrekiciman

py-why/dowhy

Overhaul GCM introduction

* Remove bibtex from GCM introduction. This is covered in docs/source/cite.rst. * Add 'Typical usage' section in GCM introduction

2022-09-05 14:12:41+00:00

2022-11-02 10:01:42+00:00

docs/source/user_guide/gcm_based_inference/introduction.rst

Introduction ============ Graphical causal model-based inference, or GCM-based inference for short, is an experimental addition to DoWhy, that currently works separately from DoWhy's main API. Its experimental status also means that its API may undergo breaking changes in the future. It will be forming a part of a joint, `new API <https://github.com/py-why/dowhy/wiki/API-proposal-for-v1>`_. We welcome your comments. The ``dowhy.gcm`` package provides a variety of ways to answer causal questions and we'll go through them in detail in section :doc:`answering_causal_questions/index`. However, before diving into them, let's understand the basic building blocks and usage patterns it is built upon. The basic building blocks ^^^^^^^^^^^^^^^^^^^^^^^^^ All main features of the GCM-based inference in DoWhy are built around the concept of **graphical causal models**. A graphical causal model consists of a causal direct acyclic graph (DAG) of variables and a **causal mechanism** for each of the variables. A causal mechanism defines the conditional distribution of a variable given its parents in the graph, or, in case of root node variables, simply its distribution. The most general case of a GCM is a **probabilistic causal model** (PCM), where causal mechanisms are defined by **conditional stochastic models** and **stochastic models**. In the ``dowhy.gcm`` package, these are represented by :class:`~ProbabilisticCausalModel`, :class:`~ConditionalStochasticModel`, and :class:`~StochasticModel`. .. image:: pcm.png :width: 80% :align: center | In practical terms however, we often use **structural causal models** (SCMs) to represent our GCMs, and the causal mechanisms are defined by **functional causal models** (FCMs) for non-root nodes and **stochastic models** for root nodes. An SCM implements the same traits as a PCM, but on top of that, its FCMs allow us to reason *further* about its data generation process based on parents and noise, and hence, allow us e.g. to compute counterfactuals. .. image:: scm.png :width: 80% :align: center | To keep this introduction simple, we will stick with SCMs for now. As mentioned above, a causal mechanism describes how the values of a node are influenced by the values of its parent nodes. We will dive much deeper into the details of causal mechanisms and their meaning in section :doc:`customizing_model_assignment`. But for this introduction, we will treat them as an opaque thing that is needed to answer causal questions. With that in mind, the typical steps involved in answering a causal question, are: 1. **Modeling cause-effect relationships as a GCM (causal graph + causal mechanisms):** :: causal_model = StructuralCausalModel(nx.DiGraph([('X', 'Y'), ('Y', 'Z')])) # X -> Y -> Z auto.assign_causal_mechanisms(causal_model, data) Or manually assign causal mechanisms: :: causal_model.set_causal_mechanism('X', EmpiricalDistribution()) causal_model.set_causal_mechanism('Y', AdditiveNoiseModel(create_linear_regressor())) causal_model.set_causal_mechanism('Z', AdditiveNoiseModel(create_linear_regressor())) 2. **Fitting the GCM to the data:** :: fit(causal_model, data) 3. **Answering a causal query based on the GCM:** :: results = <causal_query>(causal_model, ...) Where ``<causal_query>`` can be one of multiple functions explained in :doc:`answering_causal_questions/index`. Let's look at each of these steps in more detail. Step 1: Modeling cause-effect relationships as a structural causal model (SCM) ------------------------------------------------------------------------------ The first step is to model the cause-effect relationships between variables relevant to our use case. We do that in form of a causal graph. A causal graph is a directed acyclic graph (DAG) where an edge X→Y implies that X causes Y. Statistically, a causal graph encodes the conditional independence relations between variables. Using the `networkx <https://networkx .github.io/>`__ library, we can create causal graphs. In the snippet below, we create a chain X→Y→Z: >>> import networkx as nx >>> causal_graph = nx.DiGraph([('X', 'Y'), ('Y', 'Z')]) To answer causal questions using causal graphs, we also have to know the nature of underlying data-generating process of variables. A causal graph by itself, being a diagram, does not have any information about the data-generating process. To introduce this data-generating process, we use an SCM that's built on top of our causal graph: >>> from dowhy import gcm >>> causal_model = gcm.StructuralCausalModel(causal_graph) At this point we would normally load our dataset. For this introduction, we generate some synthetic data instead. The API takes data in form of Pandas DataFrames: >>> import numpy as np, pandas as pd >>> X = np.random.normal(loc=0, scale=1, size=1000) >>> Y = 2 * X + np.random.normal(loc=0, scale=1, size=1000) >>> Z = 3 * Y + np.random.normal(loc=0, scale=1, size=1000) >>> data = pd.DataFrame(data=dict(X=X, Y=Y, Z=Z)) >>> data.head() X Y Z 0 -2.253500 -3.638579 -10.370047 1 -1.078337 -2.114581 -6.028030 2 -0.962719 -2.157896 -5.750563 3 -0.300316 -0.440721 -2.619954 4 0.127419 0.158185 1.555927 Note how the columns X, Y, Z correspond to our nodes X, Y, Z in the graph constructed above. We can also see how the values of X influence the values of Y and how the values of Y influence the values of Z in that data set. The causal model created above allows us now to assign causal mechanisms to each node in the form of functional causal models. Here, these mechanism can either be assigned manually if, for instance, prior knowledge about certain causal relationships are known or they can be assigned automatically using the :mod:`~dowhy.gcm.auto` module. For the latter, we simply call: >>> gcm.auto.assign_causal_mechanisms(causal_model, data) In case we want to have more control over the assigned mechanisms, we can do this manually as well. For instance, we can can assign an empirical distribution to the root node X and linear additive noise models to nodes Y and Z: >>> causal_model.set_causal_mechanism('X', gcm.EmpiricalDistribution()) >>> causal_model.set_causal_mechanism('Y', gcm.AdditiveNoiseModel(gcm.ml.create_linear_regressor())) >>> causal_model.set_causal_mechanism('Z', gcm.AdditiveNoiseModel(gcm.ml.create_linear_regressor())) Section :doc:`customizing_model_assignment` will go into more detail on how one can even define a completely customized model or add their own implementation. In the real world, the data comes as an opaque stream of values, where we typically don't know how one variable influences another. The graphical causal models can help us to deconstruct these causal relationships again, even though we didn't know them before. Step 2: Fitting the SCM to the data ----------------------------------- With the data at hand and the graph constructed earlier, we can now train the SCM using ``fit``: >>> gcm.fit(causal_model, data) Fitting means, we learn the generative models of the variables in the SCM according to the data. Step 3: Answering a causal query based on the SCM ------------------------------------------------- The last step, answering a causal question, is our actual goal. E.g. we could ask the question: What will happen to the variable Z if I intervene on Y? This can be done via the ``interventional_samples`` function. Here's how: >>> samples = gcm.interventional_samples(causal_model, >>> {'Y': lambda y: 2.34 }, >>> num_samples_to_draw=1000) >>> samples.head() X Y Z 0 1.186229 6.918607 20.682375 1 -0.758809 -0.749365 -2.530045 2 -1.177379 -5.678514 -17.110836 3 -1.211356 -2.152073 -6.212703 4 -0.100224 -0.285047 0.256471 This intervention says: "I'll ignore any causal effects of X on Y, and set every value of Y to 2.34." So the distribution of X will remain unchanged, whereas values of Y will be at a fixed value and Z will respond according to its causal model. With this knowledge, we can now dive deep into the meaning and usages of causal queries in section :doc:`answering_causal_questions/index`.

Introduction ============ Graphical causal model-based inference, or GCM-based inference for short, is an experimental addition to DoWhy, that currently works separately from DoWhy's main API. Its experimental status also means that its API may undergo breaking changes in the future. It will be forming a part of a joint, `new API <https://github.com/py-why/dowhy/wiki/API-proposal-for-v1>`_. We welcome your comments. The ``dowhy.gcm`` package provides a variety of ways to answer causal questions and we'll go through them in detail in section :doc:`answering_causal_questions/index`. However, before diving into them, let's understand the basic building blocks and usage patterns it is built upon. The basic building blocks ^^^^^^^^^^^^^^^^^^^^^^^^^ All main features of the GCM-based inference in DoWhy are built around the concept of **graphical causal models**. A graphical causal model consists of a causal direct acyclic graph (DAG) of variables and a **causal mechanism** for each of the variables. A causal mechanism defines the conditional distribution of a variable given its parents in the graph, or, in case of root node variables, simply its distribution. The most general case of a GCM is a **probabilistic causal model** (PCM), where causal mechanisms are defined by **conditional stochastic models** and **stochastic models**. In the ``dowhy.gcm`` package, these are represented by :class:`~ProbabilisticCausalModel`, :class:`~ConditionalStochasticModel`, and :class:`~StochasticModel`. .. image:: pcm.png :width: 80% :align: center | In practical terms however, we often use **structural causal models** (SCMs) to represent our GCMs, and the causal mechanisms are defined by **functional causal models** (FCMs) for non-root nodes and **stochastic models** for root nodes. An SCM implements the same traits as a PCM, but on top of that, its FCMs allow us to reason *further* about its data generation process based on parents and noise, and hence, allow us e.g. to compute counterfactuals. .. image:: scm.png :width: 80% :align: center | To keep this introduction simple, we will stick with SCMs for now. As mentioned above, a causal mechanism describes how the values of a node are influenced by the values of its parent nodes. We will dive much deeper into the details of causal mechanisms and their meaning in section :doc:`customizing_model_assignment`. But for this introduction, we will treat them as an opaque thing that is needed to answer causal questions. With that in mind, the typical steps involved in answering a causal question, are: 1. **Modeling cause-effect relationships as a GCM (causal graph + causal mechanisms):** :: causal_model = StructuralCausalModel(nx.DiGraph([('X', 'Y'), ('Y', 'Z')])) # X -> Y -> Z auto.assign_causal_mechanisms(causal_model, data) Or manually assign causal mechanisms: :: causal_model.set_causal_mechanism('X', EmpiricalDistribution()) causal_model.set_causal_mechanism('Y', AdditiveNoiseModel(create_linear_regressor())) causal_model.set_causal_mechanism('Z', AdditiveNoiseModel(create_linear_regressor())) 2. **Fitting the GCM to the data:** :: fit(causal_model, data) 3. **Answering a causal query based on the GCM:** :: results = <causal_query>(causal_model, ...) Where ``<causal_query>`` can be one of multiple functions explained in :doc:`answering_causal_questions/index`. Let's look at each of these steps in more detail. Step 1: Modeling cause-effect relationships as a structural causal model (SCM) ------------------------------------------------------------------------------ The first step is to model the cause-effect relationships between variables relevant to our use case. We do that in form of a causal graph. A causal graph is a directed acyclic graph (DAG) where an edge X→Y implies that X causes Y. Statistically, a causal graph encodes the conditional independence relations between variables. Using the `networkx <https://networkx .github.io/>`__ library, we can create causal graphs. In the snippet below, we create a chain X→Y→Z: >>> import networkx as nx >>> causal_graph = nx.DiGraph([('X', 'Y'), ('Y', 'Z')]) To answer causal questions using causal graphs, we also have to know the nature of underlying data-generating process of variables. A causal graph by itself, being a diagram, does not have any information about the data-generating process. To introduce this data-generating process, we use an SCM that's built on top of our causal graph: >>> from dowhy import gcm >>> causal_model = gcm.StructuralCausalModel(causal_graph) At this point we would normally load our dataset. For this introduction, we generate some synthetic data instead. The API takes data in form of Pandas DataFrames: >>> import numpy as np, pandas as pd >>> X = np.random.normal(loc=0, scale=1, size=1000) >>> Y = 2 * X + np.random.normal(loc=0, scale=1, size=1000) >>> Z = 3 * Y + np.random.normal(loc=0, scale=1, size=1000) >>> data = pd.DataFrame(data=dict(X=X, Y=Y, Z=Z)) >>> data.head() X Y Z 0 -2.253500 -3.638579 -10.370047 1 -1.078337 -2.114581 -6.028030 2 -0.962719 -2.157896 -5.750563 3 -0.300316 -0.440721 -2.619954 4 0.127419 0.158185 1.555927 Note how the columns X, Y, Z correspond to our nodes X, Y, Z in the graph constructed above. We can also see how the values of X influence the values of Y and how the values of Y influence the values of Z in that data set. The causal model created above allows us now to assign causal mechanisms to each node in the form of functional causal models. Here, these mechanism can either be assigned manually if, for instance, prior knowledge about certain causal relationships are known or they can be assigned automatically using the :mod:`~dowhy.gcm.auto` module. For the latter, we simply call: >>> gcm.auto.assign_causal_mechanisms(causal_model, data) In case we want to have more control over the assigned mechanisms, we can do this manually as well. For instance, we can can assign an empirical distribution to the root node X and linear additive noise models to nodes Y and Z: >>> causal_model.set_causal_mechanism('X', gcm.EmpiricalDistribution()) >>> causal_model.set_causal_mechanism('Y', gcm.AdditiveNoiseModel(gcm.ml.create_linear_regressor())) >>> causal_model.set_causal_mechanism('Z', gcm.AdditiveNoiseModel(gcm.ml.create_linear_regressor())) Section :doc:`customizing_model_assignment` will go into more detail on how one can even define a completely customized model or add their own implementation. In the real world, the data comes as an opaque stream of values, where we typically don't know how one variable influences another. The graphical causal models can help us to deconstruct these causal relationships again, even though we didn't know them before. Step 2: Fitting the SCM to the data ----------------------------------- With the data at hand and the graph constructed earlier, we can now train the SCM using ``fit``: >>> gcm.fit(causal_model, data) Fitting means, we learn the generative models of the variables in the SCM according to the data. Step 3: Answering a causal query based on the SCM ------------------------------------------------- The last step, answering a causal question, is our actual goal. E.g. we could ask the question: What will happen to the variable Z if I intervene on Y? This can be done via the ``interventional_samples`` function. Here's how: >>> samples = gcm.interventional_samples(causal_model, >>> {'Y': lambda y: 2.34 }, >>> num_samples_to_draw=1000) >>> samples.head() X Y Z 0 1.186229 6.918607 20.682375 1 -0.758809 -0.749365 -2.530045 2 -1.177379 -5.678514 -17.110836 3 -1.211356 -2.152073 -6.212703 4 -0.100224 -0.285047 0.256471 This intervention says: "I'll ignore any causal effects of X on Y, and set every value of Y to 2.34." So the distribution of X will remain unchanged, whereas values of Y will be at a fixed value and Z will respond according to its causal model. These are the basic steps that need to happen. While we can run these steps explicitly, often they get executed as part of other steps, e.g. when fitting and re-fitting as part of computing confidence intervals. The next section therefore dives into a more typical usage pattern of the ``dowhy.gcm`` package. Typical usage of the ``dowhy.gcm`` package ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ In practice, we may not execute the steps we've learned above explicitly and in this order, but they get called by other abstractions. E.g. we usually want to use confidence intervals, when answering causal questions, to quantify our confidence in the results. In this case, ``fit`` will be called on behalf of us, but we won't call it directly. Modeling an SCM --------------- The graph modeling is the same as in `Step 1: Modeling cause-effect relationships as a structural causal model (SCM)`_. First we construct the causal graph: >>> causal_model = gcm.StructuralCausalModel(nx.DiGraph([('X', 'Y'), ('Y', 'Z')])) # X → Y → Z Answering a causal query with confidence intervals -------------------------------------------------- When we answer a causal query without computing its confidence intervals, what we effectively get, are point estimates. These are not very useful when trying to assess the confidence in our results. Instead of calling ``fit`` explicitly, we can achieve its execution by going through the API for confidence intervals. Let's say we wanted to understand the direct arrow strengths between nodes and quantify our confidence in those results. This is how we would do it: >>> strength_median, strength_intervals = gcm.confidence_intervals( >>> gcm.bootstrap_training_and_sampling(gcm.direct_arrow_strength, >>> causal_model, >>> bootstrap_training_data=data, >>> target_node='Y')) >>> strength_median, strength_intervals ({('X', 'Y'): 45.90886398636573, ('Z', 'Y'): 15.47129383737619}, {('X', 'Y'): array([42.88319632, 50.43890079]), ('Z', 'Y'): array([13.44202416, 17.74266107])}) In this case, ``fit`` will be called within ``bootstrap_training_and_sampling``, so there is no need to do this ourselves. The calling sequence of ``confidence_intervals`` and ``bootstrap_training_and_sampling`` is not trivial, but exploits the fact our APIs are composable. If not everything makes sense to you yet, we recommend to simply treat this calling sequence as a ready-to-use construct. Read: "Get confidence intervals via bootstrapping training and sampling of direct arrow strength". For a deeper understanding of this construct, see section :doc:`estimating_confidence_intervals`. With this knowledge, we can now dive deep into the meaning and usages of causal queries in section :doc:`answering_causal_questions/index`.

petergtz

b43ce50d7cf58420b88605531b34b5c86f905112

560b3460aaf1106f7a053f99ede24cfed094db6f

I am a bit concerned that most structures will be `REJECTED` due to the statistical issues with the independence tests, even if the structures are correct.

bloebp

py-why/dowhy

Overhaul GCM introduction

* Remove bibtex from GCM introduction. This is covered in docs/source/cite.rst. * Add 'Typical usage' section in GCM introduction

2022-09-05 14:12:41+00:00

2022-11-02 10:01:42+00:00

docs/source/user_guide/gcm_based_inference/introduction.rst

Introduction ============ Graphical causal model-based inference, or GCM-based inference for short, is an experimental addition to DoWhy, that currently works separately from DoWhy's main API. Its experimental status also means that its API may undergo breaking changes in the future. It will be forming a part of a joint, `new API <https://github.com/py-why/dowhy/wiki/API-proposal-for-v1>`_. We welcome your comments. The ``dowhy.gcm`` package provides a variety of ways to answer causal questions and we'll go through them in detail in section :doc:`answering_causal_questions/index`. However, before diving into them, let's understand the basic building blocks and usage patterns it is built upon. The basic building blocks ^^^^^^^^^^^^^^^^^^^^^^^^^ All main features of the GCM-based inference in DoWhy are built around the concept of **graphical causal models**. A graphical causal model consists of a causal direct acyclic graph (DAG) of variables and a **causal mechanism** for each of the variables. A causal mechanism defines the conditional distribution of a variable given its parents in the graph, or, in case of root node variables, simply its distribution. The most general case of a GCM is a **probabilistic causal model** (PCM), where causal mechanisms are defined by **conditional stochastic models** and **stochastic models**. In the ``dowhy.gcm`` package, these are represented by :class:`~ProbabilisticCausalModel`, :class:`~ConditionalStochasticModel`, and :class:`~StochasticModel`. .. image:: pcm.png :width: 80% :align: center | In practical terms however, we often use **structural causal models** (SCMs) to represent our GCMs, and the causal mechanisms are defined by **functional causal models** (FCMs) for non-root nodes and **stochastic models** for root nodes. An SCM implements the same traits as a PCM, but on top of that, its FCMs allow us to reason *further* about its data generation process based on parents and noise, and hence, allow us e.g. to compute counterfactuals. .. image:: scm.png :width: 80% :align: center | To keep this introduction simple, we will stick with SCMs for now. As mentioned above, a causal mechanism describes how the values of a node are influenced by the values of its parent nodes. We will dive much deeper into the details of causal mechanisms and their meaning in section :doc:`customizing_model_assignment`. But for this introduction, we will treat them as an opaque thing that is needed to answer causal questions. With that in mind, the typical steps involved in answering a causal question, are: 1. **Modeling cause-effect relationships as a GCM (causal graph + causal mechanisms):** :: causal_model = StructuralCausalModel(nx.DiGraph([('X', 'Y'), ('Y', 'Z')])) # X -> Y -> Z auto.assign_causal_mechanisms(causal_model, data) Or manually assign causal mechanisms: :: causal_model.set_causal_mechanism('X', EmpiricalDistribution()) causal_model.set_causal_mechanism('Y', AdditiveNoiseModel(create_linear_regressor())) causal_model.set_causal_mechanism('Z', AdditiveNoiseModel(create_linear_regressor())) 2. **Fitting the GCM to the data:** :: fit(causal_model, data) 3. **Answering a causal query based on the GCM:** :: results = <causal_query>(causal_model, ...) Where ``<causal_query>`` can be one of multiple functions explained in :doc:`answering_causal_questions/index`. Let's look at each of these steps in more detail. Step 1: Modeling cause-effect relationships as a structural causal model (SCM) ------------------------------------------------------------------------------ The first step is to model the cause-effect relationships between variables relevant to our use case. We do that in form of a causal graph. A causal graph is a directed acyclic graph (DAG) where an edge X→Y implies that X causes Y. Statistically, a causal graph encodes the conditional independence relations between variables. Using the `networkx <https://networkx .github.io/>`__ library, we can create causal graphs. In the snippet below, we create a chain X→Y→Z: >>> import networkx as nx >>> causal_graph = nx.DiGraph([('X', 'Y'), ('Y', 'Z')]) To answer causal questions using causal graphs, we also have to know the nature of underlying data-generating process of variables. A causal graph by itself, being a diagram, does not have any information about the data-generating process. To introduce this data-generating process, we use an SCM that's built on top of our causal graph: >>> from dowhy import gcm >>> causal_model = gcm.StructuralCausalModel(causal_graph) At this point we would normally load our dataset. For this introduction, we generate some synthetic data instead. The API takes data in form of Pandas DataFrames: >>> import numpy as np, pandas as pd >>> X = np.random.normal(loc=0, scale=1, size=1000) >>> Y = 2 * X + np.random.normal(loc=0, scale=1, size=1000) >>> Z = 3 * Y + np.random.normal(loc=0, scale=1, size=1000) >>> data = pd.DataFrame(data=dict(X=X, Y=Y, Z=Z)) >>> data.head() X Y Z 0 -2.253500 -3.638579 -10.370047 1 -1.078337 -2.114581 -6.028030 2 -0.962719 -2.157896 -5.750563 3 -0.300316 -0.440721 -2.619954 4 0.127419 0.158185 1.555927 Note how the columns X, Y, Z correspond to our nodes X, Y, Z in the graph constructed above. We can also see how the values of X influence the values of Y and how the values of Y influence the values of Z in that data set. The causal model created above allows us now to assign causal mechanisms to each node in the form of functional causal models. Here, these mechanism can either be assigned manually if, for instance, prior knowledge about certain causal relationships are known or they can be assigned automatically using the :mod:`~dowhy.gcm.auto` module. For the latter, we simply call: >>> gcm.auto.assign_causal_mechanisms(causal_model, data) In case we want to have more control over the assigned mechanisms, we can do this manually as well. For instance, we can can assign an empirical distribution to the root node X and linear additive noise models to nodes Y and Z: >>> causal_model.set_causal_mechanism('X', gcm.EmpiricalDistribution()) >>> causal_model.set_causal_mechanism('Y', gcm.AdditiveNoiseModel(gcm.ml.create_linear_regressor())) >>> causal_model.set_causal_mechanism('Z', gcm.AdditiveNoiseModel(gcm.ml.create_linear_regressor())) Section :doc:`customizing_model_assignment` will go into more detail on how one can even define a completely customized model or add their own implementation. In the real world, the data comes as an opaque stream of values, where we typically don't know how one variable influences another. The graphical causal models can help us to deconstruct these causal relationships again, even though we didn't know them before. Step 2: Fitting the SCM to the data ----------------------------------- With the data at hand and the graph constructed earlier, we can now train the SCM using ``fit``: >>> gcm.fit(causal_model, data) Fitting means, we learn the generative models of the variables in the SCM according to the data. Step 3: Answering a causal query based on the SCM ------------------------------------------------- The last step, answering a causal question, is our actual goal. E.g. we could ask the question: What will happen to the variable Z if I intervene on Y? This can be done via the ``interventional_samples`` function. Here's how: >>> samples = gcm.interventional_samples(causal_model, >>> {'Y': lambda y: 2.34 }, >>> num_samples_to_draw=1000) >>> samples.head() X Y Z 0 1.186229 6.918607 20.682375 1 -0.758809 -0.749365 -2.530045 2 -1.177379 -5.678514 -17.110836 3 -1.211356 -2.152073 -6.212703 4 -0.100224 -0.285047 0.256471 This intervention says: "I'll ignore any causal effects of X on Y, and set every value of Y to 2.34." So the distribution of X will remain unchanged, whereas values of Y will be at a fixed value and Z will respond according to its causal model. With this knowledge, we can now dive deep into the meaning and usages of causal queries in section :doc:`answering_causal_questions/index`.

Introduction ============ Graphical causal model-based inference, or GCM-based inference for short, is an experimental addition to DoWhy, that currently works separately from DoWhy's main API. Its experimental status also means that its API may undergo breaking changes in the future. It will be forming a part of a joint, `new API <https://github.com/py-why/dowhy/wiki/API-proposal-for-v1>`_. We welcome your comments. The ``dowhy.gcm`` package provides a variety of ways to answer causal questions and we'll go through them in detail in section :doc:`answering_causal_questions/index`. However, before diving into them, let's understand the basic building blocks and usage patterns it is built upon. The basic building blocks ^^^^^^^^^^^^^^^^^^^^^^^^^ All main features of the GCM-based inference in DoWhy are built around the concept of **graphical causal models**. A graphical causal model consists of a causal direct acyclic graph (DAG) of variables and a **causal mechanism** for each of the variables. A causal mechanism defines the conditional distribution of a variable given its parents in the graph, or, in case of root node variables, simply its distribution. The most general case of a GCM is a **probabilistic causal model** (PCM), where causal mechanisms are defined by **conditional stochastic models** and **stochastic models**. In the ``dowhy.gcm`` package, these are represented by :class:`~ProbabilisticCausalModel`, :class:`~ConditionalStochasticModel`, and :class:`~StochasticModel`. .. image:: pcm.png :width: 80% :align: center | In practical terms however, we often use **structural causal models** (SCMs) to represent our GCMs, and the causal mechanisms are defined by **functional causal models** (FCMs) for non-root nodes and **stochastic models** for root nodes. An SCM implements the same traits as a PCM, but on top of that, its FCMs allow us to reason *further* about its data generation process based on parents and noise, and hence, allow us e.g. to compute counterfactuals. .. image:: scm.png :width: 80% :align: center | To keep this introduction simple, we will stick with SCMs for now. As mentioned above, a causal mechanism describes how the values of a node are influenced by the values of its parent nodes. We will dive much deeper into the details of causal mechanisms and their meaning in section :doc:`customizing_model_assignment`. But for this introduction, we will treat them as an opaque thing that is needed to answer causal questions. With that in mind, the typical steps involved in answering a causal question, are: 1. **Modeling cause-effect relationships as a GCM (causal graph + causal mechanisms):** :: causal_model = StructuralCausalModel(nx.DiGraph([('X', 'Y'), ('Y', 'Z')])) # X -> Y -> Z auto.assign_causal_mechanisms(causal_model, data) Or manually assign causal mechanisms: :: causal_model.set_causal_mechanism('X', EmpiricalDistribution()) causal_model.set_causal_mechanism('Y', AdditiveNoiseModel(create_linear_regressor())) causal_model.set_causal_mechanism('Z', AdditiveNoiseModel(create_linear_regressor())) 2. **Fitting the GCM to the data:** :: fit(causal_model, data) 3. **Answering a causal query based on the GCM:** :: results = <causal_query>(causal_model, ...) Where ``<causal_query>`` can be one of multiple functions explained in :doc:`answering_causal_questions/index`. Let's look at each of these steps in more detail. Step 1: Modeling cause-effect relationships as a structural causal model (SCM) ------------------------------------------------------------------------------ The first step is to model the cause-effect relationships between variables relevant to our use case. We do that in form of a causal graph. A causal graph is a directed acyclic graph (DAG) where an edge X→Y implies that X causes Y. Statistically, a causal graph encodes the conditional independence relations between variables. Using the `networkx <https://networkx .github.io/>`__ library, we can create causal graphs. In the snippet below, we create a chain X→Y→Z: >>> import networkx as nx >>> causal_graph = nx.DiGraph([('X', 'Y'), ('Y', 'Z')]) To answer causal questions using causal graphs, we also have to know the nature of underlying data-generating process of variables. A causal graph by itself, being a diagram, does not have any information about the data-generating process. To introduce this data-generating process, we use an SCM that's built on top of our causal graph: >>> from dowhy import gcm >>> causal_model = gcm.StructuralCausalModel(causal_graph) At this point we would normally load our dataset. For this introduction, we generate some synthetic data instead. The API takes data in form of Pandas DataFrames: >>> import numpy as np, pandas as pd >>> X = np.random.normal(loc=0, scale=1, size=1000) >>> Y = 2 * X + np.random.normal(loc=0, scale=1, size=1000) >>> Z = 3 * Y + np.random.normal(loc=0, scale=1, size=1000) >>> data = pd.DataFrame(data=dict(X=X, Y=Y, Z=Z)) >>> data.head() X Y Z 0 -2.253500 -3.638579 -10.370047 1 -1.078337 -2.114581 -6.028030 2 -0.962719 -2.157896 -5.750563 3 -0.300316 -0.440721 -2.619954 4 0.127419 0.158185 1.555927 Note how the columns X, Y, Z correspond to our nodes X, Y, Z in the graph constructed above. We can also see how the values of X influence the values of Y and how the values of Y influence the values of Z in that data set. The causal model created above allows us now to assign causal mechanisms to each node in the form of functional causal models. Here, these mechanism can either be assigned manually if, for instance, prior knowledge about certain causal relationships are known or they can be assigned automatically using the :mod:`~dowhy.gcm.auto` module. For the latter, we simply call: >>> gcm.auto.assign_causal_mechanisms(causal_model, data) In case we want to have more control over the assigned mechanisms, we can do this manually as well. For instance, we can can assign an empirical distribution to the root node X and linear additive noise models to nodes Y and Z: >>> causal_model.set_causal_mechanism('X', gcm.EmpiricalDistribution()) >>> causal_model.set_causal_mechanism('Y', gcm.AdditiveNoiseModel(gcm.ml.create_linear_regressor())) >>> causal_model.set_causal_mechanism('Z', gcm.AdditiveNoiseModel(gcm.ml.create_linear_regressor())) Section :doc:`customizing_model_assignment` will go into more detail on how one can even define a completely customized model or add their own implementation. In the real world, the data comes as an opaque stream of values, where we typically don't know how one variable influences another. The graphical causal models can help us to deconstruct these causal relationships again, even though we didn't know them before. Step 2: Fitting the SCM to the data ----------------------------------- With the data at hand and the graph constructed earlier, we can now train the SCM using ``fit``: >>> gcm.fit(causal_model, data) Fitting means, we learn the generative models of the variables in the SCM according to the data. Step 3: Answering a causal query based on the SCM ------------------------------------------------- The last step, answering a causal question, is our actual goal. E.g. we could ask the question: What will happen to the variable Z if I intervene on Y? This can be done via the ``interventional_samples`` function. Here's how: >>> samples = gcm.interventional_samples(causal_model, >>> {'Y': lambda y: 2.34 }, >>> num_samples_to_draw=1000) >>> samples.head() X Y Z 0 1.186229 6.918607 20.682375 1 -0.758809 -0.749365 -2.530045 2 -1.177379 -5.678514 -17.110836 3 -1.211356 -2.152073 -6.212703 4 -0.100224 -0.285047 0.256471 This intervention says: "I'll ignore any causal effects of X on Y, and set every value of Y to 2.34." So the distribution of X will remain unchanged, whereas values of Y will be at a fixed value and Z will respond according to its causal model. These are the basic steps that need to happen. While we can run these steps explicitly, often they get executed as part of other steps, e.g. when fitting and re-fitting as part of computing confidence intervals. The next section therefore dives into a more typical usage pattern of the ``dowhy.gcm`` package. Typical usage of the ``dowhy.gcm`` package ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ In practice, we may not execute the steps we've learned above explicitly and in this order, but they get called by other abstractions. E.g. we usually want to use confidence intervals, when answering causal questions, to quantify our confidence in the results. In this case, ``fit`` will be called on behalf of us, but we won't call it directly. Modeling an SCM --------------- The graph modeling is the same as in `Step 1: Modeling cause-effect relationships as a structural causal model (SCM)`_. First we construct the causal graph: >>> causal_model = gcm.StructuralCausalModel(nx.DiGraph([('X', 'Y'), ('Y', 'Z')])) # X → Y → Z Answering a causal query with confidence intervals -------------------------------------------------- When we answer a causal query without computing its confidence intervals, what we effectively get, are point estimates. These are not very useful when trying to assess the confidence in our results. Instead of calling ``fit`` explicitly, we can achieve its execution by going through the API for confidence intervals. Let's say we wanted to understand the direct arrow strengths between nodes and quantify our confidence in those results. This is how we would do it: >>> strength_median, strength_intervals = gcm.confidence_intervals( >>> gcm.bootstrap_training_and_sampling(gcm.direct_arrow_strength, >>> causal_model, >>> bootstrap_training_data=data, >>> target_node='Y')) >>> strength_median, strength_intervals ({('X', 'Y'): 45.90886398636573, ('Z', 'Y'): 15.47129383737619}, {('X', 'Y'): array([42.88319632, 50.43890079]), ('Z', 'Y'): array([13.44202416, 17.74266107])}) In this case, ``fit`` will be called within ``bootstrap_training_and_sampling``, so there is no need to do this ourselves. The calling sequence of ``confidence_intervals`` and ``bootstrap_training_and_sampling`` is not trivial, but exploits the fact our APIs are composable. If not everything makes sense to you yet, we recommend to simply treat this calling sequence as a ready-to-use construct. Read: "Get confidence intervals via bootstrapping training and sampling of direct arrow strength". For a deeper understanding of this construct, see section :doc:`estimating_confidence_intervals`. With this knowledge, we can now dive deep into the meaning and usages of causal queries in section :doc:`answering_causal_questions/index`.

petergtz

b43ce50d7cf58420b88605531b34b5c86f905112

560b3460aaf1106f7a053f99ede24cfed094db6f

`quality` is by default `GOOD`. Or do you want to emphasize here that this is a parameter?

bloebp

py-why/dowhy

Overhaul GCM introduction

* Remove bibtex from GCM introduction. This is covered in docs/source/cite.rst. * Add 'Typical usage' section in GCM introduction

2022-09-05 14:12:41+00:00

2022-11-02 10:01:42+00:00

docs/source/user_guide/gcm_based_inference/introduction.rst

Introduction ============ Graphical causal model-based inference, or GCM-based inference for short, is an experimental addition to DoWhy, that currently works separately from DoWhy's main API. Its experimental status also means that its API may undergo breaking changes in the future. It will be forming a part of a joint, `new API <https://github.com/py-why/dowhy/wiki/API-proposal-for-v1>`_. We welcome your comments. The ``dowhy.gcm`` package provides a variety of ways to answer causal questions and we'll go through them in detail in section :doc:`answering_causal_questions/index`. However, before diving into them, let's understand the basic building blocks and usage patterns it is built upon. The basic building blocks ^^^^^^^^^^^^^^^^^^^^^^^^^ All main features of the GCM-based inference in DoWhy are built around the concept of **graphical causal models**. A graphical causal model consists of a causal direct acyclic graph (DAG) of variables and a **causal mechanism** for each of the variables. A causal mechanism defines the conditional distribution of a variable given its parents in the graph, or, in case of root node variables, simply its distribution. The most general case of a GCM is a **probabilistic causal model** (PCM), where causal mechanisms are defined by **conditional stochastic models** and **stochastic models**. In the ``dowhy.gcm`` package, these are represented by :class:`~ProbabilisticCausalModel`, :class:`~ConditionalStochasticModel`, and :class:`~StochasticModel`. .. image:: pcm.png :width: 80% :align: center | In practical terms however, we often use **structural causal models** (SCMs) to represent our GCMs, and the causal mechanisms are defined by **functional causal models** (FCMs) for non-root nodes and **stochastic models** for root nodes. An SCM implements the same traits as a PCM, but on top of that, its FCMs allow us to reason *further* about its data generation process based on parents and noise, and hence, allow us e.g. to compute counterfactuals. .. image:: scm.png :width: 80% :align: center | To keep this introduction simple, we will stick with SCMs for now. As mentioned above, a causal mechanism describes how the values of a node are influenced by the values of its parent nodes. We will dive much deeper into the details of causal mechanisms and their meaning in section :doc:`customizing_model_assignment`. But for this introduction, we will treat them as an opaque thing that is needed to answer causal questions. With that in mind, the typical steps involved in answering a causal question, are: 1. **Modeling cause-effect relationships as a GCM (causal graph + causal mechanisms):** :: causal_model = StructuralCausalModel(nx.DiGraph([('X', 'Y'), ('Y', 'Z')])) # X -> Y -> Z auto.assign_causal_mechanisms(causal_model, data) Or manually assign causal mechanisms: :: causal_model.set_causal_mechanism('X', EmpiricalDistribution()) causal_model.set_causal_mechanism('Y', AdditiveNoiseModel(create_linear_regressor())) causal_model.set_causal_mechanism('Z', AdditiveNoiseModel(create_linear_regressor())) 2. **Fitting the GCM to the data:** :: fit(causal_model, data) 3. **Answering a causal query based on the GCM:** :: results = <causal_query>(causal_model, ...) Where ``<causal_query>`` can be one of multiple functions explained in :doc:`answering_causal_questions/index`. Let's look at each of these steps in more detail. Step 1: Modeling cause-effect relationships as a structural causal model (SCM) ------------------------------------------------------------------------------ The first step is to model the cause-effect relationships between variables relevant to our use case. We do that in form of a causal graph. A causal graph is a directed acyclic graph (DAG) where an edge X→Y implies that X causes Y. Statistically, a causal graph encodes the conditional independence relations between variables. Using the `networkx <https://networkx .github.io/>`__ library, we can create causal graphs. In the snippet below, we create a chain X→Y→Z: >>> import networkx as nx >>> causal_graph = nx.DiGraph([('X', 'Y'), ('Y', 'Z')]) To answer causal questions using causal graphs, we also have to know the nature of underlying data-generating process of variables. A causal graph by itself, being a diagram, does not have any information about the data-generating process. To introduce this data-generating process, we use an SCM that's built on top of our causal graph: >>> from dowhy import gcm >>> causal_model = gcm.StructuralCausalModel(causal_graph) At this point we would normally load our dataset. For this introduction, we generate some synthetic data instead. The API takes data in form of Pandas DataFrames: >>> import numpy as np, pandas as pd >>> X = np.random.normal(loc=0, scale=1, size=1000) >>> Y = 2 * X + np.random.normal(loc=0, scale=1, size=1000) >>> Z = 3 * Y + np.random.normal(loc=0, scale=1, size=1000) >>> data = pd.DataFrame(data=dict(X=X, Y=Y, Z=Z)) >>> data.head() X Y Z 0 -2.253500 -3.638579 -10.370047 1 -1.078337 -2.114581 -6.028030 2 -0.962719 -2.157896 -5.750563 3 -0.300316 -0.440721 -2.619954 4 0.127419 0.158185 1.555927 Note how the columns X, Y, Z correspond to our nodes X, Y, Z in the graph constructed above. We can also see how the values of X influence the values of Y and how the values of Y influence the values of Z in that data set. The causal model created above allows us now to assign causal mechanisms to each node in the form of functional causal models. Here, these mechanism can either be assigned manually if, for instance, prior knowledge about certain causal relationships are known or they can be assigned automatically using the :mod:`~dowhy.gcm.auto` module. For the latter, we simply call: >>> gcm.auto.assign_causal_mechanisms(causal_model, data) In case we want to have more control over the assigned mechanisms, we can do this manually as well. For instance, we can can assign an empirical distribution to the root node X and linear additive noise models to nodes Y and Z: >>> causal_model.set_causal_mechanism('X', gcm.EmpiricalDistribution()) >>> causal_model.set_causal_mechanism('Y', gcm.AdditiveNoiseModel(gcm.ml.create_linear_regressor())) >>> causal_model.set_causal_mechanism('Z', gcm.AdditiveNoiseModel(gcm.ml.create_linear_regressor())) Section :doc:`customizing_model_assignment` will go into more detail on how one can even define a completely customized model or add their own implementation. In the real world, the data comes as an opaque stream of values, where we typically don't know how one variable influences another. The graphical causal models can help us to deconstruct these causal relationships again, even though we didn't know them before. Step 2: Fitting the SCM to the data ----------------------------------- With the data at hand and the graph constructed earlier, we can now train the SCM using ``fit``: >>> gcm.fit(causal_model, data) Fitting means, we learn the generative models of the variables in the SCM according to the data. Step 3: Answering a causal query based on the SCM ------------------------------------------------- The last step, answering a causal question, is our actual goal. E.g. we could ask the question: What will happen to the variable Z if I intervene on Y? This can be done via the ``interventional_samples`` function. Here's how: >>> samples = gcm.interventional_samples(causal_model, >>> {'Y': lambda y: 2.34 }, >>> num_samples_to_draw=1000) >>> samples.head() X Y Z 0 1.186229 6.918607 20.682375 1 -0.758809 -0.749365 -2.530045 2 -1.177379 -5.678514 -17.110836 3 -1.211356 -2.152073 -6.212703 4 -0.100224 -0.285047 0.256471 This intervention says: "I'll ignore any causal effects of X on Y, and set every value of Y to 2.34." So the distribution of X will remain unchanged, whereas values of Y will be at a fixed value and Z will respond according to its causal model. With this knowledge, we can now dive deep into the meaning and usages of causal queries in section :doc:`answering_causal_questions/index`.

Introduction ============ Graphical causal model-based inference, or GCM-based inference for short, is an experimental addition to DoWhy, that currently works separately from DoWhy's main API. Its experimental status also means that its API may undergo breaking changes in the future. It will be forming a part of a joint, `new API <https://github.com/py-why/dowhy/wiki/API-proposal-for-v1>`_. We welcome your comments. The ``dowhy.gcm`` package provides a variety of ways to answer causal questions and we'll go through them in detail in section :doc:`answering_causal_questions/index`. However, before diving into them, let's understand the basic building blocks and usage patterns it is built upon. The basic building blocks ^^^^^^^^^^^^^^^^^^^^^^^^^ All main features of the GCM-based inference in DoWhy are built around the concept of **graphical causal models**. A graphical causal model consists of a causal direct acyclic graph (DAG) of variables and a **causal mechanism** for each of the variables. A causal mechanism defines the conditional distribution of a variable given its parents in the graph, or, in case of root node variables, simply its distribution. The most general case of a GCM is a **probabilistic causal model** (PCM), where causal mechanisms are defined by **conditional stochastic models** and **stochastic models**. In the ``dowhy.gcm`` package, these are represented by :class:`~ProbabilisticCausalModel`, :class:`~ConditionalStochasticModel`, and :class:`~StochasticModel`. .. image:: pcm.png :width: 80% :align: center | In practical terms however, we often use **structural causal models** (SCMs) to represent our GCMs, and the causal mechanisms are defined by **functional causal models** (FCMs) for non-root nodes and **stochastic models** for root nodes. An SCM implements the same traits as a PCM, but on top of that, its FCMs allow us to reason *further* about its data generation process based on parents and noise, and hence, allow us e.g. to compute counterfactuals. .. image:: scm.png :width: 80% :align: center | To keep this introduction simple, we will stick with SCMs for now. As mentioned above, a causal mechanism describes how the values of a node are influenced by the values of its parent nodes. We will dive much deeper into the details of causal mechanisms and their meaning in section :doc:`customizing_model_assignment`. But for this introduction, we will treat them as an opaque thing that is needed to answer causal questions. With that in mind, the typical steps involved in answering a causal question, are: 1. **Modeling cause-effect relationships as a GCM (causal graph + causal mechanisms):** :: causal_model = StructuralCausalModel(nx.DiGraph([('X', 'Y'), ('Y', 'Z')])) # X -> Y -> Z auto.assign_causal_mechanisms(causal_model, data) Or manually assign causal mechanisms: :: causal_model.set_causal_mechanism('X', EmpiricalDistribution()) causal_model.set_causal_mechanism('Y', AdditiveNoiseModel(create_linear_regressor())) causal_model.set_causal_mechanism('Z', AdditiveNoiseModel(create_linear_regressor())) 2. **Fitting the GCM to the data:** :: fit(causal_model, data) 3. **Answering a causal query based on the GCM:** :: results = <causal_query>(causal_model, ...) Where ``<causal_query>`` can be one of multiple functions explained in :doc:`answering_causal_questions/index`. Let's look at each of these steps in more detail. Step 1: Modeling cause-effect relationships as a structural causal model (SCM) ------------------------------------------------------------------------------ The first step is to model the cause-effect relationships between variables relevant to our use case. We do that in form of a causal graph. A causal graph is a directed acyclic graph (DAG) where an edge X→Y implies that X causes Y. Statistically, a causal graph encodes the conditional independence relations between variables. Using the `networkx <https://networkx .github.io/>`__ library, we can create causal graphs. In the snippet below, we create a chain X→Y→Z: >>> import networkx as nx >>> causal_graph = nx.DiGraph([('X', 'Y'), ('Y', 'Z')]) To answer causal questions using causal graphs, we also have to know the nature of underlying data-generating process of variables. A causal graph by itself, being a diagram, does not have any information about the data-generating process. To introduce this data-generating process, we use an SCM that's built on top of our causal graph: >>> from dowhy import gcm >>> causal_model = gcm.StructuralCausalModel(causal_graph) At this point we would normally load our dataset. For this introduction, we generate some synthetic data instead. The API takes data in form of Pandas DataFrames: >>> import numpy as np, pandas as pd >>> X = np.random.normal(loc=0, scale=1, size=1000) >>> Y = 2 * X + np.random.normal(loc=0, scale=1, size=1000) >>> Z = 3 * Y + np.random.normal(loc=0, scale=1, size=1000) >>> data = pd.DataFrame(data=dict(X=X, Y=Y, Z=Z)) >>> data.head() X Y Z 0 -2.253500 -3.638579 -10.370047 1 -1.078337 -2.114581 -6.028030 2 -0.962719 -2.157896 -5.750563 3 -0.300316 -0.440721 -2.619954 4 0.127419 0.158185 1.555927 Note how the columns X, Y, Z correspond to our nodes X, Y, Z in the graph constructed above. We can also see how the values of X influence the values of Y and how the values of Y influence the values of Z in that data set. The causal model created above allows us now to assign causal mechanisms to each node in the form of functional causal models. Here, these mechanism can either be assigned manually if, for instance, prior knowledge about certain causal relationships are known or they can be assigned automatically using the :mod:`~dowhy.gcm.auto` module. For the latter, we simply call: >>> gcm.auto.assign_causal_mechanisms(causal_model, data) In case we want to have more control over the assigned mechanisms, we can do this manually as well. For instance, we can can assign an empirical distribution to the root node X and linear additive noise models to nodes Y and Z: >>> causal_model.set_causal_mechanism('X', gcm.EmpiricalDistribution()) >>> causal_model.set_causal_mechanism('Y', gcm.AdditiveNoiseModel(gcm.ml.create_linear_regressor())) >>> causal_model.set_causal_mechanism('Z', gcm.AdditiveNoiseModel(gcm.ml.create_linear_regressor())) Section :doc:`customizing_model_assignment` will go into more detail on how one can even define a completely customized model or add their own implementation. In the real world, the data comes as an opaque stream of values, where we typically don't know how one variable influences another. The graphical causal models can help us to deconstruct these causal relationships again, even though we didn't know them before. Step 2: Fitting the SCM to the data ----------------------------------- With the data at hand and the graph constructed earlier, we can now train the SCM using ``fit``: >>> gcm.fit(causal_model, data) Fitting means, we learn the generative models of the variables in the SCM according to the data. Step 3: Answering a causal query based on the SCM ------------------------------------------------- The last step, answering a causal question, is our actual goal. E.g. we could ask the question: What will happen to the variable Z if I intervene on Y? This can be done via the ``interventional_samples`` function. Here's how: >>> samples = gcm.interventional_samples(causal_model, >>> {'Y': lambda y: 2.34 }, >>> num_samples_to_draw=1000) >>> samples.head() X Y Z 0 1.186229 6.918607 20.682375 1 -0.758809 -0.749365 -2.530045 2 -1.177379 -5.678514 -17.110836 3 -1.211356 -2.152073 -6.212703 4 -0.100224 -0.285047 0.256471 This intervention says: "I'll ignore any causal effects of X on Y, and set every value of Y to 2.34." So the distribution of X will remain unchanged, whereas values of Y will be at a fixed value and Z will respond according to its causal model. These are the basic steps that need to happen. While we can run these steps explicitly, often they get executed as part of other steps, e.g. when fitting and re-fitting as part of computing confidence intervals. The next section therefore dives into a more typical usage pattern of the ``dowhy.gcm`` package. Typical usage of the ``dowhy.gcm`` package ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ In practice, we may not execute the steps we've learned above explicitly and in this order, but they get called by other abstractions. E.g. we usually want to use confidence intervals, when answering causal questions, to quantify our confidence in the results. In this case, ``fit`` will be called on behalf of us, but we won't call it directly. Modeling an SCM --------------- The graph modeling is the same as in `Step 1: Modeling cause-effect relationships as a structural causal model (SCM)`_. First we construct the causal graph: >>> causal_model = gcm.StructuralCausalModel(nx.DiGraph([('X', 'Y'), ('Y', 'Z')])) # X → Y → Z Answering a causal query with confidence intervals -------------------------------------------------- When we answer a causal query without computing its confidence intervals, what we effectively get, are point estimates. These are not very useful when trying to assess the confidence in our results. Instead of calling ``fit`` explicitly, we can achieve its execution by going through the API for confidence intervals. Let's say we wanted to understand the direct arrow strengths between nodes and quantify our confidence in those results. This is how we would do it: >>> strength_median, strength_intervals = gcm.confidence_intervals( >>> gcm.bootstrap_training_and_sampling(gcm.direct_arrow_strength, >>> causal_model, >>> bootstrap_training_data=data, >>> target_node='Y')) >>> strength_median, strength_intervals ({('X', 'Y'): 45.90886398636573, ('Z', 'Y'): 15.47129383737619}, {('X', 'Y'): array([42.88319632, 50.43890079]), ('Z', 'Y'): array([13.44202416, 17.74266107])}) In this case, ``fit`` will be called within ``bootstrap_training_and_sampling``, so there is no need to do this ourselves. The calling sequence of ``confidence_intervals`` and ``bootstrap_training_and_sampling`` is not trivial, but exploits the fact our APIs are composable. If not everything makes sense to you yet, we recommend to simply treat this calling sequence as a ready-to-use construct. Read: "Get confidence intervals via bootstrapping training and sampling of direct arrow strength". For a deeper understanding of this construct, see section :doc:`estimating_confidence_intervals`. With this knowledge, we can now dive deep into the meaning and usages of causal queries in section :doc:`answering_causal_questions/index`.

petergtz

b43ce50d7cf58420b88605531b34b5c86f905112

560b3460aaf1106f7a053f99ede24cfed094db6f

(Not for this PR): What about renaming `bootstrap_training_and_sampling` to `fit_and_evaluate_subset` or something along the line? For me, this makes it clearer what it actually does. The multiple samples based on different data subsets are actually due to `confidence_intervals` calling it multiple times.

bloebp

py-why/dowhy

Overhaul GCM introduction

* Remove bibtex from GCM introduction. This is covered in docs/source/cite.rst. * Add 'Typical usage' section in GCM introduction

2022-09-05 14:12:41+00:00

2022-11-02 10:01:42+00:00

docs/source/user_guide/gcm_based_inference/introduction.rst

Introduction ============ Graphical causal model-based inference, or GCM-based inference for short, is an experimental addition to DoWhy, that currently works separately from DoWhy's main API. Its experimental status also means that its API may undergo breaking changes in the future. It will be forming a part of a joint, `new API <https://github.com/py-why/dowhy/wiki/API-proposal-for-v1>`_. We welcome your comments. The ``dowhy.gcm`` package provides a variety of ways to answer causal questions and we'll go through them in detail in section :doc:`answering_causal_questions/index`. However, before diving into them, let's understand the basic building blocks and usage patterns it is built upon. The basic building blocks ^^^^^^^^^^^^^^^^^^^^^^^^^ All main features of the GCM-based inference in DoWhy are built around the concept of **graphical causal models**. A graphical causal model consists of a causal direct acyclic graph (DAG) of variables and a **causal mechanism** for each of the variables. A causal mechanism defines the conditional distribution of a variable given its parents in the graph, or, in case of root node variables, simply its distribution. The most general case of a GCM is a **probabilistic causal model** (PCM), where causal mechanisms are defined by **conditional stochastic models** and **stochastic models**. In the ``dowhy.gcm`` package, these are represented by :class:`~ProbabilisticCausalModel`, :class:`~ConditionalStochasticModel`, and :class:`~StochasticModel`. .. image:: pcm.png :width: 80% :align: center | In practical terms however, we often use **structural causal models** (SCMs) to represent our GCMs, and the causal mechanisms are defined by **functional causal models** (FCMs) for non-root nodes and **stochastic models** for root nodes. An SCM implements the same traits as a PCM, but on top of that, its FCMs allow us to reason *further* about its data generation process based on parents and noise, and hence, allow us e.g. to compute counterfactuals. .. image:: scm.png :width: 80% :align: center | To keep this introduction simple, we will stick with SCMs for now. As mentioned above, a causal mechanism describes how the values of a node are influenced by the values of its parent nodes. We will dive much deeper into the details of causal mechanisms and their meaning in section :doc:`customizing_model_assignment`. But for this introduction, we will treat them as an opaque thing that is needed to answer causal questions. With that in mind, the typical steps involved in answering a causal question, are: 1. **Modeling cause-effect relationships as a GCM (causal graph + causal mechanisms):** :: causal_model = StructuralCausalModel(nx.DiGraph([('X', 'Y'), ('Y', 'Z')])) # X -> Y -> Z auto.assign_causal_mechanisms(causal_model, data) Or manually assign causal mechanisms: :: causal_model.set_causal_mechanism('X', EmpiricalDistribution()) causal_model.set_causal_mechanism('Y', AdditiveNoiseModel(create_linear_regressor())) causal_model.set_causal_mechanism('Z', AdditiveNoiseModel(create_linear_regressor())) 2. **Fitting the GCM to the data:** :: fit(causal_model, data) 3. **Answering a causal query based on the GCM:** :: results = <causal_query>(causal_model, ...) Where ``<causal_query>`` can be one of multiple functions explained in :doc:`answering_causal_questions/index`. Let's look at each of these steps in more detail. Step 1: Modeling cause-effect relationships as a structural causal model (SCM) ------------------------------------------------------------------------------ The first step is to model the cause-effect relationships between variables relevant to our use case. We do that in form of a causal graph. A causal graph is a directed acyclic graph (DAG) where an edge X→Y implies that X causes Y. Statistically, a causal graph encodes the conditional independence relations between variables. Using the `networkx <https://networkx .github.io/>`__ library, we can create causal graphs. In the snippet below, we create a chain X→Y→Z: >>> import networkx as nx >>> causal_graph = nx.DiGraph([('X', 'Y'), ('Y', 'Z')]) To answer causal questions using causal graphs, we also have to know the nature of underlying data-generating process of variables. A causal graph by itself, being a diagram, does not have any information about the data-generating process. To introduce this data-generating process, we use an SCM that's built on top of our causal graph: >>> from dowhy import gcm >>> causal_model = gcm.StructuralCausalModel(causal_graph) At this point we would normally load our dataset. For this introduction, we generate some synthetic data instead. The API takes data in form of Pandas DataFrames: >>> import numpy as np, pandas as pd >>> X = np.random.normal(loc=0, scale=1, size=1000) >>> Y = 2 * X + np.random.normal(loc=0, scale=1, size=1000) >>> Z = 3 * Y + np.random.normal(loc=0, scale=1, size=1000) >>> data = pd.DataFrame(data=dict(X=X, Y=Y, Z=Z)) >>> data.head() X Y Z 0 -2.253500 -3.638579 -10.370047 1 -1.078337 -2.114581 -6.028030 2 -0.962719 -2.157896 -5.750563 3 -0.300316 -0.440721 -2.619954 4 0.127419 0.158185 1.555927 Note how the columns X, Y, Z correspond to our nodes X, Y, Z in the graph constructed above. We can also see how the values of X influence the values of Y and how the values of Y influence the values of Z in that data set. The causal model created above allows us now to assign causal mechanisms to each node in the form of functional causal models. Here, these mechanism can either be assigned manually if, for instance, prior knowledge about certain causal relationships are known or they can be assigned automatically using the :mod:`~dowhy.gcm.auto` module. For the latter, we simply call: >>> gcm.auto.assign_causal_mechanisms(causal_model, data) In case we want to have more control over the assigned mechanisms, we can do this manually as well. For instance, we can can assign an empirical distribution to the root node X and linear additive noise models to nodes Y and Z: >>> causal_model.set_causal_mechanism('X', gcm.EmpiricalDistribution()) >>> causal_model.set_causal_mechanism('Y', gcm.AdditiveNoiseModel(gcm.ml.create_linear_regressor())) >>> causal_model.set_causal_mechanism('Z', gcm.AdditiveNoiseModel(gcm.ml.create_linear_regressor())) Section :doc:`customizing_model_assignment` will go into more detail on how one can even define a completely customized model or add their own implementation. In the real world, the data comes as an opaque stream of values, where we typically don't know how one variable influences another. The graphical causal models can help us to deconstruct these causal relationships again, even though we didn't know them before. Step 2: Fitting the SCM to the data ----------------------------------- With the data at hand and the graph constructed earlier, we can now train the SCM using ``fit``: >>> gcm.fit(causal_model, data) Fitting means, we learn the generative models of the variables in the SCM according to the data. Step 3: Answering a causal query based on the SCM ------------------------------------------------- The last step, answering a causal question, is our actual goal. E.g. we could ask the question: What will happen to the variable Z if I intervene on Y? This can be done via the ``interventional_samples`` function. Here's how: >>> samples = gcm.interventional_samples(causal_model, >>> {'Y': lambda y: 2.34 }, >>> num_samples_to_draw=1000) >>> samples.head() X Y Z 0 1.186229 6.918607 20.682375 1 -0.758809 -0.749365 -2.530045 2 -1.177379 -5.678514 -17.110836 3 -1.211356 -2.152073 -6.212703 4 -0.100224 -0.285047 0.256471 This intervention says: "I'll ignore any causal effects of X on Y, and set every value of Y to 2.34." So the distribution of X will remain unchanged, whereas values of Y will be at a fixed value and Z will respond according to its causal model. With this knowledge, we can now dive deep into the meaning and usages of causal queries in section :doc:`answering_causal_questions/index`.

Introduction ============ Graphical causal model-based inference, or GCM-based inference for short, is an experimental addition to DoWhy, that currently works separately from DoWhy's main API. Its experimental status also means that its API may undergo breaking changes in the future. It will be forming a part of a joint, `new API <https://github.com/py-why/dowhy/wiki/API-proposal-for-v1>`_. We welcome your comments. The ``dowhy.gcm`` package provides a variety of ways to answer causal questions and we'll go through them in detail in section :doc:`answering_causal_questions/index`. However, before diving into them, let's understand the basic building blocks and usage patterns it is built upon. The basic building blocks ^^^^^^^^^^^^^^^^^^^^^^^^^ All main features of the GCM-based inference in DoWhy are built around the concept of **graphical causal models**. A graphical causal model consists of a causal direct acyclic graph (DAG) of variables and a **causal mechanism** for each of the variables. A causal mechanism defines the conditional distribution of a variable given its parents in the graph, or, in case of root node variables, simply its distribution. The most general case of a GCM is a **probabilistic causal model** (PCM), where causal mechanisms are defined by **conditional stochastic models** and **stochastic models**. In the ``dowhy.gcm`` package, these are represented by :class:`~ProbabilisticCausalModel`, :class:`~ConditionalStochasticModel`, and :class:`~StochasticModel`. .. image:: pcm.png :width: 80% :align: center | In practical terms however, we often use **structural causal models** (SCMs) to represent our GCMs, and the causal mechanisms are defined by **functional causal models** (FCMs) for non-root nodes and **stochastic models** for root nodes. An SCM implements the same traits as a PCM, but on top of that, its FCMs allow us to reason *further* about its data generation process based on parents and noise, and hence, allow us e.g. to compute counterfactuals. .. image:: scm.png :width: 80% :align: center | To keep this introduction simple, we will stick with SCMs for now. As mentioned above, a causal mechanism describes how the values of a node are influenced by the values of its parent nodes. We will dive much deeper into the details of causal mechanisms and their meaning in section :doc:`customizing_model_assignment`. But for this introduction, we will treat them as an opaque thing that is needed to answer causal questions. With that in mind, the typical steps involved in answering a causal question, are: 1. **Modeling cause-effect relationships as a GCM (causal graph + causal mechanisms):** :: causal_model = StructuralCausalModel(nx.DiGraph([('X', 'Y'), ('Y', 'Z')])) # X -> Y -> Z auto.assign_causal_mechanisms(causal_model, data) Or manually assign causal mechanisms: :: causal_model.set_causal_mechanism('X', EmpiricalDistribution()) causal_model.set_causal_mechanism('Y', AdditiveNoiseModel(create_linear_regressor())) causal_model.set_causal_mechanism('Z', AdditiveNoiseModel(create_linear_regressor())) 2. **Fitting the GCM to the data:** :: fit(causal_model, data) 3. **Answering a causal query based on the GCM:** :: results = <causal_query>(causal_model, ...) Where ``<causal_query>`` can be one of multiple functions explained in :doc:`answering_causal_questions/index`. Let's look at each of these steps in more detail. Step 1: Modeling cause-effect relationships as a structural causal model (SCM) ------------------------------------------------------------------------------ The first step is to model the cause-effect relationships between variables relevant to our use case. We do that in form of a causal graph. A causal graph is a directed acyclic graph (DAG) where an edge X→Y implies that X causes Y. Statistically, a causal graph encodes the conditional independence relations between variables. Using the `networkx <https://networkx .github.io/>`__ library, we can create causal graphs. In the snippet below, we create a chain X→Y→Z: >>> import networkx as nx >>> causal_graph = nx.DiGraph([('X', 'Y'), ('Y', 'Z')]) To answer causal questions using causal graphs, we also have to know the nature of underlying data-generating process of variables. A causal graph by itself, being a diagram, does not have any information about the data-generating process. To introduce this data-generating process, we use an SCM that's built on top of our causal graph: >>> from dowhy import gcm >>> causal_model = gcm.StructuralCausalModel(causal_graph) At this point we would normally load our dataset. For this introduction, we generate some synthetic data instead. The API takes data in form of Pandas DataFrames: >>> import numpy as np, pandas as pd >>> X = np.random.normal(loc=0, scale=1, size=1000) >>> Y = 2 * X + np.random.normal(loc=0, scale=1, size=1000) >>> Z = 3 * Y + np.random.normal(loc=0, scale=1, size=1000) >>> data = pd.DataFrame(data=dict(X=X, Y=Y, Z=Z)) >>> data.head() X Y Z 0 -2.253500 -3.638579 -10.370047 1 -1.078337 -2.114581 -6.028030 2 -0.962719 -2.157896 -5.750563 3 -0.300316 -0.440721 -2.619954 4 0.127419 0.158185 1.555927 Note how the columns X, Y, Z correspond to our nodes X, Y, Z in the graph constructed above. We can also see how the values of X influence the values of Y and how the values of Y influence the values of Z in that data set. The causal model created above allows us now to assign causal mechanisms to each node in the form of functional causal models. Here, these mechanism can either be assigned manually if, for instance, prior knowledge about certain causal relationships are known or they can be assigned automatically using the :mod:`~dowhy.gcm.auto` module. For the latter, we simply call: >>> gcm.auto.assign_causal_mechanisms(causal_model, data) In case we want to have more control over the assigned mechanisms, we can do this manually as well. For instance, we can can assign an empirical distribution to the root node X and linear additive noise models to nodes Y and Z: >>> causal_model.set_causal_mechanism('X', gcm.EmpiricalDistribution()) >>> causal_model.set_causal_mechanism('Y', gcm.AdditiveNoiseModel(gcm.ml.create_linear_regressor())) >>> causal_model.set_causal_mechanism('Z', gcm.AdditiveNoiseModel(gcm.ml.create_linear_regressor())) Section :doc:`customizing_model_assignment` will go into more detail on how one can even define a completely customized model or add their own implementation. In the real world, the data comes as an opaque stream of values, where we typically don't know how one variable influences another. The graphical causal models can help us to deconstruct these causal relationships again, even though we didn't know them before. Step 2: Fitting the SCM to the data ----------------------------------- With the data at hand and the graph constructed earlier, we can now train the SCM using ``fit``: >>> gcm.fit(causal_model, data) Fitting means, we learn the generative models of the variables in the SCM according to the data. Step 3: Answering a causal query based on the SCM ------------------------------------------------- The last step, answering a causal question, is our actual goal. E.g. we could ask the question: What will happen to the variable Z if I intervene on Y? This can be done via the ``interventional_samples`` function. Here's how: >>> samples = gcm.interventional_samples(causal_model, >>> {'Y': lambda y: 2.34 }, >>> num_samples_to_draw=1000) >>> samples.head() X Y Z 0 1.186229 6.918607 20.682375 1 -0.758809 -0.749365 -2.530045 2 -1.177379 -5.678514 -17.110836 3 -1.211356 -2.152073 -6.212703 4 -0.100224 -0.285047 0.256471 This intervention says: "I'll ignore any causal effects of X on Y, and set every value of Y to 2.34." So the distribution of X will remain unchanged, whereas values of Y will be at a fixed value and Z will respond according to its causal model. These are the basic steps that need to happen. While we can run these steps explicitly, often they get executed as part of other steps, e.g. when fitting and re-fitting as part of computing confidence intervals. The next section therefore dives into a more typical usage pattern of the ``dowhy.gcm`` package. Typical usage of the ``dowhy.gcm`` package ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ In practice, we may not execute the steps we've learned above explicitly and in this order, but they get called by other abstractions. E.g. we usually want to use confidence intervals, when answering causal questions, to quantify our confidence in the results. In this case, ``fit`` will be called on behalf of us, but we won't call it directly. Modeling an SCM --------------- The graph modeling is the same as in `Step 1: Modeling cause-effect relationships as a structural causal model (SCM)`_. First we construct the causal graph: >>> causal_model = gcm.StructuralCausalModel(nx.DiGraph([('X', 'Y'), ('Y', 'Z')])) # X → Y → Z Answering a causal query with confidence intervals -------------------------------------------------- When we answer a causal query without computing its confidence intervals, what we effectively get, are point estimates. These are not very useful when trying to assess the confidence in our results. Instead of calling ``fit`` explicitly, we can achieve its execution by going through the API for confidence intervals. Let's say we wanted to understand the direct arrow strengths between nodes and quantify our confidence in those results. This is how we would do it: >>> strength_median, strength_intervals = gcm.confidence_intervals( >>> gcm.bootstrap_training_and_sampling(gcm.direct_arrow_strength, >>> causal_model, >>> bootstrap_training_data=data, >>> target_node='Y')) >>> strength_median, strength_intervals ({('X', 'Y'): 45.90886398636573, ('Z', 'Y'): 15.47129383737619}, {('X', 'Y'): array([42.88319632, 50.43890079]), ('Z', 'Y'): array([13.44202416, 17.74266107])}) In this case, ``fit`` will be called within ``bootstrap_training_and_sampling``, so there is no need to do this ourselves. The calling sequence of ``confidence_intervals`` and ``bootstrap_training_and_sampling`` is not trivial, but exploits the fact our APIs are composable. If not everything makes sense to you yet, we recommend to simply treat this calling sequence as a ready-to-use construct. Read: "Get confidence intervals via bootstrapping training and sampling of direct arrow strength". For a deeper understanding of this construct, see section :doc:`estimating_confidence_intervals`. With this knowledge, we can now dive deep into the meaning and usages of causal queries in section :doc:`answering_causal_questions/index`.

petergtz

b43ce50d7cf58420b88605531b34b5c86f905112

560b3460aaf1106f7a053f99ede24cfed094db6f

Yea, I'm open to renaming that. We could even make it short and call it `fit_and_compute`. Then it would also nice read "fit and compute direct arrow strength" or similar.

petergtz

py-why/dowhy

Overhaul GCM introduction

* Remove bibtex from GCM introduction. This is covered in docs/source/cite.rst. * Add 'Typical usage' section in GCM introduction

2022-09-05 14:12:41+00:00

2022-11-02 10:01:42+00:00

docs/source/user_guide/gcm_based_inference/introduction.rst

Introduction ============ Graphical causal model-based inference, or GCM-based inference for short, is an experimental addition to DoWhy, that currently works separately from DoWhy's main API. Its experimental status also means that its API may undergo breaking changes in the future. It will be forming a part of a joint, `new API <https://github.com/py-why/dowhy/wiki/API-proposal-for-v1>`_. We welcome your comments. The ``dowhy.gcm`` package provides a variety of ways to answer causal questions and we'll go through them in detail in section :doc:`answering_causal_questions/index`. However, before diving into them, let's understand the basic building blocks and usage patterns it is built upon. The basic building blocks ^^^^^^^^^^^^^^^^^^^^^^^^^ All main features of the GCM-based inference in DoWhy are built around the concept of **graphical causal models**. A graphical causal model consists of a causal direct acyclic graph (DAG) of variables and a **causal mechanism** for each of the variables. A causal mechanism defines the conditional distribution of a variable given its parents in the graph, or, in case of root node variables, simply its distribution. The most general case of a GCM is a **probabilistic causal model** (PCM), where causal mechanisms are defined by **conditional stochastic models** and **stochastic models**. In the ``dowhy.gcm`` package, these are represented by :class:`~ProbabilisticCausalModel`, :class:`~ConditionalStochasticModel`, and :class:`~StochasticModel`. .. image:: pcm.png :width: 80% :align: center | In practical terms however, we often use **structural causal models** (SCMs) to represent our GCMs, and the causal mechanisms are defined by **functional causal models** (FCMs) for non-root nodes and **stochastic models** for root nodes. An SCM implements the same traits as a PCM, but on top of that, its FCMs allow us to reason *further* about its data generation process based on parents and noise, and hence, allow us e.g. to compute counterfactuals. .. image:: scm.png :width: 80% :align: center | To keep this introduction simple, we will stick with SCMs for now. As mentioned above, a causal mechanism describes how the values of a node are influenced by the values of its parent nodes. We will dive much deeper into the details of causal mechanisms and their meaning in section :doc:`customizing_model_assignment`. But for this introduction, we will treat them as an opaque thing that is needed to answer causal questions. With that in mind, the typical steps involved in answering a causal question, are: 1. **Modeling cause-effect relationships as a GCM (causal graph + causal mechanisms):** :: causal_model = StructuralCausalModel(nx.DiGraph([('X', 'Y'), ('Y', 'Z')])) # X -> Y -> Z auto.assign_causal_mechanisms(causal_model, data) Or manually assign causal mechanisms: :: causal_model.set_causal_mechanism('X', EmpiricalDistribution()) causal_model.set_causal_mechanism('Y', AdditiveNoiseModel(create_linear_regressor())) causal_model.set_causal_mechanism('Z', AdditiveNoiseModel(create_linear_regressor())) 2. **Fitting the GCM to the data:** :: fit(causal_model, data) 3. **Answering a causal query based on the GCM:** :: results = <causal_query>(causal_model, ...) Where ``<causal_query>`` can be one of multiple functions explained in :doc:`answering_causal_questions/index`. Let's look at each of these steps in more detail. Step 1: Modeling cause-effect relationships as a structural causal model (SCM) ------------------------------------------------------------------------------ The first step is to model the cause-effect relationships between variables relevant to our use case. We do that in form of a causal graph. A causal graph is a directed acyclic graph (DAG) where an edge X→Y implies that X causes Y. Statistically, a causal graph encodes the conditional independence relations between variables. Using the `networkx <https://networkx .github.io/>`__ library, we can create causal graphs. In the snippet below, we create a chain X→Y→Z: >>> import networkx as nx >>> causal_graph = nx.DiGraph([('X', 'Y'), ('Y', 'Z')]) To answer causal questions using causal graphs, we also have to know the nature of underlying data-generating process of variables. A causal graph by itself, being a diagram, does not have any information about the data-generating process. To introduce this data-generating process, we use an SCM that's built on top of our causal graph: >>> from dowhy import gcm >>> causal_model = gcm.StructuralCausalModel(causal_graph) At this point we would normally load our dataset. For this introduction, we generate some synthetic data instead. The API takes data in form of Pandas DataFrames: >>> import numpy as np, pandas as pd >>> X = np.random.normal(loc=0, scale=1, size=1000) >>> Y = 2 * X + np.random.normal(loc=0, scale=1, size=1000) >>> Z = 3 * Y + np.random.normal(loc=0, scale=1, size=1000) >>> data = pd.DataFrame(data=dict(X=X, Y=Y, Z=Z)) >>> data.head() X Y Z 0 -2.253500 -3.638579 -10.370047 1 -1.078337 -2.114581 -6.028030 2 -0.962719 -2.157896 -5.750563 3 -0.300316 -0.440721 -2.619954 4 0.127419 0.158185 1.555927 Note how the columns X, Y, Z correspond to our nodes X, Y, Z in the graph constructed above. We can also see how the values of X influence the values of Y and how the values of Y influence the values of Z in that data set. The causal model created above allows us now to assign causal mechanisms to each node in the form of functional causal models. Here, these mechanism can either be assigned manually if, for instance, prior knowledge about certain causal relationships are known or they can be assigned automatically using the :mod:`~dowhy.gcm.auto` module. For the latter, we simply call: >>> gcm.auto.assign_causal_mechanisms(causal_model, data) In case we want to have more control over the assigned mechanisms, we can do this manually as well. For instance, we can can assign an empirical distribution to the root node X and linear additive noise models to nodes Y and Z: >>> causal_model.set_causal_mechanism('X', gcm.EmpiricalDistribution()) >>> causal_model.set_causal_mechanism('Y', gcm.AdditiveNoiseModel(gcm.ml.create_linear_regressor())) >>> causal_model.set_causal_mechanism('Z', gcm.AdditiveNoiseModel(gcm.ml.create_linear_regressor())) Section :doc:`customizing_model_assignment` will go into more detail on how one can even define a completely customized model or add their own implementation. In the real world, the data comes as an opaque stream of values, where we typically don't know how one variable influences another. The graphical causal models can help us to deconstruct these causal relationships again, even though we didn't know them before. Step 2: Fitting the SCM to the data ----------------------------------- With the data at hand and the graph constructed earlier, we can now train the SCM using ``fit``: >>> gcm.fit(causal_model, data) Fitting means, we learn the generative models of the variables in the SCM according to the data. Step 3: Answering a causal query based on the SCM ------------------------------------------------- The last step, answering a causal question, is our actual goal. E.g. we could ask the question: What will happen to the variable Z if I intervene on Y? This can be done via the ``interventional_samples`` function. Here's how: >>> samples = gcm.interventional_samples(causal_model, >>> {'Y': lambda y: 2.34 }, >>> num_samples_to_draw=1000) >>> samples.head() X Y Z 0 1.186229 6.918607 20.682375 1 -0.758809 -0.749365 -2.530045 2 -1.177379 -5.678514 -17.110836 3 -1.211356 -2.152073 -6.212703 4 -0.100224 -0.285047 0.256471 This intervention says: "I'll ignore any causal effects of X on Y, and set every value of Y to 2.34." So the distribution of X will remain unchanged, whereas values of Y will be at a fixed value and Z will respond according to its causal model. With this knowledge, we can now dive deep into the meaning and usages of causal queries in section :doc:`answering_causal_questions/index`.

Introduction ============ Graphical causal model-based inference, or GCM-based inference for short, is an experimental addition to DoWhy, that currently works separately from DoWhy's main API. Its experimental status also means that its API may undergo breaking changes in the future. It will be forming a part of a joint, `new API <https://github.com/py-why/dowhy/wiki/API-proposal-for-v1>`_. We welcome your comments. The ``dowhy.gcm`` package provides a variety of ways to answer causal questions and we'll go through them in detail in section :doc:`answering_causal_questions/index`. However, before diving into them, let's understand the basic building blocks and usage patterns it is built upon. The basic building blocks ^^^^^^^^^^^^^^^^^^^^^^^^^ All main features of the GCM-based inference in DoWhy are built around the concept of **graphical causal models**. A graphical causal model consists of a causal direct acyclic graph (DAG) of variables and a **causal mechanism** for each of the variables. A causal mechanism defines the conditional distribution of a variable given its parents in the graph, or, in case of root node variables, simply its distribution. The most general case of a GCM is a **probabilistic causal model** (PCM), where causal mechanisms are defined by **conditional stochastic models** and **stochastic models**. In the ``dowhy.gcm`` package, these are represented by :class:`~ProbabilisticCausalModel`, :class:`~ConditionalStochasticModel`, and :class:`~StochasticModel`. .. image:: pcm.png :width: 80% :align: center | In practical terms however, we often use **structural causal models** (SCMs) to represent our GCMs, and the causal mechanisms are defined by **functional causal models** (FCMs) for non-root nodes and **stochastic models** for root nodes. An SCM implements the same traits as a PCM, but on top of that, its FCMs allow us to reason *further* about its data generation process based on parents and noise, and hence, allow us e.g. to compute counterfactuals. .. image:: scm.png :width: 80% :align: center | To keep this introduction simple, we will stick with SCMs for now. As mentioned above, a causal mechanism describes how the values of a node are influenced by the values of its parent nodes. We will dive much deeper into the details of causal mechanisms and their meaning in section :doc:`customizing_model_assignment`. But for this introduction, we will treat them as an opaque thing that is needed to answer causal questions. With that in mind, the typical steps involved in answering a causal question, are: 1. **Modeling cause-effect relationships as a GCM (causal graph + causal mechanisms):** :: causal_model = StructuralCausalModel(nx.DiGraph([('X', 'Y'), ('Y', 'Z')])) # X -> Y -> Z auto.assign_causal_mechanisms(causal_model, data) Or manually assign causal mechanisms: :: causal_model.set_causal_mechanism('X', EmpiricalDistribution()) causal_model.set_causal_mechanism('Y', AdditiveNoiseModel(create_linear_regressor())) causal_model.set_causal_mechanism('Z', AdditiveNoiseModel(create_linear_regressor())) 2. **Fitting the GCM to the data:** :: fit(causal_model, data) 3. **Answering a causal query based on the GCM:** :: results = <causal_query>(causal_model, ...) Where ``<causal_query>`` can be one of multiple functions explained in :doc:`answering_causal_questions/index`. Let's look at each of these steps in more detail. Step 1: Modeling cause-effect relationships as a structural causal model (SCM) ------------------------------------------------------------------------------ The first step is to model the cause-effect relationships between variables relevant to our use case. We do that in form of a causal graph. A causal graph is a directed acyclic graph (DAG) where an edge X→Y implies that X causes Y. Statistically, a causal graph encodes the conditional independence relations between variables. Using the `networkx <https://networkx .github.io/>`__ library, we can create causal graphs. In the snippet below, we create a chain X→Y→Z: >>> import networkx as nx >>> causal_graph = nx.DiGraph([('X', 'Y'), ('Y', 'Z')]) To answer causal questions using causal graphs, we also have to know the nature of underlying data-generating process of variables. A causal graph by itself, being a diagram, does not have any information about the data-generating process. To introduce this data-generating process, we use an SCM that's built on top of our causal graph: >>> from dowhy import gcm >>> causal_model = gcm.StructuralCausalModel(causal_graph) At this point we would normally load our dataset. For this introduction, we generate some synthetic data instead. The API takes data in form of Pandas DataFrames: >>> import numpy as np, pandas as pd >>> X = np.random.normal(loc=0, scale=1, size=1000) >>> Y = 2 * X + np.random.normal(loc=0, scale=1, size=1000) >>> Z = 3 * Y + np.random.normal(loc=0, scale=1, size=1000) >>> data = pd.DataFrame(data=dict(X=X, Y=Y, Z=Z)) >>> data.head() X Y Z 0 -2.253500 -3.638579 -10.370047 1 -1.078337 -2.114581 -6.028030 2 -0.962719 -2.157896 -5.750563 3 -0.300316 -0.440721 -2.619954 4 0.127419 0.158185 1.555927 Note how the columns X, Y, Z correspond to our nodes X, Y, Z in the graph constructed above. We can also see how the values of X influence the values of Y and how the values of Y influence the values of Z in that data set. The causal model created above allows us now to assign causal mechanisms to each node in the form of functional causal models. Here, these mechanism can either be assigned manually if, for instance, prior knowledge about certain causal relationships are known or they can be assigned automatically using the :mod:`~dowhy.gcm.auto` module. For the latter, we simply call: >>> gcm.auto.assign_causal_mechanisms(causal_model, data) In case we want to have more control over the assigned mechanisms, we can do this manually as well. For instance, we can can assign an empirical distribution to the root node X and linear additive noise models to nodes Y and Z: >>> causal_model.set_causal_mechanism('X', gcm.EmpiricalDistribution()) >>> causal_model.set_causal_mechanism('Y', gcm.AdditiveNoiseModel(gcm.ml.create_linear_regressor())) >>> causal_model.set_causal_mechanism('Z', gcm.AdditiveNoiseModel(gcm.ml.create_linear_regressor())) Section :doc:`customizing_model_assignment` will go into more detail on how one can even define a completely customized model or add their own implementation. In the real world, the data comes as an opaque stream of values, where we typically don't know how one variable influences another. The graphical causal models can help us to deconstruct these causal relationships again, even though we didn't know them before. Step 2: Fitting the SCM to the data ----------------------------------- With the data at hand and the graph constructed earlier, we can now train the SCM using ``fit``: >>> gcm.fit(causal_model, data) Fitting means, we learn the generative models of the variables in the SCM according to the data. Step 3: Answering a causal query based on the SCM ------------------------------------------------- The last step, answering a causal question, is our actual goal. E.g. we could ask the question: What will happen to the variable Z if I intervene on Y? This can be done via the ``interventional_samples`` function. Here's how: >>> samples = gcm.interventional_samples(causal_model, >>> {'Y': lambda y: 2.34 }, >>> num_samples_to_draw=1000) >>> samples.head() X Y Z 0 1.186229 6.918607 20.682375 1 -0.758809 -0.749365 -2.530045 2 -1.177379 -5.678514 -17.110836 3 -1.211356 -2.152073 -6.212703 4 -0.100224 -0.285047 0.256471 This intervention says: "I'll ignore any causal effects of X on Y, and set every value of Y to 2.34." So the distribution of X will remain unchanged, whereas values of Y will be at a fixed value and Z will respond according to its causal model. These are the basic steps that need to happen. While we can run these steps explicitly, often they get executed as part of other steps, e.g. when fitting and re-fitting as part of computing confidence intervals. The next section therefore dives into a more typical usage pattern of the ``dowhy.gcm`` package. Typical usage of the ``dowhy.gcm`` package ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ In practice, we may not execute the steps we've learned above explicitly and in this order, but they get called by other abstractions. E.g. we usually want to use confidence intervals, when answering causal questions, to quantify our confidence in the results. In this case, ``fit`` will be called on behalf of us, but we won't call it directly. Modeling an SCM --------------- The graph modeling is the same as in `Step 1: Modeling cause-effect relationships as a structural causal model (SCM)`_. First we construct the causal graph: >>> causal_model = gcm.StructuralCausalModel(nx.DiGraph([('X', 'Y'), ('Y', 'Z')])) # X → Y → Z Answering a causal query with confidence intervals -------------------------------------------------- When we answer a causal query without computing its confidence intervals, what we effectively get, are point estimates. These are not very useful when trying to assess the confidence in our results. Instead of calling ``fit`` explicitly, we can achieve its execution by going through the API for confidence intervals. Let's say we wanted to understand the direct arrow strengths between nodes and quantify our confidence in those results. This is how we would do it: >>> strength_median, strength_intervals = gcm.confidence_intervals( >>> gcm.bootstrap_training_and_sampling(gcm.direct_arrow_strength, >>> causal_model, >>> bootstrap_training_data=data, >>> target_node='Y')) >>> strength_median, strength_intervals ({('X', 'Y'): 45.90886398636573, ('Z', 'Y'): 15.47129383737619}, {('X', 'Y'): array([42.88319632, 50.43890079]), ('Z', 'Y'): array([13.44202416, 17.74266107])}) In this case, ``fit`` will be called within ``bootstrap_training_and_sampling``, so there is no need to do this ourselves. The calling sequence of ``confidence_intervals`` and ``bootstrap_training_and_sampling`` is not trivial, but exploits the fact our APIs are composable. If not everything makes sense to you yet, we recommend to simply treat this calling sequence as a ready-to-use construct. Read: "Get confidence intervals via bootstrapping training and sampling of direct arrow strength". For a deeper understanding of this construct, see section :doc:`estimating_confidence_intervals`. With this knowledge, we can now dive deep into the meaning and usages of causal queries in section :doc:`answering_causal_questions/index`.

petergtz

b43ce50d7cf58420b88605531b34b5c86f905112

560b3460aaf1106f7a053f99ede24cfed094db6f

No, I guess this is a copy-and-paste issue. I'll remove it.

petergtz

py-why/dowhy

Overhaul GCM introduction

* Remove bibtex from GCM introduction. This is covered in docs/source/cite.rst. * Add 'Typical usage' section in GCM introduction

2022-09-05 14:12:41+00:00

2022-11-02 10:01:42+00:00

docs/source/user_guide/gcm_based_inference/introduction.rst

Introduction ============ Graphical causal model-based inference, or GCM-based inference for short, is an experimental addition to DoWhy, that currently works separately from DoWhy's main API. Its experimental status also means that its API may undergo breaking changes in the future. It will be forming a part of a joint, `new API <https://github.com/py-why/dowhy/wiki/API-proposal-for-v1>`_. We welcome your comments. The ``dowhy.gcm`` package provides a variety of ways to answer causal questions and we'll go through them in detail in section :doc:`answering_causal_questions/index`. However, before diving into them, let's understand the basic building blocks and usage patterns it is built upon. The basic building blocks ^^^^^^^^^^^^^^^^^^^^^^^^^ All main features of the GCM-based inference in DoWhy are built around the concept of **graphical causal models**. A graphical causal model consists of a causal direct acyclic graph (DAG) of variables and a **causal mechanism** for each of the variables. A causal mechanism defines the conditional distribution of a variable given its parents in the graph, or, in case of root node variables, simply its distribution. The most general case of a GCM is a **probabilistic causal model** (PCM), where causal mechanisms are defined by **conditional stochastic models** and **stochastic models**. In the ``dowhy.gcm`` package, these are represented by :class:`~ProbabilisticCausalModel`, :class:`~ConditionalStochasticModel`, and :class:`~StochasticModel`. .. image:: pcm.png :width: 80% :align: center | In practical terms however, we often use **structural causal models** (SCMs) to represent our GCMs, and the causal mechanisms are defined by **functional causal models** (FCMs) for non-root nodes and **stochastic models** for root nodes. An SCM implements the same traits as a PCM, but on top of that, its FCMs allow us to reason *further* about its data generation process based on parents and noise, and hence, allow us e.g. to compute counterfactuals. .. image:: scm.png :width: 80% :align: center | To keep this introduction simple, we will stick with SCMs for now. As mentioned above, a causal mechanism describes how the values of a node are influenced by the values of its parent nodes. We will dive much deeper into the details of causal mechanisms and their meaning in section :doc:`customizing_model_assignment`. But for this introduction, we will treat them as an opaque thing that is needed to answer causal questions. With that in mind, the typical steps involved in answering a causal question, are: 1. **Modeling cause-effect relationships as a GCM (causal graph + causal mechanisms):** :: causal_model = StructuralCausalModel(nx.DiGraph([('X', 'Y'), ('Y', 'Z')])) # X -> Y -> Z auto.assign_causal_mechanisms(causal_model, data) Or manually assign causal mechanisms: :: causal_model.set_causal_mechanism('X', EmpiricalDistribution()) causal_model.set_causal_mechanism('Y', AdditiveNoiseModel(create_linear_regressor())) causal_model.set_causal_mechanism('Z', AdditiveNoiseModel(create_linear_regressor())) 2. **Fitting the GCM to the data:** :: fit(causal_model, data) 3. **Answering a causal query based on the GCM:** :: results = <causal_query>(causal_model, ...) Where ``<causal_query>`` can be one of multiple functions explained in :doc:`answering_causal_questions/index`. Let's look at each of these steps in more detail. Step 1: Modeling cause-effect relationships as a structural causal model (SCM) ------------------------------------------------------------------------------ The first step is to model the cause-effect relationships between variables relevant to our use case. We do that in form of a causal graph. A causal graph is a directed acyclic graph (DAG) where an edge X→Y implies that X causes Y. Statistically, a causal graph encodes the conditional independence relations between variables. Using the `networkx <https://networkx .github.io/>`__ library, we can create causal graphs. In the snippet below, we create a chain X→Y→Z: >>> import networkx as nx >>> causal_graph = nx.DiGraph([('X', 'Y'), ('Y', 'Z')]) To answer causal questions using causal graphs, we also have to know the nature of underlying data-generating process of variables. A causal graph by itself, being a diagram, does not have any information about the data-generating process. To introduce this data-generating process, we use an SCM that's built on top of our causal graph: >>> from dowhy import gcm >>> causal_model = gcm.StructuralCausalModel(causal_graph) At this point we would normally load our dataset. For this introduction, we generate some synthetic data instead. The API takes data in form of Pandas DataFrames: >>> import numpy as np, pandas as pd >>> X = np.random.normal(loc=0, scale=1, size=1000) >>> Y = 2 * X + np.random.normal(loc=0, scale=1, size=1000) >>> Z = 3 * Y + np.random.normal(loc=0, scale=1, size=1000) >>> data = pd.DataFrame(data=dict(X=X, Y=Y, Z=Z)) >>> data.head() X Y Z 0 -2.253500 -3.638579 -10.370047 1 -1.078337 -2.114581 -6.028030 2 -0.962719 -2.157896 -5.750563 3 -0.300316 -0.440721 -2.619954 4 0.127419 0.158185 1.555927 Note how the columns X, Y, Z correspond to our nodes X, Y, Z in the graph constructed above. We can also see how the values of X influence the values of Y and how the values of Y influence the values of Z in that data set. The causal model created above allows us now to assign causal mechanisms to each node in the form of functional causal models. Here, these mechanism can either be assigned manually if, for instance, prior knowledge about certain causal relationships are known or they can be assigned automatically using the :mod:`~dowhy.gcm.auto` module. For the latter, we simply call: >>> gcm.auto.assign_causal_mechanisms(causal_model, data) In case we want to have more control over the assigned mechanisms, we can do this manually as well. For instance, we can can assign an empirical distribution to the root node X and linear additive noise models to nodes Y and Z: >>> causal_model.set_causal_mechanism('X', gcm.EmpiricalDistribution()) >>> causal_model.set_causal_mechanism('Y', gcm.AdditiveNoiseModel(gcm.ml.create_linear_regressor())) >>> causal_model.set_causal_mechanism('Z', gcm.AdditiveNoiseModel(gcm.ml.create_linear_regressor())) Section :doc:`customizing_model_assignment` will go into more detail on how one can even define a completely customized model or add their own implementation. In the real world, the data comes as an opaque stream of values, where we typically don't know how one variable influences another. The graphical causal models can help us to deconstruct these causal relationships again, even though we didn't know them before. Step 2: Fitting the SCM to the data ----------------------------------- With the data at hand and the graph constructed earlier, we can now train the SCM using ``fit``: >>> gcm.fit(causal_model, data) Fitting means, we learn the generative models of the variables in the SCM according to the data. Step 3: Answering a causal query based on the SCM ------------------------------------------------- The last step, answering a causal question, is our actual goal. E.g. we could ask the question: What will happen to the variable Z if I intervene on Y? This can be done via the ``interventional_samples`` function. Here's how: >>> samples = gcm.interventional_samples(causal_model, >>> {'Y': lambda y: 2.34 }, >>> num_samples_to_draw=1000) >>> samples.head() X Y Z 0 1.186229 6.918607 20.682375 1 -0.758809 -0.749365 -2.530045 2 -1.177379 -5.678514 -17.110836 3 -1.211356 -2.152073 -6.212703 4 -0.100224 -0.285047 0.256471 This intervention says: "I'll ignore any causal effects of X on Y, and set every value of Y to 2.34." So the distribution of X will remain unchanged, whereas values of Y will be at a fixed value and Z will respond according to its causal model. With this knowledge, we can now dive deep into the meaning and usages of causal queries in section :doc:`answering_causal_questions/index`.

Introduction ============ Graphical causal model-based inference, or GCM-based inference for short, is an experimental addition to DoWhy, that currently works separately from DoWhy's main API. Its experimental status also means that its API may undergo breaking changes in the future. It will be forming a part of a joint, `new API <https://github.com/py-why/dowhy/wiki/API-proposal-for-v1>`_. We welcome your comments. The ``dowhy.gcm`` package provides a variety of ways to answer causal questions and we'll go through them in detail in section :doc:`answering_causal_questions/index`. However, before diving into them, let's understand the basic building blocks and usage patterns it is built upon. The basic building blocks ^^^^^^^^^^^^^^^^^^^^^^^^^ All main features of the GCM-based inference in DoWhy are built around the concept of **graphical causal models**. A graphical causal model consists of a causal direct acyclic graph (DAG) of variables and a **causal mechanism** for each of the variables. A causal mechanism defines the conditional distribution of a variable given its parents in the graph, or, in case of root node variables, simply its distribution. The most general case of a GCM is a **probabilistic causal model** (PCM), where causal mechanisms are defined by **conditional stochastic models** and **stochastic models**. In the ``dowhy.gcm`` package, these are represented by :class:`~ProbabilisticCausalModel`, :class:`~ConditionalStochasticModel`, and :class:`~StochasticModel`. .. image:: pcm.png :width: 80% :align: center | In practical terms however, we often use **structural causal models** (SCMs) to represent our GCMs, and the causal mechanisms are defined by **functional causal models** (FCMs) for non-root nodes and **stochastic models** for root nodes. An SCM implements the same traits as a PCM, but on top of that, its FCMs allow us to reason *further* about its data generation process based on parents and noise, and hence, allow us e.g. to compute counterfactuals. .. image:: scm.png :width: 80% :align: center | To keep this introduction simple, we will stick with SCMs for now. As mentioned above, a causal mechanism describes how the values of a node are influenced by the values of its parent nodes. We will dive much deeper into the details of causal mechanisms and their meaning in section :doc:`customizing_model_assignment`. But for this introduction, we will treat them as an opaque thing that is needed to answer causal questions. With that in mind, the typical steps involved in answering a causal question, are: 1. **Modeling cause-effect relationships as a GCM (causal graph + causal mechanisms):** :: causal_model = StructuralCausalModel(nx.DiGraph([('X', 'Y'), ('Y', 'Z')])) # X -> Y -> Z auto.assign_causal_mechanisms(causal_model, data) Or manually assign causal mechanisms: :: causal_model.set_causal_mechanism('X', EmpiricalDistribution()) causal_model.set_causal_mechanism('Y', AdditiveNoiseModel(create_linear_regressor())) causal_model.set_causal_mechanism('Z', AdditiveNoiseModel(create_linear_regressor())) 2. **Fitting the GCM to the data:** :: fit(causal_model, data) 3. **Answering a causal query based on the GCM:** :: results = <causal_query>(causal_model, ...) Where ``<causal_query>`` can be one of multiple functions explained in :doc:`answering_causal_questions/index`. Let's look at each of these steps in more detail. Step 1: Modeling cause-effect relationships as a structural causal model (SCM) ------------------------------------------------------------------------------ The first step is to model the cause-effect relationships between variables relevant to our use case. We do that in form of a causal graph. A causal graph is a directed acyclic graph (DAG) where an edge X→Y implies that X causes Y. Statistically, a causal graph encodes the conditional independence relations between variables. Using the `networkx <https://networkx .github.io/>`__ library, we can create causal graphs. In the snippet below, we create a chain X→Y→Z: >>> import networkx as nx >>> causal_graph = nx.DiGraph([('X', 'Y'), ('Y', 'Z')]) To answer causal questions using causal graphs, we also have to know the nature of underlying data-generating process of variables. A causal graph by itself, being a diagram, does not have any information about the data-generating process. To introduce this data-generating process, we use an SCM that's built on top of our causal graph: >>> from dowhy import gcm >>> causal_model = gcm.StructuralCausalModel(causal_graph) At this point we would normally load our dataset. For this introduction, we generate some synthetic data instead. The API takes data in form of Pandas DataFrames: >>> import numpy as np, pandas as pd >>> X = np.random.normal(loc=0, scale=1, size=1000) >>> Y = 2 * X + np.random.normal(loc=0, scale=1, size=1000) >>> Z = 3 * Y + np.random.normal(loc=0, scale=1, size=1000) >>> data = pd.DataFrame(data=dict(X=X, Y=Y, Z=Z)) >>> data.head() X Y Z 0 -2.253500 -3.638579 -10.370047 1 -1.078337 -2.114581 -6.028030 2 -0.962719 -2.157896 -5.750563 3 -0.300316 -0.440721 -2.619954 4 0.127419 0.158185 1.555927 Note how the columns X, Y, Z correspond to our nodes X, Y, Z in the graph constructed above. We can also see how the values of X influence the values of Y and how the values of Y influence the values of Z in that data set. The causal model created above allows us now to assign causal mechanisms to each node in the form of functional causal models. Here, these mechanism can either be assigned manually if, for instance, prior knowledge about certain causal relationships are known or they can be assigned automatically using the :mod:`~dowhy.gcm.auto` module. For the latter, we simply call: >>> gcm.auto.assign_causal_mechanisms(causal_model, data) In case we want to have more control over the assigned mechanisms, we can do this manually as well. For instance, we can can assign an empirical distribution to the root node X and linear additive noise models to nodes Y and Z: >>> causal_model.set_causal_mechanism('X', gcm.EmpiricalDistribution()) >>> causal_model.set_causal_mechanism('Y', gcm.AdditiveNoiseModel(gcm.ml.create_linear_regressor())) >>> causal_model.set_causal_mechanism('Z', gcm.AdditiveNoiseModel(gcm.ml.create_linear_regressor())) Section :doc:`customizing_model_assignment` will go into more detail on how one can even define a completely customized model or add their own implementation. In the real world, the data comes as an opaque stream of values, where we typically don't know how one variable influences another. The graphical causal models can help us to deconstruct these causal relationships again, even though we didn't know them before. Step 2: Fitting the SCM to the data ----------------------------------- With the data at hand and the graph constructed earlier, we can now train the SCM using ``fit``: >>> gcm.fit(causal_model, data) Fitting means, we learn the generative models of the variables in the SCM according to the data. Step 3: Answering a causal query based on the SCM ------------------------------------------------- The last step, answering a causal question, is our actual goal. E.g. we could ask the question: What will happen to the variable Z if I intervene on Y? This can be done via the ``interventional_samples`` function. Here's how: >>> samples = gcm.interventional_samples(causal_model, >>> {'Y': lambda y: 2.34 }, >>> num_samples_to_draw=1000) >>> samples.head() X Y Z 0 1.186229 6.918607 20.682375 1 -0.758809 -0.749365 -2.530045 2 -1.177379 -5.678514 -17.110836 3 -1.211356 -2.152073 -6.212703 4 -0.100224 -0.285047 0.256471 This intervention says: "I'll ignore any causal effects of X on Y, and set every value of Y to 2.34." So the distribution of X will remain unchanged, whereas values of Y will be at a fixed value and Z will respond according to its causal model. These are the basic steps that need to happen. While we can run these steps explicitly, often they get executed as part of other steps, e.g. when fitting and re-fitting as part of computing confidence intervals. The next section therefore dives into a more typical usage pattern of the ``dowhy.gcm`` package. Typical usage of the ``dowhy.gcm`` package ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ In practice, we may not execute the steps we've learned above explicitly and in this order, but they get called by other abstractions. E.g. we usually want to use confidence intervals, when answering causal questions, to quantify our confidence in the results. In this case, ``fit`` will be called on behalf of us, but we won't call it directly. Modeling an SCM --------------- The graph modeling is the same as in `Step 1: Modeling cause-effect relationships as a structural causal model (SCM)`_. First we construct the causal graph: >>> causal_model = gcm.StructuralCausalModel(nx.DiGraph([('X', 'Y'), ('Y', 'Z')])) # X → Y → Z Answering a causal query with confidence intervals -------------------------------------------------- When we answer a causal query without computing its confidence intervals, what we effectively get, are point estimates. These are not very useful when trying to assess the confidence in our results. Instead of calling ``fit`` explicitly, we can achieve its execution by going through the API for confidence intervals. Let's say we wanted to understand the direct arrow strengths between nodes and quantify our confidence in those results. This is how we would do it: >>> strength_median, strength_intervals = gcm.confidence_intervals( >>> gcm.bootstrap_training_and_sampling(gcm.direct_arrow_strength, >>> causal_model, >>> bootstrap_training_data=data, >>> target_node='Y')) >>> strength_median, strength_intervals ({('X', 'Y'): 45.90886398636573, ('Z', 'Y'): 15.47129383737619}, {('X', 'Y'): array([42.88319632, 50.43890079]), ('Z', 'Y'): array([13.44202416, 17.74266107])}) In this case, ``fit`` will be called within ``bootstrap_training_and_sampling``, so there is no need to do this ourselves. The calling sequence of ``confidence_intervals`` and ``bootstrap_training_and_sampling`` is not trivial, but exploits the fact our APIs are composable. If not everything makes sense to you yet, we recommend to simply treat this calling sequence as a ready-to-use construct. Read: "Get confidence intervals via bootstrapping training and sampling of direct arrow strength". For a deeper understanding of this construct, see section :doc:`estimating_confidence_intervals`. With this knowledge, we can now dive deep into the meaning and usages of causal queries in section :doc:`answering_causal_questions/index`.

petergtz

b43ce50d7cf58420b88605531b34b5c86f905112

560b3460aaf1106f7a053f99ede24cfed094db6f

Wait, but didn't we discuss this at length and said that `REJECTED` would only be returned when you really shouldn't continue, whereas in other cases it might still not be correct, but it's somewhat inconclusive. It feels like we're re-discussing something that we've already resolved, no?

petergtz

py-why/dowhy

Overhaul GCM introduction

* Remove bibtex from GCM introduction. This is covered in docs/source/cite.rst. * Add 'Typical usage' section in GCM introduction

2022-09-05 14:12:41+00:00

2022-11-02 10:01:42+00:00

docs/source/user_guide/gcm_based_inference/introduction.rst

Introduction ============ Graphical causal model-based inference, or GCM-based inference for short, is an experimental addition to DoWhy, that currently works separately from DoWhy's main API. Its experimental status also means that its API may undergo breaking changes in the future. It will be forming a part of a joint, `new API <https://github.com/py-why/dowhy/wiki/API-proposal-for-v1>`_. We welcome your comments. The ``dowhy.gcm`` package provides a variety of ways to answer causal questions and we'll go through them in detail in section :doc:`answering_causal_questions/index`. However, before diving into them, let's understand the basic building blocks and usage patterns it is built upon. The basic building blocks ^^^^^^^^^^^^^^^^^^^^^^^^^ All main features of the GCM-based inference in DoWhy are built around the concept of **graphical causal models**. A graphical causal model consists of a causal direct acyclic graph (DAG) of variables and a **causal mechanism** for each of the variables. A causal mechanism defines the conditional distribution of a variable given its parents in the graph, or, in case of root node variables, simply its distribution. The most general case of a GCM is a **probabilistic causal model** (PCM), where causal mechanisms are defined by **conditional stochastic models** and **stochastic models**. In the ``dowhy.gcm`` package, these are represented by :class:`~ProbabilisticCausalModel`, :class:`~ConditionalStochasticModel`, and :class:`~StochasticModel`. .. image:: pcm.png :width: 80% :align: center | In practical terms however, we often use **structural causal models** (SCMs) to represent our GCMs, and the causal mechanisms are defined by **functional causal models** (FCMs) for non-root nodes and **stochastic models** for root nodes. An SCM implements the same traits as a PCM, but on top of that, its FCMs allow us to reason *further* about its data generation process based on parents and noise, and hence, allow us e.g. to compute counterfactuals. .. image:: scm.png :width: 80% :align: center | To keep this introduction simple, we will stick with SCMs for now. As mentioned above, a causal mechanism describes how the values of a node are influenced by the values of its parent nodes. We will dive much deeper into the details of causal mechanisms and their meaning in section :doc:`customizing_model_assignment`. But for this introduction, we will treat them as an opaque thing that is needed to answer causal questions. With that in mind, the typical steps involved in answering a causal question, are: 1. **Modeling cause-effect relationships as a GCM (causal graph + causal mechanisms):** :: causal_model = StructuralCausalModel(nx.DiGraph([('X', 'Y'), ('Y', 'Z')])) # X -> Y -> Z auto.assign_causal_mechanisms(causal_model, data) Or manually assign causal mechanisms: :: causal_model.set_causal_mechanism('X', EmpiricalDistribution()) causal_model.set_causal_mechanism('Y', AdditiveNoiseModel(create_linear_regressor())) causal_model.set_causal_mechanism('Z', AdditiveNoiseModel(create_linear_regressor())) 2. **Fitting the GCM to the data:** :: fit(causal_model, data) 3. **Answering a causal query based on the GCM:** :: results = <causal_query>(causal_model, ...) Where ``<causal_query>`` can be one of multiple functions explained in :doc:`answering_causal_questions/index`. Let's look at each of these steps in more detail. Step 1: Modeling cause-effect relationships as a structural causal model (SCM) ------------------------------------------------------------------------------ The first step is to model the cause-effect relationships between variables relevant to our use case. We do that in form of a causal graph. A causal graph is a directed acyclic graph (DAG) where an edge X→Y implies that X causes Y. Statistically, a causal graph encodes the conditional independence relations between variables. Using the `networkx <https://networkx .github.io/>`__ library, we can create causal graphs. In the snippet below, we create a chain X→Y→Z: >>> import networkx as nx >>> causal_graph = nx.DiGraph([('X', 'Y'), ('Y', 'Z')]) To answer causal questions using causal graphs, we also have to know the nature of underlying data-generating process of variables. A causal graph by itself, being a diagram, does not have any information about the data-generating process. To introduce this data-generating process, we use an SCM that's built on top of our causal graph: >>> from dowhy import gcm >>> causal_model = gcm.StructuralCausalModel(causal_graph) At this point we would normally load our dataset. For this introduction, we generate some synthetic data instead. The API takes data in form of Pandas DataFrames: >>> import numpy as np, pandas as pd >>> X = np.random.normal(loc=0, scale=1, size=1000) >>> Y = 2 * X + np.random.normal(loc=0, scale=1, size=1000) >>> Z = 3 * Y + np.random.normal(loc=0, scale=1, size=1000) >>> data = pd.DataFrame(data=dict(X=X, Y=Y, Z=Z)) >>> data.head() X Y Z 0 -2.253500 -3.638579 -10.370047 1 -1.078337 -2.114581 -6.028030 2 -0.962719 -2.157896 -5.750563 3 -0.300316 -0.440721 -2.619954 4 0.127419 0.158185 1.555927 Note how the columns X, Y, Z correspond to our nodes X, Y, Z in the graph constructed above. We can also see how the values of X influence the values of Y and how the values of Y influence the values of Z in that data set. The causal model created above allows us now to assign causal mechanisms to each node in the form of functional causal models. Here, these mechanism can either be assigned manually if, for instance, prior knowledge about certain causal relationships are known or they can be assigned automatically using the :mod:`~dowhy.gcm.auto` module. For the latter, we simply call: >>> gcm.auto.assign_causal_mechanisms(causal_model, data) In case we want to have more control over the assigned mechanisms, we can do this manually as well. For instance, we can can assign an empirical distribution to the root node X and linear additive noise models to nodes Y and Z: >>> causal_model.set_causal_mechanism('X', gcm.EmpiricalDistribution()) >>> causal_model.set_causal_mechanism('Y', gcm.AdditiveNoiseModel(gcm.ml.create_linear_regressor())) >>> causal_model.set_causal_mechanism('Z', gcm.AdditiveNoiseModel(gcm.ml.create_linear_regressor())) Section :doc:`customizing_model_assignment` will go into more detail on how one can even define a completely customized model or add their own implementation. In the real world, the data comes as an opaque stream of values, where we typically don't know how one variable influences another. The graphical causal models can help us to deconstruct these causal relationships again, even though we didn't know them before. Step 2: Fitting the SCM to the data ----------------------------------- With the data at hand and the graph constructed earlier, we can now train the SCM using ``fit``: >>> gcm.fit(causal_model, data) Fitting means, we learn the generative models of the variables in the SCM according to the data. Step 3: Answering a causal query based on the SCM ------------------------------------------------- The last step, answering a causal question, is our actual goal. E.g. we could ask the question: What will happen to the variable Z if I intervene on Y? This can be done via the ``interventional_samples`` function. Here's how: >>> samples = gcm.interventional_samples(causal_model, >>> {'Y': lambda y: 2.34 }, >>> num_samples_to_draw=1000) >>> samples.head() X Y Z 0 1.186229 6.918607 20.682375 1 -0.758809 -0.749365 -2.530045 2 -1.177379 -5.678514 -17.110836 3 -1.211356 -2.152073 -6.212703 4 -0.100224 -0.285047 0.256471 This intervention says: "I'll ignore any causal effects of X on Y, and set every value of Y to 2.34." So the distribution of X will remain unchanged, whereas values of Y will be at a fixed value and Z will respond according to its causal model. With this knowledge, we can now dive deep into the meaning and usages of causal queries in section :doc:`answering_causal_questions/index`.

Introduction ============ Graphical causal model-based inference, or GCM-based inference for short, is an experimental addition to DoWhy, that currently works separately from DoWhy's main API. Its experimental status also means that its API may undergo breaking changes in the future. It will be forming a part of a joint, `new API <https://github.com/py-why/dowhy/wiki/API-proposal-for-v1>`_. We welcome your comments. The ``dowhy.gcm`` package provides a variety of ways to answer causal questions and we'll go through them in detail in section :doc:`answering_causal_questions/index`. However, before diving into them, let's understand the basic building blocks and usage patterns it is built upon. The basic building blocks ^^^^^^^^^^^^^^^^^^^^^^^^^ All main features of the GCM-based inference in DoWhy are built around the concept of **graphical causal models**. A graphical causal model consists of a causal direct acyclic graph (DAG) of variables and a **causal mechanism** for each of the variables. A causal mechanism defines the conditional distribution of a variable given its parents in the graph, or, in case of root node variables, simply its distribution. The most general case of a GCM is a **probabilistic causal model** (PCM), where causal mechanisms are defined by **conditional stochastic models** and **stochastic models**. In the ``dowhy.gcm`` package, these are represented by :class:`~ProbabilisticCausalModel`, :class:`~ConditionalStochasticModel`, and :class:`~StochasticModel`. .. image:: pcm.png :width: 80% :align: center | In practical terms however, we often use **structural causal models** (SCMs) to represent our GCMs, and the causal mechanisms are defined by **functional causal models** (FCMs) for non-root nodes and **stochastic models** for root nodes. An SCM implements the same traits as a PCM, but on top of that, its FCMs allow us to reason *further* about its data generation process based on parents and noise, and hence, allow us e.g. to compute counterfactuals. .. image:: scm.png :width: 80% :align: center | To keep this introduction simple, we will stick with SCMs for now. As mentioned above, a causal mechanism describes how the values of a node are influenced by the values of its parent nodes. We will dive much deeper into the details of causal mechanisms and their meaning in section :doc:`customizing_model_assignment`. But for this introduction, we will treat them as an opaque thing that is needed to answer causal questions. With that in mind, the typical steps involved in answering a causal question, are: 1. **Modeling cause-effect relationships as a GCM (causal graph + causal mechanisms):** :: causal_model = StructuralCausalModel(nx.DiGraph([('X', 'Y'), ('Y', 'Z')])) # X -> Y -> Z auto.assign_causal_mechanisms(causal_model, data) Or manually assign causal mechanisms: :: causal_model.set_causal_mechanism('X', EmpiricalDistribution()) causal_model.set_causal_mechanism('Y', AdditiveNoiseModel(create_linear_regressor())) causal_model.set_causal_mechanism('Z', AdditiveNoiseModel(create_linear_regressor())) 2. **Fitting the GCM to the data:** :: fit(causal_model, data) 3. **Answering a causal query based on the GCM:** :: results = <causal_query>(causal_model, ...) Where ``<causal_query>`` can be one of multiple functions explained in :doc:`answering_causal_questions/index`. Let's look at each of these steps in more detail. Step 1: Modeling cause-effect relationships as a structural causal model (SCM) ------------------------------------------------------------------------------ The first step is to model the cause-effect relationships between variables relevant to our use case. We do that in form of a causal graph. A causal graph is a directed acyclic graph (DAG) where an edge X→Y implies that X causes Y. Statistically, a causal graph encodes the conditional independence relations between variables. Using the `networkx <https://networkx .github.io/>`__ library, we can create causal graphs. In the snippet below, we create a chain X→Y→Z: >>> import networkx as nx >>> causal_graph = nx.DiGraph([('X', 'Y'), ('Y', 'Z')]) To answer causal questions using causal graphs, we also have to know the nature of underlying data-generating process of variables. A causal graph by itself, being a diagram, does not have any information about the data-generating process. To introduce this data-generating process, we use an SCM that's built on top of our causal graph: >>> from dowhy import gcm >>> causal_model = gcm.StructuralCausalModel(causal_graph) At this point we would normally load our dataset. For this introduction, we generate some synthetic data instead. The API takes data in form of Pandas DataFrames: >>> import numpy as np, pandas as pd >>> X = np.random.normal(loc=0, scale=1, size=1000) >>> Y = 2 * X + np.random.normal(loc=0, scale=1, size=1000) >>> Z = 3 * Y + np.random.normal(loc=0, scale=1, size=1000) >>> data = pd.DataFrame(data=dict(X=X, Y=Y, Z=Z)) >>> data.head() X Y Z 0 -2.253500 -3.638579 -10.370047 1 -1.078337 -2.114581 -6.028030 2 -0.962719 -2.157896 -5.750563 3 -0.300316 -0.440721 -2.619954 4 0.127419 0.158185 1.555927 Note how the columns X, Y, Z correspond to our nodes X, Y, Z in the graph constructed above. We can also see how the values of X influence the values of Y and how the values of Y influence the values of Z in that data set. The causal model created above allows us now to assign causal mechanisms to each node in the form of functional causal models. Here, these mechanism can either be assigned manually if, for instance, prior knowledge about certain causal relationships are known or they can be assigned automatically using the :mod:`~dowhy.gcm.auto` module. For the latter, we simply call: >>> gcm.auto.assign_causal_mechanisms(causal_model, data) In case we want to have more control over the assigned mechanisms, we can do this manually as well. For instance, we can can assign an empirical distribution to the root node X and linear additive noise models to nodes Y and Z: >>> causal_model.set_causal_mechanism('X', gcm.EmpiricalDistribution()) >>> causal_model.set_causal_mechanism('Y', gcm.AdditiveNoiseModel(gcm.ml.create_linear_regressor())) >>> causal_model.set_causal_mechanism('Z', gcm.AdditiveNoiseModel(gcm.ml.create_linear_regressor())) Section :doc:`customizing_model_assignment` will go into more detail on how one can even define a completely customized model or add their own implementation. In the real world, the data comes as an opaque stream of values, where we typically don't know how one variable influences another. The graphical causal models can help us to deconstruct these causal relationships again, even though we didn't know them before. Step 2: Fitting the SCM to the data ----------------------------------- With the data at hand and the graph constructed earlier, we can now train the SCM using ``fit``: >>> gcm.fit(causal_model, data) Fitting means, we learn the generative models of the variables in the SCM according to the data. Step 3: Answering a causal query based on the SCM ------------------------------------------------- The last step, answering a causal question, is our actual goal. E.g. we could ask the question: What will happen to the variable Z if I intervene on Y? This can be done via the ``interventional_samples`` function. Here's how: >>> samples = gcm.interventional_samples(causal_model, >>> {'Y': lambda y: 2.34 }, >>> num_samples_to_draw=1000) >>> samples.head() X Y Z 0 1.186229 6.918607 20.682375 1 -0.758809 -0.749365 -2.530045 2 -1.177379 -5.678514 -17.110836 3 -1.211356 -2.152073 -6.212703 4 -0.100224 -0.285047 0.256471 This intervention says: "I'll ignore any causal effects of X on Y, and set every value of Y to 2.34." So the distribution of X will remain unchanged, whereas values of Y will be at a fixed value and Z will respond according to its causal model. These are the basic steps that need to happen. While we can run these steps explicitly, often they get executed as part of other steps, e.g. when fitting and re-fitting as part of computing confidence intervals. The next section therefore dives into a more typical usage pattern of the ``dowhy.gcm`` package. Typical usage of the ``dowhy.gcm`` package ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ In practice, we may not execute the steps we've learned above explicitly and in this order, but they get called by other abstractions. E.g. we usually want to use confidence intervals, when answering causal questions, to quantify our confidence in the results. In this case, ``fit`` will be called on behalf of us, but we won't call it directly. Modeling an SCM --------------- The graph modeling is the same as in `Step 1: Modeling cause-effect relationships as a structural causal model (SCM)`_. First we construct the causal graph: >>> causal_model = gcm.StructuralCausalModel(nx.DiGraph([('X', 'Y'), ('Y', 'Z')])) # X → Y → Z Answering a causal query with confidence intervals -------------------------------------------------- When we answer a causal query without computing its confidence intervals, what we effectively get, are point estimates. These are not very useful when trying to assess the confidence in our results. Instead of calling ``fit`` explicitly, we can achieve its execution by going through the API for confidence intervals. Let's say we wanted to understand the direct arrow strengths between nodes and quantify our confidence in those results. This is how we would do it: >>> strength_median, strength_intervals = gcm.confidence_intervals( >>> gcm.bootstrap_training_and_sampling(gcm.direct_arrow_strength, >>> causal_model, >>> bootstrap_training_data=data, >>> target_node='Y')) >>> strength_median, strength_intervals ({('X', 'Y'): 45.90886398636573, ('Z', 'Y'): 15.47129383737619}, {('X', 'Y'): array([42.88319632, 50.43890079]), ('Z', 'Y'): array([13.44202416, 17.74266107])}) In this case, ``fit`` will be called within ``bootstrap_training_and_sampling``, so there is no need to do this ourselves. The calling sequence of ``confidence_intervals`` and ``bootstrap_training_and_sampling`` is not trivial, but exploits the fact our APIs are composable. If not everything makes sense to you yet, we recommend to simply treat this calling sequence as a ready-to-use construct. Read: "Get confidence intervals via bootstrapping training and sampling of direct arrow strength". For a deeper understanding of this construct, see section :doc:`estimating_confidence_intervals`. With this knowledge, we can now dive deep into the meaning and usages of causal queries in section :doc:`answering_causal_questions/index`.

petergtz

b43ce50d7cf58420b88605531b34b5c86f905112

560b3460aaf1106f7a053f99ede24cfed094db6f

The discussion we had was to give a clear answer whether the graph is "correct", while we can only clearly say "no" if we `REJECTED` it. However, even if the graph is completely correct, there is a (very high) chance that we still return `REJECTED` here. At least, even in our artificial notebook examples, its often rejected although the data perfectly follows the graph structure.

bloebp

py-why/dowhy

Overhaul GCM introduction

* Remove bibtex from GCM introduction. This is covered in docs/source/cite.rst. * Add 'Typical usage' section in GCM introduction

2022-09-05 14:12:41+00:00

2022-11-02 10:01:42+00:00

docs/source/user_guide/gcm_based_inference/introduction.rst

Introduction ============ Graphical causal model-based inference, or GCM-based inference for short, is an experimental addition to DoWhy, that currently works separately from DoWhy's main API. Its experimental status also means that its API may undergo breaking changes in the future. It will be forming a part of a joint, `new API <https://github.com/py-why/dowhy/wiki/API-proposal-for-v1>`_. We welcome your comments. The ``dowhy.gcm`` package provides a variety of ways to answer causal questions and we'll go through them in detail in section :doc:`answering_causal_questions/index`. However, before diving into them, let's understand the basic building blocks and usage patterns it is built upon. The basic building blocks ^^^^^^^^^^^^^^^^^^^^^^^^^ All main features of the GCM-based inference in DoWhy are built around the concept of **graphical causal models**. A graphical causal model consists of a causal direct acyclic graph (DAG) of variables and a **causal mechanism** for each of the variables. A causal mechanism defines the conditional distribution of a variable given its parents in the graph, or, in case of root node variables, simply its distribution. The most general case of a GCM is a **probabilistic causal model** (PCM), where causal mechanisms are defined by **conditional stochastic models** and **stochastic models**. In the ``dowhy.gcm`` package, these are represented by :class:`~ProbabilisticCausalModel`, :class:`~ConditionalStochasticModel`, and :class:`~StochasticModel`. .. image:: pcm.png :width: 80% :align: center | In practical terms however, we often use **structural causal models** (SCMs) to represent our GCMs, and the causal mechanisms are defined by **functional causal models** (FCMs) for non-root nodes and **stochastic models** for root nodes. An SCM implements the same traits as a PCM, but on top of that, its FCMs allow us to reason *further* about its data generation process based on parents and noise, and hence, allow us e.g. to compute counterfactuals. .. image:: scm.png :width: 80% :align: center | To keep this introduction simple, we will stick with SCMs for now. As mentioned above, a causal mechanism describes how the values of a node are influenced by the values of its parent nodes. We will dive much deeper into the details of causal mechanisms and their meaning in section :doc:`customizing_model_assignment`. But for this introduction, we will treat them as an opaque thing that is needed to answer causal questions. With that in mind, the typical steps involved in answering a causal question, are: 1. **Modeling cause-effect relationships as a GCM (causal graph + causal mechanisms):** :: causal_model = StructuralCausalModel(nx.DiGraph([('X', 'Y'), ('Y', 'Z')])) # X -> Y -> Z auto.assign_causal_mechanisms(causal_model, data) Or manually assign causal mechanisms: :: causal_model.set_causal_mechanism('X', EmpiricalDistribution()) causal_model.set_causal_mechanism('Y', AdditiveNoiseModel(create_linear_regressor())) causal_model.set_causal_mechanism('Z', AdditiveNoiseModel(create_linear_regressor())) 2. **Fitting the GCM to the data:** :: fit(causal_model, data) 3. **Answering a causal query based on the GCM:** :: results = <causal_query>(causal_model, ...) Where ``<causal_query>`` can be one of multiple functions explained in :doc:`answering_causal_questions/index`. Let's look at each of these steps in more detail. Step 1: Modeling cause-effect relationships as a structural causal model (SCM) ------------------------------------------------------------------------------ The first step is to model the cause-effect relationships between variables relevant to our use case. We do that in form of a causal graph. A causal graph is a directed acyclic graph (DAG) where an edge X→Y implies that X causes Y. Statistically, a causal graph encodes the conditional independence relations between variables. Using the `networkx <https://networkx .github.io/>`__ library, we can create causal graphs. In the snippet below, we create a chain X→Y→Z: >>> import networkx as nx >>> causal_graph = nx.DiGraph([('X', 'Y'), ('Y', 'Z')]) To answer causal questions using causal graphs, we also have to know the nature of underlying data-generating process of variables. A causal graph by itself, being a diagram, does not have any information about the data-generating process. To introduce this data-generating process, we use an SCM that's built on top of our causal graph: >>> from dowhy import gcm >>> causal_model = gcm.StructuralCausalModel(causal_graph) At this point we would normally load our dataset. For this introduction, we generate some synthetic data instead. The API takes data in form of Pandas DataFrames: >>> import numpy as np, pandas as pd >>> X = np.random.normal(loc=0, scale=1, size=1000) >>> Y = 2 * X + np.random.normal(loc=0, scale=1, size=1000) >>> Z = 3 * Y + np.random.normal(loc=0, scale=1, size=1000) >>> data = pd.DataFrame(data=dict(X=X, Y=Y, Z=Z)) >>> data.head() X Y Z 0 -2.253500 -3.638579 -10.370047 1 -1.078337 -2.114581 -6.028030 2 -0.962719 -2.157896 -5.750563 3 -0.300316 -0.440721 -2.619954 4 0.127419 0.158185 1.555927 Note how the columns X, Y, Z correspond to our nodes X, Y, Z in the graph constructed above. We can also see how the values of X influence the values of Y and how the values of Y influence the values of Z in that data set. The causal model created above allows us now to assign causal mechanisms to each node in the form of functional causal models. Here, these mechanism can either be assigned manually if, for instance, prior knowledge about certain causal relationships are known or they can be assigned automatically using the :mod:`~dowhy.gcm.auto` module. For the latter, we simply call: >>> gcm.auto.assign_causal_mechanisms(causal_model, data) In case we want to have more control over the assigned mechanisms, we can do this manually as well. For instance, we can can assign an empirical distribution to the root node X and linear additive noise models to nodes Y and Z: >>> causal_model.set_causal_mechanism('X', gcm.EmpiricalDistribution()) >>> causal_model.set_causal_mechanism('Y', gcm.AdditiveNoiseModel(gcm.ml.create_linear_regressor())) >>> causal_model.set_causal_mechanism('Z', gcm.AdditiveNoiseModel(gcm.ml.create_linear_regressor())) Section :doc:`customizing_model_assignment` will go into more detail on how one can even define a completely customized model or add their own implementation. In the real world, the data comes as an opaque stream of values, where we typically don't know how one variable influences another. The graphical causal models can help us to deconstruct these causal relationships again, even though we didn't know them before. Step 2: Fitting the SCM to the data ----------------------------------- With the data at hand and the graph constructed earlier, we can now train the SCM using ``fit``: >>> gcm.fit(causal_model, data) Fitting means, we learn the generative models of the variables in the SCM according to the data. Step 3: Answering a causal query based on the SCM ------------------------------------------------- The last step, answering a causal question, is our actual goal. E.g. we could ask the question: What will happen to the variable Z if I intervene on Y? This can be done via the ``interventional_samples`` function. Here's how: >>> samples = gcm.interventional_samples(causal_model, >>> {'Y': lambda y: 2.34 }, >>> num_samples_to_draw=1000) >>> samples.head() X Y Z 0 1.186229 6.918607 20.682375 1 -0.758809 -0.749365 -2.530045 2 -1.177379 -5.678514 -17.110836 3 -1.211356 -2.152073 -6.212703 4 -0.100224 -0.285047 0.256471 This intervention says: "I'll ignore any causal effects of X on Y, and set every value of Y to 2.34." So the distribution of X will remain unchanged, whereas values of Y will be at a fixed value and Z will respond according to its causal model. With this knowledge, we can now dive deep into the meaning and usages of causal queries in section :doc:`answering_causal_questions/index`.

Introduction ============ Graphical causal model-based inference, or GCM-based inference for short, is an experimental addition to DoWhy, that currently works separately from DoWhy's main API. Its experimental status also means that its API may undergo breaking changes in the future. It will be forming a part of a joint, `new API <https://github.com/py-why/dowhy/wiki/API-proposal-for-v1>`_. We welcome your comments. The ``dowhy.gcm`` package provides a variety of ways to answer causal questions and we'll go through them in detail in section :doc:`answering_causal_questions/index`. However, before diving into them, let's understand the basic building blocks and usage patterns it is built upon. The basic building blocks ^^^^^^^^^^^^^^^^^^^^^^^^^ All main features of the GCM-based inference in DoWhy are built around the concept of **graphical causal models**. A graphical causal model consists of a causal direct acyclic graph (DAG) of variables and a **causal mechanism** for each of the variables. A causal mechanism defines the conditional distribution of a variable given its parents in the graph, or, in case of root node variables, simply its distribution. The most general case of a GCM is a **probabilistic causal model** (PCM), where causal mechanisms are defined by **conditional stochastic models** and **stochastic models**. In the ``dowhy.gcm`` package, these are represented by :class:`~ProbabilisticCausalModel`, :class:`~ConditionalStochasticModel`, and :class:`~StochasticModel`. .. image:: pcm.png :width: 80% :align: center | In practical terms however, we often use **structural causal models** (SCMs) to represent our GCMs, and the causal mechanisms are defined by **functional causal models** (FCMs) for non-root nodes and **stochastic models** for root nodes. An SCM implements the same traits as a PCM, but on top of that, its FCMs allow us to reason *further* about its data generation process based on parents and noise, and hence, allow us e.g. to compute counterfactuals. .. image:: scm.png :width: 80% :align: center | To keep this introduction simple, we will stick with SCMs for now. As mentioned above, a causal mechanism describes how the values of a node are influenced by the values of its parent nodes. We will dive much deeper into the details of causal mechanisms and their meaning in section :doc:`customizing_model_assignment`. But for this introduction, we will treat them as an opaque thing that is needed to answer causal questions. With that in mind, the typical steps involved in answering a causal question, are: 1. **Modeling cause-effect relationships as a GCM (causal graph + causal mechanisms):** :: causal_model = StructuralCausalModel(nx.DiGraph([('X', 'Y'), ('Y', 'Z')])) # X -> Y -> Z auto.assign_causal_mechanisms(causal_model, data) Or manually assign causal mechanisms: :: causal_model.set_causal_mechanism('X', EmpiricalDistribution()) causal_model.set_causal_mechanism('Y', AdditiveNoiseModel(create_linear_regressor())) causal_model.set_causal_mechanism('Z', AdditiveNoiseModel(create_linear_regressor())) 2. **Fitting the GCM to the data:** :: fit(causal_model, data) 3. **Answering a causal query based on the GCM:** :: results = <causal_query>(causal_model, ...) Where ``<causal_query>`` can be one of multiple functions explained in :doc:`answering_causal_questions/index`. Let's look at each of these steps in more detail. Step 1: Modeling cause-effect relationships as a structural causal model (SCM) ------------------------------------------------------------------------------ The first step is to model the cause-effect relationships between variables relevant to our use case. We do that in form of a causal graph. A causal graph is a directed acyclic graph (DAG) where an edge X→Y implies that X causes Y. Statistically, a causal graph encodes the conditional independence relations between variables. Using the `networkx <https://networkx .github.io/>`__ library, we can create causal graphs. In the snippet below, we create a chain X→Y→Z: >>> import networkx as nx >>> causal_graph = nx.DiGraph([('X', 'Y'), ('Y', 'Z')]) To answer causal questions using causal graphs, we also have to know the nature of underlying data-generating process of variables. A causal graph by itself, being a diagram, does not have any information about the data-generating process. To introduce this data-generating process, we use an SCM that's built on top of our causal graph: >>> from dowhy import gcm >>> causal_model = gcm.StructuralCausalModel(causal_graph) At this point we would normally load our dataset. For this introduction, we generate some synthetic data instead. The API takes data in form of Pandas DataFrames: >>> import numpy as np, pandas as pd >>> X = np.random.normal(loc=0, scale=1, size=1000) >>> Y = 2 * X + np.random.normal(loc=0, scale=1, size=1000) >>> Z = 3 * Y + np.random.normal(loc=0, scale=1, size=1000) >>> data = pd.DataFrame(data=dict(X=X, Y=Y, Z=Z)) >>> data.head() X Y Z 0 -2.253500 -3.638579 -10.370047 1 -1.078337 -2.114581 -6.028030 2 -0.962719 -2.157896 -5.750563 3 -0.300316 -0.440721 -2.619954 4 0.127419 0.158185 1.555927 Note how the columns X, Y, Z correspond to our nodes X, Y, Z in the graph constructed above. We can also see how the values of X influence the values of Y and how the values of Y influence the values of Z in that data set. The causal model created above allows us now to assign causal mechanisms to each node in the form of functional causal models. Here, these mechanism can either be assigned manually if, for instance, prior knowledge about certain causal relationships are known or they can be assigned automatically using the :mod:`~dowhy.gcm.auto` module. For the latter, we simply call: >>> gcm.auto.assign_causal_mechanisms(causal_model, data) In case we want to have more control over the assigned mechanisms, we can do this manually as well. For instance, we can can assign an empirical distribution to the root node X and linear additive noise models to nodes Y and Z: >>> causal_model.set_causal_mechanism('X', gcm.EmpiricalDistribution()) >>> causal_model.set_causal_mechanism('Y', gcm.AdditiveNoiseModel(gcm.ml.create_linear_regressor())) >>> causal_model.set_causal_mechanism('Z', gcm.AdditiveNoiseModel(gcm.ml.create_linear_regressor())) Section :doc:`customizing_model_assignment` will go into more detail on how one can even define a completely customized model or add their own implementation. In the real world, the data comes as an opaque stream of values, where we typically don't know how one variable influences another. The graphical causal models can help us to deconstruct these causal relationships again, even though we didn't know them before. Step 2: Fitting the SCM to the data ----------------------------------- With the data at hand and the graph constructed earlier, we can now train the SCM using ``fit``: >>> gcm.fit(causal_model, data) Fitting means, we learn the generative models of the variables in the SCM according to the data. Step 3: Answering a causal query based on the SCM ------------------------------------------------- The last step, answering a causal question, is our actual goal. E.g. we could ask the question: What will happen to the variable Z if I intervene on Y? This can be done via the ``interventional_samples`` function. Here's how: >>> samples = gcm.interventional_samples(causal_model, >>> {'Y': lambda y: 2.34 }, >>> num_samples_to_draw=1000) >>> samples.head() X Y Z 0 1.186229 6.918607 20.682375 1 -0.758809 -0.749365 -2.530045 2 -1.177379 -5.678514 -17.110836 3 -1.211356 -2.152073 -6.212703 4 -0.100224 -0.285047 0.256471 This intervention says: "I'll ignore any causal effects of X on Y, and set every value of Y to 2.34." So the distribution of X will remain unchanged, whereas values of Y will be at a fixed value and Z will respond according to its causal model. These are the basic steps that need to happen. While we can run these steps explicitly, often they get executed as part of other steps, e.g. when fitting and re-fitting as part of computing confidence intervals. The next section therefore dives into a more typical usage pattern of the ``dowhy.gcm`` package. Typical usage of the ``dowhy.gcm`` package ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ In practice, we may not execute the steps we've learned above explicitly and in this order, but they get called by other abstractions. E.g. we usually want to use confidence intervals, when answering causal questions, to quantify our confidence in the results. In this case, ``fit`` will be called on behalf of us, but we won't call it directly. Modeling an SCM --------------- The graph modeling is the same as in `Step 1: Modeling cause-effect relationships as a structural causal model (SCM)`_. First we construct the causal graph: >>> causal_model = gcm.StructuralCausalModel(nx.DiGraph([('X', 'Y'), ('Y', 'Z')])) # X → Y → Z Answering a causal query with confidence intervals -------------------------------------------------- When we answer a causal query without computing its confidence intervals, what we effectively get, are point estimates. These are not very useful when trying to assess the confidence in our results. Instead of calling ``fit`` explicitly, we can achieve its execution by going through the API for confidence intervals. Let's say we wanted to understand the direct arrow strengths between nodes and quantify our confidence in those results. This is how we would do it: >>> strength_median, strength_intervals = gcm.confidence_intervals( >>> gcm.bootstrap_training_and_sampling(gcm.direct_arrow_strength, >>> causal_model, >>> bootstrap_training_data=data, >>> target_node='Y')) >>> strength_median, strength_intervals ({('X', 'Y'): 45.90886398636573, ('Z', 'Y'): 15.47129383737619}, {('X', 'Y'): array([42.88319632, 50.43890079]), ('Z', 'Y'): array([13.44202416, 17.74266107])}) In this case, ``fit`` will be called within ``bootstrap_training_and_sampling``, so there is no need to do this ourselves. The calling sequence of ``confidence_intervals`` and ``bootstrap_training_and_sampling`` is not trivial, but exploits the fact our APIs are composable. If not everything makes sense to you yet, we recommend to simply treat this calling sequence as a ready-to-use construct. Read: "Get confidence intervals via bootstrapping training and sampling of direct arrow strength". For a deeper understanding of this construct, see section :doc:`estimating_confidence_intervals`. With this knowledge, we can now dive deep into the meaning and usages of causal queries in section :doc:`answering_causal_questions/index`.

petergtz

b43ce50d7cf58420b88605531b34b5c86f905112

560b3460aaf1106f7a053f99ede24cfed094db6f

Created - https://github.com/py-why/dowhy/issues/689

petergtz

py-why/dowhy

Overhaul GCM introduction

* Remove bibtex from GCM introduction. This is covered in docs/source/cite.rst. * Add 'Typical usage' section in GCM introduction

2022-09-05 14:12:41+00:00

2022-11-02 10:01:42+00:00

docs/source/user_guide/gcm_based_inference/introduction.rst

Introduction ============ Graphical causal model-based inference, or GCM-based inference for short, is an experimental addition to DoWhy, that currently works separately from DoWhy's main API. Its experimental status also means that its API may undergo breaking changes in the future. It will be forming a part of a joint, `new API <https://github.com/py-why/dowhy/wiki/API-proposal-for-v1>`_. We welcome your comments. The ``dowhy.gcm`` package provides a variety of ways to answer causal questions and we'll go through them in detail in section :doc:`answering_causal_questions/index`. However, before diving into them, let's understand the basic building blocks and usage patterns it is built upon. The basic building blocks ^^^^^^^^^^^^^^^^^^^^^^^^^ All main features of the GCM-based inference in DoWhy are built around the concept of **graphical causal models**. A graphical causal model consists of a causal direct acyclic graph (DAG) of variables and a **causal mechanism** for each of the variables. A causal mechanism defines the conditional distribution of a variable given its parents in the graph, or, in case of root node variables, simply its distribution. The most general case of a GCM is a **probabilistic causal model** (PCM), where causal mechanisms are defined by **conditional stochastic models** and **stochastic models**. In the ``dowhy.gcm`` package, these are represented by :class:`~ProbabilisticCausalModel`, :class:`~ConditionalStochasticModel`, and :class:`~StochasticModel`. .. image:: pcm.png :width: 80% :align: center | In practical terms however, we often use **structural causal models** (SCMs) to represent our GCMs, and the causal mechanisms are defined by **functional causal models** (FCMs) for non-root nodes and **stochastic models** for root nodes. An SCM implements the same traits as a PCM, but on top of that, its FCMs allow us to reason *further* about its data generation process based on parents and noise, and hence, allow us e.g. to compute counterfactuals. .. image:: scm.png :width: 80% :align: center | To keep this introduction simple, we will stick with SCMs for now. As mentioned above, a causal mechanism describes how the values of a node are influenced by the values of its parent nodes. We will dive much deeper into the details of causal mechanisms and their meaning in section :doc:`customizing_model_assignment`. But for this introduction, we will treat them as an opaque thing that is needed to answer causal questions. With that in mind, the typical steps involved in answering a causal question, are: 1. **Modeling cause-effect relationships as a GCM (causal graph + causal mechanisms):** :: causal_model = StructuralCausalModel(nx.DiGraph([('X', 'Y'), ('Y', 'Z')])) # X -> Y -> Z auto.assign_causal_mechanisms(causal_model, data) Or manually assign causal mechanisms: :: causal_model.set_causal_mechanism('X', EmpiricalDistribution()) causal_model.set_causal_mechanism('Y', AdditiveNoiseModel(create_linear_regressor())) causal_model.set_causal_mechanism('Z', AdditiveNoiseModel(create_linear_regressor())) 2. **Fitting the GCM to the data:** :: fit(causal_model, data) 3. **Answering a causal query based on the GCM:** :: results = <causal_query>(causal_model, ...) Where ``<causal_query>`` can be one of multiple functions explained in :doc:`answering_causal_questions/index`. Let's look at each of these steps in more detail. Step 1: Modeling cause-effect relationships as a structural causal model (SCM) ------------------------------------------------------------------------------ The first step is to model the cause-effect relationships between variables relevant to our use case. We do that in form of a causal graph. A causal graph is a directed acyclic graph (DAG) where an edge X→Y implies that X causes Y. Statistically, a causal graph encodes the conditional independence relations between variables. Using the `networkx <https://networkx .github.io/>`__ library, we can create causal graphs. In the snippet below, we create a chain X→Y→Z: >>> import networkx as nx >>> causal_graph = nx.DiGraph([('X', 'Y'), ('Y', 'Z')]) To answer causal questions using causal graphs, we also have to know the nature of underlying data-generating process of variables. A causal graph by itself, being a diagram, does not have any information about the data-generating process. To introduce this data-generating process, we use an SCM that's built on top of our causal graph: >>> from dowhy import gcm >>> causal_model = gcm.StructuralCausalModel(causal_graph) At this point we would normally load our dataset. For this introduction, we generate some synthetic data instead. The API takes data in form of Pandas DataFrames: >>> import numpy as np, pandas as pd >>> X = np.random.normal(loc=0, scale=1, size=1000) >>> Y = 2 * X + np.random.normal(loc=0, scale=1, size=1000) >>> Z = 3 * Y + np.random.normal(loc=0, scale=1, size=1000) >>> data = pd.DataFrame(data=dict(X=X, Y=Y, Z=Z)) >>> data.head() X Y Z 0 -2.253500 -3.638579 -10.370047 1 -1.078337 -2.114581 -6.028030 2 -0.962719 -2.157896 -5.750563 3 -0.300316 -0.440721 -2.619954 4 0.127419 0.158185 1.555927 Note how the columns X, Y, Z correspond to our nodes X, Y, Z in the graph constructed above. We can also see how the values of X influence the values of Y and how the values of Y influence the values of Z in that data set. The causal model created above allows us now to assign causal mechanisms to each node in the form of functional causal models. Here, these mechanism can either be assigned manually if, for instance, prior knowledge about certain causal relationships are known or they can be assigned automatically using the :mod:`~dowhy.gcm.auto` module. For the latter, we simply call: >>> gcm.auto.assign_causal_mechanisms(causal_model, data) In case we want to have more control over the assigned mechanisms, we can do this manually as well. For instance, we can can assign an empirical distribution to the root node X and linear additive noise models to nodes Y and Z: >>> causal_model.set_causal_mechanism('X', gcm.EmpiricalDistribution()) >>> causal_model.set_causal_mechanism('Y', gcm.AdditiveNoiseModel(gcm.ml.create_linear_regressor())) >>> causal_model.set_causal_mechanism('Z', gcm.AdditiveNoiseModel(gcm.ml.create_linear_regressor())) Section :doc:`customizing_model_assignment` will go into more detail on how one can even define a completely customized model or add their own implementation. In the real world, the data comes as an opaque stream of values, where we typically don't know how one variable influences another. The graphical causal models can help us to deconstruct these causal relationships again, even though we didn't know them before. Step 2: Fitting the SCM to the data ----------------------------------- With the data at hand and the graph constructed earlier, we can now train the SCM using ``fit``: >>> gcm.fit(causal_model, data) Fitting means, we learn the generative models of the variables in the SCM according to the data. Step 3: Answering a causal query based on the SCM ------------------------------------------------- The last step, answering a causal question, is our actual goal. E.g. we could ask the question: What will happen to the variable Z if I intervene on Y? This can be done via the ``interventional_samples`` function. Here's how: >>> samples = gcm.interventional_samples(causal_model, >>> {'Y': lambda y: 2.34 }, >>> num_samples_to_draw=1000) >>> samples.head() X Y Z 0 1.186229 6.918607 20.682375 1 -0.758809 -0.749365 -2.530045 2 -1.177379 -5.678514 -17.110836 3 -1.211356 -2.152073 -6.212703 4 -0.100224 -0.285047 0.256471 This intervention says: "I'll ignore any causal effects of X on Y, and set every value of Y to 2.34." So the distribution of X will remain unchanged, whereas values of Y will be at a fixed value and Z will respond according to its causal model. With this knowledge, we can now dive deep into the meaning and usages of causal queries in section :doc:`answering_causal_questions/index`.

Introduction ============ Graphical causal model-based inference, or GCM-based inference for short, is an experimental addition to DoWhy, that currently works separately from DoWhy's main API. Its experimental status also means that its API may undergo breaking changes in the future. It will be forming a part of a joint, `new API <https://github.com/py-why/dowhy/wiki/API-proposal-for-v1>`_. We welcome your comments. The ``dowhy.gcm`` package provides a variety of ways to answer causal questions and we'll go through them in detail in section :doc:`answering_causal_questions/index`. However, before diving into them, let's understand the basic building blocks and usage patterns it is built upon. The basic building blocks ^^^^^^^^^^^^^^^^^^^^^^^^^ All main features of the GCM-based inference in DoWhy are built around the concept of **graphical causal models**. A graphical causal model consists of a causal direct acyclic graph (DAG) of variables and a **causal mechanism** for each of the variables. A causal mechanism defines the conditional distribution of a variable given its parents in the graph, or, in case of root node variables, simply its distribution. The most general case of a GCM is a **probabilistic causal model** (PCM), where causal mechanisms are defined by **conditional stochastic models** and **stochastic models**. In the ``dowhy.gcm`` package, these are represented by :class:`~ProbabilisticCausalModel`, :class:`~ConditionalStochasticModel`, and :class:`~StochasticModel`. .. image:: pcm.png :width: 80% :align: center | In practical terms however, we often use **structural causal models** (SCMs) to represent our GCMs, and the causal mechanisms are defined by **functional causal models** (FCMs) for non-root nodes and **stochastic models** for root nodes. An SCM implements the same traits as a PCM, but on top of that, its FCMs allow us to reason *further* about its data generation process based on parents and noise, and hence, allow us e.g. to compute counterfactuals. .. image:: scm.png :width: 80% :align: center | To keep this introduction simple, we will stick with SCMs for now. As mentioned above, a causal mechanism describes how the values of a node are influenced by the values of its parent nodes. We will dive much deeper into the details of causal mechanisms and their meaning in section :doc:`customizing_model_assignment`. But for this introduction, we will treat them as an opaque thing that is needed to answer causal questions. With that in mind, the typical steps involved in answering a causal question, are: 1. **Modeling cause-effect relationships as a GCM (causal graph + causal mechanisms):** :: causal_model = StructuralCausalModel(nx.DiGraph([('X', 'Y'), ('Y', 'Z')])) # X -> Y -> Z auto.assign_causal_mechanisms(causal_model, data) Or manually assign causal mechanisms: :: causal_model.set_causal_mechanism('X', EmpiricalDistribution()) causal_model.set_causal_mechanism('Y', AdditiveNoiseModel(create_linear_regressor())) causal_model.set_causal_mechanism('Z', AdditiveNoiseModel(create_linear_regressor())) 2. **Fitting the GCM to the data:** :: fit(causal_model, data) 3. **Answering a causal query based on the GCM:** :: results = <causal_query>(causal_model, ...) Where ``<causal_query>`` can be one of multiple functions explained in :doc:`answering_causal_questions/index`. Let's look at each of these steps in more detail. Step 1: Modeling cause-effect relationships as a structural causal model (SCM) ------------------------------------------------------------------------------ The first step is to model the cause-effect relationships between variables relevant to our use case. We do that in form of a causal graph. A causal graph is a directed acyclic graph (DAG) where an edge X→Y implies that X causes Y. Statistically, a causal graph encodes the conditional independence relations between variables. Using the `networkx <https://networkx .github.io/>`__ library, we can create causal graphs. In the snippet below, we create a chain X→Y→Z: >>> import networkx as nx >>> causal_graph = nx.DiGraph([('X', 'Y'), ('Y', 'Z')]) To answer causal questions using causal graphs, we also have to know the nature of underlying data-generating process of variables. A causal graph by itself, being a diagram, does not have any information about the data-generating process. To introduce this data-generating process, we use an SCM that's built on top of our causal graph: >>> from dowhy import gcm >>> causal_model = gcm.StructuralCausalModel(causal_graph) At this point we would normally load our dataset. For this introduction, we generate some synthetic data instead. The API takes data in form of Pandas DataFrames: >>> import numpy as np, pandas as pd >>> X = np.random.normal(loc=0, scale=1, size=1000) >>> Y = 2 * X + np.random.normal(loc=0, scale=1, size=1000) >>> Z = 3 * Y + np.random.normal(loc=0, scale=1, size=1000) >>> data = pd.DataFrame(data=dict(X=X, Y=Y, Z=Z)) >>> data.head() X Y Z 0 -2.253500 -3.638579 -10.370047 1 -1.078337 -2.114581 -6.028030 2 -0.962719 -2.157896 -5.750563 3 -0.300316 -0.440721 -2.619954 4 0.127419 0.158185 1.555927 Note how the columns X, Y, Z correspond to our nodes X, Y, Z in the graph constructed above. We can also see how the values of X influence the values of Y and how the values of Y influence the values of Z in that data set. The causal model created above allows us now to assign causal mechanisms to each node in the form of functional causal models. Here, these mechanism can either be assigned manually if, for instance, prior knowledge about certain causal relationships are known or they can be assigned automatically using the :mod:`~dowhy.gcm.auto` module. For the latter, we simply call: >>> gcm.auto.assign_causal_mechanisms(causal_model, data) In case we want to have more control over the assigned mechanisms, we can do this manually as well. For instance, we can can assign an empirical distribution to the root node X and linear additive noise models to nodes Y and Z: >>> causal_model.set_causal_mechanism('X', gcm.EmpiricalDistribution()) >>> causal_model.set_causal_mechanism('Y', gcm.AdditiveNoiseModel(gcm.ml.create_linear_regressor())) >>> causal_model.set_causal_mechanism('Z', gcm.AdditiveNoiseModel(gcm.ml.create_linear_regressor())) Section :doc:`customizing_model_assignment` will go into more detail on how one can even define a completely customized model or add their own implementation. In the real world, the data comes as an opaque stream of values, where we typically don't know how one variable influences another. The graphical causal models can help us to deconstruct these causal relationships again, even though we didn't know them before. Step 2: Fitting the SCM to the data ----------------------------------- With the data at hand and the graph constructed earlier, we can now train the SCM using ``fit``: >>> gcm.fit(causal_model, data) Fitting means, we learn the generative models of the variables in the SCM according to the data. Step 3: Answering a causal query based on the SCM ------------------------------------------------- The last step, answering a causal question, is our actual goal. E.g. we could ask the question: What will happen to the variable Z if I intervene on Y? This can be done via the ``interventional_samples`` function. Here's how: >>> samples = gcm.interventional_samples(causal_model, >>> {'Y': lambda y: 2.34 }, >>> num_samples_to_draw=1000) >>> samples.head() X Y Z 0 1.186229 6.918607 20.682375 1 -0.758809 -0.749365 -2.530045 2 -1.177379 -5.678514 -17.110836 3 -1.211356 -2.152073 -6.212703 4 -0.100224 -0.285047 0.256471 This intervention says: "I'll ignore any causal effects of X on Y, and set every value of Y to 2.34." So the distribution of X will remain unchanged, whereas values of Y will be at a fixed value and Z will respond according to its causal model. These are the basic steps that need to happen. While we can run these steps explicitly, often they get executed as part of other steps, e.g. when fitting and re-fitting as part of computing confidence intervals. The next section therefore dives into a more typical usage pattern of the ``dowhy.gcm`` package. Typical usage of the ``dowhy.gcm`` package ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ In practice, we may not execute the steps we've learned above explicitly and in this order, but they get called by other abstractions. E.g. we usually want to use confidence intervals, when answering causal questions, to quantify our confidence in the results. In this case, ``fit`` will be called on behalf of us, but we won't call it directly. Modeling an SCM --------------- The graph modeling is the same as in `Step 1: Modeling cause-effect relationships as a structural causal model (SCM)`_. First we construct the causal graph: >>> causal_model = gcm.StructuralCausalModel(nx.DiGraph([('X', 'Y'), ('Y', 'Z')])) # X → Y → Z Answering a causal query with confidence intervals -------------------------------------------------- When we answer a causal query without computing its confidence intervals, what we effectively get, are point estimates. These are not very useful when trying to assess the confidence in our results. Instead of calling ``fit`` explicitly, we can achieve its execution by going through the API for confidence intervals. Let's say we wanted to understand the direct arrow strengths between nodes and quantify our confidence in those results. This is how we would do it: >>> strength_median, strength_intervals = gcm.confidence_intervals( >>> gcm.bootstrap_training_and_sampling(gcm.direct_arrow_strength, >>> causal_model, >>> bootstrap_training_data=data, >>> target_node='Y')) >>> strength_median, strength_intervals ({('X', 'Y'): 45.90886398636573, ('Z', 'Y'): 15.47129383737619}, {('X', 'Y'): array([42.88319632, 50.43890079]), ('Z', 'Y'): array([13.44202416, 17.74266107])}) In this case, ``fit`` will be called within ``bootstrap_training_and_sampling``, so there is no need to do this ourselves. The calling sequence of ``confidence_intervals`` and ``bootstrap_training_and_sampling`` is not trivial, but exploits the fact our APIs are composable. If not everything makes sense to you yet, we recommend to simply treat this calling sequence as a ready-to-use construct. Read: "Get confidence intervals via bootstrapping training and sampling of direct arrow strength". For a deeper understanding of this construct, see section :doc:`estimating_confidence_intervals`. With this knowledge, we can now dive deep into the meaning and usages of causal queries in section :doc:`answering_causal_questions/index`.

petergtz

b43ce50d7cf58420b88605531b34b5c86f905112

560b3460aaf1106f7a053f99ede24cfed094db6f

We don't do the validation in the introduction anymore, right?

bloebp

py-why/dowhy

Overhaul GCM introduction

* Remove bibtex from GCM introduction. This is covered in docs/source/cite.rst. * Add 'Typical usage' section in GCM introduction

2022-09-05 14:12:41+00:00

2022-11-02 10:01:42+00:00

docs/source/user_guide/gcm_based_inference/introduction.rst

Introduction ============ Graphical causal model-based inference, or GCM-based inference for short, is an experimental addition to DoWhy, that currently works separately from DoWhy's main API. Its experimental status also means that its API may undergo breaking changes in the future. It will be forming a part of a joint, `new API <https://github.com/py-why/dowhy/wiki/API-proposal-for-v1>`_. We welcome your comments. The ``dowhy.gcm`` package provides a variety of ways to answer causal questions and we'll go through them in detail in section :doc:`answering_causal_questions/index`. However, before diving into them, let's understand the basic building blocks and usage patterns it is built upon. The basic building blocks ^^^^^^^^^^^^^^^^^^^^^^^^^ All main features of the GCM-based inference in DoWhy are built around the concept of **graphical causal models**. A graphical causal model consists of a causal direct acyclic graph (DAG) of variables and a **causal mechanism** for each of the variables. A causal mechanism defines the conditional distribution of a variable given its parents in the graph, or, in case of root node variables, simply its distribution. The most general case of a GCM is a **probabilistic causal model** (PCM), where causal mechanisms are defined by **conditional stochastic models** and **stochastic models**. In the ``dowhy.gcm`` package, these are represented by :class:`~ProbabilisticCausalModel`, :class:`~ConditionalStochasticModel`, and :class:`~StochasticModel`. .. image:: pcm.png :width: 80% :align: center | In practical terms however, we often use **structural causal models** (SCMs) to represent our GCMs, and the causal mechanisms are defined by **functional causal models** (FCMs) for non-root nodes and **stochastic models** for root nodes. An SCM implements the same traits as a PCM, but on top of that, its FCMs allow us to reason *further* about its data generation process based on parents and noise, and hence, allow us e.g. to compute counterfactuals. .. image:: scm.png :width: 80% :align: center | To keep this introduction simple, we will stick with SCMs for now. As mentioned above, a causal mechanism describes how the values of a node are influenced by the values of its parent nodes. We will dive much deeper into the details of causal mechanisms and their meaning in section :doc:`customizing_model_assignment`. But for this introduction, we will treat them as an opaque thing that is needed to answer causal questions. With that in mind, the typical steps involved in answering a causal question, are: 1. **Modeling cause-effect relationships as a GCM (causal graph + causal mechanisms):** :: causal_model = StructuralCausalModel(nx.DiGraph([('X', 'Y'), ('Y', 'Z')])) # X -> Y -> Z auto.assign_causal_mechanisms(causal_model, data) Or manually assign causal mechanisms: :: causal_model.set_causal_mechanism('X', EmpiricalDistribution()) causal_model.set_causal_mechanism('Y', AdditiveNoiseModel(create_linear_regressor())) causal_model.set_causal_mechanism('Z', AdditiveNoiseModel(create_linear_regressor())) 2. **Fitting the GCM to the data:** :: fit(causal_model, data) 3. **Answering a causal query based on the GCM:** :: results = <causal_query>(causal_model, ...) Where ``<causal_query>`` can be one of multiple functions explained in :doc:`answering_causal_questions/index`. Let's look at each of these steps in more detail. Step 1: Modeling cause-effect relationships as a structural causal model (SCM) ------------------------------------------------------------------------------ The first step is to model the cause-effect relationships between variables relevant to our use case. We do that in form of a causal graph. A causal graph is a directed acyclic graph (DAG) where an edge X→Y implies that X causes Y. Statistically, a causal graph encodes the conditional independence relations between variables. Using the `networkx <https://networkx .github.io/>`__ library, we can create causal graphs. In the snippet below, we create a chain X→Y→Z: >>> import networkx as nx >>> causal_graph = nx.DiGraph([('X', 'Y'), ('Y', 'Z')]) To answer causal questions using causal graphs, we also have to know the nature of underlying data-generating process of variables. A causal graph by itself, being a diagram, does not have any information about the data-generating process. To introduce this data-generating process, we use an SCM that's built on top of our causal graph: >>> from dowhy import gcm >>> causal_model = gcm.StructuralCausalModel(causal_graph) At this point we would normally load our dataset. For this introduction, we generate some synthetic data instead. The API takes data in form of Pandas DataFrames: >>> import numpy as np, pandas as pd >>> X = np.random.normal(loc=0, scale=1, size=1000) >>> Y = 2 * X + np.random.normal(loc=0, scale=1, size=1000) >>> Z = 3 * Y + np.random.normal(loc=0, scale=1, size=1000) >>> data = pd.DataFrame(data=dict(X=X, Y=Y, Z=Z)) >>> data.head() X Y Z 0 -2.253500 -3.638579 -10.370047 1 -1.078337 -2.114581 -6.028030 2 -0.962719 -2.157896 -5.750563 3 -0.300316 -0.440721 -2.619954 4 0.127419 0.158185 1.555927 Note how the columns X, Y, Z correspond to our nodes X, Y, Z in the graph constructed above. We can also see how the values of X influence the values of Y and how the values of Y influence the values of Z in that data set. The causal model created above allows us now to assign causal mechanisms to each node in the form of functional causal models. Here, these mechanism can either be assigned manually if, for instance, prior knowledge about certain causal relationships are known or they can be assigned automatically using the :mod:`~dowhy.gcm.auto` module. For the latter, we simply call: >>> gcm.auto.assign_causal_mechanisms(causal_model, data) In case we want to have more control over the assigned mechanisms, we can do this manually as well. For instance, we can can assign an empirical distribution to the root node X and linear additive noise models to nodes Y and Z: >>> causal_model.set_causal_mechanism('X', gcm.EmpiricalDistribution()) >>> causal_model.set_causal_mechanism('Y', gcm.AdditiveNoiseModel(gcm.ml.create_linear_regressor())) >>> causal_model.set_causal_mechanism('Z', gcm.AdditiveNoiseModel(gcm.ml.create_linear_regressor())) Section :doc:`customizing_model_assignment` will go into more detail on how one can even define a completely customized model or add their own implementation. In the real world, the data comes as an opaque stream of values, where we typically don't know how one variable influences another. The graphical causal models can help us to deconstruct these causal relationships again, even though we didn't know them before. Step 2: Fitting the SCM to the data ----------------------------------- With the data at hand and the graph constructed earlier, we can now train the SCM using ``fit``: >>> gcm.fit(causal_model, data) Fitting means, we learn the generative models of the variables in the SCM according to the data. Step 3: Answering a causal query based on the SCM ------------------------------------------------- The last step, answering a causal question, is our actual goal. E.g. we could ask the question: What will happen to the variable Z if I intervene on Y? This can be done via the ``interventional_samples`` function. Here's how: >>> samples = gcm.interventional_samples(causal_model, >>> {'Y': lambda y: 2.34 }, >>> num_samples_to_draw=1000) >>> samples.head() X Y Z 0 1.186229 6.918607 20.682375 1 -0.758809 -0.749365 -2.530045 2 -1.177379 -5.678514 -17.110836 3 -1.211356 -2.152073 -6.212703 4 -0.100224 -0.285047 0.256471 This intervention says: "I'll ignore any causal effects of X on Y, and set every value of Y to 2.34." So the distribution of X will remain unchanged, whereas values of Y will be at a fixed value and Z will respond according to its causal model. With this knowledge, we can now dive deep into the meaning and usages of causal queries in section :doc:`answering_causal_questions/index`.

Introduction ============ Graphical causal model-based inference, or GCM-based inference for short, is an experimental addition to DoWhy, that currently works separately from DoWhy's main API. Its experimental status also means that its API may undergo breaking changes in the future. It will be forming a part of a joint, `new API <https://github.com/py-why/dowhy/wiki/API-proposal-for-v1>`_. We welcome your comments. The ``dowhy.gcm`` package provides a variety of ways to answer causal questions and we'll go through them in detail in section :doc:`answering_causal_questions/index`. However, before diving into them, let's understand the basic building blocks and usage patterns it is built upon. The basic building blocks ^^^^^^^^^^^^^^^^^^^^^^^^^ All main features of the GCM-based inference in DoWhy are built around the concept of **graphical causal models**. A graphical causal model consists of a causal direct acyclic graph (DAG) of variables and a **causal mechanism** for each of the variables. A causal mechanism defines the conditional distribution of a variable given its parents in the graph, or, in case of root node variables, simply its distribution. The most general case of a GCM is a **probabilistic causal model** (PCM), where causal mechanisms are defined by **conditional stochastic models** and **stochastic models**. In the ``dowhy.gcm`` package, these are represented by :class:`~ProbabilisticCausalModel`, :class:`~ConditionalStochasticModel`, and :class:`~StochasticModel`. .. image:: pcm.png :width: 80% :align: center | In practical terms however, we often use **structural causal models** (SCMs) to represent our GCMs, and the causal mechanisms are defined by **functional causal models** (FCMs) for non-root nodes and **stochastic models** for root nodes. An SCM implements the same traits as a PCM, but on top of that, its FCMs allow us to reason *further* about its data generation process based on parents and noise, and hence, allow us e.g. to compute counterfactuals. .. image:: scm.png :width: 80% :align: center | To keep this introduction simple, we will stick with SCMs for now. As mentioned above, a causal mechanism describes how the values of a node are influenced by the values of its parent nodes. We will dive much deeper into the details of causal mechanisms and their meaning in section :doc:`customizing_model_assignment`. But for this introduction, we will treat them as an opaque thing that is needed to answer causal questions. With that in mind, the typical steps involved in answering a causal question, are: 1. **Modeling cause-effect relationships as a GCM (causal graph + causal mechanisms):** :: causal_model = StructuralCausalModel(nx.DiGraph([('X', 'Y'), ('Y', 'Z')])) # X -> Y -> Z auto.assign_causal_mechanisms(causal_model, data) Or manually assign causal mechanisms: :: causal_model.set_causal_mechanism('X', EmpiricalDistribution()) causal_model.set_causal_mechanism('Y', AdditiveNoiseModel(create_linear_regressor())) causal_model.set_causal_mechanism('Z', AdditiveNoiseModel(create_linear_regressor())) 2. **Fitting the GCM to the data:** :: fit(causal_model, data) 3. **Answering a causal query based on the GCM:** :: results = <causal_query>(causal_model, ...) Where ``<causal_query>`` can be one of multiple functions explained in :doc:`answering_causal_questions/index`. Let's look at each of these steps in more detail. Step 1: Modeling cause-effect relationships as a structural causal model (SCM) ------------------------------------------------------------------------------ The first step is to model the cause-effect relationships between variables relevant to our use case. We do that in form of a causal graph. A causal graph is a directed acyclic graph (DAG) where an edge X→Y implies that X causes Y. Statistically, a causal graph encodes the conditional independence relations between variables. Using the `networkx <https://networkx .github.io/>`__ library, we can create causal graphs. In the snippet below, we create a chain X→Y→Z: >>> import networkx as nx >>> causal_graph = nx.DiGraph([('X', 'Y'), ('Y', 'Z')]) To answer causal questions using causal graphs, we also have to know the nature of underlying data-generating process of variables. A causal graph by itself, being a diagram, does not have any information about the data-generating process. To introduce this data-generating process, we use an SCM that's built on top of our causal graph: >>> from dowhy import gcm >>> causal_model = gcm.StructuralCausalModel(causal_graph) At this point we would normally load our dataset. For this introduction, we generate some synthetic data instead. The API takes data in form of Pandas DataFrames: >>> import numpy as np, pandas as pd >>> X = np.random.normal(loc=0, scale=1, size=1000) >>> Y = 2 * X + np.random.normal(loc=0, scale=1, size=1000) >>> Z = 3 * Y + np.random.normal(loc=0, scale=1, size=1000) >>> data = pd.DataFrame(data=dict(X=X, Y=Y, Z=Z)) >>> data.head() X Y Z 0 -2.253500 -3.638579 -10.370047 1 -1.078337 -2.114581 -6.028030 2 -0.962719 -2.157896 -5.750563 3 -0.300316 -0.440721 -2.619954 4 0.127419 0.158185 1.555927 Note how the columns X, Y, Z correspond to our nodes X, Y, Z in the graph constructed above. We can also see how the values of X influence the values of Y and how the values of Y influence the values of Z in that data set. The causal model created above allows us now to assign causal mechanisms to each node in the form of functional causal models. Here, these mechanism can either be assigned manually if, for instance, prior knowledge about certain causal relationships are known or they can be assigned automatically using the :mod:`~dowhy.gcm.auto` module. For the latter, we simply call: >>> gcm.auto.assign_causal_mechanisms(causal_model, data) In case we want to have more control over the assigned mechanisms, we can do this manually as well. For instance, we can can assign an empirical distribution to the root node X and linear additive noise models to nodes Y and Z: >>> causal_model.set_causal_mechanism('X', gcm.EmpiricalDistribution()) >>> causal_model.set_causal_mechanism('Y', gcm.AdditiveNoiseModel(gcm.ml.create_linear_regressor())) >>> causal_model.set_causal_mechanism('Z', gcm.AdditiveNoiseModel(gcm.ml.create_linear_regressor())) Section :doc:`customizing_model_assignment` will go into more detail on how one can even define a completely customized model or add their own implementation. In the real world, the data comes as an opaque stream of values, where we typically don't know how one variable influences another. The graphical causal models can help us to deconstruct these causal relationships again, even though we didn't know them before. Step 2: Fitting the SCM to the data ----------------------------------- With the data at hand and the graph constructed earlier, we can now train the SCM using ``fit``: >>> gcm.fit(causal_model, data) Fitting means, we learn the generative models of the variables in the SCM according to the data. Step 3: Answering a causal query based on the SCM ------------------------------------------------- The last step, answering a causal question, is our actual goal. E.g. we could ask the question: What will happen to the variable Z if I intervene on Y? This can be done via the ``interventional_samples`` function. Here's how: >>> samples = gcm.interventional_samples(causal_model, >>> {'Y': lambda y: 2.34 }, >>> num_samples_to_draw=1000) >>> samples.head() X Y Z 0 1.186229 6.918607 20.682375 1 -0.758809 -0.749365 -2.530045 2 -1.177379 -5.678514 -17.110836 3 -1.211356 -2.152073 -6.212703 4 -0.100224 -0.285047 0.256471 This intervention says: "I'll ignore any causal effects of X on Y, and set every value of Y to 2.34." So the distribution of X will remain unchanged, whereas values of Y will be at a fixed value and Z will respond according to its causal model. These are the basic steps that need to happen. While we can run these steps explicitly, often they get executed as part of other steps, e.g. when fitting and re-fitting as part of computing confidence intervals. The next section therefore dives into a more typical usage pattern of the ``dowhy.gcm`` package. Typical usage of the ``dowhy.gcm`` package ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ In practice, we may not execute the steps we've learned above explicitly and in this order, but they get called by other abstractions. E.g. we usually want to use confidence intervals, when answering causal questions, to quantify our confidence in the results. In this case, ``fit`` will be called on behalf of us, but we won't call it directly. Modeling an SCM --------------- The graph modeling is the same as in `Step 1: Modeling cause-effect relationships as a structural causal model (SCM)`_. First we construct the causal graph: >>> causal_model = gcm.StructuralCausalModel(nx.DiGraph([('X', 'Y'), ('Y', 'Z')])) # X → Y → Z Answering a causal query with confidence intervals -------------------------------------------------- When we answer a causal query without computing its confidence intervals, what we effectively get, are point estimates. These are not very useful when trying to assess the confidence in our results. Instead of calling ``fit`` explicitly, we can achieve its execution by going through the API for confidence intervals. Let's say we wanted to understand the direct arrow strengths between nodes and quantify our confidence in those results. This is how we would do it: >>> strength_median, strength_intervals = gcm.confidence_intervals( >>> gcm.bootstrap_training_and_sampling(gcm.direct_arrow_strength, >>> causal_model, >>> bootstrap_training_data=data, >>> target_node='Y')) >>> strength_median, strength_intervals ({('X', 'Y'): 45.90886398636573, ('Z', 'Y'): 15.47129383737619}, {('X', 'Y'): array([42.88319632, 50.43890079]), ('Z', 'Y'): array([13.44202416, 17.74266107])}) In this case, ``fit`` will be called within ``bootstrap_training_and_sampling``, so there is no need to do this ourselves. The calling sequence of ``confidence_intervals`` and ``bootstrap_training_and_sampling`` is not trivial, but exploits the fact our APIs are composable. If not everything makes sense to you yet, we recommend to simply treat this calling sequence as a ready-to-use construct. Read: "Get confidence intervals via bootstrapping training and sampling of direct arrow strength". For a deeper understanding of this construct, see section :doc:`estimating_confidence_intervals`. With this knowledge, we can now dive deep into the meaning and usages of causal queries in section :doc:`answering_causal_questions/index`.

petergtz

b43ce50d7cf58420b88605531b34b5c86f905112

560b3460aaf1106f7a053f99ede24cfed094db6f

Removed that paragraph.

petergtz

py-why/dowhy

Add MVG projects docs

Hi @amit-sharma, @emrekiciman, @bloebp, I'm doing some basic chores here to comply with our own MVG (doing the same for the other repos). Normally, you would "sign" the maintainers file yourself by adding your name, but I figured you approving this PR is equivalent. Also, is there anyone else who should be in the maintainers table? Feel free to nominate and I'll add them, or push directly onto this branch.

2022-09-05 08:01:55+00:00

2022-09-16 07:13:16+00:00

CONTRIBUTING.md

<!-- ALL-CONTRIBUTORS-BADGE:START - Do not remove or modify this section --> [](#contributors-) <!-- ALL-CONTRIBUTORS-BADGE:END --> ## Contributors ✨ Thanks goes to these wonderful people ([emoji key](https://allcontributors.org/docs/en/emoji-key)): <!-- ALL-CONTRIBUTORS-LIST:START - Do not remove or modify this section --> <!-- prettier-ignore-start --> <!-- markdownlint-disable --> <table> <tr> <td align="center"><a href="https://github.com/emrekiciman"><img src="https://avatars3.githubusercontent.com/u/5982160?v=4?s=100" width="100px;" alt=""/><br />_{<b>emrekiciman</b>}</a><br /><a href="https://github.com/py-why/dowhy/commits?author=emrekiciman" title="Code">💻</a></td> <td align="center"><a href="https://github.com/amit-sharma"><img src="https://avatars3.githubusercontent.com/u/1775381?v=4?s=100" width="100px;" alt=""/><br />_{<b>Amit Sharma</b>}</a><br /><a href="https://github.com/py-why/dowhy/commits?author=amit-sharma" title="Code">💻</a></td> <td align="center"><a href="http://adamkelleher.com"><img src="https://avatars0.githubusercontent.com/u/1762368?v=4?s=100" width="100px;" alt=""/><br />_{<b>Adam Kelleher</b>}</a><br /><a href="https://github.com/py-why/dowhy/commits?author=akelleh" title="Code">💻</a> <a href="#content-akelleh" title="Content">🖋</a></td> <td align="center"><a href="https://github.com/Tanmay-Kulkarni101"><img src="https://avatars3.githubusercontent.com/u/17275495?v=4?s=100" width="100px;" alt=""/><br />_{<b>Tanmay Kulkarni</b>}</a><br /><a href="https://github.com/py-why/dowhy/commits?author=Tanmay-Kulkarni101" title="Code">💻</a> <a href="https://github.com/py-why/dowhy/commits?author=Tanmay-Kulkarni101" title="Documentation">📖</a></td> <td align="center"><a href="https://github.com/vojavocni"><img src="https://avatars.githubusercontent.com/u/40206443?v=4?s=100" width="100px;" alt=""/><br />_{<b>Aleksandar Jovanovic</b>}</a><br /><a href="https://github.com/py-why/dowhy/commits?author=vojavocni" title="Code">💻</a></td> <td align="center"><a href="https://github.com/n8sty"><img src="https://avatars.githubusercontent.com/u/2964996?v=4?s=100" width="100px;" alt=""/><br />_{<b>nate giraldi</b>}</a><br /><a href="https://github.com/py-why/dowhy/commits?author=n8sty" title="Documentation">📖</a> <a href="https://github.com/py-why/dowhy/commits?author=n8sty" title="Code">💻</a></td> <td align="center"><a href="https://github.com/yaakx"><img src="https://avatars.githubusercontent.com/u/54352800?v=4?s=100" width="100px;" alt=""/><br />_{<b>Julen Corral</b>}</a><br /><a href="https://github.com/py-why/dowhy/commits?author=yaakx" title="Code">💻</a></td> </tr> <tr> <td align="center"><a href="http://toppare.github.io/"><img src="https://avatars.githubusercontent.com/u/6221127?v=4?s=100" width="100px;" alt=""/><br />_{<b>Baran Toppare</b>}</a><br /><a href="https://github.com/py-why/dowhy/commits?author=toppare" title="Documentation">📖</a></td> <td align="center"><a href="https://github.com/EgorKraevTransferwise"><img src="https://avatars.githubusercontent.com/u/62890791?v=4?s=100" width="100px;" alt=""/><br />_{<b>EgorKraevTransferwise</b>}</a><br /><a href="https://github.com/py-why/dowhy/commits?author=EgorKraevTransferwise" title="Code">💻</a></td> <td align="center"><a href="https://github.com/ryanrussell"><img src="https://avatars.githubusercontent.com/u/523300?v=4?s=100" width="100px;" alt=""/><br />_{<b>Ryan Russell</b>}</a><br /><a href="https://github.com/py-why/dowhy/commits?author=ryanrussell" title="Documentation">📖</a></td> <td align="center"><a href="https://github.com/MichaelMarien"><img src="https://avatars.githubusercontent.com/u/13829139?v=4?s=100" width="100px;" alt=""/><br />_{<b>MichaelMarien</b>}</a><br /><a href="https://github.com/py-why/dowhy/commits?author=MichaelMarien" title="Code">💻</a> <a href="https://github.com/py-why/dowhy/commits?author=MichaelMarien" title="Documentation">📖</a></td> <td align="center"><a href="http://people.mpi-inf.mpg.de/~kbudhath/"><img src="https://avatars.githubusercontent.com/u/111277?v=4?s=100" width="100px;" alt=""/><br />_{<b>Kailashbuki</b>}</a><br /><a href="https://github.com/py-why/dowhy/commits?author=kailashbuki" title="Code">💻</a> <a href="https://github.com/py-why/dowhy/commits?author=kailashbuki" title="Documentation">📖</a></td> <td align="center"><a href="https://github.com/petergtz"><img src="https://avatars.githubusercontent.com/u/3618401?v=4?s=100" width="100px;" alt=""/><br />_{<b>Peter Götz</b>}</a><br /><a href="https://github.com/py-why/dowhy/commits?author=petergtz" title="Code">💻</a> <a href="https://github.com/py-why/dowhy/commits?author=petergtz" title="Documentation">📖</a></td> <td align="center"><a href="https://github.com/bloebp"><img src="https://avatars.githubusercontent.com/u/51325689?v=4?s=100" width="100px;" alt=""/><br />_{<b>Patrick Blöbaum</b>}</a><br /><a href="https://github.com/py-why/dowhy/commits?author=bloebp" title="Code">💻</a> <a href="https://github.com/py-why/dowhy/commits?author=bloebp" title="Documentation">📖</a></td> </tr> <tr> <td align="center"><a href="https://github.com/itsoum"><img src="https://avatars.githubusercontent.com/u/9675299?v=4?s=100" width="100px;" alt=""/><br />_{<b>Ilias Tsoumas</b>}</a><br /><a href="https://github.com/py-why/dowhy/commits?author=itsoum" title="Code">💻</a></td> <td align="center"><a href="https://github.com/elikling"><img src="https://avatars.githubusercontent.com/u/8556526?v=4?s=100" width="100px;" alt=""/><br />_{<b>Eli Y. Kling</b>}</a><br /><a href="https://github.com/py-why/dowhy/commits?author=elikling" title="Documentation">📖</a></td> <td align="center"><a href="http://astoeffelbauer.github.io"><img src="https://avatars.githubusercontent.com/u/54737457?v=4?s=100" width="100px;" alt=""/><br />_{<b>Andreas Stöffelbauer</b>}</a><br /><a href="https://github.com/py-why/dowhy/commits?author=astoeffelbauer" title="Code">💻</a></td> <td align="center"><a href="https://github.com/esmucler"><img src="https://avatars.githubusercontent.com/u/14080095?v=4?s=100" width="100px;" alt=""/><br />_{<b>Ezequiel Smucler</b>}</a><br /><a href="https://github.com/py-why/dowhy/commits?author=esmucler" title="Code">💻</a></td> <td align="center"><a href="https://github.com/yemaedahrav"><img src="https://avatars.githubusercontent.com/u/50958687?v=4?s=100" width="100px;" alt=""/><br />_{<b>Amey Varhade</b>}</a><br /><a href="https://github.com/py-why/dowhy/commits?author=yemaedahrav" title="Code">💻</a></td> <td align="center"><a href="https://github.com/bkowshik"><img src="https://avatars.githubusercontent.com/u/2899501?v=4?s=100" width="100px;" alt=""/><br />_{<b>Bhargav Kowshik</b>}</a><br /><a href="https://github.com/py-why/dowhy/commits?author=bkowshik" title="Code">💻</a></td> <td align="center"><a href="https://github.com/darthtrevino"><img src="https://avatars.githubusercontent.com/u/113544?v=4?s=100" width="100px;" alt=""/><br />_{<b>Chris Trevino</b>}</a><br /><a href="https://github.com/py-why/dowhy/commits?author=darthtrevino" title="Code">💻</a></td> </tr> </table> <!-- markdownlint-restore --> <!-- prettier-ignore-end --> <!-- ALL-CONTRIBUTORS-LIST:END --> ## Contributing Guide This project follows the [all-contributors](https://github.com/all-contributors/all-contributors) specification. This Project welcomes contributions, suggestions, and feedback. All contributions, suggestions, and feedback you submitted are accepted under the [Project's license](./LICENSE.md). You represent that if you do not own copyright in the code that you have the authority to submit it under the [Project's license](./LICENSE.md). All feedback, suggestions, or contributions are not confidential. There are multiple ways to contribute to DoWhy. You can help us make DoWhy better, * Adding a Jupyter notebook that describes the use of DoWhy for solving causal problems * Helping implement a new method for any of the four steps of causal analysis: model, identify, estimate, refute * Integrating DoWhy's API with external implementations for any of the four steps, so that external libraries can be called seamlessly from the `identify_effect`, `estimate_effect` or `refute_estimate` methods. * Helping extend the DoWhy API so that we can support new functionality like interpretability of the estimate, counterfactual prediction and more. * Helping update the documentation for DoWhy If you would like to contribute, you can raise a pull request. If you have questions before contributing, you can start by opening an issue on Github. The Project abides by PyWhy's [code of conduct](https://github.com/py-why/governance/blob/main/CODE-OF-CONDUCT.md) and [trademark policy](https://github.com/py-why/governance/blob/main/TRADEMARKS.md). --- Part of MVG-0.1-beta. Made with love by GitHub. Licensed under the [CC-BY 4.0 License](https://creativecommons.org/licenses/by-sa/4.0/).

<!-- ALL-CONTRIBUTORS-BADGE:START - Do not remove or modify this section --> [](#contributors-) <!-- ALL-CONTRIBUTORS-BADGE:END --> ## Contributors ✨ Thanks goes to these wonderful people ([emoji key](https://allcontributors.org/docs/en/emoji-key)): <!-- ALL-CONTRIBUTORS-LIST:START - Do not remove or modify this section --> <!-- prettier-ignore-start --> <!-- markdownlint-disable --> <table> <tr> <td align="center"><a href="https://github.com/emrekiciman"><img src="https://avatars3.githubusercontent.com/u/5982160?v=4?s=100" width="100px;" alt=""/><br />_{<b>emrekiciman</b>}</a><br /><a href="https://github.com/py-why/dowhy/commits?author=emrekiciman" title="Code">💻</a></td> <td align="center"><a href="https://github.com/amit-sharma"><img src="https://avatars3.githubusercontent.com/u/1775381?v=4?s=100" width="100px;" alt=""/><br />_{<b>Amit Sharma</b>}</a><br /><a href="https://github.com/py-why/dowhy/commits?author=amit-sharma" title="Code">💻</a></td> <td align="center"><a href="http://adamkelleher.com"><img src="https://avatars0.githubusercontent.com/u/1762368?v=4?s=100" width="100px;" alt=""/><br />_{<b>Adam Kelleher</b>}</a><br /><a href="https://github.com/py-why/dowhy/commits?author=akelleh" title="Code">💻</a> <a href="#content-akelleh" title="Content">🖋</a></td> <td align="center"><a href="https://github.com/Tanmay-Kulkarni101"><img src="https://avatars3.githubusercontent.com/u/17275495?v=4?s=100" width="100px;" alt=""/><br />_{<b>Tanmay Kulkarni</b>}</a><br /><a href="https://github.com/py-why/dowhy/commits?author=Tanmay-Kulkarni101" title="Code">💻</a> <a href="https://github.com/py-why/dowhy/commits?author=Tanmay-Kulkarni101" title="Documentation">📖</a></td> <td align="center"><a href="https://github.com/vojavocni"><img src="https://avatars.githubusercontent.com/u/40206443?v=4?s=100" width="100px;" alt=""/><br />_{<b>Aleksandar Jovanovic</b>}</a><br /><a href="https://github.com/py-why/dowhy/commits?author=vojavocni" title="Code">💻</a></td> <td align="center"><a href="https://github.com/n8sty"><img src="https://avatars.githubusercontent.com/u/2964996?v=4?s=100" width="100px;" alt=""/><br />_{<b>nate giraldi</b>}</a><br /><a href="https://github.com/py-why/dowhy/commits?author=n8sty" title="Documentation">📖</a> <a href="https://github.com/py-why/dowhy/commits?author=n8sty" title="Code">💻</a></td> <td align="center"><a href="https://github.com/yaakx"><img src="https://avatars.githubusercontent.com/u/54352800?v=4?s=100" width="100px;" alt=""/><br />_{<b>Julen Corral</b>}</a><br /><a href="https://github.com/py-why/dowhy/commits?author=yaakx" title="Code">💻</a></td> </tr> <tr> <td align="center"><a href="http://toppare.github.io/"><img src="https://avatars.githubusercontent.com/u/6221127?v=4?s=100" width="100px;" alt=""/><br />_{<b>Baran Toppare</b>}</a><br /><a href="https://github.com/py-why/dowhy/commits?author=toppare" title="Documentation">📖</a></td> <td align="center"><a href="https://github.com/EgorKraevTransferwise"><img src="https://avatars.githubusercontent.com/u/62890791?v=4?s=100" width="100px;" alt=""/><br />_{<b>EgorKraevTransferwise</b>}</a><br /><a href="https://github.com/py-why/dowhy/commits?author=EgorKraevTransferwise" title="Code">💻</a></td> <td align="center"><a href="https://github.com/ryanrussell"><img src="https://avatars.githubusercontent.com/u/523300?v=4?s=100" width="100px;" alt=""/><br />_{<b>Ryan Russell</b>}</a><br /><a href="https://github.com/py-why/dowhy/commits?author=ryanrussell" title="Documentation">📖</a></td> <td align="center"><a href="https://github.com/MichaelMarien"><img src="https://avatars.githubusercontent.com/u/13829139?v=4?s=100" width="100px;" alt=""/><br />_{<b>MichaelMarien</b>}</a><br /><a href="https://github.com/py-why/dowhy/commits?author=MichaelMarien" title="Code">💻</a> <a href="https://github.com/py-why/dowhy/commits?author=MichaelMarien" title="Documentation">📖</a></td> <td align="center"><a href="http://people.mpi-inf.mpg.de/~kbudhath/"><img src="https://avatars.githubusercontent.com/u/111277?v=4?s=100" width="100px;" alt=""/><br />_{<b>Kailashbuki</b>}</a><br /><a href="https://github.com/py-why/dowhy/commits?author=kailashbuki" title="Code">💻</a> <a href="https://github.com/py-why/dowhy/commits?author=kailashbuki" title="Documentation">📖</a></td> <td align="center"><a href="https://github.com/petergtz"><img src="https://avatars.githubusercontent.com/u/3618401?v=4?s=100" width="100px;" alt=""/><br />_{<b>Peter Götz</b>}</a><br /><a href="https://github.com/py-why/dowhy/commits?author=petergtz" title="Code">💻</a> <a href="https://github.com/py-why/dowhy/commits?author=petergtz" title="Documentation">📖</a></td> <td align="center"><a href="https://github.com/bloebp"><img src="https://avatars.githubusercontent.com/u/51325689?v=4?s=100" width="100px;" alt=""/><br />_{<b>Patrick Blöbaum</b>}</a><br /><a href="https://github.com/py-why/dowhy/commits?author=bloebp" title="Code">💻</a> <a href="https://github.com/py-why/dowhy/commits?author=bloebp" title="Documentation">📖</a></td> </tr> <tr> <td align="center"><a href="https://github.com/itsoum"><img src="https://avatars.githubusercontent.com/u/9675299?v=4?s=100" width="100px;" alt=""/><br />_{<b>Ilias Tsoumas</b>}</a><br /><a href="https://github.com/py-why/dowhy/commits?author=itsoum" title="Code">💻</a></td> <td align="center"><a href="https://github.com/elikling"><img src="https://avatars.githubusercontent.com/u/8556526?v=4?s=100" width="100px;" alt=""/><br />_{<b>Eli Y. Kling</b>}</a><br /><a href="https://github.com/py-why/dowhy/commits?author=elikling" title="Documentation">📖</a></td> <td align="center"><a href="http://astoeffelbauer.github.io"><img src="https://avatars.githubusercontent.com/u/54737457?v=4?s=100" width="100px;" alt=""/><br />_{<b>Andreas Stöffelbauer</b>}</a><br /><a href="https://github.com/py-why/dowhy/commits?author=astoeffelbauer" title="Code">💻</a></td> <td align="center"><a href="https://github.com/esmucler"><img src="https://avatars.githubusercontent.com/u/14080095?v=4?s=100" width="100px;" alt=""/><br />_{<b>Ezequiel Smucler</b>}</a><br /><a href="https://github.com/py-why/dowhy/commits?author=esmucler" title="Code">💻</a></td> <td align="center"><a href="https://github.com/yemaedahrav"><img src="https://avatars.githubusercontent.com/u/50958687?v=4?s=100" width="100px;" alt=""/><br />_{<b>Amey Varhade</b>}</a><br /><a href="https://github.com/py-why/dowhy/commits?author=yemaedahrav" title="Code">💻</a></td> <td align="center"><a href="https://github.com/bkowshik"><img src="https://avatars.githubusercontent.com/u/2899501?v=4?s=100" width="100px;" alt=""/><br />_{<b>Bhargav Kowshik</b>}</a><br /><a href="https://github.com/py-why/dowhy/commits?author=bkowshik" title="Code">💻</a></td> <td align="center"><a href="https://github.com/darthtrevino"><img src="https://avatars.githubusercontent.com/u/113544?v=4?s=100" width="100px;" alt=""/><br />_{<b>Chris Trevino</b>}</a><br /><a href="https://github.com/py-why/dowhy/commits?author=darthtrevino" title="Code">💻</a></td> </tr> </table> <!-- markdownlint-restore --> <!-- prettier-ignore-end --> <!-- ALL-CONTRIBUTORS-LIST:END --> ## Contributing Guide This project follows the [all-contributors](https://github.com/all-contributors/all-contributors) specification. This Project welcomes contributions, suggestions, and feedback. All contributions, suggestions, and feedback you submitted are accepted under the [Project's license](./LICENSE.md). You represent that if you do not own copyright in the code that you have the authority to submit it under the [Project's license](./LICENSE.md). All feedback, suggestions, or contributions are not confidential. There are multiple ways to contribute to DoWhy. You can help us make DoWhy better, * Adding a Jupyter notebook that describes the use of DoWhy for solving causal problems * Helping implement a new method for any of the four steps of causal analysis: model, identify, estimate, refute * Integrating DoWhy's API with external implementations for any of the four steps, so that external libraries can be called seamlessly from the `identify_effect`, `estimate_effect` or `refute_estimate` methods. * Helping extend the DoWhy API so that we can support new functionality like interpretability of the estimate, counterfactual prediction and more. * Helping update the documentation for DoWhy If you would like to contribute, you can raise a pull request. If you have questions before contributing, you can start by opening an issue on Github. The Project abides by PyWhy's [code of conduct](https://github.com/py-why/governance/blob/main/CODE-OF-CONDUCT.md) and [trademark policy](https://github.com/py-why/governance/blob/main/TRADEMARKS.md). --- Part of MVG-0.1-beta. Made with love by GitHub. Licensed under the [CC-BY 4.0 License](https://creativecommons.org/licenses/by-sa/4.0/).

petergtz

ad87aef3b728ec68cd81d5b33a618b543691f953

93f1852b326c06d8d06e4209078b1283555e8fc5

shall we change Organization's to PyWhy's?

amit-sharma

py-why/dowhy

Add support for controlled direct treatment effect

This PR adds a new estimand_type="nonparametric-cde" and associated identification method to compute the controlled direct effect. The estimation can still be handled using standard backdoor estimators since the estimand is always a conditional expectation.

2022-08-31 17:48:43+00:00

2022-09-02 08:37:56+00:00

dowhy/causal_graph.py

import itertools import logging import re import networkx as nx from dowhy.utils.api import parse_state from dowhy.utils.graph_operations import daggity_to_dot class CausalGraph: """Class for creating and modifying the causal graph. Accepts a graph string (or a text file) in gml format (preferred) and dot format. Graphviz-like attributes can be set for edges and nodes. E.g. style="dashed" as an edge attribute ensures that the edge is drawn with a dashed line. If a graph string is not given, names of treatment, outcome, and confounders, instruments and effect modifiers (if any) can be provided to create the graph. """ def __init__( self, treatment_name, outcome_name, graph=None, common_cause_names=None, instrument_names=None, effect_modifier_names=None, mediator_names=None, observed_node_names=None, missing_nodes_as_confounders=False, ): self.treatment_name = parse_state(treatment_name) self.outcome_name = parse_state(outcome_name) instrument_names = parse_state(instrument_names) common_cause_names = parse_state(common_cause_names) effect_modifier_names = parse_state(effect_modifier_names) mediator_names = parse_state(mediator_names) self.logger = logging.getLogger(__name__) # re.sub only takes string parameter so the first if is to avoid error # if the input is a text file, convert the contained data into string if isinstance(graph, str) and re.match(r".*\.txt", str(graph)): text_file = open(graph, "r") graph = text_file.read() text_file.close() if isinstance(graph, str) and re.match(r"^dag", graph): # Convert daggity output to dot format graph = daggity_to_dot(graph) if isinstance(graph, str): graph = graph.replace("\n", " ") if graph is None: self._graph = nx.DiGraph() self._graph = self.build_graph(common_cause_names, instrument_names, effect_modifier_names, mediator_names) elif re.match(r".*\.dot", graph): # load dot file try: import pygraphviz as pgv self._graph = nx.DiGraph(nx.drawing.nx_agraph.read_dot(graph)) except Exception as e: self.logger.error("Pygraphviz cannot be loaded. " + str(e) + "\nTrying pydot...") try: import pydot self._graph = nx.DiGraph(nx.drawing.nx_pydot.read_dot(graph)) except Exception as e: self.logger.error("Error: Pydot cannot be loaded. " + str(e)) raise e elif re.match(r".*\.gml", graph): self._graph = nx.DiGraph(nx.read_gml(graph)) elif re.match(r".*graph\s*\{.*\}\s*", graph): try: import pygraphviz as pgv self._graph = pgv.AGraph(graph, strict=True, directed=True) self._graph = nx.drawing.nx_agraph.from_agraph(self._graph) except Exception as e: self.logger.error("Error: Pygraphviz cannot be loaded. " + str(e) + "\nTrying pydot ...") try: import pydot P_list = pydot.graph_from_dot_data(graph) self._graph = nx.drawing.nx_pydot.from_pydot(P_list[0]) except Exception as e: self.logger.error("Error: Pydot cannot be loaded. " + str(e)) raise e elif re.match(".*graph\s*\[.*\]\s*", graph): self._graph = nx.DiGraph(nx.parse_gml(graph)) else: self.logger.error("Error: Please provide graph (as string or text file) in dot or gml format.") self.logger.error("Error: Incorrect graph format") raise ValueError if missing_nodes_as_confounders: self._graph = self.add_missing_nodes_as_common_causes(observed_node_names) # Adding node attributes self._graph = self.add_node_attributes(observed_node_names) def view_graph(self, layout="dot", size=(8, 6), file_name="causal_model"): out_filename = "{}.png".format(file_name) try: import pygraphviz as pgv agraph = nx.drawing.nx_agraph.to_agraph(self._graph) agraph.graph_attr.update(size="{},{}!".format(size[0], size[0])) agraph.draw(out_filename, format="png", prog=layout) except: self.logger.warning( "Warning: Pygraphviz cannot be loaded. Check that graphviz and pygraphviz are installed." ) self.logger.info("Using Matplotlib for plotting") import matplotlib.pyplot as plt plt.figure(figsize=size) solid_edges = [(n1, n2) for n1, n2, e in self._graph.edges(data=True) if "style" not in e] dashed_edges = [ (n1, n2) for n1, n2, e in self._graph.edges(data=True) if ("style" in e and e["style"] == "dashed") ] plt.clf() pos = nx.layout.shell_layout(self._graph) nx.draw_networkx_nodes(self._graph, pos, node_color="yellow", node_size=400) nx.draw_networkx_edges(self._graph, pos, edgelist=solid_edges, arrowstyle="-|>", arrowsize=12) nx.draw_networkx_edges( self._graph, pos, edgelist=dashed_edges, arrowstyle="-|>", style="dashed", arrowsize=12 ) labels = nx.draw_networkx_labels(self._graph, pos) plt.axis("off") plt.savefig(out_filename) plt.draw() def build_graph(self, common_cause_names, instrument_names, effect_modifier_names, mediator_names): """Creates nodes and edges based on variable names and their semantics. Currently only considers the graphical representation of "direct" effect modifiers. Thus, all effect modifiers are assumed to be "direct" unless otherwise expressed using a graph. Based on the taxonomy of effect modifiers by VanderWheele and Robins: "Four types of effect modification: A classification based on directed acyclic graphs. Epidemiology. 2007." """ for treatment in self.treatment_name: self._graph.add_node(treatment, observed="yes", penwidth=2) for outcome in self.outcome_name: self._graph.add_node(outcome, observed="yes", penwidth=2) for treatment, outcome in itertools.product(self.treatment_name, self.outcome_name): # adding penwidth to make the edge bold self._graph.add_edge(treatment, outcome, penwidth=2) # Adding common causes if common_cause_names is not None: for node_name in common_cause_names: for treatment, outcome in itertools.product(self.treatment_name, self.outcome_name): self._graph.add_node(node_name, observed="yes") self._graph.add_edge(node_name, treatment) self._graph.add_edge(node_name, outcome) # Adding instruments if instrument_names: if type(instrument_names[0]) != tuple: if len(self.treatment_name) > 1: self.logger.info("Assuming Instrument points to all treatments! Use tuples for more granularity.") for instrument, treatment in itertools.product(instrument_names, self.treatment_name): self._graph.add_node(instrument, observed="yes") self._graph.add_edge(instrument, treatment) else: for instrument, treatment in itertools.product(instrument_names): self._graph.add_node(instrument, observed="yes") self._graph.add_edge(instrument, treatment) # Adding effect modifiers if effect_modifier_names is not None: for node_name in effect_modifier_names: if node_name not in common_cause_names: for outcome in self.outcome_name: self._graph.add_node(node_name, observed="yes") # Assuming the simple form of effect modifier # that directly causes the outcome. self._graph.add_edge(node_name, outcome) # self._graph.add_edge(node_name, outcome, style = "dotted", headport="s", tailport="n") # self._graph.add_edge(outcome, node_name, style = "dotted", headport="n", tailport="s") # TODO make the ports more general so that they apply not just to top-bottom node configurations if mediator_names is not None: for node_name in mediator_names: for treatment, outcome in itertools.product(self.treatment_name, self.outcome_name): self._graph.add_node(node_name, observed="yes") self._graph.add_edge(treatment, node_name) self._graph.add_edge(node_name, outcome) return self._graph def add_node_attributes(self, observed_node_names): for node_name in self._graph: if node_name in observed_node_names: self._graph.nodes[node_name]["observed"] = "yes" else: self._graph.nodes[node_name]["observed"] = "no" return self._graph def add_missing_nodes_as_common_causes(self, observed_node_names): # Adding columns in the dataframe as confounders that were not in the graph for node_name in observed_node_names: if node_name not in self._graph: self._graph.add_node(node_name, observed="yes") for treatment_outcome_node in self.treatment_name + self.outcome_name: self._graph.add_edge(node_name, treatment_outcome_node) return self._graph def add_unobserved_common_cause(self, observed_node_names, color="gray"): # Adding unobserved confounders current_common_causes = self.get_common_causes(self.treatment_name, self.outcome_name) create_new_common_cause = True for node_name in current_common_causes: if self._graph.nodes[node_name]["observed"] == "no": create_new_common_cause = False if create_new_common_cause: uc_label = "Unobserved Confounders" self._graph.add_node("U", label=uc_label, observed="no", color=color, style="filled", fillcolor=color) for node in self.treatment_name + self.outcome_name: self._graph.add_edge("U", node) self.logger.info( 'If this is observed data (not from a randomized experiment), there might always be missing confounders. Adding a node named "Unobserved Confounders" to reflect this.' ) return self._graph def get_unconfounded_observed_subgraph(self): observed_nodes = [node for node in self._graph.nodes() if self._graph.nodes[node]["observed"] == "yes"] return self._graph.subgraph(observed_nodes) def do_surgery(self, node_names, remove_outgoing_edges=False, remove_incoming_edges=False): node_names = parse_state(node_names) new_graph = self._graph.copy() for node_name in node_names: if remove_outgoing_edges: children = new_graph.successors(node_name) edges_bunch = [(node_name, child) for child in children] new_graph.remove_edges_from(edges_bunch) if remove_incoming_edges: parents = new_graph.predecessors(node_name) edges_bunch = [(parent, node_name) for parent in parents] new_graph.remove_edges_from(edges_bunch) return new_graph def get_causes(self, nodes, remove_edges=None): nodes = parse_state(nodes) new_graph = None if remove_edges is not None: new_graph = self._graph.copy() # caution: shallow copy of the attributes sources = parse_state(remove_edges["sources"]) targets = parse_state(remove_edges["targets"]) for s in sources: for t in targets: new_graph.remove_edge(s, t) causes = set() for v in nodes: causes = causes.union(self.get_ancestors(v, new_graph=new_graph)) return causes def check_dseparation(self, nodes1, nodes2, nodes3, new_graph=None, dseparation_algo="default"): if dseparation_algo == "default": if new_graph is None: new_graph = self._graph dseparated = nx.algorithms.d_separated(new_graph, set(nodes1), set(nodes2), set(nodes3)) else: raise ValueError(f"{dseparation_algo} method for d-separation not supported.") return dseparated def check_valid_backdoor_set( self, nodes1, nodes2, nodes3, backdoor_paths=None, new_graph=None, dseparation_algo="default" ): """Assume that the first parameter (nodes1) is the treatment, the second is the outcome, and the third is the candidate backdoor set """ # also return the number of backdoor paths blocked by observed nodes if dseparation_algo == "default": if new_graph is None: # Assume that nodes1 is the treatment new_graph = self.do_surgery(nodes1, remove_outgoing_edges=True) dseparated = nx.algorithms.d_separated(new_graph, set(nodes1), set(nodes2), set(nodes3)) elif dseparation_algo == "naive": # ignores new_graph parameter, always uses self._graph if backdoor_paths is None: backdoor_paths = self.get_backdoor_paths(nodes1, nodes2) dseparated = all([self.is_blocked(path, nodes3) for path in backdoor_paths]) else: raise ValueError(f"{dseparation_algo} method for d-separation not supported.") return {"is_dseparated": dseparated} def get_backdoor_paths(self, nodes1, nodes2): paths = [] undirected_graph = self._graph.to_undirected() nodes12 = set(nodes1).union(nodes2) for node1 in nodes1: for node2 in nodes2: backdoor_paths = [ pth for pth in nx.all_simple_paths(undirected_graph, source=node1, target=node2) if self._graph.has_edge(pth[1], pth[0]) ] # remove paths that have nodes1\node1 or nodes2\node2 as intermediate nodes filtered_backdoor_paths = [pth for pth in backdoor_paths if len(nodes12.intersection(pth[1:-1])) == 0] paths.extend(filtered_backdoor_paths) self.logger.debug("Backdoor paths: " + str(paths)) return paths def is_blocked(self, path, conditioned_nodes): """Uses d-separation criteria to decide if conditioned_nodes block given path.""" blocked_by_conditioning = False has_unconditioned_collider = False for i in range(len(path) - 2): if self._graph.has_edge(path[i], path[i + 1]) and self._graph.has_edge( path[i + 2], path[i + 1] ): # collider collider_descendants = nx.descendants(self._graph, path[i + 1]) if path[i + 1] not in conditioned_nodes and all( cdesc not in conditioned_nodes for cdesc in collider_descendants ): has_unconditioned_collider = True else: # chain or fork if path[i + 1] in conditioned_nodes: blocked_by_conditioning = True break if blocked_by_conditioning: return True elif has_unconditioned_collider: return True else: return False def get_common_causes(self, nodes1, nodes2): """ Assume that nodes1 causes nodes2 (e.g., nodes1 are the treatments and nodes2 are the outcomes) """ # TODO Refactor to remove this from here and only implement this logic in causalIdentifier. Unnecessary assumption of nodes1 to be causing nodes2. nodes1 = parse_state(nodes1) nodes2 = parse_state(nodes2) causes_1 = set() causes_2 = set() for node in nodes1: causes_1 = causes_1.union(self.get_ancestors(node)) for node in nodes2: # Cannot simply compute ancestors, since that will also include nodes1 and its parents (e.g. instruments) parents_2 = self.get_parents(node) for parent in parents_2: if parent not in nodes1: causes_2 = causes_2.union( set( [ parent, ] ) ) causes_2 = causes_2.union(self.get_ancestors(parent)) return list(causes_1.intersection(causes_2)) def get_effect_modifiers(self, nodes1, nodes2): modifiers = set() for node in nodes2: modifiers = modifiers.union(self.get_ancestors(node)) modifiers = modifiers.difference(nodes1) for node in nodes1: modifiers = modifiers.difference(self.get_ancestors(node)) # removing all mediators for node1 in nodes1: for node2 in nodes2: all_directed_paths = nx.all_simple_paths(self._graph, node1, node2) for path in all_directed_paths: modifiers = modifiers.difference(path) return list(modifiers) def get_parents(self, node_name): return set(self._graph.predecessors(node_name)) def get_ancestors(self, node_name, new_graph=None): if new_graph is None: graph = self._graph else: graph = new_graph return set(nx.ancestors(graph, node_name)) def get_descendants(self, nodes): descendants = set() for node_name in nodes: descendants = descendants.union(set(nx.descendants(self._graph, node_name))) return descendants def all_observed(self, node_names): for node_name in node_names: if self._graph.nodes[node_name]["observed"] != "yes": return False return True def get_all_nodes(self, include_unobserved=True): nodes = self._graph.nodes if not include_unobserved: nodes = set(self.filter_unobserved_variables(nodes)) return nodes def filter_unobserved_variables(self, node_names): observed_node_names = list() for node_name in node_names: if self._graph.nodes[node_name]["observed"] == "yes": observed_node_names.append(node_name) return observed_node_names def get_instruments(self, treatment_nodes, outcome_nodes): treatment_nodes = parse_state(treatment_nodes) outcome_nodes = parse_state(outcome_nodes) parents_treatment = set() for node in treatment_nodes: parents_treatment = parents_treatment.union(self.get_parents(node)) g_no_parents_treatment = self.do_surgery(treatment_nodes, remove_incoming_edges=True) ancestors_outcome = set() for node in outcome_nodes: ancestors_outcome = ancestors_outcome.union(nx.ancestors(g_no_parents_treatment, node)) # [TODO: double check these work with multivariate implementation:] # Exclusion candidate_instruments = parents_treatment.difference(ancestors_outcome) self.logger.debug("Candidate instruments after satisfying exclusion: %s", candidate_instruments) # As-if-random setup children_causes_outcome = [nx.descendants(g_no_parents_treatment, v) for v in ancestors_outcome] children_causes_outcome = set([item for sublist in children_causes_outcome for item in sublist]) # As-if-random instruments = candidate_instruments.difference(children_causes_outcome) self.logger.debug("Candidate instruments after satisfying exclusion and as-if-random: %s", instruments) return list(instruments) def get_all_directed_paths(self, nodes1, nodes2): """Get all directed paths between sets of nodes. Currently only supports singleton sets. """ node1 = nodes1[0] node2 = nodes2[0] # convert the outputted generator into a list return [p for p in nx.all_simple_paths(self._graph, source=node1, target=node2)] def has_directed_path(self, nodes1, nodes2): """Checks if there is any directed path between two sets of nodes. Currently only supports singleton sets. """ # dpaths = self.get_all_directed_paths(nodes1, nodes2) # return len(dpaths) > 0 return nx.has_path(self._graph, nodes1[0], nodes2[0]) def get_adjacency_matrix(self, *args, **kwargs): """ Get adjacency matrix from the networkx graph """ return nx.convert_matrix.to_numpy_matrix(self._graph, *args, **kwargs) def check_valid_frontdoor_set( self, nodes1, nodes2, candidate_nodes, frontdoor_paths=None, new_graph=None, dseparation_algo="default" ): """Check if valid the frontdoor variables for set of treatments, nodes1 to set of outcomes, nodes2.""" # Condition 1: node 1 ---> node 2 is intercepted by candidate_nodes if dseparation_algo == "default": if new_graph is None: new_graph = self._graph dseparated = nx.algorithms.d_separated(new_graph, set(nodes1), set(nodes2), set(candidate_nodes)) elif dseparation_algo == "naive": if frontdoor_paths is None: frontdoor_paths = self.get_all_directed_paths(nodes1, nodes2) dseparated = all([self.is_blocked(path, candidate_nodes) for path in frontdoor_paths]) else: raise ValueError(f"{dseparation_algo} method for d-separation not supported.") return dseparated def check_valid_mediation_set(self, nodes1, nodes2, candidate_nodes, mediation_paths=None): """Check if candidate nodes are valid mediators for set of treatments, nodes1 to set of outcomes, nodes2.""" if mediation_paths is None: mediation_paths = self.get_all_directed_paths(nodes1, nodes2) is_mediator = any([self.is_blocked(path, candidate_nodes) for path in mediation_paths]) return is_mediator

import itertools import logging import re import networkx as nx from dowhy.utils.api import parse_state from dowhy.utils.graph_operations import daggity_to_dot class CausalGraph: """Class for creating and modifying the causal graph. Accepts a graph string (or a text file) in gml format (preferred) and dot format. Graphviz-like attributes can be set for edges and nodes. E.g. style="dashed" as an edge attribute ensures that the edge is drawn with a dashed line. If a graph string is not given, names of treatment, outcome, and confounders, instruments and effect modifiers (if any) can be provided to create the graph. """ def __init__( self, treatment_name, outcome_name, graph=None, common_cause_names=None, instrument_names=None, effect_modifier_names=None, mediator_names=None, observed_node_names=None, missing_nodes_as_confounders=False, ): self.treatment_name = parse_state(treatment_name) self.outcome_name = parse_state(outcome_name) instrument_names = parse_state(instrument_names) common_cause_names = parse_state(common_cause_names) effect_modifier_names = parse_state(effect_modifier_names) mediator_names = parse_state(mediator_names) self.logger = logging.getLogger(__name__) # re.sub only takes string parameter so the first if is to avoid error # if the input is a text file, convert the contained data into string if isinstance(graph, str) and re.match(r".*\.txt", str(graph)): text_file = open(graph, "r") graph = text_file.read() text_file.close() if isinstance(graph, str) and re.match(r"^dag", graph): # Convert daggity output to dot format graph = daggity_to_dot(graph) if isinstance(graph, str): graph = graph.replace("\n", " ") if graph is None: self._graph = nx.DiGraph() self._graph = self.build_graph(common_cause_names, instrument_names, effect_modifier_names, mediator_names) elif re.match(r".*\.dot", graph): # load dot file try: import pygraphviz as pgv self._graph = nx.DiGraph(nx.drawing.nx_agraph.read_dot(graph)) except Exception as e: self.logger.error("Pygraphviz cannot be loaded. " + str(e) + "\nTrying pydot...") try: import pydot self._graph = nx.DiGraph(nx.drawing.nx_pydot.read_dot(graph)) except Exception as e: self.logger.error("Error: Pydot cannot be loaded. " + str(e)) raise e elif re.match(r".*\.gml", graph): self._graph = nx.DiGraph(nx.read_gml(graph)) elif re.match(r".*graph\s*\{.*\}\s*", graph): try: import pygraphviz as pgv self._graph = pgv.AGraph(graph, strict=True, directed=True) self._graph = nx.drawing.nx_agraph.from_agraph(self._graph) except Exception as e: self.logger.error("Error: Pygraphviz cannot be loaded. " + str(e) + "\nTrying pydot ...") try: import pydot P_list = pydot.graph_from_dot_data(graph) self._graph = nx.drawing.nx_pydot.from_pydot(P_list[0]) except Exception as e: self.logger.error("Error: Pydot cannot be loaded. " + str(e)) raise e elif re.match(".*graph\s*\[.*\]\s*", graph): self._graph = nx.DiGraph(nx.parse_gml(graph)) else: self.logger.error("Error: Please provide graph (as string or text file) in dot or gml format.") self.logger.error("Error: Incorrect graph format") raise ValueError if missing_nodes_as_confounders: self._graph = self.add_missing_nodes_as_common_causes(observed_node_names) # Adding node attributes self._graph = self.add_node_attributes(observed_node_names) def view_graph(self, layout="dot", size=(8, 6), file_name="causal_model"): out_filename = "{}.png".format(file_name) try: import pygraphviz as pgv agraph = nx.drawing.nx_agraph.to_agraph(self._graph) agraph.graph_attr.update(size="{},{}!".format(size[0], size[0])) agraph.draw(out_filename, format="png", prog=layout) except: self.logger.warning( "Warning: Pygraphviz cannot be loaded. Check that graphviz and pygraphviz are installed." ) self.logger.info("Using Matplotlib for plotting") import matplotlib.pyplot as plt plt.figure(figsize=size) solid_edges = [(n1, n2) for n1, n2, e in self._graph.edges(data=True) if "style" not in e] dashed_edges = [ (n1, n2) for n1, n2, e in self._graph.edges(data=True) if ("style" in e and e["style"] == "dashed") ] plt.clf() pos = nx.layout.shell_layout(self._graph) nx.draw_networkx_nodes(self._graph, pos, node_color="yellow", node_size=400) nx.draw_networkx_edges(self._graph, pos, edgelist=solid_edges, arrowstyle="-|>", arrowsize=12) nx.draw_networkx_edges( self._graph, pos, edgelist=dashed_edges, arrowstyle="-|>", style="dashed", arrowsize=12 ) labels = nx.draw_networkx_labels(self._graph, pos) plt.axis("off") plt.savefig(out_filename) plt.draw() def build_graph(self, common_cause_names, instrument_names, effect_modifier_names, mediator_names): """Creates nodes and edges based on variable names and their semantics. Currently only considers the graphical representation of "direct" effect modifiers. Thus, all effect modifiers are assumed to be "direct" unless otherwise expressed using a graph. Based on the taxonomy of effect modifiers by VanderWheele and Robins: "Four types of effect modification: A classification based on directed acyclic graphs. Epidemiology. 2007." """ for treatment in self.treatment_name: self._graph.add_node(treatment, observed="yes", penwidth=2) for outcome in self.outcome_name: self._graph.add_node(outcome, observed="yes", penwidth=2) for treatment, outcome in itertools.product(self.treatment_name, self.outcome_name): # adding penwidth to make the edge bold self._graph.add_edge(treatment, outcome, penwidth=2) # Adding common causes if common_cause_names is not None: for node_name in common_cause_names: for treatment, outcome in itertools.product(self.treatment_name, self.outcome_name): self._graph.add_node(node_name, observed="yes") self._graph.add_edge(node_name, treatment) self._graph.add_edge(node_name, outcome) # Adding instruments if instrument_names: if type(instrument_names[0]) != tuple: if len(self.treatment_name) > 1: self.logger.info("Assuming Instrument points to all treatments! Use tuples for more granularity.") for instrument, treatment in itertools.product(instrument_names, self.treatment_name): self._graph.add_node(instrument, observed="yes") self._graph.add_edge(instrument, treatment) else: for instrument, treatment in itertools.product(instrument_names): self._graph.add_node(instrument, observed="yes") self._graph.add_edge(instrument, treatment) # Adding effect modifiers if effect_modifier_names is not None: for node_name in effect_modifier_names: if node_name not in common_cause_names: for outcome in self.outcome_name: self._graph.add_node(node_name, observed="yes") # Assuming the simple form of effect modifier # that directly causes the outcome. self._graph.add_edge(node_name, outcome) # self._graph.add_edge(node_name, outcome, style = "dotted", headport="s", tailport="n") # self._graph.add_edge(outcome, node_name, style = "dotted", headport="n", tailport="s") # TODO make the ports more general so that they apply not just to top-bottom node configurations if mediator_names is not None: for node_name in mediator_names: for treatment, outcome in itertools.product(self.treatment_name, self.outcome_name): self._graph.add_node(node_name, observed="yes") self._graph.add_edge(treatment, node_name) self._graph.add_edge(node_name, outcome) return self._graph def add_node_attributes(self, observed_node_names): for node_name in self._graph: if node_name in observed_node_names: self._graph.nodes[node_name]["observed"] = "yes" else: self._graph.nodes[node_name]["observed"] = "no" return self._graph def add_missing_nodes_as_common_causes(self, observed_node_names): # Adding columns in the dataframe as confounders that were not in the graph for node_name in observed_node_names: if node_name not in self._graph: self._graph.add_node(node_name, observed="yes") for treatment_outcome_node in self.treatment_name + self.outcome_name: self._graph.add_edge(node_name, treatment_outcome_node) return self._graph def add_unobserved_common_cause(self, observed_node_names, color="gray"): # Adding unobserved confounders current_common_causes = self.get_common_causes(self.treatment_name, self.outcome_name) create_new_common_cause = True for node_name in current_common_causes: if self._graph.nodes[node_name]["observed"] == "no": create_new_common_cause = False if create_new_common_cause: uc_label = "Unobserved Confounders" self._graph.add_node("U", label=uc_label, observed="no", color=color, style="filled", fillcolor=color) for node in self.treatment_name + self.outcome_name: self._graph.add_edge("U", node) self.logger.info( 'If this is observed data (not from a randomized experiment), there might always be missing confounders. Adding a node named "Unobserved Confounders" to reflect this.' ) return self._graph def get_unconfounded_observed_subgraph(self): observed_nodes = [node for node in self._graph.nodes() if self._graph.nodes[node]["observed"] == "yes"] return self._graph.subgraph(observed_nodes) def do_surgery( self, node_names, remove_outgoing_edges=False, remove_incoming_edges=False, target_node_names=None, remove_only_direct_edges_to_target=False, ): """Method to create a new graph based on the concept of do-surgery. :param node_names: focal nodes for the surgery :param remove_outgoing_edges: whether to remove outgoing edges from the focal nodes :param remove_incoming_edges: whether to remove incoming edges to the focal nodes :param target_node_names: target nodes (optional) for the surgery, only used when remove_only_direct_edges_to_target is True :param remove_only_direct_edges_to_target: whether to remove only the direct edges from focal nodes to the target nodes :returns: a new networkx graph after the specified removal of edges """ node_names = parse_state(node_names) new_graph = self._graph.copy() for node_name in node_names: if remove_outgoing_edges: if remove_only_direct_edges_to_target: new_graph.remove_edges_from([(node_name, v) for v in target_node_names]) else: children = new_graph.successors(node_name) edges_bunch = [(node_name, child) for child in children] new_graph.remove_edges_from(edges_bunch) if remove_incoming_edges: # removal of only direct edges wrt a target is not implemented for incoming edges parents = new_graph.predecessors(node_name) edges_bunch = [(parent, node_name) for parent in parents] new_graph.remove_edges_from(edges_bunch) return new_graph def get_causes(self, nodes, remove_edges=None): nodes = parse_state(nodes) new_graph = None if remove_edges is not None: new_graph = self._graph.copy() # caution: shallow copy of the attributes sources = parse_state(remove_edges["sources"]) targets = parse_state(remove_edges["targets"]) for s in sources: for t in targets: new_graph.remove_edge(s, t) causes = set() for v in nodes: causes = causes.union(self.get_ancestors(v, new_graph=new_graph)) return causes def check_dseparation(self, nodes1, nodes2, nodes3, new_graph=None, dseparation_algo="default"): if dseparation_algo == "default": if new_graph is None: new_graph = self._graph dseparated = nx.algorithms.d_separated(new_graph, set(nodes1), set(nodes2), set(nodes3)) else: raise ValueError(f"{dseparation_algo} method for d-separation not supported.") return dseparated def check_valid_backdoor_set( self, nodes1, nodes2, nodes3, backdoor_paths=None, new_graph=None, dseparation_algo="default" ): """Assume that the first parameter (nodes1) is the treatment, the second is the outcome, and the third is the candidate backdoor set """ # also return the number of backdoor paths blocked by observed nodes if dseparation_algo == "default": if new_graph is None: # Assume that nodes1 is the treatment new_graph = self.do_surgery(nodes1, remove_outgoing_edges=True) dseparated = nx.algorithms.d_separated(new_graph, set(nodes1), set(nodes2), set(nodes3)) elif dseparation_algo == "naive": # ignores new_graph parameter, always uses self._graph if backdoor_paths is None: backdoor_paths = self.get_backdoor_paths(nodes1, nodes2) dseparated = all([self.is_blocked(path, nodes3) for path in backdoor_paths]) else: raise ValueError(f"{dseparation_algo} method for d-separation not supported.") return {"is_dseparated": dseparated} def get_backdoor_paths(self, nodes1, nodes2): paths = [] undirected_graph = self._graph.to_undirected() nodes12 = set(nodes1).union(nodes2) for node1 in nodes1: for node2 in nodes2: backdoor_paths = [ pth for pth in nx.all_simple_paths(undirected_graph, source=node1, target=node2) if self._graph.has_edge(pth[1], pth[0]) ] # remove paths that have nodes1\node1 or nodes2\node2 as intermediate nodes filtered_backdoor_paths = [pth for pth in backdoor_paths if len(nodes12.intersection(pth[1:-1])) == 0] paths.extend(filtered_backdoor_paths) self.logger.debug("Backdoor paths: " + str(paths)) return paths def is_blocked(self, path, conditioned_nodes): """Uses d-separation criteria to decide if conditioned_nodes block given path.""" blocked_by_conditioning = False has_unconditioned_collider = False for i in range(len(path) - 2): if self._graph.has_edge(path[i], path[i + 1]) and self._graph.has_edge( path[i + 2], path[i + 1] ): # collider collider_descendants = nx.descendants(self._graph, path[i + 1]) if path[i + 1] not in conditioned_nodes and all( cdesc not in conditioned_nodes for cdesc in collider_descendants ): has_unconditioned_collider = True else: # chain or fork if path[i + 1] in conditioned_nodes: blocked_by_conditioning = True break if blocked_by_conditioning: return True elif has_unconditioned_collider: return True else: return False def get_common_causes(self, nodes1, nodes2): """ Assume that nodes1 causes nodes2 (e.g., nodes1 are the treatments and nodes2 are the outcomes) """ # TODO Refactor to remove this from here and only implement this logic in causalIdentifier. Unnecessary assumption of nodes1 to be causing nodes2. nodes1 = parse_state(nodes1) nodes2 = parse_state(nodes2) causes_1 = set() causes_2 = set() for node in nodes1: causes_1 = causes_1.union(self.get_ancestors(node)) for node in nodes2: # Cannot simply compute ancestors, since that will also include nodes1 and its parents (e.g. instruments) parents_2 = self.get_parents(node) for parent in parents_2: if parent not in nodes1: causes_2 = causes_2.union( set( [ parent, ] ) ) causes_2 = causes_2.union(self.get_ancestors(parent)) return list(causes_1.intersection(causes_2)) def get_effect_modifiers(self, nodes1, nodes2): modifiers = set() for node in nodes2: modifiers = modifiers.union(self.get_ancestors(node)) modifiers = modifiers.difference(nodes1) for node in nodes1: modifiers = modifiers.difference(self.get_ancestors(node)) # removing all mediators for node1 in nodes1: for node2 in nodes2: all_directed_paths = nx.all_simple_paths(self._graph, node1, node2) for path in all_directed_paths: modifiers = modifiers.difference(path) return list(modifiers) def get_parents(self, node_name): return set(self._graph.predecessors(node_name)) def get_ancestors(self, node_name, new_graph=None): if new_graph is None: graph = self._graph else: graph = new_graph return set(nx.ancestors(graph, node_name)) def get_descendants(self, nodes): descendants = set() for node_name in nodes: descendants = descendants.union(set(nx.descendants(self._graph, node_name))) return descendants def all_observed(self, node_names): for node_name in node_names: if self._graph.nodes[node_name]["observed"] != "yes": return False return True def get_all_nodes(self, include_unobserved=True): nodes = self._graph.nodes if not include_unobserved: nodes = set(self.filter_unobserved_variables(nodes)) return nodes def filter_unobserved_variables(self, node_names): observed_node_names = list() for node_name in node_names: if self._graph.nodes[node_name]["observed"] == "yes": observed_node_names.append(node_name) return observed_node_names def get_instruments(self, treatment_nodes, outcome_nodes): treatment_nodes = parse_state(treatment_nodes) outcome_nodes = parse_state(outcome_nodes) parents_treatment = set() for node in treatment_nodes: parents_treatment = parents_treatment.union(self.get_parents(node)) g_no_parents_treatment = self.do_surgery(treatment_nodes, remove_incoming_edges=True) ancestors_outcome = set() for node in outcome_nodes: ancestors_outcome = ancestors_outcome.union(nx.ancestors(g_no_parents_treatment, node)) # [TODO: double check these work with multivariate implementation:] # Exclusion candidate_instruments = parents_treatment.difference(ancestors_outcome) self.logger.debug("Candidate instruments after satisfying exclusion: %s", candidate_instruments) # As-if-random setup children_causes_outcome = [nx.descendants(g_no_parents_treatment, v) for v in ancestors_outcome] children_causes_outcome = set([item for sublist in children_causes_outcome for item in sublist]) # As-if-random instruments = candidate_instruments.difference(children_causes_outcome) self.logger.debug("Candidate instruments after satisfying exclusion and as-if-random: %s", instruments) return list(instruments) def get_all_directed_paths(self, nodes1, nodes2): """Get all directed paths between sets of nodes. Currently only supports singleton sets. """ node1 = nodes1[0] node2 = nodes2[0] # convert the outputted generator into a list return [p for p in nx.all_simple_paths(self._graph, source=node1, target=node2)] def has_directed_path(self, nodes1, nodes2): """Checks if there is any directed path between two sets of nodes. Currently only supports singleton sets. """ # dpaths = self.get_all_directed_paths(nodes1, nodes2) # return len(dpaths) > 0 return nx.has_path(self._graph, nodes1[0], nodes2[0]) def get_adjacency_matrix(self, *args, **kwargs): """ Get adjacency matrix from the networkx graph """ return nx.convert_matrix.to_numpy_matrix(self._graph, *args, **kwargs) def check_valid_frontdoor_set( self, nodes1, nodes2, candidate_nodes, frontdoor_paths=None, new_graph=None, dseparation_algo="default" ): """Check if valid the frontdoor variables for set of treatments, nodes1 to set of outcomes, nodes2.""" # Condition 1: node 1 ---> node 2 is intercepted by candidate_nodes if dseparation_algo == "default": if new_graph is None: new_graph = self._graph dseparated = nx.algorithms.d_separated(new_graph, set(nodes1), set(nodes2), set(candidate_nodes)) elif dseparation_algo == "naive": if frontdoor_paths is None: frontdoor_paths = self.get_all_directed_paths(nodes1, nodes2) dseparated = all([self.is_blocked(path, candidate_nodes) for path in frontdoor_paths]) else: raise ValueError(f"{dseparation_algo} method for d-separation not supported.") return dseparated def check_valid_mediation_set(self, nodes1, nodes2, candidate_nodes, mediation_paths=None): """Check if candidate nodes are valid mediators for set of treatments, nodes1 to set of outcomes, nodes2.""" if mediation_paths is None: mediation_paths = self.get_all_directed_paths(nodes1, nodes2) is_mediator = any([self.is_blocked(path, candidate_nodes) for path in mediation_paths]) return is_mediator

amit-sharma

2f2463be424093d720ebfa9cc625a06160a44cfe

d67da0e57eda5cc47d180f3de240182dde4aacad

from a variable naming perspective, the distinction between "node_names" and "target_node_names" is unclear. if target_node_names is for supporting direct_edges, can the name reflect that? Or, would it be better to have multiple surgery methods that each present cleaner APIs?

emrekiciman

py-why/dowhy

Add support for controlled direct treatment effect

This PR adds a new estimand_type="nonparametric-cde" and associated identification method to compute the controlled direct effect. The estimation can still be handled using standard backdoor estimators since the estimand is always a conditional expectation.

2022-08-31 17:48:43+00:00

2022-09-02 08:37:56+00:00

dowhy/causal_graph.py

import itertools import logging import re import networkx as nx from dowhy.utils.api import parse_state from dowhy.utils.graph_operations import daggity_to_dot class CausalGraph: """Class for creating and modifying the causal graph. Accepts a graph string (or a text file) in gml format (preferred) and dot format. Graphviz-like attributes can be set for edges and nodes. E.g. style="dashed" as an edge attribute ensures that the edge is drawn with a dashed line. If a graph string is not given, names of treatment, outcome, and confounders, instruments and effect modifiers (if any) can be provided to create the graph. """ def __init__( self, treatment_name, outcome_name, graph=None, common_cause_names=None, instrument_names=None, effect_modifier_names=None, mediator_names=None, observed_node_names=None, missing_nodes_as_confounders=False, ): self.treatment_name = parse_state(treatment_name) self.outcome_name = parse_state(outcome_name) instrument_names = parse_state(instrument_names) common_cause_names = parse_state(common_cause_names) effect_modifier_names = parse_state(effect_modifier_names) mediator_names = parse_state(mediator_names) self.logger = logging.getLogger(__name__) # re.sub only takes string parameter so the first if is to avoid error # if the input is a text file, convert the contained data into string if isinstance(graph, str) and re.match(r".*\.txt", str(graph)): text_file = open(graph, "r") graph = text_file.read() text_file.close() if isinstance(graph, str) and re.match(r"^dag", graph): # Convert daggity output to dot format graph = daggity_to_dot(graph) if isinstance(graph, str): graph = graph.replace("\n", " ") if graph is None: self._graph = nx.DiGraph() self._graph = self.build_graph(common_cause_names, instrument_names, effect_modifier_names, mediator_names) elif re.match(r".*\.dot", graph): # load dot file try: import pygraphviz as pgv self._graph = nx.DiGraph(nx.drawing.nx_agraph.read_dot(graph)) except Exception as e: self.logger.error("Pygraphviz cannot be loaded. " + str(e) + "\nTrying pydot...") try: import pydot self._graph = nx.DiGraph(nx.drawing.nx_pydot.read_dot(graph)) except Exception as e: self.logger.error("Error: Pydot cannot be loaded. " + str(e)) raise e elif re.match(r".*\.gml", graph): self._graph = nx.DiGraph(nx.read_gml(graph)) elif re.match(r".*graph\s*\{.*\}\s*", graph): try: import pygraphviz as pgv self._graph = pgv.AGraph(graph, strict=True, directed=True) self._graph = nx.drawing.nx_agraph.from_agraph(self._graph) except Exception as e: self.logger.error("Error: Pygraphviz cannot be loaded. " + str(e) + "\nTrying pydot ...") try: import pydot P_list = pydot.graph_from_dot_data(graph) self._graph = nx.drawing.nx_pydot.from_pydot(P_list[0]) except Exception as e: self.logger.error("Error: Pydot cannot be loaded. " + str(e)) raise e elif re.match(".*graph\s*\[.*\]\s*", graph): self._graph = nx.DiGraph(nx.parse_gml(graph)) else: self.logger.error("Error: Please provide graph (as string or text file) in dot or gml format.") self.logger.error("Error: Incorrect graph format") raise ValueError if missing_nodes_as_confounders: self._graph = self.add_missing_nodes_as_common_causes(observed_node_names) # Adding node attributes self._graph = self.add_node_attributes(observed_node_names) def view_graph(self, layout="dot", size=(8, 6), file_name="causal_model"): out_filename = "{}.png".format(file_name) try: import pygraphviz as pgv agraph = nx.drawing.nx_agraph.to_agraph(self._graph) agraph.graph_attr.update(size="{},{}!".format(size[0], size[0])) agraph.draw(out_filename, format="png", prog=layout) except: self.logger.warning( "Warning: Pygraphviz cannot be loaded. Check that graphviz and pygraphviz are installed." ) self.logger.info("Using Matplotlib for plotting") import matplotlib.pyplot as plt plt.figure(figsize=size) solid_edges = [(n1, n2) for n1, n2, e in self._graph.edges(data=True) if "style" not in e] dashed_edges = [ (n1, n2) for n1, n2, e in self._graph.edges(data=True) if ("style" in e and e["style"] == "dashed") ] plt.clf() pos = nx.layout.shell_layout(self._graph) nx.draw_networkx_nodes(self._graph, pos, node_color="yellow", node_size=400) nx.draw_networkx_edges(self._graph, pos, edgelist=solid_edges, arrowstyle="-|>", arrowsize=12) nx.draw_networkx_edges( self._graph, pos, edgelist=dashed_edges, arrowstyle="-|>", style="dashed", arrowsize=12 ) labels = nx.draw_networkx_labels(self._graph, pos) plt.axis("off") plt.savefig(out_filename) plt.draw() def build_graph(self, common_cause_names, instrument_names, effect_modifier_names, mediator_names): """Creates nodes and edges based on variable names and their semantics. Currently only considers the graphical representation of "direct" effect modifiers. Thus, all effect modifiers are assumed to be "direct" unless otherwise expressed using a graph. Based on the taxonomy of effect modifiers by VanderWheele and Robins: "Four types of effect modification: A classification based on directed acyclic graphs. Epidemiology. 2007." """ for treatment in self.treatment_name: self._graph.add_node(treatment, observed="yes", penwidth=2) for outcome in self.outcome_name: self._graph.add_node(outcome, observed="yes", penwidth=2) for treatment, outcome in itertools.product(self.treatment_name, self.outcome_name): # adding penwidth to make the edge bold self._graph.add_edge(treatment, outcome, penwidth=2) # Adding common causes if common_cause_names is not None: for node_name in common_cause_names: for treatment, outcome in itertools.product(self.treatment_name, self.outcome_name): self._graph.add_node(node_name, observed="yes") self._graph.add_edge(node_name, treatment) self._graph.add_edge(node_name, outcome) # Adding instruments if instrument_names: if type(instrument_names[0]) != tuple: if len(self.treatment_name) > 1: self.logger.info("Assuming Instrument points to all treatments! Use tuples for more granularity.") for instrument, treatment in itertools.product(instrument_names, self.treatment_name): self._graph.add_node(instrument, observed="yes") self._graph.add_edge(instrument, treatment) else: for instrument, treatment in itertools.product(instrument_names): self._graph.add_node(instrument, observed="yes") self._graph.add_edge(instrument, treatment) # Adding effect modifiers if effect_modifier_names is not None: for node_name in effect_modifier_names: if node_name not in common_cause_names: for outcome in self.outcome_name: self._graph.add_node(node_name, observed="yes") # Assuming the simple form of effect modifier # that directly causes the outcome. self._graph.add_edge(node_name, outcome) # self._graph.add_edge(node_name, outcome, style = "dotted", headport="s", tailport="n") # self._graph.add_edge(outcome, node_name, style = "dotted", headport="n", tailport="s") # TODO make the ports more general so that they apply not just to top-bottom node configurations if mediator_names is not None: for node_name in mediator_names: for treatment, outcome in itertools.product(self.treatment_name, self.outcome_name): self._graph.add_node(node_name, observed="yes") self._graph.add_edge(treatment, node_name) self._graph.add_edge(node_name, outcome) return self._graph def add_node_attributes(self, observed_node_names): for node_name in self._graph: if node_name in observed_node_names: self._graph.nodes[node_name]["observed"] = "yes" else: self._graph.nodes[node_name]["observed"] = "no" return self._graph def add_missing_nodes_as_common_causes(self, observed_node_names): # Adding columns in the dataframe as confounders that were not in the graph for node_name in observed_node_names: if node_name not in self._graph: self._graph.add_node(node_name, observed="yes") for treatment_outcome_node in self.treatment_name + self.outcome_name: self._graph.add_edge(node_name, treatment_outcome_node) return self._graph def add_unobserved_common_cause(self, observed_node_names, color="gray"): # Adding unobserved confounders current_common_causes = self.get_common_causes(self.treatment_name, self.outcome_name) create_new_common_cause = True for node_name in current_common_causes: if self._graph.nodes[node_name]["observed"] == "no": create_new_common_cause = False if create_new_common_cause: uc_label = "Unobserved Confounders" self._graph.add_node("U", label=uc_label, observed="no", color=color, style="filled", fillcolor=color) for node in self.treatment_name + self.outcome_name: self._graph.add_edge("U", node) self.logger.info( 'If this is observed data (not from a randomized experiment), there might always be missing confounders. Adding a node named "Unobserved Confounders" to reflect this.' ) return self._graph def get_unconfounded_observed_subgraph(self): observed_nodes = [node for node in self._graph.nodes() if self._graph.nodes[node]["observed"] == "yes"] return self._graph.subgraph(observed_nodes) def do_surgery(self, node_names, remove_outgoing_edges=False, remove_incoming_edges=False): node_names = parse_state(node_names) new_graph = self._graph.copy() for node_name in node_names: if remove_outgoing_edges: children = new_graph.successors(node_name) edges_bunch = [(node_name, child) for child in children] new_graph.remove_edges_from(edges_bunch) if remove_incoming_edges: parents = new_graph.predecessors(node_name) edges_bunch = [(parent, node_name) for parent in parents] new_graph.remove_edges_from(edges_bunch) return new_graph def get_causes(self, nodes, remove_edges=None): nodes = parse_state(nodes) new_graph = None if remove_edges is not None: new_graph = self._graph.copy() # caution: shallow copy of the attributes sources = parse_state(remove_edges["sources"]) targets = parse_state(remove_edges["targets"]) for s in sources: for t in targets: new_graph.remove_edge(s, t) causes = set() for v in nodes: causes = causes.union(self.get_ancestors(v, new_graph=new_graph)) return causes def check_dseparation(self, nodes1, nodes2, nodes3, new_graph=None, dseparation_algo="default"): if dseparation_algo == "default": if new_graph is None: new_graph = self._graph dseparated = nx.algorithms.d_separated(new_graph, set(nodes1), set(nodes2), set(nodes3)) else: raise ValueError(f"{dseparation_algo} method for d-separation not supported.") return dseparated def check_valid_backdoor_set( self, nodes1, nodes2, nodes3, backdoor_paths=None, new_graph=None, dseparation_algo="default" ): """Assume that the first parameter (nodes1) is the treatment, the second is the outcome, and the third is the candidate backdoor set """ # also return the number of backdoor paths blocked by observed nodes if dseparation_algo == "default": if new_graph is None: # Assume that nodes1 is the treatment new_graph = self.do_surgery(nodes1, remove_outgoing_edges=True) dseparated = nx.algorithms.d_separated(new_graph, set(nodes1), set(nodes2), set(nodes3)) elif dseparation_algo == "naive": # ignores new_graph parameter, always uses self._graph if backdoor_paths is None: backdoor_paths = self.get_backdoor_paths(nodes1, nodes2) dseparated = all([self.is_blocked(path, nodes3) for path in backdoor_paths]) else: raise ValueError(f"{dseparation_algo} method for d-separation not supported.") return {"is_dseparated": dseparated} def get_backdoor_paths(self, nodes1, nodes2): paths = [] undirected_graph = self._graph.to_undirected() nodes12 = set(nodes1).union(nodes2) for node1 in nodes1: for node2 in nodes2: backdoor_paths = [ pth for pth in nx.all_simple_paths(undirected_graph, source=node1, target=node2) if self._graph.has_edge(pth[1], pth[0]) ] # remove paths that have nodes1\node1 or nodes2\node2 as intermediate nodes filtered_backdoor_paths = [pth for pth in backdoor_paths if len(nodes12.intersection(pth[1:-1])) == 0] paths.extend(filtered_backdoor_paths) self.logger.debug("Backdoor paths: " + str(paths)) return paths def is_blocked(self, path, conditioned_nodes): """Uses d-separation criteria to decide if conditioned_nodes block given path.""" blocked_by_conditioning = False has_unconditioned_collider = False for i in range(len(path) - 2): if self._graph.has_edge(path[i], path[i + 1]) and self._graph.has_edge( path[i + 2], path[i + 1] ): # collider collider_descendants = nx.descendants(self._graph, path[i + 1]) if path[i + 1] not in conditioned_nodes and all( cdesc not in conditioned_nodes for cdesc in collider_descendants ): has_unconditioned_collider = True else: # chain or fork if path[i + 1] in conditioned_nodes: blocked_by_conditioning = True break if blocked_by_conditioning: return True elif has_unconditioned_collider: return True else: return False def get_common_causes(self, nodes1, nodes2): """ Assume that nodes1 causes nodes2 (e.g., nodes1 are the treatments and nodes2 are the outcomes) """ # TODO Refactor to remove this from here and only implement this logic in causalIdentifier. Unnecessary assumption of nodes1 to be causing nodes2. nodes1 = parse_state(nodes1) nodes2 = parse_state(nodes2) causes_1 = set() causes_2 = set() for node in nodes1: causes_1 = causes_1.union(self.get_ancestors(node)) for node in nodes2: # Cannot simply compute ancestors, since that will also include nodes1 and its parents (e.g. instruments) parents_2 = self.get_parents(node) for parent in parents_2: if parent not in nodes1: causes_2 = causes_2.union( set( [ parent, ] ) ) causes_2 = causes_2.union(self.get_ancestors(parent)) return list(causes_1.intersection(causes_2)) def get_effect_modifiers(self, nodes1, nodes2): modifiers = set() for node in nodes2: modifiers = modifiers.union(self.get_ancestors(node)) modifiers = modifiers.difference(nodes1) for node in nodes1: modifiers = modifiers.difference(self.get_ancestors(node)) # removing all mediators for node1 in nodes1: for node2 in nodes2: all_directed_paths = nx.all_simple_paths(self._graph, node1, node2) for path in all_directed_paths: modifiers = modifiers.difference(path) return list(modifiers) def get_parents(self, node_name): return set(self._graph.predecessors(node_name)) def get_ancestors(self, node_name, new_graph=None): if new_graph is None: graph = self._graph else: graph = new_graph return set(nx.ancestors(graph, node_name)) def get_descendants(self, nodes): descendants = set() for node_name in nodes: descendants = descendants.union(set(nx.descendants(self._graph, node_name))) return descendants def all_observed(self, node_names): for node_name in node_names: if self._graph.nodes[node_name]["observed"] != "yes": return False return True def get_all_nodes(self, include_unobserved=True): nodes = self._graph.nodes if not include_unobserved: nodes = set(self.filter_unobserved_variables(nodes)) return nodes def filter_unobserved_variables(self, node_names): observed_node_names = list() for node_name in node_names: if self._graph.nodes[node_name]["observed"] == "yes": observed_node_names.append(node_name) return observed_node_names def get_instruments(self, treatment_nodes, outcome_nodes): treatment_nodes = parse_state(treatment_nodes) outcome_nodes = parse_state(outcome_nodes) parents_treatment = set() for node in treatment_nodes: parents_treatment = parents_treatment.union(self.get_parents(node)) g_no_parents_treatment = self.do_surgery(treatment_nodes, remove_incoming_edges=True) ancestors_outcome = set() for node in outcome_nodes: ancestors_outcome = ancestors_outcome.union(nx.ancestors(g_no_parents_treatment, node)) # [TODO: double check these work with multivariate implementation:] # Exclusion candidate_instruments = parents_treatment.difference(ancestors_outcome) self.logger.debug("Candidate instruments after satisfying exclusion: %s", candidate_instruments) # As-if-random setup children_causes_outcome = [nx.descendants(g_no_parents_treatment, v) for v in ancestors_outcome] children_causes_outcome = set([item for sublist in children_causes_outcome for item in sublist]) # As-if-random instruments = candidate_instruments.difference(children_causes_outcome) self.logger.debug("Candidate instruments after satisfying exclusion and as-if-random: %s", instruments) return list(instruments) def get_all_directed_paths(self, nodes1, nodes2): """Get all directed paths between sets of nodes. Currently only supports singleton sets. """ node1 = nodes1[0] node2 = nodes2[0] # convert the outputted generator into a list return [p for p in nx.all_simple_paths(self._graph, source=node1, target=node2)] def has_directed_path(self, nodes1, nodes2): """Checks if there is any directed path between two sets of nodes. Currently only supports singleton sets. """ # dpaths = self.get_all_directed_paths(nodes1, nodes2) # return len(dpaths) > 0 return nx.has_path(self._graph, nodes1[0], nodes2[0]) def get_adjacency_matrix(self, *args, **kwargs): """ Get adjacency matrix from the networkx graph """ return nx.convert_matrix.to_numpy_matrix(self._graph, *args, **kwargs) def check_valid_frontdoor_set( self, nodes1, nodes2, candidate_nodes, frontdoor_paths=None, new_graph=None, dseparation_algo="default" ): """Check if valid the frontdoor variables for set of treatments, nodes1 to set of outcomes, nodes2.""" # Condition 1: node 1 ---> node 2 is intercepted by candidate_nodes if dseparation_algo == "default": if new_graph is None: new_graph = self._graph dseparated = nx.algorithms.d_separated(new_graph, set(nodes1), set(nodes2), set(candidate_nodes)) elif dseparation_algo == "naive": if frontdoor_paths is None: frontdoor_paths = self.get_all_directed_paths(nodes1, nodes2) dseparated = all([self.is_blocked(path, candidate_nodes) for path in frontdoor_paths]) else: raise ValueError(f"{dseparation_algo} method for d-separation not supported.") return dseparated def check_valid_mediation_set(self, nodes1, nodes2, candidate_nodes, mediation_paths=None): """Check if candidate nodes are valid mediators for set of treatments, nodes1 to set of outcomes, nodes2.""" if mediation_paths is None: mediation_paths = self.get_all_directed_paths(nodes1, nodes2) is_mediator = any([self.is_blocked(path, candidate_nodes) for path in mediation_paths]) return is_mediator

import itertools import logging import re import networkx as nx from dowhy.utils.api import parse_state from dowhy.utils.graph_operations import daggity_to_dot class CausalGraph: """Class for creating and modifying the causal graph. Accepts a graph string (or a text file) in gml format (preferred) and dot format. Graphviz-like attributes can be set for edges and nodes. E.g. style="dashed" as an edge attribute ensures that the edge is drawn with a dashed line. If a graph string is not given, names of treatment, outcome, and confounders, instruments and effect modifiers (if any) can be provided to create the graph. """ def __init__( self, treatment_name, outcome_name, graph=None, common_cause_names=None, instrument_names=None, effect_modifier_names=None, mediator_names=None, observed_node_names=None, missing_nodes_as_confounders=False, ): self.treatment_name = parse_state(treatment_name) self.outcome_name = parse_state(outcome_name) instrument_names = parse_state(instrument_names) common_cause_names = parse_state(common_cause_names) effect_modifier_names = parse_state(effect_modifier_names) mediator_names = parse_state(mediator_names) self.logger = logging.getLogger(__name__) # re.sub only takes string parameter so the first if is to avoid error # if the input is a text file, convert the contained data into string if isinstance(graph, str) and re.match(r".*\.txt", str(graph)): text_file = open(graph, "r") graph = text_file.read() text_file.close() if isinstance(graph, str) and re.match(r"^dag", graph): # Convert daggity output to dot format graph = daggity_to_dot(graph) if isinstance(graph, str): graph = graph.replace("\n", " ") if graph is None: self._graph = nx.DiGraph() self._graph = self.build_graph(common_cause_names, instrument_names, effect_modifier_names, mediator_names) elif re.match(r".*\.dot", graph): # load dot file try: import pygraphviz as pgv self._graph = nx.DiGraph(nx.drawing.nx_agraph.read_dot(graph)) except Exception as e: self.logger.error("Pygraphviz cannot be loaded. " + str(e) + "\nTrying pydot...") try: import pydot self._graph = nx.DiGraph(nx.drawing.nx_pydot.read_dot(graph)) except Exception as e: self.logger.error("Error: Pydot cannot be loaded. " + str(e)) raise e elif re.match(r".*\.gml", graph): self._graph = nx.DiGraph(nx.read_gml(graph)) elif re.match(r".*graph\s*\{.*\}\s*", graph): try: import pygraphviz as pgv self._graph = pgv.AGraph(graph, strict=True, directed=True) self._graph = nx.drawing.nx_agraph.from_agraph(self._graph) except Exception as e: self.logger.error("Error: Pygraphviz cannot be loaded. " + str(e) + "\nTrying pydot ...") try: import pydot P_list = pydot.graph_from_dot_data(graph) self._graph = nx.drawing.nx_pydot.from_pydot(P_list[0]) except Exception as e: self.logger.error("Error: Pydot cannot be loaded. " + str(e)) raise e elif re.match(".*graph\s*\[.*\]\s*", graph): self._graph = nx.DiGraph(nx.parse_gml(graph)) else: self.logger.error("Error: Please provide graph (as string or text file) in dot or gml format.") self.logger.error("Error: Incorrect graph format") raise ValueError if missing_nodes_as_confounders: self._graph = self.add_missing_nodes_as_common_causes(observed_node_names) # Adding node attributes self._graph = self.add_node_attributes(observed_node_names) def view_graph(self, layout="dot", size=(8, 6), file_name="causal_model"): out_filename = "{}.png".format(file_name) try: import pygraphviz as pgv agraph = nx.drawing.nx_agraph.to_agraph(self._graph) agraph.graph_attr.update(size="{},{}!".format(size[0], size[0])) agraph.draw(out_filename, format="png", prog=layout) except: self.logger.warning( "Warning: Pygraphviz cannot be loaded. Check that graphviz and pygraphviz are installed." ) self.logger.info("Using Matplotlib for plotting") import matplotlib.pyplot as plt plt.figure(figsize=size) solid_edges = [(n1, n2) for n1, n2, e in self._graph.edges(data=True) if "style" not in e] dashed_edges = [ (n1, n2) for n1, n2, e in self._graph.edges(data=True) if ("style" in e and e["style"] == "dashed") ] plt.clf() pos = nx.layout.shell_layout(self._graph) nx.draw_networkx_nodes(self._graph, pos, node_color="yellow", node_size=400) nx.draw_networkx_edges(self._graph, pos, edgelist=solid_edges, arrowstyle="-|>", arrowsize=12) nx.draw_networkx_edges( self._graph, pos, edgelist=dashed_edges, arrowstyle="-|>", style="dashed", arrowsize=12 ) labels = nx.draw_networkx_labels(self._graph, pos) plt.axis("off") plt.savefig(out_filename) plt.draw() def build_graph(self, common_cause_names, instrument_names, effect_modifier_names, mediator_names): """Creates nodes and edges based on variable names and their semantics. Currently only considers the graphical representation of "direct" effect modifiers. Thus, all effect modifiers are assumed to be "direct" unless otherwise expressed using a graph. Based on the taxonomy of effect modifiers by VanderWheele and Robins: "Four types of effect modification: A classification based on directed acyclic graphs. Epidemiology. 2007." """ for treatment in self.treatment_name: self._graph.add_node(treatment, observed="yes", penwidth=2) for outcome in self.outcome_name: self._graph.add_node(outcome, observed="yes", penwidth=2) for treatment, outcome in itertools.product(self.treatment_name, self.outcome_name): # adding penwidth to make the edge bold self._graph.add_edge(treatment, outcome, penwidth=2) # Adding common causes if common_cause_names is not None: for node_name in common_cause_names: for treatment, outcome in itertools.product(self.treatment_name, self.outcome_name): self._graph.add_node(node_name, observed="yes") self._graph.add_edge(node_name, treatment) self._graph.add_edge(node_name, outcome) # Adding instruments if instrument_names: if type(instrument_names[0]) != tuple: if len(self.treatment_name) > 1: self.logger.info("Assuming Instrument points to all treatments! Use tuples for more granularity.") for instrument, treatment in itertools.product(instrument_names, self.treatment_name): self._graph.add_node(instrument, observed="yes") self._graph.add_edge(instrument, treatment) else: for instrument, treatment in itertools.product(instrument_names): self._graph.add_node(instrument, observed="yes") self._graph.add_edge(instrument, treatment) # Adding effect modifiers if effect_modifier_names is not None: for node_name in effect_modifier_names: if node_name not in common_cause_names: for outcome in self.outcome_name: self._graph.add_node(node_name, observed="yes") # Assuming the simple form of effect modifier # that directly causes the outcome. self._graph.add_edge(node_name, outcome) # self._graph.add_edge(node_name, outcome, style = "dotted", headport="s", tailport="n") # self._graph.add_edge(outcome, node_name, style = "dotted", headport="n", tailport="s") # TODO make the ports more general so that they apply not just to top-bottom node configurations if mediator_names is not None: for node_name in mediator_names: for treatment, outcome in itertools.product(self.treatment_name, self.outcome_name): self._graph.add_node(node_name, observed="yes") self._graph.add_edge(treatment, node_name) self._graph.add_edge(node_name, outcome) return self._graph def add_node_attributes(self, observed_node_names): for node_name in self._graph: if node_name in observed_node_names: self._graph.nodes[node_name]["observed"] = "yes" else: self._graph.nodes[node_name]["observed"] = "no" return self._graph def add_missing_nodes_as_common_causes(self, observed_node_names): # Adding columns in the dataframe as confounders that were not in the graph for node_name in observed_node_names: if node_name not in self._graph: self._graph.add_node(node_name, observed="yes") for treatment_outcome_node in self.treatment_name + self.outcome_name: self._graph.add_edge(node_name, treatment_outcome_node) return self._graph def add_unobserved_common_cause(self, observed_node_names, color="gray"): # Adding unobserved confounders current_common_causes = self.get_common_causes(self.treatment_name, self.outcome_name) create_new_common_cause = True for node_name in current_common_causes: if self._graph.nodes[node_name]["observed"] == "no": create_new_common_cause = False if create_new_common_cause: uc_label = "Unobserved Confounders" self._graph.add_node("U", label=uc_label, observed="no", color=color, style="filled", fillcolor=color) for node in self.treatment_name + self.outcome_name: self._graph.add_edge("U", node) self.logger.info( 'If this is observed data (not from a randomized experiment), there might always be missing confounders. Adding a node named "Unobserved Confounders" to reflect this.' ) return self._graph def get_unconfounded_observed_subgraph(self): observed_nodes = [node for node in self._graph.nodes() if self._graph.nodes[node]["observed"] == "yes"] return self._graph.subgraph(observed_nodes) def do_surgery( self, node_names, remove_outgoing_edges=False, remove_incoming_edges=False, target_node_names=None, remove_only_direct_edges_to_target=False, ): """Method to create a new graph based on the concept of do-surgery. :param node_names: focal nodes for the surgery :param remove_outgoing_edges: whether to remove outgoing edges from the focal nodes :param remove_incoming_edges: whether to remove incoming edges to the focal nodes :param target_node_names: target nodes (optional) for the surgery, only used when remove_only_direct_edges_to_target is True :param remove_only_direct_edges_to_target: whether to remove only the direct edges from focal nodes to the target nodes :returns: a new networkx graph after the specified removal of edges """ node_names = parse_state(node_names) new_graph = self._graph.copy() for node_name in node_names: if remove_outgoing_edges: if remove_only_direct_edges_to_target: new_graph.remove_edges_from([(node_name, v) for v in target_node_names]) else: children = new_graph.successors(node_name) edges_bunch = [(node_name, child) for child in children] new_graph.remove_edges_from(edges_bunch) if remove_incoming_edges: # removal of only direct edges wrt a target is not implemented for incoming edges parents = new_graph.predecessors(node_name) edges_bunch = [(parent, node_name) for parent in parents] new_graph.remove_edges_from(edges_bunch) return new_graph def get_causes(self, nodes, remove_edges=None): nodes = parse_state(nodes) new_graph = None if remove_edges is not None: new_graph = self._graph.copy() # caution: shallow copy of the attributes sources = parse_state(remove_edges["sources"]) targets = parse_state(remove_edges["targets"]) for s in sources: for t in targets: new_graph.remove_edge(s, t) causes = set() for v in nodes: causes = causes.union(self.get_ancestors(v, new_graph=new_graph)) return causes def check_dseparation(self, nodes1, nodes2, nodes3, new_graph=None, dseparation_algo="default"): if dseparation_algo == "default": if new_graph is None: new_graph = self._graph dseparated = nx.algorithms.d_separated(new_graph, set(nodes1), set(nodes2), set(nodes3)) else: raise ValueError(f"{dseparation_algo} method for d-separation not supported.") return dseparated def check_valid_backdoor_set( self, nodes1, nodes2, nodes3, backdoor_paths=None, new_graph=None, dseparation_algo="default" ): """Assume that the first parameter (nodes1) is the treatment, the second is the outcome, and the third is the candidate backdoor set """ # also return the number of backdoor paths blocked by observed nodes if dseparation_algo == "default": if new_graph is None: # Assume that nodes1 is the treatment new_graph = self.do_surgery(nodes1, remove_outgoing_edges=True) dseparated = nx.algorithms.d_separated(new_graph, set(nodes1), set(nodes2), set(nodes3)) elif dseparation_algo == "naive": # ignores new_graph parameter, always uses self._graph if backdoor_paths is None: backdoor_paths = self.get_backdoor_paths(nodes1, nodes2) dseparated = all([self.is_blocked(path, nodes3) for path in backdoor_paths]) else: raise ValueError(f"{dseparation_algo} method for d-separation not supported.") return {"is_dseparated": dseparated} def get_backdoor_paths(self, nodes1, nodes2): paths = [] undirected_graph = self._graph.to_undirected() nodes12 = set(nodes1).union(nodes2) for node1 in nodes1: for node2 in nodes2: backdoor_paths = [ pth for pth in nx.all_simple_paths(undirected_graph, source=node1, target=node2) if self._graph.has_edge(pth[1], pth[0]) ] # remove paths that have nodes1\node1 or nodes2\node2 as intermediate nodes filtered_backdoor_paths = [pth for pth in backdoor_paths if len(nodes12.intersection(pth[1:-1])) == 0] paths.extend(filtered_backdoor_paths) self.logger.debug("Backdoor paths: " + str(paths)) return paths def is_blocked(self, path, conditioned_nodes): """Uses d-separation criteria to decide if conditioned_nodes block given path.""" blocked_by_conditioning = False has_unconditioned_collider = False for i in range(len(path) - 2): if self._graph.has_edge(path[i], path[i + 1]) and self._graph.has_edge( path[i + 2], path[i + 1] ): # collider collider_descendants = nx.descendants(self._graph, path[i + 1]) if path[i + 1] not in conditioned_nodes and all( cdesc not in conditioned_nodes for cdesc in collider_descendants ): has_unconditioned_collider = True else: # chain or fork if path[i + 1] in conditioned_nodes: blocked_by_conditioning = True break if blocked_by_conditioning: return True elif has_unconditioned_collider: return True else: return False def get_common_causes(self, nodes1, nodes2): """ Assume that nodes1 causes nodes2 (e.g., nodes1 are the treatments and nodes2 are the outcomes) """ # TODO Refactor to remove this from here and only implement this logic in causalIdentifier. Unnecessary assumption of nodes1 to be causing nodes2. nodes1 = parse_state(nodes1) nodes2 = parse_state(nodes2) causes_1 = set() causes_2 = set() for node in nodes1: causes_1 = causes_1.union(self.get_ancestors(node)) for node in nodes2: # Cannot simply compute ancestors, since that will also include nodes1 and its parents (e.g. instruments) parents_2 = self.get_parents(node) for parent in parents_2: if parent not in nodes1: causes_2 = causes_2.union( set( [ parent, ] ) ) causes_2 = causes_2.union(self.get_ancestors(parent)) return list(causes_1.intersection(causes_2)) def get_effect_modifiers(self, nodes1, nodes2): modifiers = set() for node in nodes2: modifiers = modifiers.union(self.get_ancestors(node)) modifiers = modifiers.difference(nodes1) for node in nodes1: modifiers = modifiers.difference(self.get_ancestors(node)) # removing all mediators for node1 in nodes1: for node2 in nodes2: all_directed_paths = nx.all_simple_paths(self._graph, node1, node2) for path in all_directed_paths: modifiers = modifiers.difference(path) return list(modifiers) def get_parents(self, node_name): return set(self._graph.predecessors(node_name)) def get_ancestors(self, node_name, new_graph=None): if new_graph is None: graph = self._graph else: graph = new_graph return set(nx.ancestors(graph, node_name)) def get_descendants(self, nodes): descendants = set() for node_name in nodes: descendants = descendants.union(set(nx.descendants(self._graph, node_name))) return descendants def all_observed(self, node_names): for node_name in node_names: if self._graph.nodes[node_name]["observed"] != "yes": return False return True def get_all_nodes(self, include_unobserved=True): nodes = self._graph.nodes if not include_unobserved: nodes = set(self.filter_unobserved_variables(nodes)) return nodes def filter_unobserved_variables(self, node_names): observed_node_names = list() for node_name in node_names: if self._graph.nodes[node_name]["observed"] == "yes": observed_node_names.append(node_name) return observed_node_names def get_instruments(self, treatment_nodes, outcome_nodes): treatment_nodes = parse_state(treatment_nodes) outcome_nodes = parse_state(outcome_nodes) parents_treatment = set() for node in treatment_nodes: parents_treatment = parents_treatment.union(self.get_parents(node)) g_no_parents_treatment = self.do_surgery(treatment_nodes, remove_incoming_edges=True) ancestors_outcome = set() for node in outcome_nodes: ancestors_outcome = ancestors_outcome.union(nx.ancestors(g_no_parents_treatment, node)) # [TODO: double check these work with multivariate implementation:] # Exclusion candidate_instruments = parents_treatment.difference(ancestors_outcome) self.logger.debug("Candidate instruments after satisfying exclusion: %s", candidate_instruments) # As-if-random setup children_causes_outcome = [nx.descendants(g_no_parents_treatment, v) for v in ancestors_outcome] children_causes_outcome = set([item for sublist in children_causes_outcome for item in sublist]) # As-if-random instruments = candidate_instruments.difference(children_causes_outcome) self.logger.debug("Candidate instruments after satisfying exclusion and as-if-random: %s", instruments) return list(instruments) def get_all_directed_paths(self, nodes1, nodes2): """Get all directed paths between sets of nodes. Currently only supports singleton sets. """ node1 = nodes1[0] node2 = nodes2[0] # convert the outputted generator into a list return [p for p in nx.all_simple_paths(self._graph, source=node1, target=node2)] def has_directed_path(self, nodes1, nodes2): """Checks if there is any directed path between two sets of nodes. Currently only supports singleton sets. """ # dpaths = self.get_all_directed_paths(nodes1, nodes2) # return len(dpaths) > 0 return nx.has_path(self._graph, nodes1[0], nodes2[0]) def get_adjacency_matrix(self, *args, **kwargs): """ Get adjacency matrix from the networkx graph """ return nx.convert_matrix.to_numpy_matrix(self._graph, *args, **kwargs) def check_valid_frontdoor_set( self, nodes1, nodes2, candidate_nodes, frontdoor_paths=None, new_graph=None, dseparation_algo="default" ): """Check if valid the frontdoor variables for set of treatments, nodes1 to set of outcomes, nodes2.""" # Condition 1: node 1 ---> node 2 is intercepted by candidate_nodes if dseparation_algo == "default": if new_graph is None: new_graph = self._graph dseparated = nx.algorithms.d_separated(new_graph, set(nodes1), set(nodes2), set(candidate_nodes)) elif dseparation_algo == "naive": if frontdoor_paths is None: frontdoor_paths = self.get_all_directed_paths(nodes1, nodes2) dseparated = all([self.is_blocked(path, candidate_nodes) for path in frontdoor_paths]) else: raise ValueError(f"{dseparation_algo} method for d-separation not supported.") return dseparated def check_valid_mediation_set(self, nodes1, nodes2, candidate_nodes, mediation_paths=None): """Check if candidate nodes are valid mediators for set of treatments, nodes1 to set of outcomes, nodes2.""" if mediation_paths is None: mediation_paths = self.get_all_directed_paths(nodes1, nodes2) is_mediator = any([self.is_blocked(path, candidate_nodes) for path in mediation_paths]) return is_mediator

amit-sharma

2f2463be424093d720ebfa9cc625a06160a44cfe

d67da0e57eda5cc47d180f3de240182dde4aacad

instead of renaming target_node_names, maybe "remove_only_direct_edges" could be renamed to "remove_edges_to_targets"?

emrekiciman

py-why/dowhy

Add support for controlled direct treatment effect

This PR adds a new estimand_type="nonparametric-cde" and associated identification method to compute the controlled direct effect. The estimation can still be handled using standard backdoor estimators since the estimand is always a conditional expectation.

2022-08-31 17:48:43+00:00

2022-09-02 08:37:56+00:00

dowhy/causal_graph.py

import itertools import logging import re import networkx as nx from dowhy.utils.api import parse_state from dowhy.utils.graph_operations import daggity_to_dot class CausalGraph: """Class for creating and modifying the causal graph. Accepts a graph string (or a text file) in gml format (preferred) and dot format. Graphviz-like attributes can be set for edges and nodes. E.g. style="dashed" as an edge attribute ensures that the edge is drawn with a dashed line. If a graph string is not given, names of treatment, outcome, and confounders, instruments and effect modifiers (if any) can be provided to create the graph. """ def __init__( self, treatment_name, outcome_name, graph=None, common_cause_names=None, instrument_names=None, effect_modifier_names=None, mediator_names=None, observed_node_names=None, missing_nodes_as_confounders=False, ): self.treatment_name = parse_state(treatment_name) self.outcome_name = parse_state(outcome_name) instrument_names = parse_state(instrument_names) common_cause_names = parse_state(common_cause_names) effect_modifier_names = parse_state(effect_modifier_names) mediator_names = parse_state(mediator_names) self.logger = logging.getLogger(__name__) # re.sub only takes string parameter so the first if is to avoid error # if the input is a text file, convert the contained data into string if isinstance(graph, str) and re.match(r".*\.txt", str(graph)): text_file = open(graph, "r") graph = text_file.read() text_file.close() if isinstance(graph, str) and re.match(r"^dag", graph): # Convert daggity output to dot format graph = daggity_to_dot(graph) if isinstance(graph, str): graph = graph.replace("\n", " ") if graph is None: self._graph = nx.DiGraph() self._graph = self.build_graph(common_cause_names, instrument_names, effect_modifier_names, mediator_names) elif re.match(r".*\.dot", graph): # load dot file try: import pygraphviz as pgv self._graph = nx.DiGraph(nx.drawing.nx_agraph.read_dot(graph)) except Exception as e: self.logger.error("Pygraphviz cannot be loaded. " + str(e) + "\nTrying pydot...") try: import pydot self._graph = nx.DiGraph(nx.drawing.nx_pydot.read_dot(graph)) except Exception as e: self.logger.error("Error: Pydot cannot be loaded. " + str(e)) raise e elif re.match(r".*\.gml", graph): self._graph = nx.DiGraph(nx.read_gml(graph)) elif re.match(r".*graph\s*\{.*\}\s*", graph): try: import pygraphviz as pgv self._graph = pgv.AGraph(graph, strict=True, directed=True) self._graph = nx.drawing.nx_agraph.from_agraph(self._graph) except Exception as e: self.logger.error("Error: Pygraphviz cannot be loaded. " + str(e) + "\nTrying pydot ...") try: import pydot P_list = pydot.graph_from_dot_data(graph) self._graph = nx.drawing.nx_pydot.from_pydot(P_list[0]) except Exception as e: self.logger.error("Error: Pydot cannot be loaded. " + str(e)) raise e elif re.match(".*graph\s*\[.*\]\s*", graph): self._graph = nx.DiGraph(nx.parse_gml(graph)) else: self.logger.error("Error: Please provide graph (as string or text file) in dot or gml format.") self.logger.error("Error: Incorrect graph format") raise ValueError if missing_nodes_as_confounders: self._graph = self.add_missing_nodes_as_common_causes(observed_node_names) # Adding node attributes self._graph = self.add_node_attributes(observed_node_names) def view_graph(self, layout="dot", size=(8, 6), file_name="causal_model"): out_filename = "{}.png".format(file_name) try: import pygraphviz as pgv agraph = nx.drawing.nx_agraph.to_agraph(self._graph) agraph.graph_attr.update(size="{},{}!".format(size[0], size[0])) agraph.draw(out_filename, format="png", prog=layout) except: self.logger.warning( "Warning: Pygraphviz cannot be loaded. Check that graphviz and pygraphviz are installed." ) self.logger.info("Using Matplotlib for plotting") import matplotlib.pyplot as plt plt.figure(figsize=size) solid_edges = [(n1, n2) for n1, n2, e in self._graph.edges(data=True) if "style" not in e] dashed_edges = [ (n1, n2) for n1, n2, e in self._graph.edges(data=True) if ("style" in e and e["style"] == "dashed") ] plt.clf() pos = nx.layout.shell_layout(self._graph) nx.draw_networkx_nodes(self._graph, pos, node_color="yellow", node_size=400) nx.draw_networkx_edges(self._graph, pos, edgelist=solid_edges, arrowstyle="-|>", arrowsize=12) nx.draw_networkx_edges( self._graph, pos, edgelist=dashed_edges, arrowstyle="-|>", style="dashed", arrowsize=12 ) labels = nx.draw_networkx_labels(self._graph, pos) plt.axis("off") plt.savefig(out_filename) plt.draw() def build_graph(self, common_cause_names, instrument_names, effect_modifier_names, mediator_names): """Creates nodes and edges based on variable names and their semantics. Currently only considers the graphical representation of "direct" effect modifiers. Thus, all effect modifiers are assumed to be "direct" unless otherwise expressed using a graph. Based on the taxonomy of effect modifiers by VanderWheele and Robins: "Four types of effect modification: A classification based on directed acyclic graphs. Epidemiology. 2007." """ for treatment in self.treatment_name: self._graph.add_node(treatment, observed="yes", penwidth=2) for outcome in self.outcome_name: self._graph.add_node(outcome, observed="yes", penwidth=2) for treatment, outcome in itertools.product(self.treatment_name, self.outcome_name): # adding penwidth to make the edge bold self._graph.add_edge(treatment, outcome, penwidth=2) # Adding common causes if common_cause_names is not None: for node_name in common_cause_names: for treatment, outcome in itertools.product(self.treatment_name, self.outcome_name): self._graph.add_node(node_name, observed="yes") self._graph.add_edge(node_name, treatment) self._graph.add_edge(node_name, outcome) # Adding instruments if instrument_names: if type(instrument_names[0]) != tuple: if len(self.treatment_name) > 1: self.logger.info("Assuming Instrument points to all treatments! Use tuples for more granularity.") for instrument, treatment in itertools.product(instrument_names, self.treatment_name): self._graph.add_node(instrument, observed="yes") self._graph.add_edge(instrument, treatment) else: for instrument, treatment in itertools.product(instrument_names): self._graph.add_node(instrument, observed="yes") self._graph.add_edge(instrument, treatment) # Adding effect modifiers if effect_modifier_names is not None: for node_name in effect_modifier_names: if node_name not in common_cause_names: for outcome in self.outcome_name: self._graph.add_node(node_name, observed="yes") # Assuming the simple form of effect modifier # that directly causes the outcome. self._graph.add_edge(node_name, outcome) # self._graph.add_edge(node_name, outcome, style = "dotted", headport="s", tailport="n") # self._graph.add_edge(outcome, node_name, style = "dotted", headport="n", tailport="s") # TODO make the ports more general so that they apply not just to top-bottom node configurations if mediator_names is not None: for node_name in mediator_names: for treatment, outcome in itertools.product(self.treatment_name, self.outcome_name): self._graph.add_node(node_name, observed="yes") self._graph.add_edge(treatment, node_name) self._graph.add_edge(node_name, outcome) return self._graph def add_node_attributes(self, observed_node_names): for node_name in self._graph: if node_name in observed_node_names: self._graph.nodes[node_name]["observed"] = "yes" else: self._graph.nodes[node_name]["observed"] = "no" return self._graph def add_missing_nodes_as_common_causes(self, observed_node_names): # Adding columns in the dataframe as confounders that were not in the graph for node_name in observed_node_names: if node_name not in self._graph: self._graph.add_node(node_name, observed="yes") for treatment_outcome_node in self.treatment_name + self.outcome_name: self._graph.add_edge(node_name, treatment_outcome_node) return self._graph def add_unobserved_common_cause(self, observed_node_names, color="gray"): # Adding unobserved confounders current_common_causes = self.get_common_causes(self.treatment_name, self.outcome_name) create_new_common_cause = True for node_name in current_common_causes: if self._graph.nodes[node_name]["observed"] == "no": create_new_common_cause = False if create_new_common_cause: uc_label = "Unobserved Confounders" self._graph.add_node("U", label=uc_label, observed="no", color=color, style="filled", fillcolor=color) for node in self.treatment_name + self.outcome_name: self._graph.add_edge("U", node) self.logger.info( 'If this is observed data (not from a randomized experiment), there might always be missing confounders. Adding a node named "Unobserved Confounders" to reflect this.' ) return self._graph def get_unconfounded_observed_subgraph(self): observed_nodes = [node for node in self._graph.nodes() if self._graph.nodes[node]["observed"] == "yes"] return self._graph.subgraph(observed_nodes) def do_surgery(self, node_names, remove_outgoing_edges=False, remove_incoming_edges=False): node_names = parse_state(node_names) new_graph = self._graph.copy() for node_name in node_names: if remove_outgoing_edges: children = new_graph.successors(node_name) edges_bunch = [(node_name, child) for child in children] new_graph.remove_edges_from(edges_bunch) if remove_incoming_edges: parents = new_graph.predecessors(node_name) edges_bunch = [(parent, node_name) for parent in parents] new_graph.remove_edges_from(edges_bunch) return new_graph def get_causes(self, nodes, remove_edges=None): nodes = parse_state(nodes) new_graph = None if remove_edges is not None: new_graph = self._graph.copy() # caution: shallow copy of the attributes sources = parse_state(remove_edges["sources"]) targets = parse_state(remove_edges["targets"]) for s in sources: for t in targets: new_graph.remove_edge(s, t) causes = set() for v in nodes: causes = causes.union(self.get_ancestors(v, new_graph=new_graph)) return causes def check_dseparation(self, nodes1, nodes2, nodes3, new_graph=None, dseparation_algo="default"): if dseparation_algo == "default": if new_graph is None: new_graph = self._graph dseparated = nx.algorithms.d_separated(new_graph, set(nodes1), set(nodes2), set(nodes3)) else: raise ValueError(f"{dseparation_algo} method for d-separation not supported.") return dseparated def check_valid_backdoor_set( self, nodes1, nodes2, nodes3, backdoor_paths=None, new_graph=None, dseparation_algo="default" ): """Assume that the first parameter (nodes1) is the treatment, the second is the outcome, and the third is the candidate backdoor set """ # also return the number of backdoor paths blocked by observed nodes if dseparation_algo == "default": if new_graph is None: # Assume that nodes1 is the treatment new_graph = self.do_surgery(nodes1, remove_outgoing_edges=True) dseparated = nx.algorithms.d_separated(new_graph, set(nodes1), set(nodes2), set(nodes3)) elif dseparation_algo == "naive": # ignores new_graph parameter, always uses self._graph if backdoor_paths is None: backdoor_paths = self.get_backdoor_paths(nodes1, nodes2) dseparated = all([self.is_blocked(path, nodes3) for path in backdoor_paths]) else: raise ValueError(f"{dseparation_algo} method for d-separation not supported.") return {"is_dseparated": dseparated} def get_backdoor_paths(self, nodes1, nodes2): paths = [] undirected_graph = self._graph.to_undirected() nodes12 = set(nodes1).union(nodes2) for node1 in nodes1: for node2 in nodes2: backdoor_paths = [ pth for pth in nx.all_simple_paths(undirected_graph, source=node1, target=node2) if self._graph.has_edge(pth[1], pth[0]) ] # remove paths that have nodes1\node1 or nodes2\node2 as intermediate nodes filtered_backdoor_paths = [pth for pth in backdoor_paths if len(nodes12.intersection(pth[1:-1])) == 0] paths.extend(filtered_backdoor_paths) self.logger.debug("Backdoor paths: " + str(paths)) return paths def is_blocked(self, path, conditioned_nodes): """Uses d-separation criteria to decide if conditioned_nodes block given path.""" blocked_by_conditioning = False has_unconditioned_collider = False for i in range(len(path) - 2): if self._graph.has_edge(path[i], path[i + 1]) and self._graph.has_edge( path[i + 2], path[i + 1] ): # collider collider_descendants = nx.descendants(self._graph, path[i + 1]) if path[i + 1] not in conditioned_nodes and all( cdesc not in conditioned_nodes for cdesc in collider_descendants ): has_unconditioned_collider = True else: # chain or fork if path[i + 1] in conditioned_nodes: blocked_by_conditioning = True break if blocked_by_conditioning: return True elif has_unconditioned_collider: return True else: return False def get_common_causes(self, nodes1, nodes2): """ Assume that nodes1 causes nodes2 (e.g., nodes1 are the treatments and nodes2 are the outcomes) """ # TODO Refactor to remove this from here and only implement this logic in causalIdentifier. Unnecessary assumption of nodes1 to be causing nodes2. nodes1 = parse_state(nodes1) nodes2 = parse_state(nodes2) causes_1 = set() causes_2 = set() for node in nodes1: causes_1 = causes_1.union(self.get_ancestors(node)) for node in nodes2: # Cannot simply compute ancestors, since that will also include nodes1 and its parents (e.g. instruments) parents_2 = self.get_parents(node) for parent in parents_2: if parent not in nodes1: causes_2 = causes_2.union( set( [ parent, ] ) ) causes_2 = causes_2.union(self.get_ancestors(parent)) return list(causes_1.intersection(causes_2)) def get_effect_modifiers(self, nodes1, nodes2): modifiers = set() for node in nodes2: modifiers = modifiers.union(self.get_ancestors(node)) modifiers = modifiers.difference(nodes1) for node in nodes1: modifiers = modifiers.difference(self.get_ancestors(node)) # removing all mediators for node1 in nodes1: for node2 in nodes2: all_directed_paths = nx.all_simple_paths(self._graph, node1, node2) for path in all_directed_paths: modifiers = modifiers.difference(path) return list(modifiers) def get_parents(self, node_name): return set(self._graph.predecessors(node_name)) def get_ancestors(self, node_name, new_graph=None): if new_graph is None: graph = self._graph else: graph = new_graph return set(nx.ancestors(graph, node_name)) def get_descendants(self, nodes): descendants = set() for node_name in nodes: descendants = descendants.union(set(nx.descendants(self._graph, node_name))) return descendants def all_observed(self, node_names): for node_name in node_names: if self._graph.nodes[node_name]["observed"] != "yes": return False return True def get_all_nodes(self, include_unobserved=True): nodes = self._graph.nodes if not include_unobserved: nodes = set(self.filter_unobserved_variables(nodes)) return nodes def filter_unobserved_variables(self, node_names): observed_node_names = list() for node_name in node_names: if self._graph.nodes[node_name]["observed"] == "yes": observed_node_names.append(node_name) return observed_node_names def get_instruments(self, treatment_nodes, outcome_nodes): treatment_nodes = parse_state(treatment_nodes) outcome_nodes = parse_state(outcome_nodes) parents_treatment = set() for node in treatment_nodes: parents_treatment = parents_treatment.union(self.get_parents(node)) g_no_parents_treatment = self.do_surgery(treatment_nodes, remove_incoming_edges=True) ancestors_outcome = set() for node in outcome_nodes: ancestors_outcome = ancestors_outcome.union(nx.ancestors(g_no_parents_treatment, node)) # [TODO: double check these work with multivariate implementation:] # Exclusion candidate_instruments = parents_treatment.difference(ancestors_outcome) self.logger.debug("Candidate instruments after satisfying exclusion: %s", candidate_instruments) # As-if-random setup children_causes_outcome = [nx.descendants(g_no_parents_treatment, v) for v in ancestors_outcome] children_causes_outcome = set([item for sublist in children_causes_outcome for item in sublist]) # As-if-random instruments = candidate_instruments.difference(children_causes_outcome) self.logger.debug("Candidate instruments after satisfying exclusion and as-if-random: %s", instruments) return list(instruments) def get_all_directed_paths(self, nodes1, nodes2): """Get all directed paths between sets of nodes. Currently only supports singleton sets. """ node1 = nodes1[0] node2 = nodes2[0] # convert the outputted generator into a list return [p for p in nx.all_simple_paths(self._graph, source=node1, target=node2)] def has_directed_path(self, nodes1, nodes2): """Checks if there is any directed path between two sets of nodes. Currently only supports singleton sets. """ # dpaths = self.get_all_directed_paths(nodes1, nodes2) # return len(dpaths) > 0 return nx.has_path(self._graph, nodes1[0], nodes2[0]) def get_adjacency_matrix(self, *args, **kwargs): """ Get adjacency matrix from the networkx graph """ return nx.convert_matrix.to_numpy_matrix(self._graph, *args, **kwargs) def check_valid_frontdoor_set( self, nodes1, nodes2, candidate_nodes, frontdoor_paths=None, new_graph=None, dseparation_algo="default" ): """Check if valid the frontdoor variables for set of treatments, nodes1 to set of outcomes, nodes2.""" # Condition 1: node 1 ---> node 2 is intercepted by candidate_nodes if dseparation_algo == "default": if new_graph is None: new_graph = self._graph dseparated = nx.algorithms.d_separated(new_graph, set(nodes1), set(nodes2), set(candidate_nodes)) elif dseparation_algo == "naive": if frontdoor_paths is None: frontdoor_paths = self.get_all_directed_paths(nodes1, nodes2) dseparated = all([self.is_blocked(path, candidate_nodes) for path in frontdoor_paths]) else: raise ValueError(f"{dseparation_algo} method for d-separation not supported.") return dseparated def check_valid_mediation_set(self, nodes1, nodes2, candidate_nodes, mediation_paths=None): """Check if candidate nodes are valid mediators for set of treatments, nodes1 to set of outcomes, nodes2.""" if mediation_paths is None: mediation_paths = self.get_all_directed_paths(nodes1, nodes2) is_mediator = any([self.is_blocked(path, candidate_nodes) for path in mediation_paths]) return is_mediator

import itertools import logging import re import networkx as nx from dowhy.utils.api import parse_state from dowhy.utils.graph_operations import daggity_to_dot class CausalGraph: """Class for creating and modifying the causal graph. Accepts a graph string (or a text file) in gml format (preferred) and dot format. Graphviz-like attributes can be set for edges and nodes. E.g. style="dashed" as an edge attribute ensures that the edge is drawn with a dashed line. If a graph string is not given, names of treatment, outcome, and confounders, instruments and effect modifiers (if any) can be provided to create the graph. """ def __init__( self, treatment_name, outcome_name, graph=None, common_cause_names=None, instrument_names=None, effect_modifier_names=None, mediator_names=None, observed_node_names=None, missing_nodes_as_confounders=False, ): self.treatment_name = parse_state(treatment_name) self.outcome_name = parse_state(outcome_name) instrument_names = parse_state(instrument_names) common_cause_names = parse_state(common_cause_names) effect_modifier_names = parse_state(effect_modifier_names) mediator_names = parse_state(mediator_names) self.logger = logging.getLogger(__name__) # re.sub only takes string parameter so the first if is to avoid error # if the input is a text file, convert the contained data into string if isinstance(graph, str) and re.match(r".*\.txt", str(graph)): text_file = open(graph, "r") graph = text_file.read() text_file.close() if isinstance(graph, str) and re.match(r"^dag", graph): # Convert daggity output to dot format graph = daggity_to_dot(graph) if isinstance(graph, str): graph = graph.replace("\n", " ") if graph is None: self._graph = nx.DiGraph() self._graph = self.build_graph(common_cause_names, instrument_names, effect_modifier_names, mediator_names) elif re.match(r".*\.dot", graph): # load dot file try: import pygraphviz as pgv self._graph = nx.DiGraph(nx.drawing.nx_agraph.read_dot(graph)) except Exception as e: self.logger.error("Pygraphviz cannot be loaded. " + str(e) + "\nTrying pydot...") try: import pydot self._graph = nx.DiGraph(nx.drawing.nx_pydot.read_dot(graph)) except Exception as e: self.logger.error("Error: Pydot cannot be loaded. " + str(e)) raise e elif re.match(r".*\.gml", graph): self._graph = nx.DiGraph(nx.read_gml(graph)) elif re.match(r".*graph\s*\{.*\}\s*", graph): try: import pygraphviz as pgv self._graph = pgv.AGraph(graph, strict=True, directed=True) self._graph = nx.drawing.nx_agraph.from_agraph(self._graph) except Exception as e: self.logger.error("Error: Pygraphviz cannot be loaded. " + str(e) + "\nTrying pydot ...") try: import pydot P_list = pydot.graph_from_dot_data(graph) self._graph = nx.drawing.nx_pydot.from_pydot(P_list[0]) except Exception as e: self.logger.error("Error: Pydot cannot be loaded. " + str(e)) raise e elif re.match(".*graph\s*\[.*\]\s*", graph): self._graph = nx.DiGraph(nx.parse_gml(graph)) else: self.logger.error("Error: Please provide graph (as string or text file) in dot or gml format.") self.logger.error("Error: Incorrect graph format") raise ValueError if missing_nodes_as_confounders: self._graph = self.add_missing_nodes_as_common_causes(observed_node_names) # Adding node attributes self._graph = self.add_node_attributes(observed_node_names) def view_graph(self, layout="dot", size=(8, 6), file_name="causal_model"): out_filename = "{}.png".format(file_name) try: import pygraphviz as pgv agraph = nx.drawing.nx_agraph.to_agraph(self._graph) agraph.graph_attr.update(size="{},{}!".format(size[0], size[0])) agraph.draw(out_filename, format="png", prog=layout) except: self.logger.warning( "Warning: Pygraphviz cannot be loaded. Check that graphviz and pygraphviz are installed." ) self.logger.info("Using Matplotlib for plotting") import matplotlib.pyplot as plt plt.figure(figsize=size) solid_edges = [(n1, n2) for n1, n2, e in self._graph.edges(data=True) if "style" not in e] dashed_edges = [ (n1, n2) for n1, n2, e in self._graph.edges(data=True) if ("style" in e and e["style"] == "dashed") ] plt.clf() pos = nx.layout.shell_layout(self._graph) nx.draw_networkx_nodes(self._graph, pos, node_color="yellow", node_size=400) nx.draw_networkx_edges(self._graph, pos, edgelist=solid_edges, arrowstyle="-|>", arrowsize=12) nx.draw_networkx_edges( self._graph, pos, edgelist=dashed_edges, arrowstyle="-|>", style="dashed", arrowsize=12 ) labels = nx.draw_networkx_labels(self._graph, pos) plt.axis("off") plt.savefig(out_filename) plt.draw() def build_graph(self, common_cause_names, instrument_names, effect_modifier_names, mediator_names): """Creates nodes and edges based on variable names and their semantics. Currently only considers the graphical representation of "direct" effect modifiers. Thus, all effect modifiers are assumed to be "direct" unless otherwise expressed using a graph. Based on the taxonomy of effect modifiers by VanderWheele and Robins: "Four types of effect modification: A classification based on directed acyclic graphs. Epidemiology. 2007." """ for treatment in self.treatment_name: self._graph.add_node(treatment, observed="yes", penwidth=2) for outcome in self.outcome_name: self._graph.add_node(outcome, observed="yes", penwidth=2) for treatment, outcome in itertools.product(self.treatment_name, self.outcome_name): # adding penwidth to make the edge bold self._graph.add_edge(treatment, outcome, penwidth=2) # Adding common causes if common_cause_names is not None: for node_name in common_cause_names: for treatment, outcome in itertools.product(self.treatment_name, self.outcome_name): self._graph.add_node(node_name, observed="yes") self._graph.add_edge(node_name, treatment) self._graph.add_edge(node_name, outcome) # Adding instruments if instrument_names: if type(instrument_names[0]) != tuple: if len(self.treatment_name) > 1: self.logger.info("Assuming Instrument points to all treatments! Use tuples for more granularity.") for instrument, treatment in itertools.product(instrument_names, self.treatment_name): self._graph.add_node(instrument, observed="yes") self._graph.add_edge(instrument, treatment) else: for instrument, treatment in itertools.product(instrument_names): self._graph.add_node(instrument, observed="yes") self._graph.add_edge(instrument, treatment) # Adding effect modifiers if effect_modifier_names is not None: for node_name in effect_modifier_names: if node_name not in common_cause_names: for outcome in self.outcome_name: self._graph.add_node(node_name, observed="yes") # Assuming the simple form of effect modifier # that directly causes the outcome. self._graph.add_edge(node_name, outcome) # self._graph.add_edge(node_name, outcome, style = "dotted", headport="s", tailport="n") # self._graph.add_edge(outcome, node_name, style = "dotted", headport="n", tailport="s") # TODO make the ports more general so that they apply not just to top-bottom node configurations if mediator_names is not None: for node_name in mediator_names: for treatment, outcome in itertools.product(self.treatment_name, self.outcome_name): self._graph.add_node(node_name, observed="yes") self._graph.add_edge(treatment, node_name) self._graph.add_edge(node_name, outcome) return self._graph def add_node_attributes(self, observed_node_names): for node_name in self._graph: if node_name in observed_node_names: self._graph.nodes[node_name]["observed"] = "yes" else: self._graph.nodes[node_name]["observed"] = "no" return self._graph def add_missing_nodes_as_common_causes(self, observed_node_names): # Adding columns in the dataframe as confounders that were not in the graph for node_name in observed_node_names: if node_name not in self._graph: self._graph.add_node(node_name, observed="yes") for treatment_outcome_node in self.treatment_name + self.outcome_name: self._graph.add_edge(node_name, treatment_outcome_node) return self._graph def add_unobserved_common_cause(self, observed_node_names, color="gray"): # Adding unobserved confounders current_common_causes = self.get_common_causes(self.treatment_name, self.outcome_name) create_new_common_cause = True for node_name in current_common_causes: if self._graph.nodes[node_name]["observed"] == "no": create_new_common_cause = False if create_new_common_cause: uc_label = "Unobserved Confounders" self._graph.add_node("U", label=uc_label, observed="no", color=color, style="filled", fillcolor=color) for node in self.treatment_name + self.outcome_name: self._graph.add_edge("U", node) self.logger.info( 'If this is observed data (not from a randomized experiment), there might always be missing confounders. Adding a node named "Unobserved Confounders" to reflect this.' ) return self._graph def get_unconfounded_observed_subgraph(self): observed_nodes = [node for node in self._graph.nodes() if self._graph.nodes[node]["observed"] == "yes"] return self._graph.subgraph(observed_nodes) def do_surgery( self, node_names, remove_outgoing_edges=False, remove_incoming_edges=False, target_node_names=None, remove_only_direct_edges_to_target=False, ): """Method to create a new graph based on the concept of do-surgery. :param node_names: focal nodes for the surgery :param remove_outgoing_edges: whether to remove outgoing edges from the focal nodes :param remove_incoming_edges: whether to remove incoming edges to the focal nodes :param target_node_names: target nodes (optional) for the surgery, only used when remove_only_direct_edges_to_target is True :param remove_only_direct_edges_to_target: whether to remove only the direct edges from focal nodes to the target nodes :returns: a new networkx graph after the specified removal of edges """ node_names = parse_state(node_names) new_graph = self._graph.copy() for node_name in node_names: if remove_outgoing_edges: if remove_only_direct_edges_to_target: new_graph.remove_edges_from([(node_name, v) for v in target_node_names]) else: children = new_graph.successors(node_name) edges_bunch = [(node_name, child) for child in children] new_graph.remove_edges_from(edges_bunch) if remove_incoming_edges: # removal of only direct edges wrt a target is not implemented for incoming edges parents = new_graph.predecessors(node_name) edges_bunch = [(parent, node_name) for parent in parents] new_graph.remove_edges_from(edges_bunch) return new_graph def get_causes(self, nodes, remove_edges=None): nodes = parse_state(nodes) new_graph = None if remove_edges is not None: new_graph = self._graph.copy() # caution: shallow copy of the attributes sources = parse_state(remove_edges["sources"]) targets = parse_state(remove_edges["targets"]) for s in sources: for t in targets: new_graph.remove_edge(s, t) causes = set() for v in nodes: causes = causes.union(self.get_ancestors(v, new_graph=new_graph)) return causes def check_dseparation(self, nodes1, nodes2, nodes3, new_graph=None, dseparation_algo="default"): if dseparation_algo == "default": if new_graph is None: new_graph = self._graph dseparated = nx.algorithms.d_separated(new_graph, set(nodes1), set(nodes2), set(nodes3)) else: raise ValueError(f"{dseparation_algo} method for d-separation not supported.") return dseparated def check_valid_backdoor_set( self, nodes1, nodes2, nodes3, backdoor_paths=None, new_graph=None, dseparation_algo="default" ): """Assume that the first parameter (nodes1) is the treatment, the second is the outcome, and the third is the candidate backdoor set """ # also return the number of backdoor paths blocked by observed nodes if dseparation_algo == "default": if new_graph is None: # Assume that nodes1 is the treatment new_graph = self.do_surgery(nodes1, remove_outgoing_edges=True) dseparated = nx.algorithms.d_separated(new_graph, set(nodes1), set(nodes2), set(nodes3)) elif dseparation_algo == "naive": # ignores new_graph parameter, always uses self._graph if backdoor_paths is None: backdoor_paths = self.get_backdoor_paths(nodes1, nodes2) dseparated = all([self.is_blocked(path, nodes3) for path in backdoor_paths]) else: raise ValueError(f"{dseparation_algo} method for d-separation not supported.") return {"is_dseparated": dseparated} def get_backdoor_paths(self, nodes1, nodes2): paths = [] undirected_graph = self._graph.to_undirected() nodes12 = set(nodes1).union(nodes2) for node1 in nodes1: for node2 in nodes2: backdoor_paths = [ pth for pth in nx.all_simple_paths(undirected_graph, source=node1, target=node2) if self._graph.has_edge(pth[1], pth[0]) ] # remove paths that have nodes1\node1 or nodes2\node2 as intermediate nodes filtered_backdoor_paths = [pth for pth in backdoor_paths if len(nodes12.intersection(pth[1:-1])) == 0] paths.extend(filtered_backdoor_paths) self.logger.debug("Backdoor paths: " + str(paths)) return paths def is_blocked(self, path, conditioned_nodes): """Uses d-separation criteria to decide if conditioned_nodes block given path.""" blocked_by_conditioning = False has_unconditioned_collider = False for i in range(len(path) - 2): if self._graph.has_edge(path[i], path[i + 1]) and self._graph.has_edge( path[i + 2], path[i + 1] ): # collider collider_descendants = nx.descendants(self._graph, path[i + 1]) if path[i + 1] not in conditioned_nodes and all( cdesc not in conditioned_nodes for cdesc in collider_descendants ): has_unconditioned_collider = True else: # chain or fork if path[i + 1] in conditioned_nodes: blocked_by_conditioning = True break if blocked_by_conditioning: return True elif has_unconditioned_collider: return True else: return False def get_common_causes(self, nodes1, nodes2): """ Assume that nodes1 causes nodes2 (e.g., nodes1 are the treatments and nodes2 are the outcomes) """ # TODO Refactor to remove this from here and only implement this logic in causalIdentifier. Unnecessary assumption of nodes1 to be causing nodes2. nodes1 = parse_state(nodes1) nodes2 = parse_state(nodes2) causes_1 = set() causes_2 = set() for node in nodes1: causes_1 = causes_1.union(self.get_ancestors(node)) for node in nodes2: # Cannot simply compute ancestors, since that will also include nodes1 and its parents (e.g. instruments) parents_2 = self.get_parents(node) for parent in parents_2: if parent not in nodes1: causes_2 = causes_2.union( set( [ parent, ] ) ) causes_2 = causes_2.union(self.get_ancestors(parent)) return list(causes_1.intersection(causes_2)) def get_effect_modifiers(self, nodes1, nodes2): modifiers = set() for node in nodes2: modifiers = modifiers.union(self.get_ancestors(node)) modifiers = modifiers.difference(nodes1) for node in nodes1: modifiers = modifiers.difference(self.get_ancestors(node)) # removing all mediators for node1 in nodes1: for node2 in nodes2: all_directed_paths = nx.all_simple_paths(self._graph, node1, node2) for path in all_directed_paths: modifiers = modifiers.difference(path) return list(modifiers) def get_parents(self, node_name): return set(self._graph.predecessors(node_name)) def get_ancestors(self, node_name, new_graph=None): if new_graph is None: graph = self._graph else: graph = new_graph return set(nx.ancestors(graph, node_name)) def get_descendants(self, nodes): descendants = set() for node_name in nodes: descendants = descendants.union(set(nx.descendants(self._graph, node_name))) return descendants def all_observed(self, node_names): for node_name in node_names: if self._graph.nodes[node_name]["observed"] != "yes": return False return True def get_all_nodes(self, include_unobserved=True): nodes = self._graph.nodes if not include_unobserved: nodes = set(self.filter_unobserved_variables(nodes)) return nodes def filter_unobserved_variables(self, node_names): observed_node_names = list() for node_name in node_names: if self._graph.nodes[node_name]["observed"] == "yes": observed_node_names.append(node_name) return observed_node_names def get_instruments(self, treatment_nodes, outcome_nodes): treatment_nodes = parse_state(treatment_nodes) outcome_nodes = parse_state(outcome_nodes) parents_treatment = set() for node in treatment_nodes: parents_treatment = parents_treatment.union(self.get_parents(node)) g_no_parents_treatment = self.do_surgery(treatment_nodes, remove_incoming_edges=True) ancestors_outcome = set() for node in outcome_nodes: ancestors_outcome = ancestors_outcome.union(nx.ancestors(g_no_parents_treatment, node)) # [TODO: double check these work with multivariate implementation:] # Exclusion candidate_instruments = parents_treatment.difference(ancestors_outcome) self.logger.debug("Candidate instruments after satisfying exclusion: %s", candidate_instruments) # As-if-random setup children_causes_outcome = [nx.descendants(g_no_parents_treatment, v) for v in ancestors_outcome] children_causes_outcome = set([item for sublist in children_causes_outcome for item in sublist]) # As-if-random instruments = candidate_instruments.difference(children_causes_outcome) self.logger.debug("Candidate instruments after satisfying exclusion and as-if-random: %s", instruments) return list(instruments) def get_all_directed_paths(self, nodes1, nodes2): """Get all directed paths between sets of nodes. Currently only supports singleton sets. """ node1 = nodes1[0] node2 = nodes2[0] # convert the outputted generator into a list return [p for p in nx.all_simple_paths(self._graph, source=node1, target=node2)] def has_directed_path(self, nodes1, nodes2): """Checks if there is any directed path between two sets of nodes. Currently only supports singleton sets. """ # dpaths = self.get_all_directed_paths(nodes1, nodes2) # return len(dpaths) > 0 return nx.has_path(self._graph, nodes1[0], nodes2[0]) def get_adjacency_matrix(self, *args, **kwargs): """ Get adjacency matrix from the networkx graph """ return nx.convert_matrix.to_numpy_matrix(self._graph, *args, **kwargs) def check_valid_frontdoor_set( self, nodes1, nodes2, candidate_nodes, frontdoor_paths=None, new_graph=None, dseparation_algo="default" ): """Check if valid the frontdoor variables for set of treatments, nodes1 to set of outcomes, nodes2.""" # Condition 1: node 1 ---> node 2 is intercepted by candidate_nodes if dseparation_algo == "default": if new_graph is None: new_graph = self._graph dseparated = nx.algorithms.d_separated(new_graph, set(nodes1), set(nodes2), set(candidate_nodes)) elif dseparation_algo == "naive": if frontdoor_paths is None: frontdoor_paths = self.get_all_directed_paths(nodes1, nodes2) dseparated = all([self.is_blocked(path, candidate_nodes) for path in frontdoor_paths]) else: raise ValueError(f"{dseparation_algo} method for d-separation not supported.") return dseparated def check_valid_mediation_set(self, nodes1, nodes2, candidate_nodes, mediation_paths=None): """Check if candidate nodes are valid mediators for set of treatments, nodes1 to set of outcomes, nodes2.""" if mediation_paths is None: mediation_paths = self.get_all_directed_paths(nodes1, nodes2) is_mediator = any([self.is_blocked(path, candidate_nodes) for path in mediation_paths]) return is_mediator

amit-sharma

2f2463be424093d720ebfa9cc625a06160a44cfe

d67da0e57eda5cc47d180f3de240182dde4aacad

thanks for the suggestion. I've renamed "remove_only_direct_edges" to "remove_only_direct_edges_to_targets", since we only want to remove the direct edges. It is long but I thought it is best to err on the side of clarity here.

amit-sharma

py-why/dowhy

CI: Split tests into groups to speed them up

* Mark some slow tests as advanced * Split tests into 4 shards in CI

2022-08-25 22:09:18+00:00

2022-09-01 22:51:03+00:00

poetry.lock

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darthtrevino

ead8d47102f0ac6db51d84432874c331fb84f3cb

2f2463be424093d720ebfa9cc625a06160a44cfe

Are the changes to lib versions in poetry.lock due to splitting the tests into groups, or are they unrelated changes?

emrekiciman

py-why/dowhy

CI: Split tests into groups to speed them up

* Mark some slow tests as advanced * Split tests into 4 shards in CI

2022-08-25 22:09:18+00:00

2022-09-01 22:51:03+00:00

poetry.lock

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[[package]] name = "argon2-cffi-bindings" version = "21.2.0" description = "Low-level CFFI bindings for Argon2" category = "dev" optional = false python-versions = ">=3.6" [package.dependencies] cffi = ">=1.0.1" [package.extras] dev = ["pytest", "cogapp", "pre-commit", "wheel"] tests = ["pytest"] [[package]] name = "asttokens" version = "2.0.8" description = "Annotate AST trees with source code positions" category = "dev" optional = false python-versions = "*" [package.dependencies] six = "*" [package.extras] test = ["pytest", "astroid (<=2.5.3)"] [[package]] name = "astunparse" version = "1.6.3" description = "An AST unparser for Python" category = "dev" optional = false python-versions = "*" [package.dependencies] six = ">=1.6.1,<2.0" [[package]] name = "atomicwrites" version = "1.4.1" description = "Atomic file writes." category = "dev" optional = false python-versions = ">=2.7, !=3.0.*, !=3.1.*, !=3.2.*, !=3.3.*" [[package]] name = "attrs" version = "22.1.0" description = "Classes Without Boilerplate" category = "dev" optional = false python-versions = ">=3.5" [package.extras] dev = ["coverage[toml] (>=5.0.2)", "hypothesis", "pympler", "pytest (>=4.3.0)", "mypy (>=0.900,!=0.940)", "pytest-mypy-plugins", "zope.interface", "furo", "sphinx", "sphinx-notfound-page", "pre-commit", "cloudpickle"] docs = ["furo", "sphinx", "zope.interface", "sphinx-notfound-page"] tests = ["coverage[toml] (>=5.0.2)", "hypothesis", "pympler", "pytest (>=4.3.0)", "mypy (>=0.900,!=0.940)", "pytest-mypy-plugins", "zope.interface", "cloudpickle"] tests_no_zope = ["coverage[toml] (>=5.0.2)", "hypothesis", "pympler", "pytest (>=4.3.0)", "mypy (>=0.900,!=0.940)", "pytest-mypy-plugins", "cloudpickle"] [[package]] name = "babel" version = "2.10.3" description = "Internationalization utilities" category = "dev" optional = false python-versions = ">=3.6" [package.dependencies] pytz = ">=2015.7" [[package]] name = "backcall" version = "0.2.0" description = "Specifications for callback functions 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description = "The Cython compiler for writing C extensions for the Python language." category = "main" optional = true python-versions = ">=2.6, !=3.0.*, !=3.1.*, !=3.2.*" [[package]] name = "debugpy" version = "1.6.3" description = "An implementation of the Debug Adapter Protocol for Python" category = "dev" optional = false python-versions = ">=3.7" [[package]] name = "decorator" version = "5.1.1" description = "Decorators for Humans" category = "dev" optional = false python-versions = ">=3.5" [[package]] name = "defusedxml" version = "0.7.1" description = "XML bomb protection for Python stdlib modules" category = "dev" optional = false python-versions = ">=2.7, !=3.0.*, !=3.1.*, !=3.2.*, !=3.3.*, !=3.4.*" [[package]] name = "dill" version = "0.3.5.1" description = "serialize all of python" category = "main" optional = true python-versions = ">=2.7, !=3.0.*, !=3.1.*, !=3.2.*, !=3.3.*, !=3.4.*, !=3.5.*, !=3.6.*" [package.extras] graph = ["objgraph (>=1.7.2)"] [[package]] name = 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[[package]] name = "google-auth-oauthlib" version = "0.4.6" description = "Google Authentication Library" category = "dev" optional = false python-versions = ">=3.6" [package.dependencies] google-auth = ">=1.0.0" requests-oauthlib = ">=0.7.0" [package.extras] tool = ["click (>=6.0.0)"] [[package]] name = "google-pasta" version = "0.2.0" description = "pasta is an AST-based Python refactoring library" category = "dev" optional = false python-versions = "*" [package.dependencies] six = "*" [[package]] name = "graphviz" version = "0.20.1" description = "Simple Python interface for Graphviz" category = "main" optional = true python-versions = ">=3.7" [package.extras] dev = ["tox (>=3)", "flake8", "pep8-naming", "wheel", "twine"] docs = ["sphinx (>=5)", "sphinx-autodoc-typehints", "sphinx-rtd-theme"] test = ["pytest (>=7)", "pytest-mock (>=3)", "mock (>=4)", "pytest-cov", "coverage"] [[package]] name = "grpcio" version = "1.48.0" description = "HTTP/2-based RPC framework" category = "dev" 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"rst.linker (>=1.9)"] perf = ["ipython"] testing = ["pytest (>=6)", "pytest-checkdocs (>=2.4)", "pytest-flake8", "pytest-cov", "pytest-enabler (>=1.3)", "packaging", "pyfakefs", "flufl.flake8", "pytest-perf (>=0.9.2)", "pytest-black (>=0.3.7)", "pytest-mypy (>=0.9.1)", "importlib-resources (>=1.3)"] [[package]] name = "importlib-resources" version = "5.9.0" description = "Read resources from Python packages" category = "dev" optional = false python-versions = ">=3.7" [package.dependencies] zipp = {version = ">=3.1.0", markers = "python_version < \"3.10\""} [package.extras] docs = ["sphinx", "jaraco.packaging (>=9)", "rst.linker (>=1.9)", "jaraco.tidelift (>=1.4)"] testing = ["pytest (>=6)", "pytest-checkdocs (>=2.4)", "pytest-flake8", "pytest-cov", "pytest-enabler (>=1.3)", "pytest-black (>=0.3.7)", "pytest-mypy (>=0.9.1)"] [[package]] name = "iniconfig" version = "1.1.1" description = "iniconfig: brain-dead simple config-ini parsing" category = "dev" optional = false python-versions = 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darthtrevino

ead8d47102f0ac6db51d84432874c331fb84f3cb

2f2463be424093d720ebfa9cc625a06160a44cfe

Some are related to adding the new dependency, but it looks like it runs the solution engine whenever you add a dependency. We have a handful of deps that are tied to `main` branches on github, which will be resolved fresh - and there may be some path-version updates from other dependencies.

darthtrevino

py-why/dowhy

CI: Split tests into groups to speed them up

* Mark some slow tests as advanced * Split tests into 4 shards in CI

2022-08-25 22:09:18+00:00

2022-09-01 22:51:03+00:00

tests/causal_refuters/test_data_subset_refuter.py

import numpy as np import pytest from .base import TestRefuter @pytest.mark.usefixtures("fixed_seed") class TestDataSubsetRefuter(object): @pytest.mark.parametrize(["error_tolerance", "estimator_method"], [(0.01, "iv.instrumental_variable")]) def test_refutation_data_subset_refuter_continuous(self, error_tolerance, estimator_method): refuter_tester = TestRefuter(error_tolerance, estimator_method, "data_subset_refuter") refuter_tester.continuous_treatment_testsuite() # Run both @pytest.mark.parametrize(["error_tolerance", "estimator_method"], [(0.01, "backdoor.propensity_score_matching")]) def test_refutation_data_subset_refuter_binary(self, error_tolerance, estimator_method): refuter_tester = TestRefuter(error_tolerance, estimator_method, "data_subset_refuter") refuter_tester.binary_treatment_testsuite(tests_to_run="atleast-one-common-cause")

import numpy as np import pytest from pytest import mark from .base import TestRefuter @mark.usefixtures("fixed_seed") class TestDataSubsetRefuter(object): @mark.parametrize(["error_tolerance", "estimator_method"], [(0.01, "iv.instrumental_variable")]) def test_refutation_data_subset_refuter_continuous(self, error_tolerance, estimator_method): refuter_tester = TestRefuter(error_tolerance, estimator_method, "data_subset_refuter") refuter_tester.continuous_treatment_testsuite() # Run both @mark.advanced @mark.parametrize(["error_tolerance", "estimator_method"], [(0.01, "backdoor.propensity_score_matching")]) def test_refutation_data_subset_refuter_binary(self, error_tolerance, estimator_method): refuter_tester = TestRefuter(error_tolerance, estimator_method, "data_subset_refuter") refuter_tester.binary_treatment_testsuite(tests_to_run="atleast-one-common-cause")

darthtrevino

ead8d47102f0ac6db51d84432874c331fb84f3cb

2f2463be424093d720ebfa9cc625a06160a44cfe

Most of the files use "mark.advanced" rather than pytest.mark.advanced. Is this contextual or would it be better to be consistent? or am I being too pedantic :)

emrekiciman

py-why/dowhy

CI: Split tests into groups to speed them up

* Mark some slow tests as advanced * Split tests into 4 shards in CI

2022-08-25 22:09:18+00:00

2022-09-01 22:51:03+00:00

tests/causal_refuters/test_data_subset_refuter.py

import numpy as np import pytest from .base import TestRefuter @pytest.mark.usefixtures("fixed_seed") class TestDataSubsetRefuter(object): @pytest.mark.parametrize(["error_tolerance", "estimator_method"], [(0.01, "iv.instrumental_variable")]) def test_refutation_data_subset_refuter_continuous(self, error_tolerance, estimator_method): refuter_tester = TestRefuter(error_tolerance, estimator_method, "data_subset_refuter") refuter_tester.continuous_treatment_testsuite() # Run both @pytest.mark.parametrize(["error_tolerance", "estimator_method"], [(0.01, "backdoor.propensity_score_matching")]) def test_refutation_data_subset_refuter_binary(self, error_tolerance, estimator_method): refuter_tester = TestRefuter(error_tolerance, estimator_method, "data_subset_refuter") refuter_tester.binary_treatment_testsuite(tests_to_run="atleast-one-common-cause")

import numpy as np import pytest from pytest import mark from .base import TestRefuter @mark.usefixtures("fixed_seed") class TestDataSubsetRefuter(object): @mark.parametrize(["error_tolerance", "estimator_method"], [(0.01, "iv.instrumental_variable")]) def test_refutation_data_subset_refuter_continuous(self, error_tolerance, estimator_method): refuter_tester = TestRefuter(error_tolerance, estimator_method, "data_subset_refuter") refuter_tester.continuous_treatment_testsuite() # Run both @mark.advanced @mark.parametrize(["error_tolerance", "estimator_method"], [(0.01, "backdoor.propensity_score_matching")]) def test_refutation_data_subset_refuter_binary(self, error_tolerance, estimator_method): refuter_tester = TestRefuter(error_tolerance, estimator_method, "data_subset_refuter") refuter_tester.binary_treatment_testsuite(tests_to_run="atleast-one-common-cause")

darthtrevino

ead8d47102f0ac6db51d84432874c331fb84f3cb

2f2463be424093d720ebfa9cc625a06160a44cfe

I've found both in the codebase - basically which one you use depends on whether you have `import pytest` or `from pytest import mark` in your file. I'm fine standardizing on using `@mark.advanced` though.

darthtrevino

py-why/dowhy

CI: Split tests into groups to speed them up

* Mark some slow tests as advanced * Split tests into 4 shards in CI

2022-08-25 22:09:18+00:00

2022-09-01 22:51:03+00:00

tests/causal_refuters/test_data_subset_refuter.py

import numpy as np import pytest from .base import TestRefuter @pytest.mark.usefixtures("fixed_seed") class TestDataSubsetRefuter(object): @pytest.mark.parametrize(["error_tolerance", "estimator_method"], [(0.01, "iv.instrumental_variable")]) def test_refutation_data_subset_refuter_continuous(self, error_tolerance, estimator_method): refuter_tester = TestRefuter(error_tolerance, estimator_method, "data_subset_refuter") refuter_tester.continuous_treatment_testsuite() # Run both @pytest.mark.parametrize(["error_tolerance", "estimator_method"], [(0.01, "backdoor.propensity_score_matching")]) def test_refutation_data_subset_refuter_binary(self, error_tolerance, estimator_method): refuter_tester = TestRefuter(error_tolerance, estimator_method, "data_subset_refuter") refuter_tester.binary_treatment_testsuite(tests_to_run="atleast-one-common-cause")

import numpy as np import pytest from pytest import mark from .base import TestRefuter @mark.usefixtures("fixed_seed") class TestDataSubsetRefuter(object): @mark.parametrize(["error_tolerance", "estimator_method"], [(0.01, "iv.instrumental_variable")]) def test_refutation_data_subset_refuter_continuous(self, error_tolerance, estimator_method): refuter_tester = TestRefuter(error_tolerance, estimator_method, "data_subset_refuter") refuter_tester.continuous_treatment_testsuite() # Run both @mark.advanced @mark.parametrize(["error_tolerance", "estimator_method"], [(0.01, "backdoor.propensity_score_matching")]) def test_refutation_data_subset_refuter_binary(self, error_tolerance, estimator_method): refuter_tester = TestRefuter(error_tolerance, estimator_method, "data_subset_refuter") refuter_tester.binary_treatment_testsuite(tests_to_run="atleast-one-common-cause")

darthtrevino

ead8d47102f0ac6db51d84432874c331fb84f3cb

2f2463be424093d720ebfa9cc625a06160a44cfe

Ok, let's standardize on mark.advanced then.

emrekiciman

py-why/dowhy

Add dependency to resolve security alert

https://github.com/py-why/dowhy/security/dependabot/1 * Updates nbconvert to 7.0rc3 & mistune to a safe version * Move documentation-generation dependencies into devDependencies area * Run `poetry update` for dependency refresh

2022-08-13 01:40:09+00:00

2022-08-19 21:01:53+00:00

poetry.lock

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darthtrevino

f947d98ffbc9d96b91be9bcfc43cf142fc2c0cd5

eadb99cbe104d89dda62f73e331515df484e8d5a

Are all the other changes in this file a consequence of updating mistune?

emrekiciman

py-why/dowhy

Add dependency to resolve security alert

https://github.com/py-why/dowhy/security/dependabot/1 * Updates nbconvert to 7.0rc3 & mistune to a safe version * Move documentation-generation dependencies into devDependencies area * Run `poetry update` for dependency refresh

2022-08-13 01:40:09+00:00

2022-08-19 21:01:53+00:00

poetry.lock

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darthtrevino

f947d98ffbc9d96b91be9bcfc43cf142fc2c0cd5

eadb99cbe104d89dda62f73e331515df484e8d5a

It looks like it - I believe that it's generally recommended to run `poetry update` once in a while, which will update the resolved versions of your dependencies to the latest that matches the semver range, but these are all from just running `poetry add mistune`

darthtrevino

py-why/dowhy

Add dependency to resolve security alert

https://github.com/py-why/dowhy/security/dependabot/1 * Updates nbconvert to 7.0rc3 & mistune to a safe version * Move documentation-generation dependencies into devDependencies area * Run `poetry update` for dependency refresh

2022-08-13 01:40:09+00:00

2022-08-19 21:01:53+00:00

pyproject.toml

[tool.poetry] name = "dowhy" # # 0.0.0 is standard placeholder for poetry-dynamic-versioning # any changes to this should not be checked in # version = "0.0.0" description = "DoWhy is a Python library for causal inference that supports explicit modeling and testing of causal assumptions" authors = [ "PyWhy Community <amshar@microsoft.com>" ] maintainers = [] license = "MIT" documentation = "https://py-why.github.io/dowhy" repository = "https://github.com/pywhy/dowhy" classifiers = [ 'Development Status :: 4 - Beta', 'License :: OSI Approved :: MIT License', 'Programming Language :: Python :: 3.8', 'Programming Language :: Python :: 3.9', ] keywords = [ 'causality', 'machine-learning', 'causal-inference', 'statistics', 'graphical-model' ] include = ['docs', 'tests', 'CONTRIBUTING.md', 'LICENSE'] readme = 'README.rst' [tool.poetry-dynamic-versioning] enable = true vcs = "git" [tool.poetry-dynamic-versioning.substitution] files = ["dowhy/__init__.py"] # # Dependency compatibility notes: # * xgboost requires Python >=3.7,<3.11 # * pygraphviz requires Python >=3.8 # * networkx requires Python >= 3.8 # * llvmlite requires Python >=3.6,<3.11 # [tool.poetry.dependencies] python = ">=3.8,<3.10" scipy = "^1.8.1" statsmodels = "^0.13.2" numpy = "^1.23.1" pandas = "^1.4.3" networkx = "^2.8.5" sympy = "^1.10.1" scikit-learn = "1.0.2" pydot = "^1.4.2" joblib = "^1.1.0" # causalml is wired to use llvmlite 0.36 causalml = {version = "^0.12.3", optional = true} llvmlite = {version = "^0.36.0", optional = true} pygraphviz = {version = "^1.9", optional = true} matplotlib = {version = "^3.5.2", optional = true} econml = {version = "*", optional = true} tqdm = "^4.64.0" # # Dependencies for Documentation Generation # rpy2 = {version = "^3.5.2", optional = true} sphinx-multiversion = { git = "https://github.com/petergtz/sphinx-multiversion.git", branch = "override-version-with-refname", optional = true} sphinxcontrib-googleanalytics = { git = "https://github.com/petergtz/googleanalytics.git", branch = "master", optional = true} nbsphinx = {version = "^0.8.9", optional = true} sphinx-rtd-theme = {version = "^1.0.0", optional = true} pydata-sphinx-theme = {version = "^0.9.0", optional = true} pandoc = {version = "^2.2", optional = true} ipykernel = {version = "^6.15.1", optional = true} [tool.poetry.extras] plotting = ["matplotlib"] causalml = ["causalml", "llvmlite"] docs = [ "rpy2", "sphinx-multiversion", "sphinxcontrib-googleanalytics", "nbsphinx", "sphinx-rtd-theme", "pydata-sphinx-theme", "sympy", "ipykernel" ] [tool.poetry.dev-dependencies] poethepoet = "^0.16.0" flake8 = "^4.0.1" black = "^22.6.0" isort = "^5.10.1" pytest = "^7.1.2" twine = "^4.0.1" nbformat = "^5.4.0" jupyter = "^1.0.0" flaky = "^3.7.0" tensorflow = "^2.9.1" keras = "^2.9.0" xgboost = "^1.6.1" mypy = "^0.971" econml = "*" pygraphviz = "^1.9" [build-system] requires = ["poetry-core>=1.0.0", "poetry-dynamic-versioning"] build-backend = "poetry.core.masonry.api" [tool.pytest.ini_options] markers = [ "advanced: not be to run each time. only on package updates." ] [tool.poe.tasks] # stop the build if there are Python syntax errors or undefined names _flake8Errors = "flake8 . --count --select=E9,F63,F7,F82 --show-source --statistics" _flake8Warnings = "flake8 . --count --exit-zero --statistics" _black = 'black .' _isort = 'isort .' # testing tasks test = "pytest -v -m 'not advanced' --durations=0 --durations-min=60.0" test_focused = "pytest -v -m 'focused'" verifyPackage = "twine check dist/*" # TODO: replace with `poetry publish` uploadPackage = "twine upload dist/*" # TODO: add formatting to build process [tool.poe.tasks.format] sequence = ['_black', '_isort'] ignore_fail = 'return_non_zero' [tool.poe.tasks.lint] sequence = ['_flake8Errors', '_flake8Warnings'] ignore_fail = 'return_non_zero' [tool.poe.tasks.verify] sequence = ['lint', 'test'] ignore_fail = "return_non_zero"

[tool.poetry] name = "dowhy" # # 0.0.0 is standard placeholder for poetry-dynamic-versioning # any changes to this should not be checked in # version = "0.0.0" description = "DoWhy is a Python library for causal inference that supports explicit modeling and testing of causal assumptions" authors = [ "PyWhy Community <amshar@microsoft.com>" ] maintainers = [] license = "MIT" documentation = "https://py-why.github.io/dowhy" repository = "https://github.com/pywhy/dowhy" classifiers = [ 'Development Status :: 4 - Beta', 'License :: OSI Approved :: MIT License', 'Programming Language :: Python :: 3.8', 'Programming Language :: Python :: 3.9', ] keywords = [ 'causality', 'machine-learning', 'causal-inference', 'statistics', 'graphical-model' ] include = ['docs', 'tests', 'CONTRIBUTING.md', 'LICENSE'] readme = 'README.rst' [tool.poetry-dynamic-versioning] enable = true vcs = "git" [tool.poetry-dynamic-versioning.substitution] files = ["dowhy/__init__.py"] # # Dependency compatibility notes: # * xgboost requires Python >=3.7,<3.11 # * pygraphviz requires Python >=3.8 # * networkx requires Python >= 3.8 # * llvmlite requires Python >=3.6,<3.11 # [tool.poetry.dependencies] python = ">=3.8,<3.10" scipy = "^1.8.1" statsmodels = "^0.13.2" numpy = "^1.23.1" pandas = "^1.4.3" networkx = "^2.8.5" sympy = "^1.10.1" scikit-learn = "1.0.2" pydot = "^1.4.2" joblib = "^1.1.0" pygraphviz = {version = "^1.9", optional = true} matplotlib = {version = "^3.5.2", optional = true} econml = {version = "*", optional = true} tqdm = "^4.64.0" # # CausalML Extra (causalml is wired to use llvmlite 0.36) # causalml = {version = "^0.12.3", optional = true} llvmlite = {version = "^0.36.0", optional = true} [tool.poetry.extras] plotting = ["matplotlib"] causalml = ["causalml", "llvmlite"] [tool.poetry.dev-dependencies] poethepoet = "^0.16.0" flake8 = "^4.0.1" black = "^22.6.0" isort = "^5.10.1" pytest = "^7.1.2" twine = "^4.0.1" nbformat = "^5.4.0" jupyter = "^1.0.0" flaky = "^3.7.0" tensorflow = "^2.9.1" keras = "^2.9.0" xgboost = "^1.6.1" mypy = "^0.971" econml = "*" pygraphviz = "^1.9" # # Dependencies for Documentation Generation # rpy2 = "^3.5.2" sphinx-multiversion = { git = "https://github.com/petergtz/sphinx-multiversion.git", branch = "override-version-with-refname"} sphinxcontrib-googleanalytics = { git = "https://github.com/petergtz/googleanalytics.git", branch = "master"} nbsphinx = "^0.8.9" sphinx-rtd-theme = "^1.0.0" pydata-sphinx-theme = "^0.9.0" pandoc = "^2.2" ipykernel = "^6.15.1" # # Versions defined for security reasons # # https://github.com/py-why/dowhy/security/dependabot/1 - CVE-2022-34749 nbconvert = {version = "7.0.0rc3", allow-prereleases = true} [build-system] requires = ["poetry-core>=1.0.0", "poetry-dynamic-versioning"] build-backend = "poetry.core.masonry.api" [tool.pytest.ini_options] markers = [ "advanced: not be to run each time. only on package updates." ] [tool.poe.tasks] # stop the build if there are Python syntax errors or undefined names _flake8Errors = "flake8 . --count --select=E9,F63,F7,F82 --show-source --statistics" _flake8Warnings = "flake8 . --count --exit-zero --statistics" _black = 'black .' _isort = 'isort .' # testing tasks test = "pytest -v -m 'not advanced' --durations=0 --durations-min=60.0" test_focused = "pytest -v -m 'focused'" verifyPackage = "twine check dist/*" # TODO: replace with `poetry publish` uploadPackage = "twine upload dist/*" # TODO: add formatting to build process [tool.poe.tasks.format] sequence = ['_black', '_isort'] ignore_fail = 'return_non_zero' [tool.poe.tasks.lint] sequence = ['_flake8Errors', '_flake8Warnings'] ignore_fail = 'return_non_zero' [tool.poe.tasks.verify] sequence = ['lint', 'test'] ignore_fail = "return_non_zero"

darthtrevino

f947d98ffbc9d96b91be9bcfc43cf142fc2c0cd5

eadb99cbe104d89dda62f73e331515df484e8d5a

Is there a reason these lines related to causalml have changed together with the update to the mistune version?

emrekiciman

py-why/dowhy

Add dependency to resolve security alert

https://github.com/py-why/dowhy/security/dependabot/1 * Updates nbconvert to 7.0rc3 & mistune to a safe version * Move documentation-generation dependencies into devDependencies area * Run `poetry update` for dependency refresh

2022-08-13 01:40:09+00:00

2022-08-19 21:01:53+00:00

pyproject.toml

[tool.poetry] name = "dowhy" # # 0.0.0 is standard placeholder for poetry-dynamic-versioning # any changes to this should not be checked in # version = "0.0.0" description = "DoWhy is a Python library for causal inference that supports explicit modeling and testing of causal assumptions" authors = [ "PyWhy Community <amshar@microsoft.com>" ] maintainers = [] license = "MIT" documentation = "https://py-why.github.io/dowhy" repository = "https://github.com/pywhy/dowhy" classifiers = [ 'Development Status :: 4 - Beta', 'License :: OSI Approved :: MIT License', 'Programming Language :: Python :: 3.8', 'Programming Language :: Python :: 3.9', ] keywords = [ 'causality', 'machine-learning', 'causal-inference', 'statistics', 'graphical-model' ] include = ['docs', 'tests', 'CONTRIBUTING.md', 'LICENSE'] readme = 'README.rst' [tool.poetry-dynamic-versioning] enable = true vcs = "git" [tool.poetry-dynamic-versioning.substitution] files = ["dowhy/__init__.py"] # # Dependency compatibility notes: # * xgboost requires Python >=3.7,<3.11 # * pygraphviz requires Python >=3.8 # * networkx requires Python >= 3.8 # * llvmlite requires Python >=3.6,<3.11 # [tool.poetry.dependencies] python = ">=3.8,<3.10" scipy = "^1.8.1" statsmodels = "^0.13.2" numpy = "^1.23.1" pandas = "^1.4.3" networkx = "^2.8.5" sympy = "^1.10.1" scikit-learn = "1.0.2" pydot = "^1.4.2" joblib = "^1.1.0" # causalml is wired to use llvmlite 0.36 causalml = {version = "^0.12.3", optional = true} llvmlite = {version = "^0.36.0", optional = true} pygraphviz = {version = "^1.9", optional = true} matplotlib = {version = "^3.5.2", optional = true} econml = {version = "*", optional = true} tqdm = "^4.64.0" # # Dependencies for Documentation Generation # rpy2 = {version = "^3.5.2", optional = true} sphinx-multiversion = { git = "https://github.com/petergtz/sphinx-multiversion.git", branch = "override-version-with-refname", optional = true} sphinxcontrib-googleanalytics = { git = "https://github.com/petergtz/googleanalytics.git", branch = "master", optional = true} nbsphinx = {version = "^0.8.9", optional = true} sphinx-rtd-theme = {version = "^1.0.0", optional = true} pydata-sphinx-theme = {version = "^0.9.0", optional = true} pandoc = {version = "^2.2", optional = true} ipykernel = {version = "^6.15.1", optional = true} [tool.poetry.extras] plotting = ["matplotlib"] causalml = ["causalml", "llvmlite"] docs = [ "rpy2", "sphinx-multiversion", "sphinxcontrib-googleanalytics", "nbsphinx", "sphinx-rtd-theme", "pydata-sphinx-theme", "sympy", "ipykernel" ] [tool.poetry.dev-dependencies] poethepoet = "^0.16.0" flake8 = "^4.0.1" black = "^22.6.0" isort = "^5.10.1" pytest = "^7.1.2" twine = "^4.0.1" nbformat = "^5.4.0" jupyter = "^1.0.0" flaky = "^3.7.0" tensorflow = "^2.9.1" keras = "^2.9.0" xgboost = "^1.6.1" mypy = "^0.971" econml = "*" pygraphviz = "^1.9" [build-system] requires = ["poetry-core>=1.0.0", "poetry-dynamic-versioning"] build-backend = "poetry.core.masonry.api" [tool.pytest.ini_options] markers = [ "advanced: not be to run each time. only on package updates." ] [tool.poe.tasks] # stop the build if there are Python syntax errors or undefined names _flake8Errors = "flake8 . --count --select=E9,F63,F7,F82 --show-source --statistics" _flake8Warnings = "flake8 . --count --exit-zero --statistics" _black = 'black .' _isort = 'isort .' # testing tasks test = "pytest -v -m 'not advanced' --durations=0 --durations-min=60.0" test_focused = "pytest -v -m 'focused'" verifyPackage = "twine check dist/*" # TODO: replace with `poetry publish` uploadPackage = "twine upload dist/*" # TODO: add formatting to build process [tool.poe.tasks.format] sequence = ['_black', '_isort'] ignore_fail = 'return_non_zero' [tool.poe.tasks.lint] sequence = ['_flake8Errors', '_flake8Warnings'] ignore_fail = 'return_non_zero' [tool.poe.tasks.verify] sequence = ['lint', 'test'] ignore_fail = "return_non_zero"

[tool.poetry] name = "dowhy" # # 0.0.0 is standard placeholder for poetry-dynamic-versioning # any changes to this should not be checked in # version = "0.0.0" description = "DoWhy is a Python library for causal inference that supports explicit modeling and testing of causal assumptions" authors = [ "PyWhy Community <amshar@microsoft.com>" ] maintainers = [] license = "MIT" documentation = "https://py-why.github.io/dowhy" repository = "https://github.com/pywhy/dowhy" classifiers = [ 'Development Status :: 4 - Beta', 'License :: OSI Approved :: MIT License', 'Programming Language :: Python :: 3.8', 'Programming Language :: Python :: 3.9', ] keywords = [ 'causality', 'machine-learning', 'causal-inference', 'statistics', 'graphical-model' ] include = ['docs', 'tests', 'CONTRIBUTING.md', 'LICENSE'] readme = 'README.rst' [tool.poetry-dynamic-versioning] enable = true vcs = "git" [tool.poetry-dynamic-versioning.substitution] files = ["dowhy/__init__.py"] # # Dependency compatibility notes: # * xgboost requires Python >=3.7,<3.11 # * pygraphviz requires Python >=3.8 # * networkx requires Python >= 3.8 # * llvmlite requires Python >=3.6,<3.11 # [tool.poetry.dependencies] python = ">=3.8,<3.10" scipy = "^1.8.1" statsmodels = "^0.13.2" numpy = "^1.23.1" pandas = "^1.4.3" networkx = "^2.8.5" sympy = "^1.10.1" scikit-learn = "1.0.2" pydot = "^1.4.2" joblib = "^1.1.0" pygraphviz = {version = "^1.9", optional = true} matplotlib = {version = "^3.5.2", optional = true} econml = {version = "*", optional = true} tqdm = "^4.64.0" # # CausalML Extra (causalml is wired to use llvmlite 0.36) # causalml = {version = "^0.12.3", optional = true} llvmlite = {version = "^0.36.0", optional = true} [tool.poetry.extras] plotting = ["matplotlib"] causalml = ["causalml", "llvmlite"] [tool.poetry.dev-dependencies] poethepoet = "^0.16.0" flake8 = "^4.0.1" black = "^22.6.0" isort = "^5.10.1" pytest = "^7.1.2" twine = "^4.0.1" nbformat = "^5.4.0" jupyter = "^1.0.0" flaky = "^3.7.0" tensorflow = "^2.9.1" keras = "^2.9.0" xgboost = "^1.6.1" mypy = "^0.971" econml = "*" pygraphviz = "^1.9" # # Dependencies for Documentation Generation # rpy2 = "^3.5.2" sphinx-multiversion = { git = "https://github.com/petergtz/sphinx-multiversion.git", branch = "override-version-with-refname"} sphinxcontrib-googleanalytics = { git = "https://github.com/petergtz/googleanalytics.git", branch = "master"} nbsphinx = "^0.8.9" sphinx-rtd-theme = "^1.0.0" pydata-sphinx-theme = "^0.9.0" pandoc = "^2.2" ipykernel = "^6.15.1" # # Versions defined for security reasons # # https://github.com/py-why/dowhy/security/dependabot/1 - CVE-2022-34749 nbconvert = {version = "7.0.0rc3", allow-prereleases = true} [build-system] requires = ["poetry-core>=1.0.0", "poetry-dynamic-versioning"] build-backend = "poetry.core.masonry.api" [tool.pytest.ini_options] markers = [ "advanced: not be to run each time. only on package updates." ] [tool.poe.tasks] # stop the build if there are Python syntax errors or undefined names _flake8Errors = "flake8 . --count --select=E9,F63,F7,F82 --show-source --statistics" _flake8Warnings = "flake8 . --count --exit-zero --statistics" _black = 'black .' _isort = 'isort .' # testing tasks test = "pytest -v -m 'not advanced' --durations=0 --durations-min=60.0" test_focused = "pytest -v -m 'focused'" verifyPackage = "twine check dist/*" # TODO: replace with `poetry publish` uploadPackage = "twine upload dist/*" # TODO: add formatting to build process [tool.poe.tasks.format] sequence = ['_black', '_isort'] ignore_fail = 'return_non_zero' [tool.poe.tasks.lint] sequence = ['_flake8Errors', '_flake8Warnings'] ignore_fail = 'return_non_zero' [tool.poe.tasks.verify] sequence = ['lint', 'test'] ignore_fail = "return_non_zero"

darthtrevino

f947d98ffbc9d96b91be9bcfc43cf142fc2c0cd5

eadb99cbe104d89dda62f73e331515df484e8d5a

Those dependencies didn't change, but I grouped them together so it was clear that they were related.

darthtrevino

py-why/dowhy

Use Poetry for Managing Dependencies, Tasks, and Package Builds

This PR includes the [Poetry](https://python-poetry.org/) tool for managing dependencies and packaging the library. This reduces a lot of boilerplate involved in defining and executing sequences of common tasks and with packaging & publishing the library. * Use pytest-xdist; other test updates will be deferred for another PR * Add poetry tasks for lint, build, verifyPackage, etc.. The CI uses these tasks instead of libraries like flake8 and pytest individually. This is useful for local development, and will let us chain tools together easily. * Remove pythonic build plumbing (setup.cfg, setup.py, manifest.in) - as Poetry takes over packaging. * Remove all requirements.txt files, as Poetry takes over dependency management. * Remove versioneer; poetry-dynamic-versioning will apply version substition Signed-off-by: Chris Trevino <chtrevin@microsoft.com>

2022-07-29 20:10:26+00:00

2022-08-13 01:12:53+00:00

.github/workflows/python-package.yml

# This workflow will install Python dependencies, run tests and lint with a variety of Python versions # For more information see: https://help.github.com/actions/language-and-framework-guides/using-python-with-github-actions name: DoWhy CI on: push: branches: [ main ] pull_request: branches: [ main ] jobs: build: runs-on: ubuntu-latest strategy: matrix: python-version: [3.7, 3.8, 3.9] steps: - uses: actions/checkout@v2 - name: Set up Python ${{ matrix.python-version }} uses: actions/setup-python@v2 with: python-version: ${{ matrix.python-version }} - name: Install graphviz run: | sudo apt install graphviz libgraphviz-dev graphviz-dev pkg-config - name: Install dependencies run: | python -m pip install --upgrade pip if [ -f requirements.txt ]; then pip install -r requirements.txt; fi if [ -f requirements-plotting.txt ]; then pip install -r requirements-plotting.txt; fi pip install 'scikit-learn==1.0.2' --force-reinstall if [ -f requirements-test.txt ]; then pip install -r requirements-test.txt --use-deprecated=legacy-resolver; fi pip install 'numpy<=1.21' --force-reinstall - name: Lint with flake8 run: | # stop the build if there are Python syntax errors or undefined names flake8 . --count --select=E9,F63,F7,F82 --show-source --statistics # exit-zero treats all errors as warnings. The GitHub editor is 127 chars wide flake8 . --count --exit-zero --max-complexity=10 --max-line-length=127 --statistics - name: Test with pytest run: | pytest -v -m "not advanced" - name: Check package consistency with twine run: | python setup.py check sdist bdist_wheel twine check dist/*

# This workflow will install Python dependencies, run tests and lint with a variety of Python versions # For more information see: https://help.github.com/actions/language-and-framework-guides/using-python-with-github-actions name: DoWhy CI on: push: branches: [ main ] pull_request: branches: [ main ] jobs: build: runs-on: ubuntu-latest strategy: matrix: python-version: [3.8, 3.9] poetry-version: [1.1.14] steps: - uses: actions/checkout@v2 - name: Set up Python ${{ matrix.python-version }} uses: actions/setup-python@v2 with: python-version: ${{ matrix.python-version }} - name: Install Poetry ${{ matrix.poetry-version }} uses: abatilo/actions-poetry@v2.0.0 with: poetry-version: ${{ matrix.poetry-version }} - name: Install Poetry Dynamic Versioning Plugin run: pip install poetry-dynamic-versioning - name: Install graphviz run: | sudo apt install graphviz libgraphviz-dev graphviz-dev pkg-config - name: Install dependencies run: | python -m pip install --upgrade pip echo "installing poetry dependencies" poetry install -E plotting -E causalml - name: Lint run: poetry run poe lint - name: Test run: poetry run poe test - name: Check package consistency run: | poetry build poetry run poe verifyPackage

darthtrevino

eba2c1cc8217495797f9d5ed34cffe7ed457fe40

2b4832a91e7ab54d31b116d19958fddecc2c8510

Sorry, you might have already commented somewhere, but why is it necessary to remove 3.7?

petergtz

py-why/dowhy

Use Poetry for Managing Dependencies, Tasks, and Package Builds

This PR includes the [Poetry](https://python-poetry.org/) tool for managing dependencies and packaging the library. This reduces a lot of boilerplate involved in defining and executing sequences of common tasks and with packaging & publishing the library. * Use pytest-xdist; other test updates will be deferred for another PR * Add poetry tasks for lint, build, verifyPackage, etc.. The CI uses these tasks instead of libraries like flake8 and pytest individually. This is useful for local development, and will let us chain tools together easily. * Remove pythonic build plumbing (setup.cfg, setup.py, manifest.in) - as Poetry takes over packaging. * Remove all requirements.txt files, as Poetry takes over dependency management. * Remove versioneer; poetry-dynamic-versioning will apply version substition Signed-off-by: Chris Trevino <chtrevin@microsoft.com>

2022-07-29 20:10:26+00:00

2022-08-13 01:12:53+00:00

.github/workflows/python-package.yml

# This workflow will install Python dependencies, run tests and lint with a variety of Python versions # For more information see: https://help.github.com/actions/language-and-framework-guides/using-python-with-github-actions name: DoWhy CI on: push: branches: [ main ] pull_request: branches: [ main ] jobs: build: runs-on: ubuntu-latest strategy: matrix: python-version: [3.7, 3.8, 3.9] steps: - uses: actions/checkout@v2 - name: Set up Python ${{ matrix.python-version }} uses: actions/setup-python@v2 with: python-version: ${{ matrix.python-version }} - name: Install graphviz run: | sudo apt install graphviz libgraphviz-dev graphviz-dev pkg-config - name: Install dependencies run: | python -m pip install --upgrade pip if [ -f requirements.txt ]; then pip install -r requirements.txt; fi if [ -f requirements-plotting.txt ]; then pip install -r requirements-plotting.txt; fi pip install 'scikit-learn==1.0.2' --force-reinstall if [ -f requirements-test.txt ]; then pip install -r requirements-test.txt --use-deprecated=legacy-resolver; fi pip install 'numpy<=1.21' --force-reinstall - name: Lint with flake8 run: | # stop the build if there are Python syntax errors or undefined names flake8 . --count --select=E9,F63,F7,F82 --show-source --statistics # exit-zero treats all errors as warnings. The GitHub editor is 127 chars wide flake8 . --count --exit-zero --max-complexity=10 --max-line-length=127 --statistics - name: Test with pytest run: | pytest -v -m "not advanced" - name: Check package consistency with twine run: | python setup.py check sdist bdist_wheel twine check dist/*

# This workflow will install Python dependencies, run tests and lint with a variety of Python versions # For more information see: https://help.github.com/actions/language-and-framework-guides/using-python-with-github-actions name: DoWhy CI on: push: branches: [ main ] pull_request: branches: [ main ] jobs: build: runs-on: ubuntu-latest strategy: matrix: python-version: [3.8, 3.9] poetry-version: [1.1.14] steps: - uses: actions/checkout@v2 - name: Set up Python ${{ matrix.python-version }} uses: actions/setup-python@v2 with: python-version: ${{ matrix.python-version }} - name: Install Poetry ${{ matrix.poetry-version }} uses: abatilo/actions-poetry@v2.0.0 with: poetry-version: ${{ matrix.poetry-version }} - name: Install Poetry Dynamic Versioning Plugin run: pip install poetry-dynamic-versioning - name: Install graphviz run: | sudo apt install graphviz libgraphviz-dev graphviz-dev pkg-config - name: Install dependencies run: | python -m pip install --upgrade pip echo "installing poetry dependencies" poetry install -E plotting -E causalml - name: Lint run: poetry run poe lint - name: Test run: poetry run poe test - name: Check package consistency run: | poetry build poetry run poe verifyPackage

darthtrevino

eba2c1cc8217495797f9d5ed34cffe7ed457fe40

2b4832a91e7ab54d31b116d19958fddecc2c8510

I tracked my compatibility notes in pyproject.toml here: https://github.com/py-why/dowhy/blob/0bd42158d7aadcd2e4e5c5c9497b1df1c2e0967d/pyproject.toml#L40-L46 Basically, `pygraphviz` and `networkx` - at least recent versions of them - require >= 3.8. Since there's a proposal to extend networkx with causal graphs, it seemed to make sense to stay recent with them.

darthtrevino

py-why/dowhy

Use Poetry for Managing Dependencies, Tasks, and Package Builds

This PR includes the [Poetry](https://python-poetry.org/) tool for managing dependencies and packaging the library. This reduces a lot of boilerplate involved in defining and executing sequences of common tasks and with packaging & publishing the library. * Use pytest-xdist; other test updates will be deferred for another PR * Add poetry tasks for lint, build, verifyPackage, etc.. The CI uses these tasks instead of libraries like flake8 and pytest individually. This is useful for local development, and will let us chain tools together easily. * Remove pythonic build plumbing (setup.cfg, setup.py, manifest.in) - as Poetry takes over packaging. * Remove all requirements.txt files, as Poetry takes over dependency management. * Remove versioneer; poetry-dynamic-versioning will apply version substition Signed-off-by: Chris Trevino <chtrevin@microsoft.com>

2022-07-29 20:10:26+00:00

2022-08-13 01:12:53+00:00

pyproject.toml

[tool.pytest.ini_options] markers = [ "advanced: not be to run each time. only on package updates." ]

[tool.poetry] name = "dowhy" # # 0.0.0 is standard placeholder for poetry-dynamic-versioning # any changes to this should not be checked in # version = "0.0.0" description = "DoWhy is a Python library for causal inference that supports explicit modeling and testing of causal assumptions" authors = [ "PyWhy Community <amshar@microsoft.com>" ] maintainers = [] license = "MIT" documentation = "https://py-why.github.io/dowhy" repository = "https://github.com/pywhy/dowhy" classifiers = [ 'Development Status :: 4 - Beta', 'License :: OSI Approved :: MIT License', 'Programming Language :: Python :: 3.8', 'Programming Language :: Python :: 3.9', ] keywords = [ 'causality', 'machine-learning', 'causal-inference', 'statistics', 'graphical-model' ] include = ['docs', 'tests', 'CONTRIBUTING.md', 'LICENSE'] readme = 'README.rst' [tool.poetry-dynamic-versioning] enable = true vcs = "git" [tool.poetry-dynamic-versioning.substitution] files = ["dowhy/__init__.py"] # # Dependency compatibility notes: # * xgboost requires Python >=3.7,<3.11 # * pygraphviz requires Python >=3.8 # * networkx requires Python >= 3.8 # * llvmlite requires Python >=3.6,<3.11 # [tool.poetry.dependencies] python = ">=3.8,<3.10" scipy = "^1.8.1" statsmodels = "^0.13.2" numpy = "^1.23.1" pandas = "^1.4.3" networkx = "^2.8.5" sympy = "^1.10.1" scikit-learn = "1.0.2" pydot = "^1.4.2" joblib = "^1.1.0" # causalml is wired to use llvmlite 0.36 causalml = {version = "^0.12.3", optional = true} llvmlite = {version = "^0.36.0", optional = true} pygraphviz = {version = "^1.9", optional = true} matplotlib = {version = "^3.5.2", optional = true} econml = {version = "*", optional = true} tqdm = "^4.64.0" # # Dependencies for Documentation Generation # rpy2 = {version = "^3.5.2", optional = true} sphinx-multiversion = { git = "https://github.com/petergtz/sphinx-multiversion.git", branch = "override-version-with-refname", optional = true} sphinxcontrib-googleanalytics = { git = "https://github.com/petergtz/googleanalytics.git", branch = "master", optional = true} nbsphinx = {version = "^0.8.9", optional = true} sphinx-rtd-theme = {version = "^1.0.0", optional = true} pydata-sphinx-theme = {version = "^0.9.0", optional = true} pandoc = {version = "^2.2", optional = true} ipykernel = {version = "^6.15.1", optional = true} [tool.poetry.extras] plotting = ["matplotlib"] causalml = ["causalml", "llvmlite"] docs = [ "rpy2", "sphinx-multiversion", "sphinxcontrib-googleanalytics", "nbsphinx", "sphinx-rtd-theme", "pydata-sphinx-theme", "sympy", "ipykernel" ] [tool.poetry.dev-dependencies] poethepoet = "^0.16.0" flake8 = "^4.0.1" black = "^22.6.0" isort = "^5.10.1" pytest = "^7.1.2" twine = "^4.0.1" nbformat = "^5.4.0" jupyter = "^1.0.0" flaky = "^3.7.0" tensorflow = "^2.9.1" keras = "^2.9.0" xgboost = "^1.6.1" mypy = "^0.971" econml = "*" pygraphviz = "^1.9" [build-system] requires = ["poetry-core>=1.0.0", "poetry-dynamic-versioning"] build-backend = "poetry.core.masonry.api" [tool.pytest.ini_options] markers = [ "advanced: not be to run each time. only on package updates." ] [tool.poe.tasks] # stop the build if there are Python syntax errors or undefined names _flake8Errors = "flake8 . --count --select=E9,F63,F7,F82 --show-source --statistics" _flake8Warnings = "flake8 . --count --exit-zero --statistics" _black = 'black .' _isort = 'isort .' # testing tasks test = "pytest -v -m 'not advanced' --durations=0 --durations-min=60.0" test_focused = "pytest -v -m 'focused'" verifyPackage = "twine check dist/*" # TODO: replace with `poetry publish` uploadPackage = "twine upload dist/*" # TODO: add formatting to build process [tool.poe.tasks.format] sequence = ['_black', '_isort'] ignore_fail = 'return_non_zero' [tool.poe.tasks.lint] sequence = ['_flake8Errors', '_flake8Warnings'] ignore_fail = 'return_non_zero' [tool.poe.tasks.verify] sequence = ['lint', 'test'] ignore_fail = "return_non_zero"

darthtrevino

eba2c1cc8217495797f9d5ed34cffe7ed457fe40

2b4832a91e7ab54d31b116d19958fddecc2c8510

should we include the LICENSE file here?

amit-sharma

py-why/dowhy

Use Poetry for Managing Dependencies, Tasks, and Package Builds

This PR includes the [Poetry](https://python-poetry.org/) tool for managing dependencies and packaging the library. This reduces a lot of boilerplate involved in defining and executing sequences of common tasks and with packaging & publishing the library. * Use pytest-xdist; other test updates will be deferred for another PR * Add poetry tasks for lint, build, verifyPackage, etc.. The CI uses these tasks instead of libraries like flake8 and pytest individually. This is useful for local development, and will let us chain tools together easily. * Remove pythonic build plumbing (setup.cfg, setup.py, manifest.in) - as Poetry takes over packaging. * Remove all requirements.txt files, as Poetry takes over dependency management. * Remove versioneer; poetry-dynamic-versioning will apply version substition Signed-off-by: Chris Trevino <chtrevin@microsoft.com>

2022-07-29 20:10:26+00:00

2022-08-13 01:12:53+00:00

pyproject.toml

[tool.pytest.ini_options] markers = [ "advanced: not be to run each time. only on package updates." ]

[tool.poetry] name = "dowhy" # # 0.0.0 is standard placeholder for poetry-dynamic-versioning # any changes to this should not be checked in # version = "0.0.0" description = "DoWhy is a Python library for causal inference that supports explicit modeling and testing of causal assumptions" authors = [ "PyWhy Community <amshar@microsoft.com>" ] maintainers = [] license = "MIT" documentation = "https://py-why.github.io/dowhy" repository = "https://github.com/pywhy/dowhy" classifiers = [ 'Development Status :: 4 - Beta', 'License :: OSI Approved :: MIT License', 'Programming Language :: Python :: 3.8', 'Programming Language :: Python :: 3.9', ] keywords = [ 'causality', 'machine-learning', 'causal-inference', 'statistics', 'graphical-model' ] include = ['docs', 'tests', 'CONTRIBUTING.md', 'LICENSE'] readme = 'README.rst' [tool.poetry-dynamic-versioning] enable = true vcs = "git" [tool.poetry-dynamic-versioning.substitution] files = ["dowhy/__init__.py"] # # Dependency compatibility notes: # * xgboost requires Python >=3.7,<3.11 # * pygraphviz requires Python >=3.8 # * networkx requires Python >= 3.8 # * llvmlite requires Python >=3.6,<3.11 # [tool.poetry.dependencies] python = ">=3.8,<3.10" scipy = "^1.8.1" statsmodels = "^0.13.2" numpy = "^1.23.1" pandas = "^1.4.3" networkx = "^2.8.5" sympy = "^1.10.1" scikit-learn = "1.0.2" pydot = "^1.4.2" joblib = "^1.1.0" # causalml is wired to use llvmlite 0.36 causalml = {version = "^0.12.3", optional = true} llvmlite = {version = "^0.36.0", optional = true} pygraphviz = {version = "^1.9", optional = true} matplotlib = {version = "^3.5.2", optional = true} econml = {version = "*", optional = true} tqdm = "^4.64.0" # # Dependencies for Documentation Generation # rpy2 = {version = "^3.5.2", optional = true} sphinx-multiversion = { git = "https://github.com/petergtz/sphinx-multiversion.git", branch = "override-version-with-refname", optional = true} sphinxcontrib-googleanalytics = { git = "https://github.com/petergtz/googleanalytics.git", branch = "master", optional = true} nbsphinx = {version = "^0.8.9", optional = true} sphinx-rtd-theme = {version = "^1.0.0", optional = true} pydata-sphinx-theme = {version = "^0.9.0", optional = true} pandoc = {version = "^2.2", optional = true} ipykernel = {version = "^6.15.1", optional = true} [tool.poetry.extras] plotting = ["matplotlib"] causalml = ["causalml", "llvmlite"] docs = [ "rpy2", "sphinx-multiversion", "sphinxcontrib-googleanalytics", "nbsphinx", "sphinx-rtd-theme", "pydata-sphinx-theme", "sympy", "ipykernel" ] [tool.poetry.dev-dependencies] poethepoet = "^0.16.0" flake8 = "^4.0.1" black = "^22.6.0" isort = "^5.10.1" pytest = "^7.1.2" twine = "^4.0.1" nbformat = "^5.4.0" jupyter = "^1.0.0" flaky = "^3.7.0" tensorflow = "^2.9.1" keras = "^2.9.0" xgboost = "^1.6.1" mypy = "^0.971" econml = "*" pygraphviz = "^1.9" [build-system] requires = ["poetry-core>=1.0.0", "poetry-dynamic-versioning"] build-backend = "poetry.core.masonry.api" [tool.pytest.ini_options] markers = [ "advanced: not be to run each time. only on package updates." ] [tool.poe.tasks] # stop the build if there are Python syntax errors or undefined names _flake8Errors = "flake8 . --count --select=E9,F63,F7,F82 --show-source --statistics" _flake8Warnings = "flake8 . --count --exit-zero --statistics" _black = 'black .' _isort = 'isort .' # testing tasks test = "pytest -v -m 'not advanced' --durations=0 --durations-min=60.0" test_focused = "pytest -v -m 'focused'" verifyPackage = "twine check dist/*" # TODO: replace with `poetry publish` uploadPackage = "twine upload dist/*" # TODO: add formatting to build process [tool.poe.tasks.format] sequence = ['_black', '_isort'] ignore_fail = 'return_non_zero' [tool.poe.tasks.lint] sequence = ['_flake8Errors', '_flake8Warnings'] ignore_fail = 'return_non_zero' [tool.poe.tasks.verify] sequence = ['lint', 'test'] ignore_fail = "return_non_zero"

darthtrevino

eba2c1cc8217495797f9d5ed34cffe7ed457fe40

2b4832a91e7ab54d31b116d19958fddecc2c8510

curious: why do we need to convert this notebook to html?

amit-sharma

py-why/dowhy

Use Poetry for Managing Dependencies, Tasks, and Package Builds

This PR includes the [Poetry](https://python-poetry.org/) tool for managing dependencies and packaging the library. This reduces a lot of boilerplate involved in defining and executing sequences of common tasks and with packaging & publishing the library. * Use pytest-xdist; other test updates will be deferred for another PR * Add poetry tasks for lint, build, verifyPackage, etc.. The CI uses these tasks instead of libraries like flake8 and pytest individually. This is useful for local development, and will let us chain tools together easily. * Remove pythonic build plumbing (setup.cfg, setup.py, manifest.in) - as Poetry takes over packaging. * Remove all requirements.txt files, as Poetry takes over dependency management. * Remove versioneer; poetry-dynamic-versioning will apply version substition Signed-off-by: Chris Trevino <chtrevin@microsoft.com>

2022-07-29 20:10:26+00:00

2022-08-13 01:12:53+00:00

pyproject.toml

[tool.pytest.ini_options] markers = [ "advanced: not be to run each time. only on package updates." ]

[tool.poetry] name = "dowhy" # # 0.0.0 is standard placeholder for poetry-dynamic-versioning # any changes to this should not be checked in # version = "0.0.0" description = "DoWhy is a Python library for causal inference that supports explicit modeling and testing of causal assumptions" authors = [ "PyWhy Community <amshar@microsoft.com>" ] maintainers = [] license = "MIT" documentation = "https://py-why.github.io/dowhy" repository = "https://github.com/pywhy/dowhy" classifiers = [ 'Development Status :: 4 - Beta', 'License :: OSI Approved :: MIT License', 'Programming Language :: Python :: 3.8', 'Programming Language :: Python :: 3.9', ] keywords = [ 'causality', 'machine-learning', 'causal-inference', 'statistics', 'graphical-model' ] include = ['docs', 'tests', 'CONTRIBUTING.md', 'LICENSE'] readme = 'README.rst' [tool.poetry-dynamic-versioning] enable = true vcs = "git" [tool.poetry-dynamic-versioning.substitution] files = ["dowhy/__init__.py"] # # Dependency compatibility notes: # * xgboost requires Python >=3.7,<3.11 # * pygraphviz requires Python >=3.8 # * networkx requires Python >= 3.8 # * llvmlite requires Python >=3.6,<3.11 # [tool.poetry.dependencies] python = ">=3.8,<3.10" scipy = "^1.8.1" statsmodels = "^0.13.2" numpy = "^1.23.1" pandas = "^1.4.3" networkx = "^2.8.5" sympy = "^1.10.1" scikit-learn = "1.0.2" pydot = "^1.4.2" joblib = "^1.1.0" # causalml is wired to use llvmlite 0.36 causalml = {version = "^0.12.3", optional = true} llvmlite = {version = "^0.36.0", optional = true} pygraphviz = {version = "^1.9", optional = true} matplotlib = {version = "^3.5.2", optional = true} econml = {version = "*", optional = true} tqdm = "^4.64.0" # # Dependencies for Documentation Generation # rpy2 = {version = "^3.5.2", optional = true} sphinx-multiversion = { git = "https://github.com/petergtz/sphinx-multiversion.git", branch = "override-version-with-refname", optional = true} sphinxcontrib-googleanalytics = { git = "https://github.com/petergtz/googleanalytics.git", branch = "master", optional = true} nbsphinx = {version = "^0.8.9", optional = true} sphinx-rtd-theme = {version = "^1.0.0", optional = true} pydata-sphinx-theme = {version = "^0.9.0", optional = true} pandoc = {version = "^2.2", optional = true} ipykernel = {version = "^6.15.1", optional = true} [tool.poetry.extras] plotting = ["matplotlib"] causalml = ["causalml", "llvmlite"] docs = [ "rpy2", "sphinx-multiversion", "sphinxcontrib-googleanalytics", "nbsphinx", "sphinx-rtd-theme", "pydata-sphinx-theme", "sympy", "ipykernel" ] [tool.poetry.dev-dependencies] poethepoet = "^0.16.0" flake8 = "^4.0.1" black = "^22.6.0" isort = "^5.10.1" pytest = "^7.1.2" twine = "^4.0.1" nbformat = "^5.4.0" jupyter = "^1.0.0" flaky = "^3.7.0" tensorflow = "^2.9.1" keras = "^2.9.0" xgboost = "^1.6.1" mypy = "^0.971" econml = "*" pygraphviz = "^1.9" [build-system] requires = ["poetry-core>=1.0.0", "poetry-dynamic-versioning"] build-backend = "poetry.core.masonry.api" [tool.pytest.ini_options] markers = [ "advanced: not be to run each time. only on package updates." ] [tool.poe.tasks] # stop the build if there are Python syntax errors or undefined names _flake8Errors = "flake8 . --count --select=E9,F63,F7,F82 --show-source --statistics" _flake8Warnings = "flake8 . --count --exit-zero --statistics" _black = 'black .' _isort = 'isort .' # testing tasks test = "pytest -v -m 'not advanced' --durations=0 --durations-min=60.0" test_focused = "pytest -v -m 'focused'" verifyPackage = "twine check dist/*" # TODO: replace with `poetry publish` uploadPackage = "twine upload dist/*" # TODO: add formatting to build process [tool.poe.tasks.format] sequence = ['_black', '_isort'] ignore_fail = 'return_non_zero' [tool.poe.tasks.lint] sequence = ['_flake8Errors', '_flake8Warnings'] ignore_fail = 'return_non_zero' [tool.poe.tasks.verify] sequence = ['lint', 'test'] ignore_fail = "return_non_zero"

darthtrevino

eba2c1cc8217495797f9d5ed34cffe7ed457fe40

2b4832a91e7ab54d31b116d19958fddecc2c8510

should we put llmvlite as a dev-dependency? It is not used by dowhy, but only relevant if someone is using causalml. Another option is to mark it as an optional dependency.

amit-sharma

py-why/dowhy

Use Poetry for Managing Dependencies, Tasks, and Package Builds

This PR includes the [Poetry](https://python-poetry.org/) tool for managing dependencies and packaging the library. This reduces a lot of boilerplate involved in defining and executing sequences of common tasks and with packaging & publishing the library. * Use pytest-xdist; other test updates will be deferred for another PR * Add poetry tasks for lint, build, verifyPackage, etc.. The CI uses these tasks instead of libraries like flake8 and pytest individually. This is useful for local development, and will let us chain tools together easily. * Remove pythonic build plumbing (setup.cfg, setup.py, manifest.in) - as Poetry takes over packaging. * Remove all requirements.txt files, as Poetry takes over dependency management. * Remove versioneer; poetry-dynamic-versioning will apply version substition Signed-off-by: Chris Trevino <chtrevin@microsoft.com>

2022-07-29 20:10:26+00:00

2022-08-13 01:12:53+00:00

pyproject.toml

[tool.pytest.ini_options] markers = [ "advanced: not be to run each time. only on package updates." ]

[tool.poetry] name = "dowhy" # # 0.0.0 is standard placeholder for poetry-dynamic-versioning # any changes to this should not be checked in # version = "0.0.0" description = "DoWhy is a Python library for causal inference that supports explicit modeling and testing of causal assumptions" authors = [ "PyWhy Community <amshar@microsoft.com>" ] maintainers = [] license = "MIT" documentation = "https://py-why.github.io/dowhy" repository = "https://github.com/pywhy/dowhy" classifiers = [ 'Development Status :: 4 - Beta', 'License :: OSI Approved :: MIT License', 'Programming Language :: Python :: 3.8', 'Programming Language :: Python :: 3.9', ] keywords = [ 'causality', 'machine-learning', 'causal-inference', 'statistics', 'graphical-model' ] include = ['docs', 'tests', 'CONTRIBUTING.md', 'LICENSE'] readme = 'README.rst' [tool.poetry-dynamic-versioning] enable = true vcs = "git" [tool.poetry-dynamic-versioning.substitution] files = ["dowhy/__init__.py"] # # Dependency compatibility notes: # * xgboost requires Python >=3.7,<3.11 # * pygraphviz requires Python >=3.8 # * networkx requires Python >= 3.8 # * llvmlite requires Python >=3.6,<3.11 # [tool.poetry.dependencies] python = ">=3.8,<3.10" scipy = "^1.8.1" statsmodels = "^0.13.2" numpy = "^1.23.1" pandas = "^1.4.3" networkx = "^2.8.5" sympy = "^1.10.1" scikit-learn = "1.0.2" pydot = "^1.4.2" joblib = "^1.1.0" # causalml is wired to use llvmlite 0.36 causalml = {version = "^0.12.3", optional = true} llvmlite = {version = "^0.36.0", optional = true} pygraphviz = {version = "^1.9", optional = true} matplotlib = {version = "^3.5.2", optional = true} econml = {version = "*", optional = true} tqdm = "^4.64.0" # # Dependencies for Documentation Generation # rpy2 = {version = "^3.5.2", optional = true} sphinx-multiversion = { git = "https://github.com/petergtz/sphinx-multiversion.git", branch = "override-version-with-refname", optional = true} sphinxcontrib-googleanalytics = { git = "https://github.com/petergtz/googleanalytics.git", branch = "master", optional = true} nbsphinx = {version = "^0.8.9", optional = true} sphinx-rtd-theme = {version = "^1.0.0", optional = true} pydata-sphinx-theme = {version = "^0.9.0", optional = true} pandoc = {version = "^2.2", optional = true} ipykernel = {version = "^6.15.1", optional = true} [tool.poetry.extras] plotting = ["matplotlib"] causalml = ["causalml", "llvmlite"] docs = [ "rpy2", "sphinx-multiversion", "sphinxcontrib-googleanalytics", "nbsphinx", "sphinx-rtd-theme", "pydata-sphinx-theme", "sympy", "ipykernel" ] [tool.poetry.dev-dependencies] poethepoet = "^0.16.0" flake8 = "^4.0.1" black = "^22.6.0" isort = "^5.10.1" pytest = "^7.1.2" twine = "^4.0.1" nbformat = "^5.4.0" jupyter = "^1.0.0" flaky = "^3.7.0" tensorflow = "^2.9.1" keras = "^2.9.0" xgboost = "^1.6.1" mypy = "^0.971" econml = "*" pygraphviz = "^1.9" [build-system] requires = ["poetry-core>=1.0.0", "poetry-dynamic-versioning"] build-backend = "poetry.core.masonry.api" [tool.pytest.ini_options] markers = [ "advanced: not be to run each time. only on package updates." ] [tool.poe.tasks] # stop the build if there are Python syntax errors or undefined names _flake8Errors = "flake8 . --count --select=E9,F63,F7,F82 --show-source --statistics" _flake8Warnings = "flake8 . --count --exit-zero --statistics" _black = 'black .' _isort = 'isort .' # testing tasks test = "pytest -v -m 'not advanced' --durations=0 --durations-min=60.0" test_focused = "pytest -v -m 'focused'" verifyPackage = "twine check dist/*" # TODO: replace with `poetry publish` uploadPackage = "twine upload dist/*" # TODO: add formatting to build process [tool.poe.tasks.format] sequence = ['_black', '_isort'] ignore_fail = 'return_non_zero' [tool.poe.tasks.lint] sequence = ['_flake8Errors', '_flake8Warnings'] ignore_fail = 'return_non_zero' [tool.poe.tasks.verify] sequence = ['lint', 'test'] ignore_fail = "return_non_zero"

darthtrevino

eba2c1cc8217495797f9d5ed34cffe7ed457fe40

2b4832a91e7ab54d31b116d19958fddecc2c8510

Honestly I just moved this script over from the makefile. I'm not sure if it was part of your workflow for some reason

darthtrevino

py-why/dowhy

Use Poetry for Managing Dependencies, Tasks, and Package Builds

This PR includes the [Poetry](https://python-poetry.org/) tool for managing dependencies and packaging the library. This reduces a lot of boilerplate involved in defining and executing sequences of common tasks and with packaging & publishing the library. * Use pytest-xdist; other test updates will be deferred for another PR * Add poetry tasks for lint, build, verifyPackage, etc.. The CI uses these tasks instead of libraries like flake8 and pytest individually. This is useful for local development, and will let us chain tools together easily. * Remove pythonic build plumbing (setup.cfg, setup.py, manifest.in) - as Poetry takes over packaging. * Remove all requirements.txt files, as Poetry takes over dependency management. * Remove versioneer; poetry-dynamic-versioning will apply version substition Signed-off-by: Chris Trevino <chtrevin@microsoft.com>

2022-07-29 20:10:26+00:00

2022-08-13 01:12:53+00:00

pyproject.toml

[tool.pytest.ini_options] markers = [ "advanced: not be to run each time. only on package updates." ]

[tool.poetry] name = "dowhy" # # 0.0.0 is standard placeholder for poetry-dynamic-versioning # any changes to this should not be checked in # version = "0.0.0" description = "DoWhy is a Python library for causal inference that supports explicit modeling and testing of causal assumptions" authors = [ "PyWhy Community <amshar@microsoft.com>" ] maintainers = [] license = "MIT" documentation = "https://py-why.github.io/dowhy" repository = "https://github.com/pywhy/dowhy" classifiers = [ 'Development Status :: 4 - Beta', 'License :: OSI Approved :: MIT License', 'Programming Language :: Python :: 3.8', 'Programming Language :: Python :: 3.9', ] keywords = [ 'causality', 'machine-learning', 'causal-inference', 'statistics', 'graphical-model' ] include = ['docs', 'tests', 'CONTRIBUTING.md', 'LICENSE'] readme = 'README.rst' [tool.poetry-dynamic-versioning] enable = true vcs = "git" [tool.poetry-dynamic-versioning.substitution] files = ["dowhy/__init__.py"] # # Dependency compatibility notes: # * xgboost requires Python >=3.7,<3.11 # * pygraphviz requires Python >=3.8 # * networkx requires Python >= 3.8 # * llvmlite requires Python >=3.6,<3.11 # [tool.poetry.dependencies] python = ">=3.8,<3.10" scipy = "^1.8.1" statsmodels = "^0.13.2" numpy = "^1.23.1" pandas = "^1.4.3" networkx = "^2.8.5" sympy = "^1.10.1" scikit-learn = "1.0.2" pydot = "^1.4.2" joblib = "^1.1.0" # causalml is wired to use llvmlite 0.36 causalml = {version = "^0.12.3", optional = true} llvmlite = {version = "^0.36.0", optional = true} pygraphviz = {version = "^1.9", optional = true} matplotlib = {version = "^3.5.2", optional = true} econml = {version = "*", optional = true} tqdm = "^4.64.0" # # Dependencies for Documentation Generation # rpy2 = {version = "^3.5.2", optional = true} sphinx-multiversion = { git = "https://github.com/petergtz/sphinx-multiversion.git", branch = "override-version-with-refname", optional = true} sphinxcontrib-googleanalytics = { git = "https://github.com/petergtz/googleanalytics.git", branch = "master", optional = true} nbsphinx = {version = "^0.8.9", optional = true} sphinx-rtd-theme = {version = "^1.0.0", optional = true} pydata-sphinx-theme = {version = "^0.9.0", optional = true} pandoc = {version = "^2.2", optional = true} ipykernel = {version = "^6.15.1", optional = true} [tool.poetry.extras] plotting = ["matplotlib"] causalml = ["causalml", "llvmlite"] docs = [ "rpy2", "sphinx-multiversion", "sphinxcontrib-googleanalytics", "nbsphinx", "sphinx-rtd-theme", "pydata-sphinx-theme", "sympy", "ipykernel" ] [tool.poetry.dev-dependencies] poethepoet = "^0.16.0" flake8 = "^4.0.1" black = "^22.6.0" isort = "^5.10.1" pytest = "^7.1.2" twine = "^4.0.1" nbformat = "^5.4.0" jupyter = "^1.0.0" flaky = "^3.7.0" tensorflow = "^2.9.1" keras = "^2.9.0" xgboost = "^1.6.1" mypy = "^0.971" econml = "*" pygraphviz = "^1.9" [build-system] requires = ["poetry-core>=1.0.0", "poetry-dynamic-versioning"] build-backend = "poetry.core.masonry.api" [tool.pytest.ini_options] markers = [ "advanced: not be to run each time. only on package updates." ] [tool.poe.tasks] # stop the build if there are Python syntax errors or undefined names _flake8Errors = "flake8 . --count --select=E9,F63,F7,F82 --show-source --statistics" _flake8Warnings = "flake8 . --count --exit-zero --statistics" _black = 'black .' _isort = 'isort .' # testing tasks test = "pytest -v -m 'not advanced' --durations=0 --durations-min=60.0" test_focused = "pytest -v -m 'focused'" verifyPackage = "twine check dist/*" # TODO: replace with `poetry publish` uploadPackage = "twine upload dist/*" # TODO: add formatting to build process [tool.poe.tasks.format] sequence = ['_black', '_isort'] ignore_fail = 'return_non_zero' [tool.poe.tasks.lint] sequence = ['_flake8Errors', '_flake8Warnings'] ignore_fail = 'return_non_zero' [tool.poe.tasks.verify] sequence = ['lint', 'test'] ignore_fail = "return_non_zero"

darthtrevino

eba2c1cc8217495797f9d5ed34cffe7ed457fe40

2b4832a91e7ab54d31b116d19958fddecc2c8510

There's a license field above, which I think covers it

darthtrevino

py-why/dowhy

Use Poetry for Managing Dependencies, Tasks, and Package Builds

This PR includes the [Poetry](https://python-poetry.org/) tool for managing dependencies and packaging the library. This reduces a lot of boilerplate involved in defining and executing sequences of common tasks and with packaging & publishing the library. * Use pytest-xdist; other test updates will be deferred for another PR * Add poetry tasks for lint, build, verifyPackage, etc.. The CI uses these tasks instead of libraries like flake8 and pytest individually. This is useful for local development, and will let us chain tools together easily. * Remove pythonic build plumbing (setup.cfg, setup.py, manifest.in) - as Poetry takes over packaging. * Remove all requirements.txt files, as Poetry takes over dependency management. * Remove versioneer; poetry-dynamic-versioning will apply version substition Signed-off-by: Chris Trevino <chtrevin@microsoft.com>

2022-07-29 20:10:26+00:00

2022-08-13 01:12:53+00:00

pyproject.toml

[tool.pytest.ini_options] markers = [ "advanced: not be to run each time. only on package updates." ]

[tool.poetry] name = "dowhy" # # 0.0.0 is standard placeholder for poetry-dynamic-versioning # any changes to this should not be checked in # version = "0.0.0" description = "DoWhy is a Python library for causal inference that supports explicit modeling and testing of causal assumptions" authors = [ "PyWhy Community <amshar@microsoft.com>" ] maintainers = [] license = "MIT" documentation = "https://py-why.github.io/dowhy" repository = "https://github.com/pywhy/dowhy" classifiers = [ 'Development Status :: 4 - Beta', 'License :: OSI Approved :: MIT License', 'Programming Language :: Python :: 3.8', 'Programming Language :: Python :: 3.9', ] keywords = [ 'causality', 'machine-learning', 'causal-inference', 'statistics', 'graphical-model' ] include = ['docs', 'tests', 'CONTRIBUTING.md', 'LICENSE'] readme = 'README.rst' [tool.poetry-dynamic-versioning] enable = true vcs = "git" [tool.poetry-dynamic-versioning.substitution] files = ["dowhy/__init__.py"] # # Dependency compatibility notes: # * xgboost requires Python >=3.7,<3.11 # * pygraphviz requires Python >=3.8 # * networkx requires Python >= 3.8 # * llvmlite requires Python >=3.6,<3.11 # [tool.poetry.dependencies] python = ">=3.8,<3.10" scipy = "^1.8.1" statsmodels = "^0.13.2" numpy = "^1.23.1" pandas = "^1.4.3" networkx = "^2.8.5" sympy = "^1.10.1" scikit-learn = "1.0.2" pydot = "^1.4.2" joblib = "^1.1.0" # causalml is wired to use llvmlite 0.36 causalml = {version = "^0.12.3", optional = true} llvmlite = {version = "^0.36.0", optional = true} pygraphviz = {version = "^1.9", optional = true} matplotlib = {version = "^3.5.2", optional = true} econml = {version = "*", optional = true} tqdm = "^4.64.0" # # Dependencies for Documentation Generation # rpy2 = {version = "^3.5.2", optional = true} sphinx-multiversion = { git = "https://github.com/petergtz/sphinx-multiversion.git", branch = "override-version-with-refname", optional = true} sphinxcontrib-googleanalytics = { git = "https://github.com/petergtz/googleanalytics.git", branch = "master", optional = true} nbsphinx = {version = "^0.8.9", optional = true} sphinx-rtd-theme = {version = "^1.0.0", optional = true} pydata-sphinx-theme = {version = "^0.9.0", optional = true} pandoc = {version = "^2.2", optional = true} ipykernel = {version = "^6.15.1", optional = true} [tool.poetry.extras] plotting = ["matplotlib"] causalml = ["causalml", "llvmlite"] docs = [ "rpy2", "sphinx-multiversion", "sphinxcontrib-googleanalytics", "nbsphinx", "sphinx-rtd-theme", "pydata-sphinx-theme", "sympy", "ipykernel" ] [tool.poetry.dev-dependencies] poethepoet = "^0.16.0" flake8 = "^4.0.1" black = "^22.6.0" isort = "^5.10.1" pytest = "^7.1.2" twine = "^4.0.1" nbformat = "^5.4.0" jupyter = "^1.0.0" flaky = "^3.7.0" tensorflow = "^2.9.1" keras = "^2.9.0" xgboost = "^1.6.1" mypy = "^0.971" econml = "*" pygraphviz = "^1.9" [build-system] requires = ["poetry-core>=1.0.0", "poetry-dynamic-versioning"] build-backend = "poetry.core.masonry.api" [tool.pytest.ini_options] markers = [ "advanced: not be to run each time. only on package updates." ] [tool.poe.tasks] # stop the build if there are Python syntax errors or undefined names _flake8Errors = "flake8 . --count --select=E9,F63,F7,F82 --show-source --statistics" _flake8Warnings = "flake8 . --count --exit-zero --statistics" _black = 'black .' _isort = 'isort .' # testing tasks test = "pytest -v -m 'not advanced' --durations=0 --durations-min=60.0" test_focused = "pytest -v -m 'focused'" verifyPackage = "twine check dist/*" # TODO: replace with `poetry publish` uploadPackage = "twine upload dist/*" # TODO: add formatting to build process [tool.poe.tasks.format] sequence = ['_black', '_isort'] ignore_fail = 'return_non_zero' [tool.poe.tasks.lint] sequence = ['_flake8Errors', '_flake8Warnings'] ignore_fail = 'return_non_zero' [tool.poe.tasks.verify] sequence = ['lint', 'test'] ignore_fail = "return_non_zero"

darthtrevino

eba2c1cc8217495797f9d5ed34cffe7ed457fe40

2b4832a91e7ab54d31b116d19958fddecc2c8510

I can do that; if it's optional we would probably add it as a devDep and mark it as optional in the main deps. Should causalml be optional as well?

darthtrevino

py-why/dowhy

Use Poetry for Managing Dependencies, Tasks, and Package Builds

This PR includes the [Poetry](https://python-poetry.org/) tool for managing dependencies and packaging the library. This reduces a lot of boilerplate involved in defining and executing sequences of common tasks and with packaging & publishing the library. * Use pytest-xdist; other test updates will be deferred for another PR * Add poetry tasks for lint, build, verifyPackage, etc.. The CI uses these tasks instead of libraries like flake8 and pytest individually. This is useful for local development, and will let us chain tools together easily. * Remove pythonic build plumbing (setup.cfg, setup.py, manifest.in) - as Poetry takes over packaging. * Remove all requirements.txt files, as Poetry takes over dependency management. * Remove versioneer; poetry-dynamic-versioning will apply version substition Signed-off-by: Chris Trevino <chtrevin@microsoft.com>

2022-07-29 20:10:26+00:00

2022-08-13 01:12:53+00:00

pyproject.toml

[tool.pytest.ini_options] markers = [ "advanced: not be to run each time. only on package updates." ]

[tool.poetry] name = "dowhy" # # 0.0.0 is standard placeholder for poetry-dynamic-versioning # any changes to this should not be checked in # version = "0.0.0" description = "DoWhy is a Python library for causal inference that supports explicit modeling and testing of causal assumptions" authors = [ "PyWhy Community <amshar@microsoft.com>" ] maintainers = [] license = "MIT" documentation = "https://py-why.github.io/dowhy" repository = "https://github.com/pywhy/dowhy" classifiers = [ 'Development Status :: 4 - Beta', 'License :: OSI Approved :: MIT License', 'Programming Language :: Python :: 3.8', 'Programming Language :: Python :: 3.9', ] keywords = [ 'causality', 'machine-learning', 'causal-inference', 'statistics', 'graphical-model' ] include = ['docs', 'tests', 'CONTRIBUTING.md', 'LICENSE'] readme = 'README.rst' [tool.poetry-dynamic-versioning] enable = true vcs = "git" [tool.poetry-dynamic-versioning.substitution] files = ["dowhy/__init__.py"] # # Dependency compatibility notes: # * xgboost requires Python >=3.7,<3.11 # * pygraphviz requires Python >=3.8 # * networkx requires Python >= 3.8 # * llvmlite requires Python >=3.6,<3.11 # [tool.poetry.dependencies] python = ">=3.8,<3.10" scipy = "^1.8.1" statsmodels = "^0.13.2" numpy = "^1.23.1" pandas = "^1.4.3" networkx = "^2.8.5" sympy = "^1.10.1" scikit-learn = "1.0.2" pydot = "^1.4.2" joblib = "^1.1.0" # causalml is wired to use llvmlite 0.36 causalml = {version = "^0.12.3", optional = true} llvmlite = {version = "^0.36.0", optional = true} pygraphviz = {version = "^1.9", optional = true} matplotlib = {version = "^3.5.2", optional = true} econml = {version = "*", optional = true} tqdm = "^4.64.0" # # Dependencies for Documentation Generation # rpy2 = {version = "^3.5.2", optional = true} sphinx-multiversion = { git = "https://github.com/petergtz/sphinx-multiversion.git", branch = "override-version-with-refname", optional = true} sphinxcontrib-googleanalytics = { git = "https://github.com/petergtz/googleanalytics.git", branch = "master", optional = true} nbsphinx = {version = "^0.8.9", optional = true} sphinx-rtd-theme = {version = "^1.0.0", optional = true} pydata-sphinx-theme = {version = "^0.9.0", optional = true} pandoc = {version = "^2.2", optional = true} ipykernel = {version = "^6.15.1", optional = true} [tool.poetry.extras] plotting = ["matplotlib"] causalml = ["causalml", "llvmlite"] docs = [ "rpy2", "sphinx-multiversion", "sphinxcontrib-googleanalytics", "nbsphinx", "sphinx-rtd-theme", "pydata-sphinx-theme", "sympy", "ipykernel" ] [tool.poetry.dev-dependencies] poethepoet = "^0.16.0" flake8 = "^4.0.1" black = "^22.6.0" isort = "^5.10.1" pytest = "^7.1.2" twine = "^4.0.1" nbformat = "^5.4.0" jupyter = "^1.0.0" flaky = "^3.7.0" tensorflow = "^2.9.1" keras = "^2.9.0" xgboost = "^1.6.1" mypy = "^0.971" econml = "*" pygraphviz = "^1.9" [build-system] requires = ["poetry-core>=1.0.0", "poetry-dynamic-versioning"] build-backend = "poetry.core.masonry.api" [tool.pytest.ini_options] markers = [ "advanced: not be to run each time. only on package updates." ] [tool.poe.tasks] # stop the build if there are Python syntax errors or undefined names _flake8Errors = "flake8 . --count --select=E9,F63,F7,F82 --show-source --statistics" _flake8Warnings = "flake8 . --count --exit-zero --statistics" _black = 'black .' _isort = 'isort .' # testing tasks test = "pytest -v -m 'not advanced' --durations=0 --durations-min=60.0" test_focused = "pytest -v -m 'focused'" verifyPackage = "twine check dist/*" # TODO: replace with `poetry publish` uploadPackage = "twine upload dist/*" # TODO: add formatting to build process [tool.poe.tasks.format] sequence = ['_black', '_isort'] ignore_fail = 'return_non_zero' [tool.poe.tasks.lint] sequence = ['_flake8Errors', '_flake8Warnings'] ignore_fail = 'return_non_zero' [tool.poe.tasks.verify] sequence = ['lint', 'test'] ignore_fail = "return_non_zero"

darthtrevino

eba2c1cc8217495797f9d5ed34cffe7ed457fe40

2b4832a91e7ab54d31b116d19958fddecc2c8510

yes, causalml should be optional too.

amit-sharma

py-why/dowhy

Use Poetry for Managing Dependencies, Tasks, and Package Builds

This PR includes the [Poetry](https://python-poetry.org/) tool for managing dependencies and packaging the library. This reduces a lot of boilerplate involved in defining and executing sequences of common tasks and with packaging & publishing the library. * Use pytest-xdist; other test updates will be deferred for another PR * Add poetry tasks for lint, build, verifyPackage, etc.. The CI uses these tasks instead of libraries like flake8 and pytest individually. This is useful for local development, and will let us chain tools together easily. * Remove pythonic build plumbing (setup.cfg, setup.py, manifest.in) - as Poetry takes over packaging. * Remove all requirements.txt files, as Poetry takes over dependency management. * Remove versioneer; poetry-dynamic-versioning will apply version substition Signed-off-by: Chris Trevino <chtrevin@microsoft.com>

2022-07-29 20:10:26+00:00

2022-08-13 01:12:53+00:00

pyproject.toml

[tool.pytest.ini_options] markers = [ "advanced: not be to run each time. only on package updates." ]

[tool.poetry] name = "dowhy" # # 0.0.0 is standard placeholder for poetry-dynamic-versioning # any changes to this should not be checked in # version = "0.0.0" description = "DoWhy is a Python library for causal inference that supports explicit modeling and testing of causal assumptions" authors = [ "PyWhy Community <amshar@microsoft.com>" ] maintainers = [] license = "MIT" documentation = "https://py-why.github.io/dowhy" repository = "https://github.com/pywhy/dowhy" classifiers = [ 'Development Status :: 4 - Beta', 'License :: OSI Approved :: MIT License', 'Programming Language :: Python :: 3.8', 'Programming Language :: Python :: 3.9', ] keywords = [ 'causality', 'machine-learning', 'causal-inference', 'statistics', 'graphical-model' ] include = ['docs', 'tests', 'CONTRIBUTING.md', 'LICENSE'] readme = 'README.rst' [tool.poetry-dynamic-versioning] enable = true vcs = "git" [tool.poetry-dynamic-versioning.substitution] files = ["dowhy/__init__.py"] # # Dependency compatibility notes: # * xgboost requires Python >=3.7,<3.11 # * pygraphviz requires Python >=3.8 # * networkx requires Python >= 3.8 # * llvmlite requires Python >=3.6,<3.11 # [tool.poetry.dependencies] python = ">=3.8,<3.10" scipy = "^1.8.1" statsmodels = "^0.13.2" numpy = "^1.23.1" pandas = "^1.4.3" networkx = "^2.8.5" sympy = "^1.10.1" scikit-learn = "1.0.2" pydot = "^1.4.2" joblib = "^1.1.0" # causalml is wired to use llvmlite 0.36 causalml = {version = "^0.12.3", optional = true} llvmlite = {version = "^0.36.0", optional = true} pygraphviz = {version = "^1.9", optional = true} matplotlib = {version = "^3.5.2", optional = true} econml = {version = "*", optional = true} tqdm = "^4.64.0" # # Dependencies for Documentation Generation # rpy2 = {version = "^3.5.2", optional = true} sphinx-multiversion = { git = "https://github.com/petergtz/sphinx-multiversion.git", branch = "override-version-with-refname", optional = true} sphinxcontrib-googleanalytics = { git = "https://github.com/petergtz/googleanalytics.git", branch = "master", optional = true} nbsphinx = {version = "^0.8.9", optional = true} sphinx-rtd-theme = {version = "^1.0.0", optional = true} pydata-sphinx-theme = {version = "^0.9.0", optional = true} pandoc = {version = "^2.2", optional = true} ipykernel = {version = "^6.15.1", optional = true} [tool.poetry.extras] plotting = ["matplotlib"] causalml = ["causalml", "llvmlite"] docs = [ "rpy2", "sphinx-multiversion", "sphinxcontrib-googleanalytics", "nbsphinx", "sphinx-rtd-theme", "pydata-sphinx-theme", "sympy", "ipykernel" ] [tool.poetry.dev-dependencies] poethepoet = "^0.16.0" flake8 = "^4.0.1" black = "^22.6.0" isort = "^5.10.1" pytest = "^7.1.2" twine = "^4.0.1" nbformat = "^5.4.0" jupyter = "^1.0.0" flaky = "^3.7.0" tensorflow = "^2.9.1" keras = "^2.9.0" xgboost = "^1.6.1" mypy = "^0.971" econml = "*" pygraphviz = "^1.9" [build-system] requires = ["poetry-core>=1.0.0", "poetry-dynamic-versioning"] build-backend = "poetry.core.masonry.api" [tool.pytest.ini_options] markers = [ "advanced: not be to run each time. only on package updates." ] [tool.poe.tasks] # stop the build if there are Python syntax errors or undefined names _flake8Errors = "flake8 . --count --select=E9,F63,F7,F82 --show-source --statistics" _flake8Warnings = "flake8 . --count --exit-zero --statistics" _black = 'black .' _isort = 'isort .' # testing tasks test = "pytest -v -m 'not advanced' --durations=0 --durations-min=60.0" test_focused = "pytest -v -m 'focused'" verifyPackage = "twine check dist/*" # TODO: replace with `poetry publish` uploadPackage = "twine upload dist/*" # TODO: add formatting to build process [tool.poe.tasks.format] sequence = ['_black', '_isort'] ignore_fail = 'return_non_zero' [tool.poe.tasks.lint] sequence = ['_flake8Errors', '_flake8Warnings'] ignore_fail = 'return_non_zero' [tool.poe.tasks.verify] sequence = ['lint', 'test'] ignore_fail = "return_non_zero"

darthtrevino

eba2c1cc8217495797f9d5ed34cffe7ed457fe40

2b4832a91e7ab54d31b116d19958fddecc2c8510

haha, I also don't remember now why it was there. I guess we can safely remove it. Does not appear to do anything critical.

amit-sharma

py-why/dowhy

CI: Update GH Action Trigger

The current trigger fired on 'master', which has been deprecated.

2022-07-28 20:18:53+00:00

2022-07-29 09:18:25+00:00

.github/workflows/python-package.yml

# This workflow will install Python dependencies, run tests and lint with a variety of Python versions # For more information see: https://help.github.com/actions/language-and-framework-guides/using-python-with-github-actions name: Python package on: push: branches: [ master ] pull_request: branches: [ master ] jobs: build: runs-on: ubuntu-latest strategy: matrix: python-version: [3.7, 3.8, 3.9] steps: - uses: actions/checkout@v2 - name: Set up Python ${{ matrix.python-version }} uses: actions/setup-python@v2 with: python-version: ${{ matrix.python-version }} - name: Install graphviz run: | sudo apt install graphviz libgraphviz-dev graphviz-dev pkg-config - name: Install dependencies run: | python -m pip install --upgrade pip if [ -f requirements.txt ]; then pip install -r requirements.txt; fi if [ -f requirements-plotting.txt ]; then pip install -r requirements-plotting.txt; fi pip install 'scikit-learn==1.0.2' --force-reinstall if [ -f requirements-test.txt ]; then pip install -r requirements-test.txt --use-deprecated=legacy-resolver; fi pip install 'numpy<=1.21' --force-reinstall - name: Lint with flake8 run: | # stop the build if there are Python syntax errors or undefined names flake8 . --count --select=E9,F63,F7,F82 --show-source --statistics # exit-zero treats all errors as warnings. The GitHub editor is 127 chars wide flake8 . --count --exit-zero --max-complexity=10 --max-line-length=127 --statistics - name: Test with pytest run: | pytest -v -m "not advanced" - name: Check package consistency with twine run: | python setup.py check sdist bdist_wheel twine check dist/*

# This workflow will install Python dependencies, run tests and lint with a variety of Python versions # For more information see: https://help.github.com/actions/language-and-framework-guides/using-python-with-github-actions name: DoWhy CI on: push: branches: [ main ] pull_request: branches: [ main ] jobs: build: runs-on: ubuntu-latest strategy: matrix: python-version: [3.7, 3.8, 3.9] steps: - uses: actions/checkout@v2 - name: Set up Python ${{ matrix.python-version }} uses: actions/setup-python@v2 with: python-version: ${{ matrix.python-version }} - name: Install graphviz run: | sudo apt install graphviz libgraphviz-dev graphviz-dev pkg-config - name: Install dependencies run: | python -m pip install --upgrade pip if [ -f requirements.txt ]; then pip install -r requirements.txt; fi if [ -f requirements-plotting.txt ]; then pip install -r requirements-plotting.txt; fi pip install 'scikit-learn==1.0.2' --force-reinstall if [ -f requirements-test.txt ]; then pip install -r requirements-test.txt --use-deprecated=legacy-resolver; fi pip install 'numpy<=1.21' --force-reinstall - name: Lint with flake8 run: | # stop the build if there are Python syntax errors or undefined names flake8 . --count --select=E9,F63,F7,F82 --show-source --statistics # exit-zero treats all errors as warnings. The GitHub editor is 127 chars wide flake8 . --count --exit-zero --max-complexity=10 --max-line-length=127 --statistics - name: Test with pytest run: | pytest -v -m "not advanced" - name: Check package consistency with twine run: | python setup.py check sdist bdist_wheel twine check dist/*

darthtrevino

96fa21848c4edcaa5e8c57a5d4c5efcbe39c408d

0464798b03b6d19e81b8db71d4451ab30d20eac9

You've removed the restriction to a specific branch (now `main`). What's the idea behind it? Do you think that's more appropriate? Asking, because I'm not sure we'd want to run this on every push to an arbitrary branch.

petergtz

py-why/dowhy

CI: Update GH Action Trigger

The current trigger fired on 'master', which has been deprecated.

2022-07-28 20:18:53+00:00

2022-07-29 09:18:25+00:00

.github/workflows/python-package.yml

# This workflow will install Python dependencies, run tests and lint with a variety of Python versions # For more information see: https://help.github.com/actions/language-and-framework-guides/using-python-with-github-actions name: Python package on: push: branches: [ master ] pull_request: branches: [ master ] jobs: build: runs-on: ubuntu-latest strategy: matrix: python-version: [3.7, 3.8, 3.9] steps: - uses: actions/checkout@v2 - name: Set up Python ${{ matrix.python-version }} uses: actions/setup-python@v2 with: python-version: ${{ matrix.python-version }} - name: Install graphviz run: | sudo apt install graphviz libgraphviz-dev graphviz-dev pkg-config - name: Install dependencies run: | python -m pip install --upgrade pip if [ -f requirements.txt ]; then pip install -r requirements.txt; fi if [ -f requirements-plotting.txt ]; then pip install -r requirements-plotting.txt; fi pip install 'scikit-learn==1.0.2' --force-reinstall if [ -f requirements-test.txt ]; then pip install -r requirements-test.txt --use-deprecated=legacy-resolver; fi pip install 'numpy<=1.21' --force-reinstall - name: Lint with flake8 run: | # stop the build if there are Python syntax errors or undefined names flake8 . --count --select=E9,F63,F7,F82 --show-source --statistics # exit-zero treats all errors as warnings. The GitHub editor is 127 chars wide flake8 . --count --exit-zero --max-complexity=10 --max-line-length=127 --statistics - name: Test with pytest run: | pytest -v -m "not advanced" - name: Check package consistency with twine run: | python setup.py check sdist bdist_wheel twine check dist/*

# This workflow will install Python dependencies, run tests and lint with a variety of Python versions # For more information see: https://help.github.com/actions/language-and-framework-guides/using-python-with-github-actions name: DoWhy CI on: push: branches: [ main ] pull_request: branches: [ main ] jobs: build: runs-on: ubuntu-latest strategy: matrix: python-version: [3.7, 3.8, 3.9] steps: - uses: actions/checkout@v2 - name: Set up Python ${{ matrix.python-version }} uses: actions/setup-python@v2 with: python-version: ${{ matrix.python-version }} - name: Install graphviz run: | sudo apt install graphviz libgraphviz-dev graphviz-dev pkg-config - name: Install dependencies run: | python -m pip install --upgrade pip if [ -f requirements.txt ]; then pip install -r requirements.txt; fi if [ -f requirements-plotting.txt ]; then pip install -r requirements-plotting.txt; fi pip install 'scikit-learn==1.0.2' --force-reinstall if [ -f requirements-test.txt ]; then pip install -r requirements-test.txt --use-deprecated=legacy-resolver; fi pip install 'numpy<=1.21' --force-reinstall - name: Lint with flake8 run: | # stop the build if there are Python syntax errors or undefined names flake8 . --count --select=E9,F63,F7,F82 --show-source --statistics # exit-zero treats all errors as warnings. The GitHub editor is 127 chars wide flake8 . --count --exit-zero --max-complexity=10 --max-line-length=127 --statistics - name: Test with pytest run: | pytest -v -m "not advanced" - name: Check package consistency with twine run: | python setup.py check sdist bdist_wheel twine check dist/*

darthtrevino

96fa21848c4edcaa5e8c57a5d4c5efcbe39c408d

0464798b03b6d19e81b8db71d4451ab30d20eac9

That's fair - we use this terser form on some other open-source projects but I don't mind restoring the branch selector.

darthtrevino

py-why/dowhy

Introduce PyData Sphinx theme and restructure docs accordingly

The PyData theme is being used by NumPy, Pandas, NetworkX, and others. I've re-arranged some sections to make it play nicely with the theme. The result can be seen here: https://petergtz.github.io/dowhy/master There is one open question, where I'd be curious for input: older versions of the documentation will now get messed up, e.g. see https://petergtz.github.io/dowhy/v0.7.1/. This is because they were structured for the RTD theme and it doesn't play well. Ideally, old documentation would keep the old theme, but there's no out-of-the-box solution using sphinx-multiversion. Curious if someone has ideas.

2022-07-21 07:48:55+00:00

2022-08-03 12:56:58+00:00

docs/source/conf.py

# -*- coding: utf-8 -*- # # Configuration file for the Sphinx documentation builder. # # This file does only contain a selection of the most common options. For a # full list see the documentation: # http://www.sphinx-doc.org/en/stable/config # -- Path setup -------------------------------------------------------------- # If extensions (or modules to document with autodoc) are in another directory, # add these directories to sys.path here. If the directory is relative to the # documentation root, use os.path.abspath to make it absolute, like shown here. # import os import sys sys.path.insert(0, os.path.abspath("../../")) # -- Project information ----------------------------------------------------- project = 'DoWhy' copyright = '2022, PyWhy contributors' author = 'PyWhy community' # -- General configuration --------------------------------------------------- # If your documentation needs a minimal Sphinx version, state it here. # # needs_sphinx = '1.0' # Add any Sphinx extension module names here, as strings. They can be # extensions coming with Sphinx (named 'sphinx.ext.*') or your custom # ones. extensions = [ 'sphinx.ext.autodoc', 'sphinx.ext.viewcode', 'sphinx.ext.todo', 'nbsphinx', 'sphinx_rtd_theme', "sphinx_multiversion", 'sphinxcontrib.googleanalytics', ] googleanalytics_id = 'G-B139P18WHM' autodoc_mock_imports = ['matplotlib', 'causalml', 'pymc3', 'econml'] # Add any paths that contain templates here, relative to this directory. templates_path = ['_templates'] # The suffix(es) of source filenames. # You can specify multiple suffix as a list of string: # # source_suffix = ['.rst', '.md'] source_suffix = '.rst' # The master toctree document. master_doc = 'index' # The language for content autogenerated by Sphinx. Refer to documentation # for a list of supported languages. # # This is also used if you do content translation via gettext catalogs. # Usually you set "language" from the command line for these cases. language = 'en' # List of patterns, relative to source directory, that match files and # directories to ignore when looking for source files. # This pattern also affects html_static_path and html_extra_path . exclude_patterns = [ '_build', 'Thumbs.db', '.DS_Store', '.ipynb_checkpoints', 'example_notebooks/dowhy_ranking_methods.ipynb', 'example_notebooks/dowhy_optimize_backdoor_example.ipynb', # need to check why str_to_dot fails here 'example_notebooks/dowhy_causal_discovery_example.ipynb', # need to check why str_to_dot fails here 'example_notebooks/dowhy_twins_example.ipynb', ] # The name of the Pygments (syntax highlighting) style to use. pygments_style = 'sphinx' # -- Options for HTML output ------------------------------------------------- # The theme to use for HTML and HTML Help pages. See the documentation for # a list of builtin themes. # html_theme = "pydata_sphinx_theme" # Theme options are theme-specific and customize the look and feel of a theme # further. For a list of options available for each theme, see the # documentation. # html_theme_options = { "navbar_end": ["navbar-icon-links", "versions"] } # Add any paths that contain custom static files (such as style sheets) here, # relative to this directory. They are copied after the builtin static files, # so a file named "default.css" will overwrite the builtin "default.css". html_static_path = ['_static'] # Custom sidebar templates, must be a dictionary that maps document names # to template names. # # The default sidebars (for documents that don't match any pattern) are # defined by theme itself. Builtin themes are using these templates by # default: ``['localtoc.html', 'relations.html', 'sourcelink.html', # 'searchbox.html']``. # # html_sidebars = {} # -- Options for HTMLHelp output --------------------------------------------- # Output file base name for HTML help builder. htmlhelp_basename = 'dowhydoc' # -- Options for LaTeX output ------------------------------------------------ latex_elements = { # The paper size ('letterpaper' or 'a4paper'). # # 'papersize': 'letterpaper', # The font size ('10pt', '11pt' or '12pt'). # # 'pointsize': '10pt', # Additional stuff for the LaTeX preamble. # # 'preamble': '', # Latex figure (float) alignment # # 'figure_align': 'htbp', } # Grouping the document tree into LaTeX files. List of tuples # (source start file, target name, title, # author, documentclass [howto, manual, or own class]). latex_documents = [ (master_doc, 'dowhy.tex', 'dowhy Documentation', 'Author', 'manual'), ] # -- Options for manual page output ------------------------------------------ # One entry per manual page. List of tuples # (source start file, name, description, authors, manual section). man_pages = [ (master_doc, 'dowhy', 'dowhy Documentation', [author], 1) ] # -- Options for Texinfo output ---------------------------------------------- # Grouping the document tree into Texinfo files. List of tuples # (source start file, target name, title, author, # dir menu entry, description, category) texinfo_documents = [ (master_doc, 'dowhy', 'dowhy Documentation', author, 'dowhy', 'One line description of project.', 'Miscellaneous'), ] # -- Options for Epub output ------------------------------------------------- # Bibliographic Dublin Core info. epub_title = project epub_author = author epub_publisher = author epub_copyright = copyright # The unique identifier of the text. This can be a ISBN number # or the project homepage. # # epub_identifier = '' # A unique identification for the text. # # epub_uid = '' # A list of files that should not be packed into the epub file. epub_exclude_files = ['search.html'] # -- Extension configuration ------------------------------------------------- # -- Options for todo extension ---------------------------------------------- # If true, `todo` and `todoList` produce output, else they produce nothing. todo_include_todos = True # init docstrings should also be included in class autoclass_content = "both" smv_tag_whitelist = r'^v\d*\.(9|\d{2,})(\..*)?$' smv_branch_whitelist = "main" smv_released_pattern = r"refs/tags/v.*"

# -*- coding: utf-8 -*- # # Configuration file for the Sphinx documentation builder. # # This file does only contain a selection of the most common options. For a # full list see the documentation: # http://www.sphinx-doc.org/en/stable/config # -- Path setup -------------------------------------------------------------- # If extensions (or modules to document with autodoc) are in another directory, # add these directories to sys.path here. If the directory is relative to the # documentation root, use os.path.abspath to make it absolute, like shown here. # import os import sys sys.path.insert(0, os.path.abspath("../../")) # -- Project information ----------------------------------------------------- project = 'DoWhy' copyright = '2022, PyWhy contributors' author = 'PyWhy community' # -- General configuration --------------------------------------------------- # If your documentation needs a minimal Sphinx version, state it here. # # needs_sphinx = '1.0' # Add any Sphinx extension module names here, as strings. They can be # extensions coming with Sphinx (named 'sphinx.ext.*') or your custom # ones. extensions = [ 'sphinx.ext.autodoc', 'sphinx.ext.viewcode', 'sphinx.ext.todo', 'nbsphinx', 'sphinx_rtd_theme', "sphinx_multiversion", 'sphinxcontrib.googleanalytics', ] googleanalytics_id = 'G-B139P18WHM' autodoc_mock_imports = ['matplotlib', 'causalml', 'pymc3', 'econml'] # Add any paths that contain templates here, relative to this directory. templates_path = ['_templates'] # The suffix(es) of source filenames. # You can specify multiple suffix as a list of string: # # source_suffix = ['.rst', '.md'] source_suffix = '.rst' # The master toctree document. master_doc = 'index' # The language for content autogenerated by Sphinx. Refer to documentation # for a list of supported languages. # # This is also used if you do content translation via gettext catalogs. # Usually you set "language" from the command line for these cases. language = 'en' # List of patterns, relative to source directory, that match files and # directories to ignore when looking for source files. # This pattern also affects html_static_path and html_extra_path . exclude_patterns = [ '_build', 'Thumbs.db', '.DS_Store', '.ipynb_checkpoints', 'example_notebooks/dowhy_ranking_methods.ipynb', 'example_notebooks/dowhy_optimize_backdoor_example.ipynb', # need to check why str_to_dot fails here 'example_notebooks/dowhy_causal_discovery_example.ipynb', # need to check why str_to_dot fails here 'example_notebooks/dowhy_twins_example.ipynb', ] # The name of the Pygments (syntax highlighting) style to use. pygments_style = 'sphinx' # -- Options for HTML output ------------------------------------------------- # The theme to use for HTML and HTML Help pages. See the documentation for # a list of builtin themes. # html_theme = "pydata_sphinx_theme" # Theme options are theme-specific and customize the look and feel of a theme # further. For a list of options available for each theme, see the # documentation. # html_theme_options = { "navbar_end": ["navbar-icon-links", "versions"] } # Add any paths that contain custom static files (such as style sheets) here, # relative to this directory. They are copied after the builtin static files, # so a file named "default.css" will overwrite the builtin "default.css". html_static_path = ['_static'] # Custom sidebar templates, must be a dictionary that maps document names # to template names. # # The default sidebars (for documents that don't match any pattern) are # defined by theme itself. Builtin themes are using these templates by # default: ``['localtoc.html', 'relations.html', 'sourcelink.html', # 'searchbox.html']``. # # html_sidebars = {} # -- Options for HTMLHelp output --------------------------------------------- # Output file base name for HTML help builder. htmlhelp_basename = 'dowhydoc' # -- Options for LaTeX output ------------------------------------------------ latex_elements = { # The paper size ('letterpaper' or 'a4paper'). # # 'papersize': 'letterpaper', # The font size ('10pt', '11pt' or '12pt'). # # 'pointsize': '10pt', # Additional stuff for the LaTeX preamble. # # 'preamble': '', # Latex figure (float) alignment # # 'figure_align': 'htbp', } # Grouping the document tree into LaTeX files. List of tuples # (source start file, target name, title, # author, documentclass [howto, manual, or own class]). latex_documents = [ (master_doc, 'dowhy.tex', 'dowhy Documentation', 'Author', 'manual'), ] # -- Options for manual page output ------------------------------------------ # One entry per manual page. List of tuples # (source start file, name, description, authors, manual section). man_pages = [ (master_doc, 'dowhy', 'dowhy Documentation', [author], 1) ] # -- Options for Texinfo output ---------------------------------------------- # Grouping the document tree into Texinfo files. List of tuples # (source start file, target name, title, author, # dir menu entry, description, category) texinfo_documents = [ (master_doc, 'dowhy', 'dowhy Documentation', author, 'dowhy', 'One line description of project.', 'Miscellaneous'), ] # -- Options for Epub output ------------------------------------------------- # Bibliographic Dublin Core info. epub_title = project epub_author = author epub_publisher = author epub_copyright = copyright # The unique identifier of the text. This can be a ISBN number # or the project homepage. # # epub_identifier = '' # A unique identification for the text. # # epub_uid = '' # A list of files that should not be packed into the epub file. epub_exclude_files = ['search.html'] # -- Extension configuration ------------------------------------------------- # -- Options for todo extension ---------------------------------------------- # If true, `todo` and `todoList` produce output, else they produce nothing. todo_include_todos = True # init docstrings should also be included in class autoclass_content = "both" smv_tag_whitelist = r'^v\d*\.(9|\d{2,})(\..*)?$' smv_branch_whitelist = "main" smv_released_pattern = r"refs/tags/v.*"

petergtz

3db32b638414aea85ee3518afbc92b655db54a95

77f7064c85b3de740b5beefb0ad7067ffdb024fd

will be good to remove/comment this out.

amit-sharma

py-why/dowhy

Introduce PyData Sphinx theme and restructure docs accordingly

The PyData theme is being used by NumPy, Pandas, NetworkX, and others. I've re-arranged some sections to make it play nicely with the theme. The result can be seen here: https://petergtz.github.io/dowhy/master There is one open question, where I'd be curious for input: older versions of the documentation will now get messed up, e.g. see https://petergtz.github.io/dowhy/v0.7.1/. This is because they were structured for the RTD theme and it doesn't play well. Ideally, old documentation would keep the old theme, but there's no out-of-the-box solution using sphinx-multiversion. Curious if someone has ideas.

2022-07-21 07:48:55+00:00

2022-08-03 12:56:58+00:00

docs/source/conf.py

# -*- coding: utf-8 -*- # # Configuration file for the Sphinx documentation builder. # # This file does only contain a selection of the most common options. For a # full list see the documentation: # http://www.sphinx-doc.org/en/stable/config # -- Path setup -------------------------------------------------------------- # If extensions (or modules to document with autodoc) are in another directory, # add these directories to sys.path here. If the directory is relative to the # documentation root, use os.path.abspath to make it absolute, like shown here. # import os import sys sys.path.insert(0, os.path.abspath("../../")) # -- Project information ----------------------------------------------------- project = 'DoWhy' copyright = '2022, PyWhy contributors' author = 'PyWhy community' # -- General configuration --------------------------------------------------- # If your documentation needs a minimal Sphinx version, state it here. # # needs_sphinx = '1.0' # Add any Sphinx extension module names here, as strings. They can be # extensions coming with Sphinx (named 'sphinx.ext.*') or your custom # ones. extensions = [ 'sphinx.ext.autodoc', 'sphinx.ext.viewcode', 'sphinx.ext.todo', 'nbsphinx', 'sphinx_rtd_theme', "sphinx_multiversion", 'sphinxcontrib.googleanalytics', ] googleanalytics_id = 'G-B139P18WHM' autodoc_mock_imports = ['matplotlib', 'causalml', 'pymc3', 'econml'] # Add any paths that contain templates here, relative to this directory. templates_path = ['_templates'] # The suffix(es) of source filenames. # You can specify multiple suffix as a list of string: # # source_suffix = ['.rst', '.md'] source_suffix = '.rst' # The master toctree document. master_doc = 'index' # The language for content autogenerated by Sphinx. Refer to documentation # for a list of supported languages. # # This is also used if you do content translation via gettext catalogs. # Usually you set "language" from the command line for these cases. language = 'en' # List of patterns, relative to source directory, that match files and # directories to ignore when looking for source files. # This pattern also affects html_static_path and html_extra_path . exclude_patterns = [ '_build', 'Thumbs.db', '.DS_Store', '.ipynb_checkpoints', 'example_notebooks/dowhy_ranking_methods.ipynb', 'example_notebooks/dowhy_optimize_backdoor_example.ipynb', # need to check why str_to_dot fails here 'example_notebooks/dowhy_causal_discovery_example.ipynb', # need to check why str_to_dot fails here 'example_notebooks/dowhy_twins_example.ipynb', ] # The name of the Pygments (syntax highlighting) style to use. pygments_style = 'sphinx' # -- Options for HTML output ------------------------------------------------- # The theme to use for HTML and HTML Help pages. See the documentation for # a list of builtin themes. # html_theme = "pydata_sphinx_theme" # Theme options are theme-specific and customize the look and feel of a theme # further. For a list of options available for each theme, see the # documentation. # html_theme_options = { "navbar_end": ["navbar-icon-links", "versions"] } # Add any paths that contain custom static files (such as style sheets) here, # relative to this directory. They are copied after the builtin static files, # so a file named "default.css" will overwrite the builtin "default.css". html_static_path = ['_static'] # Custom sidebar templates, must be a dictionary that maps document names # to template names. # # The default sidebars (for documents that don't match any pattern) are # defined by theme itself. Builtin themes are using these templates by # default: ``['localtoc.html', 'relations.html', 'sourcelink.html', # 'searchbox.html']``. # # html_sidebars = {} # -- Options for HTMLHelp output --------------------------------------------- # Output file base name for HTML help builder. htmlhelp_basename = 'dowhydoc' # -- Options for LaTeX output ------------------------------------------------ latex_elements = { # The paper size ('letterpaper' or 'a4paper'). # # 'papersize': 'letterpaper', # The font size ('10pt', '11pt' or '12pt'). # # 'pointsize': '10pt', # Additional stuff for the LaTeX preamble. # # 'preamble': '', # Latex figure (float) alignment # # 'figure_align': 'htbp', } # Grouping the document tree into LaTeX files. List of tuples # (source start file, target name, title, # author, documentclass [howto, manual, or own class]). latex_documents = [ (master_doc, 'dowhy.tex', 'dowhy Documentation', 'Author', 'manual'), ] # -- Options for manual page output ------------------------------------------ # One entry per manual page. List of tuples # (source start file, name, description, authors, manual section). man_pages = [ (master_doc, 'dowhy', 'dowhy Documentation', [author], 1) ] # -- Options for Texinfo output ---------------------------------------------- # Grouping the document tree into Texinfo files. List of tuples # (source start file, target name, title, author, # dir menu entry, description, category) texinfo_documents = [ (master_doc, 'dowhy', 'dowhy Documentation', author, 'dowhy', 'One line description of project.', 'Miscellaneous'), ] # -- Options for Epub output ------------------------------------------------- # Bibliographic Dublin Core info. epub_title = project epub_author = author epub_publisher = author epub_copyright = copyright # The unique identifier of the text. This can be a ISBN number # or the project homepage. # # epub_identifier = '' # A unique identification for the text. # # epub_uid = '' # A list of files that should not be packed into the epub file. epub_exclude_files = ['search.html'] # -- Extension configuration ------------------------------------------------- # -- Options for todo extension ---------------------------------------------- # If true, `todo` and `todoList` produce output, else they produce nothing. todo_include_todos = True # init docstrings should also be included in class autoclass_content = "both" smv_tag_whitelist = r'^v\d*\.(9|\d{2,})(\..*)?$' smv_branch_whitelist = "main" smv_released_pattern = r"refs/tags/v.*"

# -*- coding: utf-8 -*- # # Configuration file for the Sphinx documentation builder. # # This file does only contain a selection of the most common options. For a # full list see the documentation: # http://www.sphinx-doc.org/en/stable/config # -- Path setup -------------------------------------------------------------- # If extensions (or modules to document with autodoc) are in another directory, # add these directories to sys.path here. If the directory is relative to the # documentation root, use os.path.abspath to make it absolute, like shown here. # import os import sys sys.path.insert(0, os.path.abspath("../../")) # -- Project information ----------------------------------------------------- project = 'DoWhy' copyright = '2022, PyWhy contributors' author = 'PyWhy community' # -- General configuration --------------------------------------------------- # If your documentation needs a minimal Sphinx version, state it here. # # needs_sphinx = '1.0' # Add any Sphinx extension module names here, as strings. They can be # extensions coming with Sphinx (named 'sphinx.ext.*') or your custom # ones. extensions = [ 'sphinx.ext.autodoc', 'sphinx.ext.viewcode', 'sphinx.ext.todo', 'nbsphinx', 'sphinx_rtd_theme', "sphinx_multiversion", 'sphinxcontrib.googleanalytics', ] googleanalytics_id = 'G-B139P18WHM' autodoc_mock_imports = ['matplotlib', 'causalml', 'pymc3', 'econml'] # Add any paths that contain templates here, relative to this directory. templates_path = ['_templates'] # The suffix(es) of source filenames. # You can specify multiple suffix as a list of string: # # source_suffix = ['.rst', '.md'] source_suffix = '.rst' # The master toctree document. master_doc = 'index' # The language for content autogenerated by Sphinx. Refer to documentation # for a list of supported languages. # # This is also used if you do content translation via gettext catalogs. # Usually you set "language" from the command line for these cases. language = 'en' # List of patterns, relative to source directory, that match files and # directories to ignore when looking for source files. # This pattern also affects html_static_path and html_extra_path . exclude_patterns = [ '_build', 'Thumbs.db', '.DS_Store', '.ipynb_checkpoints', 'example_notebooks/dowhy_ranking_methods.ipynb', 'example_notebooks/dowhy_optimize_backdoor_example.ipynb', # need to check why str_to_dot fails here 'example_notebooks/dowhy_causal_discovery_example.ipynb', # need to check why str_to_dot fails here 'example_notebooks/dowhy_twins_example.ipynb', ] # The name of the Pygments (syntax highlighting) style to use. pygments_style = 'sphinx' # -- Options for HTML output ------------------------------------------------- # The theme to use for HTML and HTML Help pages. See the documentation for # a list of builtin themes. # html_theme = "pydata_sphinx_theme" # Theme options are theme-specific and customize the look and feel of a theme # further. For a list of options available for each theme, see the # documentation. # html_theme_options = { "navbar_end": ["navbar-icon-links", "versions"] } # Add any paths that contain custom static files (such as style sheets) here, # relative to this directory. They are copied after the builtin static files, # so a file named "default.css" will overwrite the builtin "default.css". html_static_path = ['_static'] # Custom sidebar templates, must be a dictionary that maps document names # to template names. # # The default sidebars (for documents that don't match any pattern) are # defined by theme itself. Builtin themes are using these templates by # default: ``['localtoc.html', 'relations.html', 'sourcelink.html', # 'searchbox.html']``. # # html_sidebars = {} # -- Options for HTMLHelp output --------------------------------------------- # Output file base name for HTML help builder. htmlhelp_basename = 'dowhydoc' # -- Options for LaTeX output ------------------------------------------------ latex_elements = { # The paper size ('letterpaper' or 'a4paper'). # # 'papersize': 'letterpaper', # The font size ('10pt', '11pt' or '12pt'). # # 'pointsize': '10pt', # Additional stuff for the LaTeX preamble. # # 'preamble': '', # Latex figure (float) alignment # # 'figure_align': 'htbp', } # Grouping the document tree into LaTeX files. List of tuples # (source start file, target name, title, # author, documentclass [howto, manual, or own class]). latex_documents = [ (master_doc, 'dowhy.tex', 'dowhy Documentation', 'Author', 'manual'), ] # -- Options for manual page output ------------------------------------------ # One entry per manual page. List of tuples # (source start file, name, description, authors, manual section). man_pages = [ (master_doc, 'dowhy', 'dowhy Documentation', [author], 1) ] # -- Options for Texinfo output ---------------------------------------------- # Grouping the document tree into Texinfo files. List of tuples # (source start file, target name, title, author, # dir menu entry, description, category) texinfo_documents = [ (master_doc, 'dowhy', 'dowhy Documentation', author, 'dowhy', 'One line description of project.', 'Miscellaneous'), ] # -- Options for Epub output ------------------------------------------------- # Bibliographic Dublin Core info. epub_title = project epub_author = author epub_publisher = author epub_copyright = copyright # The unique identifier of the text. This can be a ISBN number # or the project homepage. # # epub_identifier = '' # A unique identification for the text. # # epub_uid = '' # A list of files that should not be packed into the epub file. epub_exclude_files = ['search.html'] # -- Extension configuration ------------------------------------------------- # -- Options for todo extension ---------------------------------------------- # If true, `todo` and `todoList` produce output, else they produce nothing. todo_include_todos = True # init docstrings should also be included in class autoclass_content = "both" smv_tag_whitelist = r'^v\d*\.(9|\d{2,})(\..*)?$' smv_branch_whitelist = "main" smv_released_pattern = r"refs/tags/v.*"

petergtz

3db32b638414aea85ee3518afbc92b655db54a95

77f7064c85b3de740b5beefb0ad7067ffdb024fd

🤦 Removed

petergtz

py-why/dowhy

Introduce PyData Sphinx theme and restructure docs accordingly

The PyData theme is being used by NumPy, Pandas, NetworkX, and others. I've re-arranged some sections to make it play nicely with the theme. The result can be seen here: https://petergtz.github.io/dowhy/master There is one open question, where I'd be curious for input: older versions of the documentation will now get messed up, e.g. see https://petergtz.github.io/dowhy/v0.7.1/. This is because they were structured for the RTD theme and it doesn't play well. Ideally, old documentation would keep the old theme, but there's no out-of-the-box solution using sphinx-multiversion. Curious if someone has ideas.

2022-07-21 07:48:55+00:00

2022-08-03 12:56:58+00:00

docs/source/index.rst

DoWhy documentation =================== .. toctree:: :maxdepth: 3 :hidden: :glob: getting_started/index User Guide <user_guide/index> Examples <example_notebooks/nb_index> dowhy Contributing <contributing> code_repo .. image:: https://raw.githubusercontent.com/py-why/dowhy/master/docs/images/dowhy-schematic.png Much like machine learning libraries have done for prediction, **"DoWhy" is a Python library that aims to spark causal thinking and analysis**. DoWhy provides a principled four-step interface for causal inference that focuses on explicitly modeling causal assumptions and validating them as much as possible. The key feature of DoWhy is its state-of-the-art refutation API that can automatically test causal assumptions for any estimation method, thus making inference more robust and accessible to non-experts. DoWhy supports estimation of the average causal effect for backdoor, frontdoor, instrumental variable and other identification methods, and estimation of the conditional effect (CATE) through an integration with the EconML library. Getting started --------------- New to DoWhy? Our :doc:`getting_started/index` guide will get you up to speed in minutes. Once completed, you'll be ready to check out our :doc:`example_notebooks/nb_index`, :doc:`user_guide/index`, and other sections. User Guide ---------- Complete newbie when it comes to causal inference and DoWhy? Then you probably want to read our comprehensive :doc:`user_guide/index`. It guides you through everything you need to know, including the concepts and science you need to know when trying to solve non-trivial problems. Examples -------- If you prefer to learn by example, we recommend our :doc:`example_notebooks/nb_index`. API Reference ------------- The :doc:`dowhy` guide contains a detailed description of the functions, modules, and objects included in DoWhy. The reference describes how the methods work and which parameters can be used. It assumes that you have an understanding of the key concepts. Contributing ------------ Want to add to the codebase or documentation? Check out our :doc:`contributing` guide. .. include:: cite.rst

DoWhy documentation =================== .. toctree:: :maxdepth: 3 :hidden: :glob: getting_started/index User Guide <user_guide/index> Examples <example_notebooks/nb_index> dowhy Contributing <contributing> code_repo .. image:: https://raw.githubusercontent.com/py-why/dowhy/master/docs/images/dowhy-schematic.png Much like machine learning libraries have done for prediction, **"DoWhy" is a Python library that aims to spark causal thinking and analysis**. DoWhy provides a principled four-step interface for causal inference that focuses on explicitly modeling causal assumptions and validating them as much as possible. The key feature of DoWhy is its state-of-the-art refutation API that can automatically test causal assumptions for any estimation method, thus making inference more robust and accessible to non-experts. DoWhy supports estimation of the average causal effect for backdoor, frontdoor, instrumental variable and other identification methods, and estimation of the conditional effect (CATE) through an integration with the EconML library. Getting started --------------- New to DoWhy? Our :doc:`getting_started/index` guide will get you up to speed in minutes. Once completed, you'll be ready to check out our :doc:`example_notebooks/nb_index`, :doc:`user_guide/index`, and other sections. User Guide ---------- Complete newbie when it comes to causal inference and DoWhy? Then you probably want to read our comprehensive :doc:`user_guide/index`. It guides you through everything you need to know, including the concepts and science you need to know when trying to solve non-trivial problems. Examples -------- If you prefer to learn by example, we recommend our :doc:`example_notebooks/nb_index`. API Reference ------------- The :doc:`dowhy` guide contains a detailed description of the functions, modules, and objects included in DoWhy. The reference describes how the methods work and which parameters can be used. It assumes that you have an understanding of the key concepts. Contributing ------------ Want to add to the codebase or documentation? Check out our :doc:`contributing` guide. .. include:: cite.rst

petergtz

3db32b638414aea85ee3518afbc92b655db54a95

77f7064c85b3de740b5beefb0ad7067ffdb024fd

TBD text can be removed?

amit-sharma

py-why/dowhy

Introduce PyData Sphinx theme and restructure docs accordingly

The PyData theme is being used by NumPy, Pandas, NetworkX, and others. I've re-arranged some sections to make it play nicely with the theme. The result can be seen here: https://petergtz.github.io/dowhy/master There is one open question, where I'd be curious for input: older versions of the documentation will now get messed up, e.g. see https://petergtz.github.io/dowhy/v0.7.1/. This is because they were structured for the RTD theme and it doesn't play well. Ideally, old documentation would keep the old theme, but there's no out-of-the-box solution using sphinx-multiversion. Curious if someone has ideas.

2022-07-21 07:48:55+00:00

2022-08-03 12:56:58+00:00

docs/source/index.rst

DoWhy documentation =================== .. toctree:: :maxdepth: 3 :hidden: :glob: getting_started/index User Guide <user_guide/index> Examples <example_notebooks/nb_index> dowhy Contributing <contributing> code_repo .. image:: https://raw.githubusercontent.com/py-why/dowhy/master/docs/images/dowhy-schematic.png Much like machine learning libraries have done for prediction, **"DoWhy" is a Python library that aims to spark causal thinking and analysis**. DoWhy provides a principled four-step interface for causal inference that focuses on explicitly modeling causal assumptions and validating them as much as possible. The key feature of DoWhy is its state-of-the-art refutation API that can automatically test causal assumptions for any estimation method, thus making inference more robust and accessible to non-experts. DoWhy supports estimation of the average causal effect for backdoor, frontdoor, instrumental variable and other identification methods, and estimation of the conditional effect (CATE) through an integration with the EconML library. Getting started --------------- New to DoWhy? Our :doc:`getting_started/index` guide will get you up to speed in minutes. Once completed, you'll be ready to check out our :doc:`example_notebooks/nb_index`, :doc:`user_guide/index`, and other sections. User Guide ---------- Complete newbie when it comes to causal inference and DoWhy? Then you probably want to read our comprehensive :doc:`user_guide/index`. It guides you through everything you need to know, including the concepts and science you need to know when trying to solve non-trivial problems. Examples -------- If you prefer to learn by example, we recommend our :doc:`example_notebooks/nb_index`. API Reference ------------- The :doc:`dowhy` guide contains a detailed description of the functions, modules, and objects included in DoWhy. The reference describes how the methods work and which parameters can be used. It assumes that you have an understanding of the key concepts. Contributing ------------ Want to add to the codebase or documentation? Check out our :doc:`contributing` guide. .. include:: cite.rst

DoWhy documentation =================== .. toctree:: :maxdepth: 3 :hidden: :glob: getting_started/index User Guide <user_guide/index> Examples <example_notebooks/nb_index> dowhy Contributing <contributing> code_repo .. image:: https://raw.githubusercontent.com/py-why/dowhy/master/docs/images/dowhy-schematic.png Much like machine learning libraries have done for prediction, **"DoWhy" is a Python library that aims to spark causal thinking and analysis**. DoWhy provides a principled four-step interface for causal inference that focuses on explicitly modeling causal assumptions and validating them as much as possible. The key feature of DoWhy is its state-of-the-art refutation API that can automatically test causal assumptions for any estimation method, thus making inference more robust and accessible to non-experts. DoWhy supports estimation of the average causal effect for backdoor, frontdoor, instrumental variable and other identification methods, and estimation of the conditional effect (CATE) through an integration with the EconML library. Getting started --------------- New to DoWhy? Our :doc:`getting_started/index` guide will get you up to speed in minutes. Once completed, you'll be ready to check out our :doc:`example_notebooks/nb_index`, :doc:`user_guide/index`, and other sections. User Guide ---------- Complete newbie when it comes to causal inference and DoWhy? Then you probably want to read our comprehensive :doc:`user_guide/index`. It guides you through everything you need to know, including the concepts and science you need to know when trying to solve non-trivial problems. Examples -------- If you prefer to learn by example, we recommend our :doc:`example_notebooks/nb_index`. API Reference ------------- The :doc:`dowhy` guide contains a detailed description of the functions, modules, and objects included in DoWhy. The reference describes how the methods work and which parameters can be used. It assumes that you have an understanding of the key concepts. Contributing ------------ Want to add to the codebase or documentation? Check out our :doc:`contributing` guide. .. include:: cite.rst

petergtz

3db32b638414aea85ee3518afbc92b655db54a95

77f7064c85b3de740b5beefb0ad7067ffdb024fd

Well, I planned to put some text around it as in the other sections.

petergtz

py-why/dowhy

Introduce PyData Sphinx theme and restructure docs accordingly

The PyData theme is being used by NumPy, Pandas, NetworkX, and others. I've re-arranged some sections to make it play nicely with the theme. The result can be seen here: https://petergtz.github.io/dowhy/master There is one open question, where I'd be curious for input: older versions of the documentation will now get messed up, e.g. see https://petergtz.github.io/dowhy/v0.7.1/. This is because they were structured for the RTD theme and it doesn't play well. Ideally, old documentation would keep the old theme, but there's no out-of-the-box solution using sphinx-multiversion. Curious if someone has ideas.

2022-07-21 07:48:55+00:00

2022-08-03 12:56:58+00:00

docs/source/index.rst

DoWhy documentation =================== .. toctree:: :maxdepth: 3 :hidden: :glob: getting_started/index User Guide <user_guide/index> Examples <example_notebooks/nb_index> dowhy Contributing <contributing> code_repo .. image:: https://raw.githubusercontent.com/py-why/dowhy/master/docs/images/dowhy-schematic.png Much like machine learning libraries have done for prediction, **"DoWhy" is a Python library that aims to spark causal thinking and analysis**. DoWhy provides a principled four-step interface for causal inference that focuses on explicitly modeling causal assumptions and validating them as much as possible. The key feature of DoWhy is its state-of-the-art refutation API that can automatically test causal assumptions for any estimation method, thus making inference more robust and accessible to non-experts. DoWhy supports estimation of the average causal effect for backdoor, frontdoor, instrumental variable and other identification methods, and estimation of the conditional effect (CATE) through an integration with the EconML library. Getting started --------------- New to DoWhy? Our :doc:`getting_started/index` guide will get you up to speed in minutes. Once completed, you'll be ready to check out our :doc:`example_notebooks/nb_index`, :doc:`user_guide/index`, and other sections. User Guide ---------- Complete newbie when it comes to causal inference and DoWhy? Then you probably want to read our comprehensive :doc:`user_guide/index`. It guides you through everything you need to know, including the concepts and science you need to know when trying to solve non-trivial problems. Examples -------- If you prefer to learn by example, we recommend our :doc:`example_notebooks/nb_index`. API Reference ------------- The :doc:`dowhy` guide contains a detailed description of the functions, modules, and objects included in DoWhy. The reference describes how the methods work and which parameters can be used. It assumes that you have an understanding of the key concepts. Contributing ------------ Want to add to the codebase or documentation? Check out our :doc:`contributing` guide. .. include:: cite.rst

DoWhy documentation =================== .. toctree:: :maxdepth: 3 :hidden: :glob: getting_started/index User Guide <user_guide/index> Examples <example_notebooks/nb_index> dowhy Contributing <contributing> code_repo .. image:: https://raw.githubusercontent.com/py-why/dowhy/master/docs/images/dowhy-schematic.png Much like machine learning libraries have done for prediction, **"DoWhy" is a Python library that aims to spark causal thinking and analysis**. DoWhy provides a principled four-step interface for causal inference that focuses on explicitly modeling causal assumptions and validating them as much as possible. The key feature of DoWhy is its state-of-the-art refutation API that can automatically test causal assumptions for any estimation method, thus making inference more robust and accessible to non-experts. DoWhy supports estimation of the average causal effect for backdoor, frontdoor, instrumental variable and other identification methods, and estimation of the conditional effect (CATE) through an integration with the EconML library. Getting started --------------- New to DoWhy? Our :doc:`getting_started/index` guide will get you up to speed in minutes. Once completed, you'll be ready to check out our :doc:`example_notebooks/nb_index`, :doc:`user_guide/index`, and other sections. User Guide ---------- Complete newbie when it comes to causal inference and DoWhy? Then you probably want to read our comprehensive :doc:`user_guide/index`. It guides you through everything you need to know, including the concepts and science you need to know when trying to solve non-trivial problems. Examples -------- If you prefer to learn by example, we recommend our :doc:`example_notebooks/nb_index`. API Reference ------------- The :doc:`dowhy` guide contains a detailed description of the functions, modules, and objects included in DoWhy. The reference describes how the methods work and which parameters can be used. It assumes that you have an understanding of the key concepts. Contributing ------------ Want to add to the codebase or documentation? Check out our :doc:`contributing` guide. .. include:: cite.rst

petergtz

3db32b638414aea85ee3518afbc92b655db54a95

77f7064c85b3de740b5beefb0ad7067ffdb024fd

Added a little text around it.

petergtz

py-why/dowhy

fixed warnings and progrss bar improvements

Fixed the warnings arising in propensity score estimators and added optional progress bars for refuters Signed-off-by: Amey Varhade <ameyvarhade@gmail.com>

2022-07-20 18:03:07+00:00

2022-08-19 03:36:42+00:00

docs/source/example_notebooks/dowhy_simple_example.ipynb

{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Getting started with DoWhy: A simple example\n", "This is a quick introduction to the DoWhy causal inference library.\n", "We will load in a sample dataset and estimate the causal effect of a (pre-specified) treatment variable on a (pre-specified) outcome variable.\n", "\n", "First, let us load all required packages." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import pandas as pd\n", "\n", "from dowhy import CausalModel\n", "import dowhy.datasets \n", "\n", "# Avoid printing dataconversion warnings from sklearn and numpy\n", "import warnings\n", "from sklearn.exceptions import DataConversionWarning\n", "warnings.filterwarnings(action='ignore', category=DataConversionWarning)\n", "warnings.filterwarnings(action='ignore', category=FutureWarning)\n", "\n", "# Config dict to set the logging level\n", "import logging\n", "import logging.config\n", "DEFAULT_LOGGING = {\n", " 'version': 1,\n", " 'disable_existing_loggers': False,\n", " 'loggers': {\n", " '': {\n", " 'level': 'WARN',\n", " },\n", " }\n", "}\n", "\n", "logging.config.dictConfig(DEFAULT_LOGGING)\n", "logging.info(\"Getting started with DoWhy. Running notebook...\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now, let us load a dataset. For simplicity, we simulate a dataset with linear relationships between common causes and treatment, and common causes and outcome. \n", "\n", "Beta is the true causal effect. " ] }, { "cell_type": "code", "execution_count": null, "metadata": { "scrolled": true }, "outputs": [], "source": [ "data = dowhy.datasets.linear_dataset(beta=10,\n", " num_common_causes=5,\n", " num_instruments = 2,\n", " num_effect_modifiers=1,\n", " num_samples=5000, \n", " treatment_is_binary=True,\n", " stddev_treatment_noise=10,\n", " num_discrete_common_causes=1)\n", "df = data[\"df\"]\n", "print(df.head())\n", "print(data[\"dot_graph\"])\n", "print(\"\\n\")\n", "print(data[\"gml_graph\"])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Note that we are using a pandas dataframe to load the data. At present, DoWhy only supports pandas dataframe as input." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Interface 1 (recommended): Input causal graph" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We now input a causal graph in the GML graph format (recommended). You can also use the DOT format.\n", "\n", "To create the causal graph for your dataset, you can use a tool like [DAGitty](http://dagitty.net/dags.html#) that provides a GUI to construct the graph. You can export the graph string that it generates. The graph string is very close to the DOT format: just rename `dag` to `digraph`, remove newlines and add a semicolon after every line, to convert it to the DOT format and input to DoWhy. " ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# With graph\n", "model=CausalModel(\n", " data = df,\n", " treatment=data[\"treatment_name\"],\n", " outcome=data[\"outcome_name\"],\n", " graph=data[\"gml_graph\"]\n", " )" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "model.view_model()" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "scrolled": true }, "outputs": [], "source": [ "from IPython.display import Image, display\n", "display(Image(filename=\"causal_model.png\"))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The above causal graph shows the assumptions encoded in the causal model. We can now use this graph to first identify \n", "the causal effect (go from a causal estimand to a probability expression), and then estimate the causal effect." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### DoWhy philosophy: Keep identification and estimation separate\n", "\n", "Identification can be achieved without access to the data, acccesing only the graph. This results in an expression to be computed. This expression can then be evaluated using the available data in the estimation step.\n", "It is important to understand that these are orthogonal steps.\n", "\n", "#### Identification" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "identified_estimand = model.identify_effect(proceed_when_unidentifiable=True)\n", "print(identified_estimand)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Note the parameter flag *proceed\\_when\\_unidentifiable*. It needs to be set to *True* to convey the assumption that we are ignoring any unobserved confounding. The default behavior is to prompt the user to double-check that the unobserved confounders can be ignored. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Estimation" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "scrolled": true }, "outputs": [], "source": [ "causal_estimate = model.estimate_effect(identified_estimand,\n", " method_name=\"backdoor.propensity_score_stratification\")\n", "print(causal_estimate)\n", "print(\"Causal Estimate is \" + str(causal_estimate.value))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "You can input additional parameters to the estimate_effect method. For instance, to estimate the effect on any subset of the units, you can specify the \"target_units\" parameter which can be a string (\"ate\", \"att\", or \"atc\"), lambda function that filters rows of the data frame, or a new dataframe on which to compute the effect. You can also specify \"effect modifiers\" to estimate heterogeneous effects across these variables. See `help(CausalModel.estimate_effect)`. " ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Causal effect on the control group (ATC)\n", "causal_estimate_att = model.estimate_effect(identified_estimand,\n", " method_name=\"backdoor.propensity_score_stratification\",\n", " target_units = \"atc\")\n", "print(causal_estimate_att)\n", "print(\"Causal Estimate is \" + str(causal_estimate_att.value))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Interface 2: Specify common causes and instruments" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "scrolled": true }, "outputs": [], "source": [ "# Without graph \n", "model= CausalModel( \n", " data=df, \n", " treatment=data[\"treatment_name\"], \n", " outcome=data[\"outcome_name\"], \n", " common_causes=data[\"common_causes_names\"],\n", " effect_modifiers=data[\"effect_modifier_names\"]) " ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "model.view_model()" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "from IPython.display import Image, display\n", "display(Image(filename=\"causal_model.png\"))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We get the same causal graph. Now identification and estimation is done as before.\n", "\n", "#### Identification" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "identified_estimand = model.identify_effect(proceed_when_unidentifiable=True) " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Estimation" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "estimate = model.estimate_effect(identified_estimand,\n", " method_name=\"backdoor.propensity_score_stratification\") \n", "print(estimate)\n", "print(\"Causal Estimate is \" + str(estimate.value))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Refuting the estimate\n", "\n", "Let us now look at ways of refuting the estimate obtained. Refutation methods provide tests that every correct estimator should pass. So if an estimator fails the refutation test (p-value is <0.05), then it means that there is some problem with the estimator. \n", "\n", "Note that we cannot verify that the estimate is correct, but we can reject it if it violates certain expected behavior (this is analogous to scientific theories that can be falsified but not proven true). The below refutation tests are based on either \n", " 1) **Invariant transformations**: changes in the data that should not change the estimate. Any estimator whose result varies significantly between the original data and the modified data fails the test; \n", " \n", " a) Random Common Cause\n", " \n", " b) Data Subset\n", " \n", " \n", " 2) **Nullifying transformations**: after the data change, the causal true estimate is zero. Any estimator whose result varies significantly from zero on the new data fails the test.\n", " \n", " a) Placebo Treatment" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Adding a random common cause variable" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "res_random=model.refute_estimate(identified_estimand, estimate, method_name=\"random_common_cause\")\n", "print(res_random)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Replacing treatment with a random (placebo) variable" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "res_placebo=model.refute_estimate(identified_estimand, estimate,\n", " method_name=\"placebo_treatment_refuter\", placebo_type=\"permute\")\n", "print(res_placebo)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Removing a random subset of the data" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "res_subset=model.refute_estimate(identified_estimand, estimate,\n", " method_name=\"data_subset_refuter\", subset_fraction=0.9)\n", "print(res_subset)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As you can see, the propensity score stratification estimator is reasonably robust to refutations.\n", "\n", "**Reproducability**: For reproducibility, you can add a parameter \"random_seed\" to any refutation method, as shown below.\n", "\n", "**Parallelization**: You can also use built-in parallelization to speed up the refutation process. Simply set `n_jobs` to a value greater than 1 to spread the workload to multiple CPUs, or set `n_jobs=-1` to use all CPUs. Currently, this is available only for `random_common_cause`, `placebo_treatment_refuter`, and `data_subset_refuter`." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "res_subset=model.refute_estimate(identified_estimand, estimate,\n", " method_name=\"data_subset_refuter\", subset_fraction=0.9, random_seed = 1, n_jobs=-1, verbose=10)\n", "print(res_subset)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Adding an unobserved common cause variable\n", "\n", "This refutation does not return a p-value. Instead, it provides a _sensitivity_ test on how quickly the estimate changes if the identifying assumptions (used in `identify_effect`) are not valid. Specifically, it checks sensitivity to violation of the backdoor assumption: that all common causes are observed. \n", "\n", "To do so, it creates a new dataset with an additional common cause between treatment and outcome. To capture the effect of the common cause, the method takes as input the strength of common cause's effect on treatment and outcome. Based on these inputs on the common cause's effects, it changes the treatment and outcome values and then reruns the estimator. The hope is that the new estimate does not change drastically with a small effect of the unobserved common cause, indicating a robustness to any unobserved confounding.\n", "\n", "Another equivalent way of interpreting this procedure is to assume that there was already unobserved confounding present in the input data. The change in treatment and outcome values _removes_ the effect of whatever unobserved common cause was present in the original data. Then rerunning the estimator on this modified data provides the correct identified estimate and we hope that the difference between the new estimate and the original estimate is not too high, for some bounded value of the unobserved common cause's effect.\n", "\n", "**Importance of domain knowledge**: This test requires _domain knowledge_ to set plausible input values of the effect of unobserved confounding. We first show the result for a single value of confounder's effect on treatment and outcome." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "res_unobserved=model.refute_estimate(identified_estimand, estimate, method_name=\"add_unobserved_common_cause\",\n", " confounders_effect_on_treatment=\"binary_flip\", confounders_effect_on_outcome=\"linear\",\n", " effect_strength_on_treatment=0.01, effect_strength_on_outcome=0.02)\n", "print(res_unobserved)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "It is often more useful to inspect the trend as the effect of unobserved confounding is increased. For that, we can provide an array of hypothesized confounders' effects. The output is the *(min, max)* range of the estimated effects under different unobserved confounding." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "res_unobserved_range=model.refute_estimate(identified_estimand, estimate, method_name=\"add_unobserved_common_cause\",\n", " confounders_effect_on_treatment=\"binary_flip\", confounders_effect_on_outcome=\"linear\",\n", " effect_strength_on_treatment=np.array([0.001, 0.005, 0.01, 0.02]), effect_strength_on_outcome=0.01)\n", "print(res_unobserved_range)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The above plot shows how the estimate decreases as the hypothesized confounding on treatment increases. By domain knowledge, we may know the maximum plausible confounding effect on treatment. Since we see that the effect does not go beyond zero, we can safely conclude that the causal effect of treatment `v0` is positive.\n", "\n", "We can also vary the confounding effect on both treatment and outcome. We obtain a heatmap." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "res_unobserved_range=model.refute_estimate(identified_estimand, estimate, method_name=\"add_unobserved_common_cause\",\n", " confounders_effect_on_treatment=\"binary_flip\", confounders_effect_on_outcome=\"linear\",\n", " effect_strength_on_treatment=[0.001, 0.005, 0.01, 0.02], \n", " effect_strength_on_outcome=[0.001, 0.005, 0.01,0.02])\n", "print(res_unobserved_range)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Automatically inferring effect strength parameters.** Finally, DoWhy supports automatic selection of the effect strength parameters. This is based on an assumption that the effect of the unobserved confounder on treatment or outcome cannot be stronger than that of any observed confounder. That is, we have collected data at least for the most relevant confounder. If that is the case, then we can bound the range of `effect_strength_on_treatment` and `effect_strength_on_outcome` by the effect strength of observed confounders. There is an additional optional parameter signifying whether the effect strength of unobserved confounder should be as high as the highest observed, or a fraction of it. You can set it using the optional `effect_fraction_on_treatment` and `effect_fraction_on_outcome` parameters. By default, these two parameters are 1." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "res_unobserved_auto = model.refute_estimate(identified_estimand, estimate, method_name=\"add_unobserved_common_cause\",\n", " confounders_effect_on_treatment=\"binary_flip\", confounders_effect_on_outcome=\"linear\")\n", "print(res_unobserved_auto)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Conclusion**: Assuming that the unobserved confounder does not affect the treatment or outcome more strongly than any observed confounder, the causal effect can be concluded to be positive." ] } ], "metadata": { "kernelspec": { "display_name": "Python 3.7.10 ('venvrl')", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.7.10" }, "toc": { "base_numbering": 1, "nav_menu": {}, "number_sections": false, "sideBar": true, "skip_h1_title": true, "title_cell": "Table of Contents", "title_sidebar": "Contents", "toc_cell": false, "toc_position": {}, "toc_section_display": true, "toc_window_display": false } }, "nbformat": 4, "nbformat_minor": 4 }

{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Getting started with DoWhy: A simple example\n", "This is a quick introduction to the DoWhy causal inference library.\n", "We will load in a sample dataset and estimate the causal effect of a (pre-specified) treatment variable on a (pre-specified) outcome variable.\n", "\n", "First, let us load all required packages." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import pandas as pd\n", "\n", "from dowhy import CausalModel\n", "import dowhy.datasets \n", "\n", "# Avoid printing dataconversion warnings from sklearn and numpy\n", "import warnings\n", "from sklearn.exceptions import DataConversionWarning\n", "warnings.filterwarnings(action='ignore', category=DataConversionWarning)\n", "warnings.filterwarnings(action='ignore', category=FutureWarning)\n", "\n", "# Config dict to set the logging level\n", "import logging\n", "import logging.config\n", "DEFAULT_LOGGING = {\n", " 'version': 1,\n", " 'disable_existing_loggers': False,\n", " 'loggers': {\n", " '': {\n", " 'level': 'WARN',\n", " },\n", " }\n", "}\n", "\n", "logging.config.dictConfig(DEFAULT_LOGGING)\n", "logging.info(\"Getting started with DoWhy. Running notebook...\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now, let us load a dataset. For simplicity, we simulate a dataset with linear relationships between common causes and treatment, and common causes and outcome. \n", "\n", "Beta is the true causal effect. " ] }, { "cell_type": "code", "execution_count": null, "metadata": { "scrolled": true }, "outputs": [], "source": [ "data = dowhy.datasets.linear_dataset(beta=10,\n", " num_common_causes=5,\n", " num_instruments = 2,\n", " num_effect_modifiers=1,\n", " num_samples=5000, \n", " treatment_is_binary=True,\n", " stddev_treatment_noise=10,\n", " num_discrete_common_causes=1)\n", "df = data[\"df\"]\n", "print(df.head())\n", "print(data[\"dot_graph\"])\n", "print(\"\\n\")\n", "print(data[\"gml_graph\"])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Note that we are using a pandas dataframe to load the data. At present, DoWhy only supports pandas dataframe as input." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Interface 1 (recommended): Input causal graph" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We now input a causal graph in the GML graph format (recommended). You can also use the DOT format.\n", "\n", "To create the causal graph for your dataset, you can use a tool like [DAGitty](http://dagitty.net/dags.html#) that provides a GUI to construct the graph. You can export the graph string that it generates. The graph string is very close to the DOT format: just rename `dag` to `digraph`, remove newlines and add a semicolon after every line, to convert it to the DOT format and input to DoWhy. " ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# With graph\n", "model=CausalModel(\n", " data = df,\n", " treatment=data[\"treatment_name\"],\n", " outcome=data[\"outcome_name\"],\n", " graph=data[\"gml_graph\"]\n", " )" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "model.view_model()" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "scrolled": true }, "outputs": [], "source": [ "from IPython.display import Image, display\n", "display(Image(filename=\"causal_model.png\"))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The above causal graph shows the assumptions encoded in the causal model. We can now use this graph to first identify \n", "the causal effect (go from a causal estimand to a probability expression), and then estimate the causal effect." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### DoWhy philosophy: Keep identification and estimation separate\n", "\n", "Identification can be achieved without access to the data, acccesing only the graph. This results in an expression to be computed. This expression can then be evaluated using the available data in the estimation step.\n", "It is important to understand that these are orthogonal steps.\n", "\n", "#### Identification" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "identified_estimand = model.identify_effect(proceed_when_unidentifiable=True)\n", "print(identified_estimand)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Note the parameter flag *proceed\\_when\\_unidentifiable*. It needs to be set to *True* to convey the assumption that we are ignoring any unobserved confounding. The default behavior is to prompt the user to double-check that the unobserved confounders can be ignored. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Estimation" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "scrolled": true }, "outputs": [], "source": [ "causal_estimate = model.estimate_effect(identified_estimand,\n", " method_name=\"backdoor.propensity_score_stratification\")\n", "print(causal_estimate)\n", "print(\"Causal Estimate is \" + str(causal_estimate.value))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "You can input additional parameters to the estimate_effect method. For instance, to estimate the effect on any subset of the units, you can specify the \"target_units\" parameter which can be a string (\"ate\", \"att\", or \"atc\"), lambda function that filters rows of the data frame, or a new dataframe on which to compute the effect. You can also specify \"effect modifiers\" to estimate heterogeneous effects across these variables. See `help(CausalModel.estimate_effect)`. " ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Causal effect on the control group (ATC)\n", "causal_estimate_att = model.estimate_effect(identified_estimand,\n", " method_name=\"backdoor.propensity_score_stratification\",\n", " target_units = \"atc\")\n", "print(causal_estimate_att)\n", "print(\"Causal Estimate is \" + str(causal_estimate_att.value))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Interface 2: Specify common causes and instruments" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "scrolled": true }, "outputs": [], "source": [ "# Without graph \n", "model= CausalModel( \n", " data=df, \n", " treatment=data[\"treatment_name\"], \n", " outcome=data[\"outcome_name\"], \n", " common_causes=data[\"common_causes_names\"],\n", " effect_modifiers=data[\"effect_modifier_names\"]) " ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "model.view_model()" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "from IPython.display import Image, display\n", "display(Image(filename=\"causal_model.png\"))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We get the same causal graph. Now identification and estimation is done as before.\n", "\n", "#### Identification" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "identified_estimand = model.identify_effect(proceed_when_unidentifiable=True) " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Estimation" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "estimate = model.estimate_effect(identified_estimand,\n", " method_name=\"backdoor.propensity_score_stratification\") \n", "print(estimate)\n", "print(\"Causal Estimate is \" + str(estimate.value))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Refuting the estimate\n", "\n", "Let us now look at ways of refuting the estimate obtained. Refutation methods provide tests that every correct estimator should pass. So if an estimator fails the refutation test (p-value is <0.05), then it means that there is some problem with the estimator. \n", "\n", "Note that we cannot verify that the estimate is correct, but we can reject it if it violates certain expected behavior (this is analogous to scientific theories that can be falsified but not proven true). The below refutation tests are based on either \n", " 1) **Invariant transformations**: changes in the data that should not change the estimate. Any estimator whose result varies significantly between the original data and the modified data fails the test; \n", " \n", " a) Random Common Cause\n", " \n", " b) Data Subset\n", " \n", " \n", " 2) **Nullifying transformations**: after the data change, the causal true estimate is zero. Any estimator whose result varies significantly from zero on the new data fails the test.\n", " \n", " a) Placebo Treatment" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Adding a random common cause variable" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "res_random=model.refute_estimate(identified_estimand, estimate, method_name=\"random_common_cause\", show_progress_bar=True)\n", "print(res_random)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Replacing treatment with a random (placebo) variable" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "res_placebo=model.refute_estimate(identified_estimand, estimate,\n", " method_name=\"placebo_treatment_refuter\", show_progress_bar=True, placebo_type=\"permute\")\n", "print(res_placebo)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Removing a random subset of the data" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "res_subset=model.refute_estimate(identified_estimand, estimate,\n", " method_name=\"data_subset_refuter\", show_progress_bar=True, subset_fraction=0.9)\n", "print(res_subset)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As you can see, the propensity score stratification estimator is reasonably robust to refutations.\n", "\n", "**Reproducability**: For reproducibility, you can add a parameter \"random_seed\" to any refutation method, as shown below.\n", "\n", "**Parallelization**: You can also use built-in parallelization to speed up the refutation process. Simply set `n_jobs` to a value greater than 1 to spread the workload to multiple CPUs, or set `n_jobs=-1` to use all CPUs. Currently, this is available only for `random_common_cause`, `placebo_treatment_refuter`, and `data_subset_refuter`." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "res_subset=model.refute_estimate(identified_estimand, estimate,\n", " method_name=\"data_subset_refuter\", show_progress_bar=True, subset_fraction=0.9, random_seed = 1, n_jobs=-1, verbose=10)\n", "print(res_subset)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Adding an unobserved common cause variable\n", "\n", "This refutation does not return a p-value. Instead, it provides a _sensitivity_ test on how quickly the estimate changes if the identifying assumptions (used in `identify_effect`) are not valid. Specifically, it checks sensitivity to violation of the backdoor assumption: that all common causes are observed. \n", "\n", "To do so, it creates a new dataset with an additional common cause between treatment and outcome. To capture the effect of the common cause, the method takes as input the strength of common cause's effect on treatment and outcome. Based on these inputs on the common cause's effects, it changes the treatment and outcome values and then reruns the estimator. The hope is that the new estimate does not change drastically with a small effect of the unobserved common cause, indicating a robustness to any unobserved confounding.\n", "\n", "Another equivalent way of interpreting this procedure is to assume that there was already unobserved confounding present in the input data. The change in treatment and outcome values _removes_ the effect of whatever unobserved common cause was present in the original data. Then rerunning the estimator on this modified data provides the correct identified estimate and we hope that the difference between the new estimate and the original estimate is not too high, for some bounded value of the unobserved common cause's effect.\n", "\n", "**Importance of domain knowledge**: This test requires _domain knowledge_ to set plausible input values of the effect of unobserved confounding. We first show the result for a single value of confounder's effect on treatment and outcome." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "res_unobserved=model.refute_estimate(identified_estimand, estimate, method_name=\"add_unobserved_common_cause\",\n", " confounders_effect_on_treatment=\"binary_flip\", confounders_effect_on_outcome=\"linear\",\n", " effect_strength_on_treatment=0.01, effect_strength_on_outcome=0.02)\n", "print(res_unobserved)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "It is often more useful to inspect the trend as the effect of unobserved confounding is increased. For that, we can provide an array of hypothesized confounders' effects. The output is the *(min, max)* range of the estimated effects under different unobserved confounding." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "res_unobserved_range=model.refute_estimate(identified_estimand, estimate, method_name=\"add_unobserved_common_cause\",\n", " confounders_effect_on_treatment=\"binary_flip\", confounders_effect_on_outcome=\"linear\",\n", " effect_strength_on_treatment=np.array([0.001, 0.005, 0.01, 0.02]), effect_strength_on_outcome=0.01)\n", "print(res_unobserved_range)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The above plot shows how the estimate decreases as the hypothesized confounding on treatment increases. By domain knowledge, we may know the maximum plausible confounding effect on treatment. Since we see that the effect does not go beyond zero, we can safely conclude that the causal effect of treatment `v0` is positive.\n", "\n", "We can also vary the confounding effect on both treatment and outcome. We obtain a heatmap." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "res_unobserved_range=model.refute_estimate(identified_estimand, estimate, method_name=\"add_unobserved_common_cause\",\n", " confounders_effect_on_treatment=\"binary_flip\", confounders_effect_on_outcome=\"linear\",\n", " effect_strength_on_treatment=[0.001, 0.005, 0.01, 0.02], \n", " effect_strength_on_outcome=[0.001, 0.005, 0.01,0.02])\n", "print(res_unobserved_range)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Automatically inferring effect strength parameters.** Finally, DoWhy supports automatic selection of the effect strength parameters. This is based on an assumption that the effect of the unobserved confounder on treatment or outcome cannot be stronger than that of any observed confounder. That is, we have collected data at least for the most relevant confounder. If that is the case, then we can bound the range of `effect_strength_on_treatment` and `effect_strength_on_outcome` by the effect strength of observed confounders. There is an additional optional parameter signifying whether the effect strength of unobserved confounder should be as high as the highest observed, or a fraction of it. You can set it using the optional `effect_fraction_on_treatment` and `effect_fraction_on_outcome` parameters. By default, these two parameters are 1." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "res_unobserved_auto = model.refute_estimate(identified_estimand, estimate, method_name=\"add_unobserved_common_cause\",\n", " confounders_effect_on_treatment=\"binary_flip\", confounders_effect_on_outcome=\"linear\")\n", "print(res_unobserved_auto)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Conclusion**: Assuming that the unobserved confounder does not affect the treatment or outcome more strongly than any observed confounder, the causal effect can be concluded to be positive." ] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.8.13" }, "toc": { "base_numbering": 1, "nav_menu": {}, "number_sections": false, "sideBar": true, "skip_h1_title": true, "title_cell": "Table of Contents", "title_sidebar": "Contents", "toc_cell": false, "toc_position": {}, "toc_section_display": true, "toc_window_display": false } }, "nbformat": 4, "nbformat_minor": 4 }

yemaedahrav

a38a03f8b2daa0627833821e92c1b9117925e331

f94638633ef23064c69c261c324cc4739d036ac0

good to remove the vscode metadata. (you can just delete it)

amit-sharma

py-why/dowhy

fixed warnings and progrss bar improvements

Fixed the warnings arising in propensity score estimators and added optional progress bars for refuters Signed-off-by: Amey Varhade <ameyvarhade@gmail.com>

2022-07-20 18:03:07+00:00

2022-08-19 03:36:42+00:00

docs/source/example_notebooks/dowhy_simple_example.ipynb

{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Getting started with DoWhy: A simple example\n", "This is a quick introduction to the DoWhy causal inference library.\n", "We will load in a sample dataset and estimate the causal effect of a (pre-specified) treatment variable on a (pre-specified) outcome variable.\n", "\n", "First, let us load all required packages." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import pandas as pd\n", "\n", "from dowhy import CausalModel\n", "import dowhy.datasets \n", "\n", "# Avoid printing dataconversion warnings from sklearn and numpy\n", "import warnings\n", "from sklearn.exceptions import DataConversionWarning\n", "warnings.filterwarnings(action='ignore', category=DataConversionWarning)\n", "warnings.filterwarnings(action='ignore', category=FutureWarning)\n", "\n", "# Config dict to set the logging level\n", "import logging\n", "import logging.config\n", "DEFAULT_LOGGING = {\n", " 'version': 1,\n", " 'disable_existing_loggers': False,\n", " 'loggers': {\n", " '': {\n", " 'level': 'WARN',\n", " },\n", " }\n", "}\n", "\n", "logging.config.dictConfig(DEFAULT_LOGGING)\n", "logging.info(\"Getting started with DoWhy. Running notebook...\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now, let us load a dataset. For simplicity, we simulate a dataset with linear relationships between common causes and treatment, and common causes and outcome. \n", "\n", "Beta is the true causal effect. " ] }, { "cell_type": "code", "execution_count": null, "metadata": { "scrolled": true }, "outputs": [], "source": [ "data = dowhy.datasets.linear_dataset(beta=10,\n", " num_common_causes=5,\n", " num_instruments = 2,\n", " num_effect_modifiers=1,\n", " num_samples=5000, \n", " treatment_is_binary=True,\n", " stddev_treatment_noise=10,\n", " num_discrete_common_causes=1)\n", "df = data[\"df\"]\n", "print(df.head())\n", "print(data[\"dot_graph\"])\n", "print(\"\\n\")\n", "print(data[\"gml_graph\"])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Note that we are using a pandas dataframe to load the data. At present, DoWhy only supports pandas dataframe as input." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Interface 1 (recommended): Input causal graph" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We now input a causal graph in the GML graph format (recommended). You can also use the DOT format.\n", "\n", "To create the causal graph for your dataset, you can use a tool like [DAGitty](http://dagitty.net/dags.html#) that provides a GUI to construct the graph. You can export the graph string that it generates. The graph string is very close to the DOT format: just rename `dag` to `digraph`, remove newlines and add a semicolon after every line, to convert it to the DOT format and input to DoWhy. " ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# With graph\n", "model=CausalModel(\n", " data = df,\n", " treatment=data[\"treatment_name\"],\n", " outcome=data[\"outcome_name\"],\n", " graph=data[\"gml_graph\"]\n", " )" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "model.view_model()" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "scrolled": true }, "outputs": [], "source": [ "from IPython.display import Image, display\n", "display(Image(filename=\"causal_model.png\"))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The above causal graph shows the assumptions encoded in the causal model. We can now use this graph to first identify \n", "the causal effect (go from a causal estimand to a probability expression), and then estimate the causal effect." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### DoWhy philosophy: Keep identification and estimation separate\n", "\n", "Identification can be achieved without access to the data, acccesing only the graph. This results in an expression to be computed. This expression can then be evaluated using the available data in the estimation step.\n", "It is important to understand that these are orthogonal steps.\n", "\n", "#### Identification" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "identified_estimand = model.identify_effect(proceed_when_unidentifiable=True)\n", "print(identified_estimand)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Note the parameter flag *proceed\\_when\\_unidentifiable*. It needs to be set to *True* to convey the assumption that we are ignoring any unobserved confounding. The default behavior is to prompt the user to double-check that the unobserved confounders can be ignored. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Estimation" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "scrolled": true }, "outputs": [], "source": [ "causal_estimate = model.estimate_effect(identified_estimand,\n", " method_name=\"backdoor.propensity_score_stratification\")\n", "print(causal_estimate)\n", "print(\"Causal Estimate is \" + str(causal_estimate.value))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "You can input additional parameters to the estimate_effect method. For instance, to estimate the effect on any subset of the units, you can specify the \"target_units\" parameter which can be a string (\"ate\", \"att\", or \"atc\"), lambda function that filters rows of the data frame, or a new dataframe on which to compute the effect. You can also specify \"effect modifiers\" to estimate heterogeneous effects across these variables. See `help(CausalModel.estimate_effect)`. " ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Causal effect on the control group (ATC)\n", "causal_estimate_att = model.estimate_effect(identified_estimand,\n", " method_name=\"backdoor.propensity_score_stratification\",\n", " target_units = \"atc\")\n", "print(causal_estimate_att)\n", "print(\"Causal Estimate is \" + str(causal_estimate_att.value))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Interface 2: Specify common causes and instruments" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "scrolled": true }, "outputs": [], "source": [ "# Without graph \n", "model= CausalModel( \n", " data=df, \n", " treatment=data[\"treatment_name\"], \n", " outcome=data[\"outcome_name\"], \n", " common_causes=data[\"common_causes_names\"],\n", " effect_modifiers=data[\"effect_modifier_names\"]) " ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "model.view_model()" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "from IPython.display import Image, display\n", "display(Image(filename=\"causal_model.png\"))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We get the same causal graph. Now identification and estimation is done as before.\n", "\n", "#### Identification" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "identified_estimand = model.identify_effect(proceed_when_unidentifiable=True) " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Estimation" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "estimate = model.estimate_effect(identified_estimand,\n", " method_name=\"backdoor.propensity_score_stratification\") \n", "print(estimate)\n", "print(\"Causal Estimate is \" + str(estimate.value))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Refuting the estimate\n", "\n", "Let us now look at ways of refuting the estimate obtained. Refutation methods provide tests that every correct estimator should pass. So if an estimator fails the refutation test (p-value is <0.05), then it means that there is some problem with the estimator. \n", "\n", "Note that we cannot verify that the estimate is correct, but we can reject it if it violates certain expected behavior (this is analogous to scientific theories that can be falsified but not proven true). The below refutation tests are based on either \n", " 1) **Invariant transformations**: changes in the data that should not change the estimate. Any estimator whose result varies significantly between the original data and the modified data fails the test; \n", " \n", " a) Random Common Cause\n", " \n", " b) Data Subset\n", " \n", " \n", " 2) **Nullifying transformations**: after the data change, the causal true estimate is zero. Any estimator whose result varies significantly from zero on the new data fails the test.\n", " \n", " a) Placebo Treatment" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Adding a random common cause variable" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "res_random=model.refute_estimate(identified_estimand, estimate, method_name=\"random_common_cause\")\n", "print(res_random)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Replacing treatment with a random (placebo) variable" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "res_placebo=model.refute_estimate(identified_estimand, estimate,\n", " method_name=\"placebo_treatment_refuter\", placebo_type=\"permute\")\n", "print(res_placebo)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Removing a random subset of the data" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "res_subset=model.refute_estimate(identified_estimand, estimate,\n", " method_name=\"data_subset_refuter\", subset_fraction=0.9)\n", "print(res_subset)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As you can see, the propensity score stratification estimator is reasonably robust to refutations.\n", "\n", "**Reproducability**: For reproducibility, you can add a parameter \"random_seed\" to any refutation method, as shown below.\n", "\n", "**Parallelization**: You can also use built-in parallelization to speed up the refutation process. Simply set `n_jobs` to a value greater than 1 to spread the workload to multiple CPUs, or set `n_jobs=-1` to use all CPUs. Currently, this is available only for `random_common_cause`, `placebo_treatment_refuter`, and `data_subset_refuter`." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "res_subset=model.refute_estimate(identified_estimand, estimate,\n", " method_name=\"data_subset_refuter\", subset_fraction=0.9, random_seed = 1, n_jobs=-1, verbose=10)\n", "print(res_subset)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Adding an unobserved common cause variable\n", "\n", "This refutation does not return a p-value. Instead, it provides a _sensitivity_ test on how quickly the estimate changes if the identifying assumptions (used in `identify_effect`) are not valid. Specifically, it checks sensitivity to violation of the backdoor assumption: that all common causes are observed. \n", "\n", "To do so, it creates a new dataset with an additional common cause between treatment and outcome. To capture the effect of the common cause, the method takes as input the strength of common cause's effect on treatment and outcome. Based on these inputs on the common cause's effects, it changes the treatment and outcome values and then reruns the estimator. The hope is that the new estimate does not change drastically with a small effect of the unobserved common cause, indicating a robustness to any unobserved confounding.\n", "\n", "Another equivalent way of interpreting this procedure is to assume that there was already unobserved confounding present in the input data. The change in treatment and outcome values _removes_ the effect of whatever unobserved common cause was present in the original data. Then rerunning the estimator on this modified data provides the correct identified estimate and we hope that the difference between the new estimate and the original estimate is not too high, for some bounded value of the unobserved common cause's effect.\n", "\n", "**Importance of domain knowledge**: This test requires _domain knowledge_ to set plausible input values of the effect of unobserved confounding. We first show the result for a single value of confounder's effect on treatment and outcome." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "res_unobserved=model.refute_estimate(identified_estimand, estimate, method_name=\"add_unobserved_common_cause\",\n", " confounders_effect_on_treatment=\"binary_flip\", confounders_effect_on_outcome=\"linear\",\n", " effect_strength_on_treatment=0.01, effect_strength_on_outcome=0.02)\n", "print(res_unobserved)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "It is often more useful to inspect the trend as the effect of unobserved confounding is increased. For that, we can provide an array of hypothesized confounders' effects. The output is the *(min, max)* range of the estimated effects under different unobserved confounding." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "res_unobserved_range=model.refute_estimate(identified_estimand, estimate, method_name=\"add_unobserved_common_cause\",\n", " confounders_effect_on_treatment=\"binary_flip\", confounders_effect_on_outcome=\"linear\",\n", " effect_strength_on_treatment=np.array([0.001, 0.005, 0.01, 0.02]), effect_strength_on_outcome=0.01)\n", "print(res_unobserved_range)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The above plot shows how the estimate decreases as the hypothesized confounding on treatment increases. By domain knowledge, we may know the maximum plausible confounding effect on treatment. Since we see that the effect does not go beyond zero, we can safely conclude that the causal effect of treatment `v0` is positive.\n", "\n", "We can also vary the confounding effect on both treatment and outcome. We obtain a heatmap." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "res_unobserved_range=model.refute_estimate(identified_estimand, estimate, method_name=\"add_unobserved_common_cause\",\n", " confounders_effect_on_treatment=\"binary_flip\", confounders_effect_on_outcome=\"linear\",\n", " effect_strength_on_treatment=[0.001, 0.005, 0.01, 0.02], \n", " effect_strength_on_outcome=[0.001, 0.005, 0.01,0.02])\n", "print(res_unobserved_range)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Automatically inferring effect strength parameters.** Finally, DoWhy supports automatic selection of the effect strength parameters. This is based on an assumption that the effect of the unobserved confounder on treatment or outcome cannot be stronger than that of any observed confounder. That is, we have collected data at least for the most relevant confounder. If that is the case, then we can bound the range of `effect_strength_on_treatment` and `effect_strength_on_outcome` by the effect strength of observed confounders. There is an additional optional parameter signifying whether the effect strength of unobserved confounder should be as high as the highest observed, or a fraction of it. You can set it using the optional `effect_fraction_on_treatment` and `effect_fraction_on_outcome` parameters. By default, these two parameters are 1." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "res_unobserved_auto = model.refute_estimate(identified_estimand, estimate, method_name=\"add_unobserved_common_cause\",\n", " confounders_effect_on_treatment=\"binary_flip\", confounders_effect_on_outcome=\"linear\")\n", "print(res_unobserved_auto)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Conclusion**: Assuming that the unobserved confounder does not affect the treatment or outcome more strongly than any observed confounder, the causal effect can be concluded to be positive." ] } ], "metadata": { "kernelspec": { "display_name": "Python 3.7.10 ('venvrl')", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.7.10" }, "toc": { "base_numbering": 1, "nav_menu": {}, "number_sections": false, "sideBar": true, "skip_h1_title": true, "title_cell": "Table of Contents", "title_sidebar": "Contents", "toc_cell": false, "toc_position": {}, "toc_section_display": true, "toc_window_display": false } }, "nbformat": 4, "nbformat_minor": 4 }

{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Getting started with DoWhy: A simple example\n", "This is a quick introduction to the DoWhy causal inference library.\n", "We will load in a sample dataset and estimate the causal effect of a (pre-specified) treatment variable on a (pre-specified) outcome variable.\n", "\n", "First, let us load all required packages." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import pandas as pd\n", "\n", "from dowhy import CausalModel\n", "import dowhy.datasets \n", "\n", "# Avoid printing dataconversion warnings from sklearn and numpy\n", "import warnings\n", "from sklearn.exceptions import DataConversionWarning\n", "warnings.filterwarnings(action='ignore', category=DataConversionWarning)\n", "warnings.filterwarnings(action='ignore', category=FutureWarning)\n", "\n", "# Config dict to set the logging level\n", "import logging\n", "import logging.config\n", "DEFAULT_LOGGING = {\n", " 'version': 1,\n", " 'disable_existing_loggers': False,\n", " 'loggers': {\n", " '': {\n", " 'level': 'WARN',\n", " },\n", " }\n", "}\n", "\n", "logging.config.dictConfig(DEFAULT_LOGGING)\n", "logging.info(\"Getting started with DoWhy. Running notebook...\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now, let us load a dataset. For simplicity, we simulate a dataset with linear relationships between common causes and treatment, and common causes and outcome. \n", "\n", "Beta is the true causal effect. " ] }, { "cell_type": "code", "execution_count": null, "metadata": { "scrolled": true }, "outputs": [], "source": [ "data = dowhy.datasets.linear_dataset(beta=10,\n", " num_common_causes=5,\n", " num_instruments = 2,\n", " num_effect_modifiers=1,\n", " num_samples=5000, \n", " treatment_is_binary=True,\n", " stddev_treatment_noise=10,\n", " num_discrete_common_causes=1)\n", "df = data[\"df\"]\n", "print(df.head())\n", "print(data[\"dot_graph\"])\n", "print(\"\\n\")\n", "print(data[\"gml_graph\"])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Note that we are using a pandas dataframe to load the data. At present, DoWhy only supports pandas dataframe as input." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Interface 1 (recommended): Input causal graph" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We now input a causal graph in the GML graph format (recommended). You can also use the DOT format.\n", "\n", "To create the causal graph for your dataset, you can use a tool like [DAGitty](http://dagitty.net/dags.html#) that provides a GUI to construct the graph. You can export the graph string that it generates. The graph string is very close to the DOT format: just rename `dag` to `digraph`, remove newlines and add a semicolon after every line, to convert it to the DOT format and input to DoWhy. " ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# With graph\n", "model=CausalModel(\n", " data = df,\n", " treatment=data[\"treatment_name\"],\n", " outcome=data[\"outcome_name\"],\n", " graph=data[\"gml_graph\"]\n", " )" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "model.view_model()" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "scrolled": true }, "outputs": [], "source": [ "from IPython.display import Image, display\n", "display(Image(filename=\"causal_model.png\"))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The above causal graph shows the assumptions encoded in the causal model. We can now use this graph to first identify \n", "the causal effect (go from a causal estimand to a probability expression), and then estimate the causal effect." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### DoWhy philosophy: Keep identification and estimation separate\n", "\n", "Identification can be achieved without access to the data, acccesing only the graph. This results in an expression to be computed. This expression can then be evaluated using the available data in the estimation step.\n", "It is important to understand that these are orthogonal steps.\n", "\n", "#### Identification" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "identified_estimand = model.identify_effect(proceed_when_unidentifiable=True)\n", "print(identified_estimand)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Note the parameter flag *proceed\\_when\\_unidentifiable*. It needs to be set to *True* to convey the assumption that we are ignoring any unobserved confounding. The default behavior is to prompt the user to double-check that the unobserved confounders can be ignored. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Estimation" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "scrolled": true }, "outputs": [], "source": [ "causal_estimate = model.estimate_effect(identified_estimand,\n", " method_name=\"backdoor.propensity_score_stratification\")\n", "print(causal_estimate)\n", "print(\"Causal Estimate is \" + str(causal_estimate.value))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "You can input additional parameters to the estimate_effect method. For instance, to estimate the effect on any subset of the units, you can specify the \"target_units\" parameter which can be a string (\"ate\", \"att\", or \"atc\"), lambda function that filters rows of the data frame, or a new dataframe on which to compute the effect. You can also specify \"effect modifiers\" to estimate heterogeneous effects across these variables. See `help(CausalModel.estimate_effect)`. " ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Causal effect on the control group (ATC)\n", "causal_estimate_att = model.estimate_effect(identified_estimand,\n", " method_name=\"backdoor.propensity_score_stratification\",\n", " target_units = \"atc\")\n", "print(causal_estimate_att)\n", "print(\"Causal Estimate is \" + str(causal_estimate_att.value))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Interface 2: Specify common causes and instruments" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "scrolled": true }, "outputs": [], "source": [ "# Without graph \n", "model= CausalModel( \n", " data=df, \n", " treatment=data[\"treatment_name\"], \n", " outcome=data[\"outcome_name\"], \n", " common_causes=data[\"common_causes_names\"],\n", " effect_modifiers=data[\"effect_modifier_names\"]) " ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "model.view_model()" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "from IPython.display import Image, display\n", "display(Image(filename=\"causal_model.png\"))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We get the same causal graph. Now identification and estimation is done as before.\n", "\n", "#### Identification" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "identified_estimand = model.identify_effect(proceed_when_unidentifiable=True) " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Estimation" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "estimate = model.estimate_effect(identified_estimand,\n", " method_name=\"backdoor.propensity_score_stratification\") \n", "print(estimate)\n", "print(\"Causal Estimate is \" + str(estimate.value))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Refuting the estimate\n", "\n", "Let us now look at ways of refuting the estimate obtained. Refutation methods provide tests that every correct estimator should pass. So if an estimator fails the refutation test (p-value is <0.05), then it means that there is some problem with the estimator. \n", "\n", "Note that we cannot verify that the estimate is correct, but we can reject it if it violates certain expected behavior (this is analogous to scientific theories that can be falsified but not proven true). The below refutation tests are based on either \n", " 1) **Invariant transformations**: changes in the data that should not change the estimate. Any estimator whose result varies significantly between the original data and the modified data fails the test; \n", " \n", " a) Random Common Cause\n", " \n", " b) Data Subset\n", " \n", " \n", " 2) **Nullifying transformations**: after the data change, the causal true estimate is zero. Any estimator whose result varies significantly from zero on the new data fails the test.\n", " \n", " a) Placebo Treatment" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Adding a random common cause variable" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "res_random=model.refute_estimate(identified_estimand, estimate, method_name=\"random_common_cause\", show_progress_bar=True)\n", "print(res_random)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Replacing treatment with a random (placebo) variable" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "res_placebo=model.refute_estimate(identified_estimand, estimate,\n", " method_name=\"placebo_treatment_refuter\", show_progress_bar=True, placebo_type=\"permute\")\n", "print(res_placebo)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Removing a random subset of the data" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "res_subset=model.refute_estimate(identified_estimand, estimate,\n", " method_name=\"data_subset_refuter\", show_progress_bar=True, subset_fraction=0.9)\n", "print(res_subset)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As you can see, the propensity score stratification estimator is reasonably robust to refutations.\n", "\n", "**Reproducability**: For reproducibility, you can add a parameter \"random_seed\" to any refutation method, as shown below.\n", "\n", "**Parallelization**: You can also use built-in parallelization to speed up the refutation process. Simply set `n_jobs` to a value greater than 1 to spread the workload to multiple CPUs, or set `n_jobs=-1` to use all CPUs. Currently, this is available only for `random_common_cause`, `placebo_treatment_refuter`, and `data_subset_refuter`." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "res_subset=model.refute_estimate(identified_estimand, estimate,\n", " method_name=\"data_subset_refuter\", show_progress_bar=True, subset_fraction=0.9, random_seed = 1, n_jobs=-1, verbose=10)\n", "print(res_subset)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Adding an unobserved common cause variable\n", "\n", "This refutation does not return a p-value. Instead, it provides a _sensitivity_ test on how quickly the estimate changes if the identifying assumptions (used in `identify_effect`) are not valid. Specifically, it checks sensitivity to violation of the backdoor assumption: that all common causes are observed. \n", "\n", "To do so, it creates a new dataset with an additional common cause between treatment and outcome. To capture the effect of the common cause, the method takes as input the strength of common cause's effect on treatment and outcome. Based on these inputs on the common cause's effects, it changes the treatment and outcome values and then reruns the estimator. The hope is that the new estimate does not change drastically with a small effect of the unobserved common cause, indicating a robustness to any unobserved confounding.\n", "\n", "Another equivalent way of interpreting this procedure is to assume that there was already unobserved confounding present in the input data. The change in treatment and outcome values _removes_ the effect of whatever unobserved common cause was present in the original data. Then rerunning the estimator on this modified data provides the correct identified estimate and we hope that the difference between the new estimate and the original estimate is not too high, for some bounded value of the unobserved common cause's effect.\n", "\n", "**Importance of domain knowledge**: This test requires _domain knowledge_ to set plausible input values of the effect of unobserved confounding. We first show the result for a single value of confounder's effect on treatment and outcome." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "res_unobserved=model.refute_estimate(identified_estimand, estimate, method_name=\"add_unobserved_common_cause\",\n", " confounders_effect_on_treatment=\"binary_flip\", confounders_effect_on_outcome=\"linear\",\n", " effect_strength_on_treatment=0.01, effect_strength_on_outcome=0.02)\n", "print(res_unobserved)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "It is often more useful to inspect the trend as the effect of unobserved confounding is increased. For that, we can provide an array of hypothesized confounders' effects. The output is the *(min, max)* range of the estimated effects under different unobserved confounding." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "res_unobserved_range=model.refute_estimate(identified_estimand, estimate, method_name=\"add_unobserved_common_cause\",\n", " confounders_effect_on_treatment=\"binary_flip\", confounders_effect_on_outcome=\"linear\",\n", " effect_strength_on_treatment=np.array([0.001, 0.005, 0.01, 0.02]), effect_strength_on_outcome=0.01)\n", "print(res_unobserved_range)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The above plot shows how the estimate decreases as the hypothesized confounding on treatment increases. By domain knowledge, we may know the maximum plausible confounding effect on treatment. Since we see that the effect does not go beyond zero, we can safely conclude that the causal effect of treatment `v0` is positive.\n", "\n", "We can also vary the confounding effect on both treatment and outcome. We obtain a heatmap." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "res_unobserved_range=model.refute_estimate(identified_estimand, estimate, method_name=\"add_unobserved_common_cause\",\n", " confounders_effect_on_treatment=\"binary_flip\", confounders_effect_on_outcome=\"linear\",\n", " effect_strength_on_treatment=[0.001, 0.005, 0.01, 0.02], \n", " effect_strength_on_outcome=[0.001, 0.005, 0.01,0.02])\n", "print(res_unobserved_range)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Automatically inferring effect strength parameters.** Finally, DoWhy supports automatic selection of the effect strength parameters. This is based on an assumption that the effect of the unobserved confounder on treatment or outcome cannot be stronger than that of any observed confounder. That is, we have collected data at least for the most relevant confounder. If that is the case, then we can bound the range of `effect_strength_on_treatment` and `effect_strength_on_outcome` by the effect strength of observed confounders. There is an additional optional parameter signifying whether the effect strength of unobserved confounder should be as high as the highest observed, or a fraction of it. You can set it using the optional `effect_fraction_on_treatment` and `effect_fraction_on_outcome` parameters. By default, these two parameters are 1." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "res_unobserved_auto = model.refute_estimate(identified_estimand, estimate, method_name=\"add_unobserved_common_cause\",\n", " confounders_effect_on_treatment=\"binary_flip\", confounders_effect_on_outcome=\"linear\")\n", "print(res_unobserved_auto)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Conclusion**: Assuming that the unobserved confounder does not affect the treatment or outcome more strongly than any observed confounder, the causal effect can be concluded to be positive." ] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.8.13" }, "toc": { "base_numbering": 1, "nav_menu": {}, "number_sections": false, "sideBar": true, "skip_h1_title": true, "title_cell": "Table of Contents", "title_sidebar": "Contents", "toc_cell": false, "toc_position": {}, "toc_section_display": true, "toc_window_display": false } }, "nbformat": 4, "nbformat_minor": 4 }

yemaedahrav

a38a03f8b2daa0627833821e92c1b9117925e331

f94638633ef23064c69c261c324cc4739d036ac0

can you add the show_progress_bar=True to random common cause and placebo treatment refuter too?

amit-sharma

py-why/dowhy

fixed warnings and progrss bar improvements

Fixed the warnings arising in propensity score estimators and added optional progress bars for refuters Signed-off-by: Amey Varhade <ameyvarhade@gmail.com>

2022-07-20 18:03:07+00:00

2022-08-19 03:36:42+00:00

dowhy/causal_refuters/add_unobserved_common_cause.py

import copy import logging import numpy as np import pandas as pd import scipy.stats import math import statsmodels.api as sm from sklearn.preprocessing import StandardScaler from sklearn.linear_model import LogisticRegression from dowhy.causal_refuter import CausalRefutation from dowhy.causal_refuter import CausalRefuter from dowhy.causal_estimator import CausalEstimator from dowhy.causal_refuters.linear_sensitivity_analyzer import LinearSensitivityAnalyzer from dowhy.causal_estimators.linear_regression_estimator import LinearRegressionEstimator class AddUnobservedCommonCause(CausalRefuter): """Add an unobserved confounder for refutation. Supports additional parameters that can be specified in the refute_estimate() method. - 'confounders_effect_on_treatment': how the simulated confounder affects the value of treatment. This can be linear (for continuous treatment) or binary_flip (for binary treatment) - 'confounders_effect_on_outcome': how the simulated confounder affects the value of outcome. This can be linear (for continuous outcome) or binary_flip (for binary outcome) - 'effect_strength_on_treatment': parameter for the strength of the effect of simulated confounder on treatment. For linear effect, it is the regression coeffient. For binary_flip, it is the probability that simulated confounder's effect flips the value of treatment from 0 to 1 (or vice-versa). - 'effect_strength_on_outcome': parameter for the strength of the effect of simulated confounder on outcome. For linear effect, it is the regression coeffient. For binary_flip, it is the probability that simulated confounder's effect flips the value of outcome from 0 to 1 (or vice-versa). TODO: Needs an interpretation module """ def __init__(self, *args, **kwargs): """ Initialize the parameters required for the refuter. If effect_strength_on_treatment or effect_strength_on_outcome is not given, it is calculated automatically as a range between the minimum and maximum effect strength of observed confounders on treatment and outcome respectively. :param confounders_effect_on_treatment: str : The type of effect on the treatment due to the unobserved confounder. Possible values are ['binary_flip', 'linear'] :param confounders_effect_on_outcome: str : The type of effect on the outcome due to the unobserved confounder. Possible values are ['binary_flip', 'linear'] :param effect_strength_on_treatment: float, numpy.ndarray: This refers to the strength of the confounder on treatment. For a linear effect, it behaves like the regression coeffecient. For a binary flip it is the probability with which it can invert the value of the treatment. :param effect_strength_on_outcome: float, numpy.ndarray: This refers to the strength of the confounder on outcome. For a linear effect, it behaves like the regression coefficient. For a binary flip, it is the probability with which it can invert the value of the outcome. :param effect_fraction_on_treatment: float: If effect_strength_on_treatment is not provided, this parameter decides the effect strength of the simulated confounder as a fraction of the effect strength of observed confounders on treatment. Defaults to 1. :param effect_fraction_on_outcome: float: If effect_strength_on_outcome is not provided, this parameter decides the effect strength of the simulated confounder as a fraction of the effect strength of observed confounders on outcome. Defaults to 1. :param plotmethod: string: Type of plot to be shown. If None, no plot is generated. This parameter is used only only when more than one treatment confounder effect values or outcome confounder effect values are provided. Default is "colormesh". Supported values are "contour", "colormesh" when more than one value is provided for both confounder effect value parameters; "line" when provided for only one of them. :param simulated_method_name: method type to add unobserved common cause. "linear-partial-R2" for linear sensitivity analysis :param percent_change_estimate: It is the percentage of reduction of treatment estimate that could alter the results (default = 1) if percent_change_estimate = 1, the robustness value describes the strength of association of confounders with treatment and outcome in order to reduce the estimate by 100% i.e bring it down to 0. :param confounder_increases_estimate: True implies that confounder increases the absolute value of estimate and vice versa. (Default = False) :param benchmark_common_causes: names of variables for bounding strength of confounders :param significance_level: confidence interval for statistical inference(default = 0.05) :param null_hypothesis_effect: assumed effect under the null hypothesis :param plot_estimate: Generate contour plot for estimate while performing sensitivity analysis. (default = True). To override the setting, set plot_estimate = False. """ super().__init__(*args, **kwargs) self.effect_on_t = kwargs["confounders_effect_on_treatment"] if "confounders_effect_on_treatment" in kwargs else "binary_flip" self.effect_on_y = kwargs["confounders_effect_on_outcome"] if "confounders_effect_on_outcome" in kwargs else "linear" self.kappa_t = kwargs["effect_strength_on_treatment"] if "effect_strength_on_treatment" in kwargs else None self.kappa_y = kwargs["effect_strength_on_outcome"] if "effect_strength_on_outcome" in kwargs else None self.frac_strength_treatment = kwargs["effect_fraction_on_treatment"] if "effect_fraction_on_treatment" in kwargs else 1 self.frac_strength_outcome = kwargs["effect_fraction_on_outcome"] if "effect_fraction_on_outcome" in kwargs else 1 self.simulated_method_name = kwargs["simulated_method_name"] if "simulated_method_name" in kwargs else "linear_based" self.plotmethod = kwargs['plotmethod'] if "plotmethod" in kwargs else "colormesh" self.percent_change_estimate = kwargs["percent_change_estimate"] if 'percent_change_estimate' in kwargs else 1.0 self.significance_level = kwargs["significance_level"] if "significance_level" in kwargs else 0.05 self.confounder_increases_estimate = kwargs["confounder_increases_estimate"] if "confounder_increases_estimate" in kwargs else False self.benchmark_common_causes = kwargs["benchmark_common_causes"] if "benchmark_common_causes" in kwargs else None self.null_hypothesis_effect = kwargs["null_hypothesis_effect"] if "null_hypothesis_effect" in kwargs else 0 self.plot_estimate = kwargs["plot_estimate"] if "plot_estimate" in kwargs else True self.logger = logging.getLogger(__name__) def infer_default_kappa_t(self, len_kappa_t = 10): """ Infer default effect strength of simulated confounder on treatment. """ observed_common_causes_names = self._target_estimand.get_backdoor_variables() if len(observed_common_causes_names)>0: observed_common_causes = self._data[observed_common_causes_names] observed_common_causes = pd.get_dummies(observed_common_causes, drop_first=True) else: raise ValueError("There needs to be at least one common cause to" + "automatically compute the default value of kappa_t."+ " Provide a value for kappa_t") t = self._data[self._treatment_name] # Standardizing the data observed_common_causes = StandardScaler().fit_transform(observed_common_causes) if self.effect_on_t == "binary_flip": # Fit a model containing all confounders and compare predictions # using all features compared to all features except a given # confounder. tmodel = LogisticRegression().fit(observed_common_causes, t) tpred = tmodel.predict(observed_common_causes).astype(int) flips = [] for i in range(observed_common_causes.shape[1]): oldval = np.copy(observed_common_causes[:, i]) observed_common_causes[:,i] = 0 tcap = tmodel.predict(observed_common_causes).astype(int) observed_common_causes[:,i] = oldval flips.append(np.sum(abs(tcap-tpred))/tpred.shape[0]) min_coeff, max_coeff = min(flips), max(flips) elif self.effect_on_t == "linear": # Estimating the regression coefficient from standardized features to t corrcoef_var_t = np.corrcoef(observed_common_causes, t, rowvar=False)[-1, :-1] std_dev_t = np.std(t)[0] max_coeff = max(corrcoef_var_t) * std_dev_t min_coeff = min(corrcoef_var_t) * std_dev_t else: raise NotImplementedError("'" + self.effect_on_t + "' method not supported for confounders' effect on treatment") min_coeff, max_coeff = self._compute_min_max_coeff(min_coeff, max_coeff, self.frac_strength_treatment) # By default, return a plot with 10 points # consider 10 values of the effect of the unobserved confounder step = (max_coeff - min_coeff)/len_kappa_t self.logger.info("(Min, Max) kappa_t for observed common causes, ({0}, {1})".format( min_coeff, max_coeff)) if np.equal(max_coeff, min_coeff): return max_coeff else: return np.arange(min_coeff, max_coeff, step) def _compute_min_max_coeff(self, min_coeff, max_coeff, effect_strength_fraction): max_coeff = effect_strength_fraction * max_coeff min_coeff = effect_strength_fraction * min_coeff return min_coeff, max_coeff def infer_default_kappa_y(self, len_kappa_y = 10): """ Infer default effect strength of simulated confounder on treatment. """ observed_common_causes_names = self._target_estimand.get_backdoor_variables() if len(observed_common_causes_names)>0: observed_common_causes = self._data[observed_common_causes_names] observed_common_causes = pd.get_dummies(observed_common_causes, drop_first=True) else: raise ValueError("There needs to be at least one common cause to" + "automatically compute the default value of kappa_y."+ " Provide a value for kappa_y") y = self._data[self._outcome_name] # Standardizing the data observed_common_causes = StandardScaler().fit_transform(observed_common_causes) if self.effect_on_y == "binary_flip": # Fit a model containing all confounders and compare predictions # using all features compared to all features except a given # confounder. ymodel = LogisticRegression().fit(observed_common_causes, y) ypred = ymodel.predict(observed_common_causes).astype(int) flips = [] for i in range(observed_common_causes.shape[1]): oldval = np.copy(observed_common_causes[:, i]) observed_common_causes[:,i] = 0 ycap = ymodel.predict(observed_common_causes).astype(int) observed_common_causes[:,i] = oldval flips.append(np.sum(abs(ycap-ypred))/ypred.shape[0]) min_coeff, max_coeff = min(flips), max(flips) elif self.effect_on_y == "linear": corrcoef_var_y = np.corrcoef(observed_common_causes, y, rowvar=False)[-1, :-1] std_dev_y = np.std(y)[0] max_coeff = max(corrcoef_var_y) * std_dev_y min_coeff = min(corrcoef_var_y) * std_dev_y else: raise NotImplementedError("'" + self.effect_on_y + "' method not supported for confounders' effect on outcome") min_coeff, max_coeff = self._compute_min_max_coeff(min_coeff, max_coeff, self.frac_strength_outcome) # By default, return a plot with 10 points # consider 10 values of the effect of the unobserved confounder step = (max_coeff - min_coeff)/len_kappa_y self.logger.info("(Min, Max) kappa_y for observed common causes, ({0}, {1})".format( min_coeff, max_coeff)) if np.equal(max_coeff, min_coeff): return max_coeff else: return np.arange(min_coeff, max_coeff, step) def refute_estimate(self): """ This function attempts to add an unobserved common cause to the outcome and the treatment. At present, we have implemented the behavior for one dimensional behaviors for continuous and binary variables. This function can either take single valued inputs or a range of inputs. The function then looks at the data type of the input and then decides on the course of action. :return: CausalRefuter: An object that contains the estimated effect and a new effect and the name of the refutation used. """ if self.simulated_method_name == "linear-partial-R2": if not(isinstance(self._estimate.estimator, LinearRegressionEstimator)): raise NotImplementedError("Currently only LinearRegressionEstimator is supported for Sensitivity Analysis") if(len(self._estimate.estimator._effect_modifier_names) > 0): raise NotImplementedError("The current implementation does not support effect modifiers") if(self.frac_strength_outcome == 1): self.frac_strength_outcome = self.frac_strength_treatment analyzer = LinearSensitivityAnalyzer(estimator = self._estimate.estimator, data = self._data, treatment_name = self._treatment_name, percent_change_estimate = self.percent_change_estimate, significance_level = self.significance_level, benchmark_common_causes= self.benchmark_common_causes, null_hypothesis_effect = self.null_hypothesis_effect, frac_strength_treatment = self.frac_strength_treatment, frac_strength_outcome = self.frac_strength_outcome, common_causes_order = self._estimate.estimator._observed_common_causes.columns) analyzer.check_sensitivity(plot = self.plot_estimate) return analyzer if self.kappa_t is None: self.kappa_t = self.infer_default_kappa_t() if self.kappa_y is None: self.kappa_y = self.infer_default_kappa_y() if not isinstance(self.kappa_t, (list, np.ndarray)) and not isinstance(self.kappa_y, (list,np.ndarray)): # Deal with single value inputs new_data = copy.deepcopy(self._data) new_data = self.include_confounders_effect(new_data, self.kappa_t, self.kappa_y) new_estimator = CausalEstimator.get_estimator_object(new_data, self._target_estimand, self._estimate) new_effect = new_estimator.estimate_effect() refute = CausalRefutation(self._estimate.value, new_effect.value, refutation_type="Refute: Add an Unobserved Common Cause") refute.new_effect_array = np.array(new_effect.value) refute.new_effect = new_effect.value refute.add_refuter(self) return refute else: # Deal with multiple value inputs if isinstance(self.kappa_t, (list, np.ndarray)) and isinstance(self.kappa_y, (list, np.ndarray)): # Deal with range inputs # Get a 2D matrix of values #x,y = np.meshgrid(self.kappa_t, self.kappa_y) # x,y are both MxN results_matrix = np.random.rand(len(self.kappa_t),len(self.kappa_y)) # Matrix to hold all the results of NxM orig_data = copy.deepcopy(self._data) for i in range(len(self.kappa_t)): for j in range(len(self.kappa_y)): new_data = self.include_confounders_effect(orig_data, self.kappa_t[i], self.kappa_y[j]) new_estimator = CausalEstimator.get_estimator_object(new_data, self._target_estimand, self._estimate) new_effect = new_estimator.estimate_effect() refute = CausalRefutation(self._estimate.value, new_effect.value, refutation_type="Refute: Add an Unobserved Common Cause") results_matrix[i][j] = refute.new_effect # Populate the results refute.new_effect_array = results_matrix refute.new_effect = (np.min(results_matrix), np.max(results_matrix)) # Store the values into the refute object refute.add_refuter(self) if self.plotmethod is None: return refute import matplotlib import matplotlib.pyplot as plt fig = plt.figure(figsize=(6,5)) left, bottom, width, height = 0.1, 0.1, 0.8, 0.8 ax = fig.add_axes([left, bottom, width, height]) oe = self._estimate.value contour_levels = [oe/4.0, oe/2.0, (3.0/4)*oe, oe] contour_levels.extend([0, np.min(results_matrix), np.max(results_matrix)]) if self.plotmethod=="contour": cp = plt.contourf(self.kappa_y, self.kappa_t, results_matrix, levels=sorted(contour_levels)) # Adding a label on the contour line for the original estimate fmt = {} trueeffect_index = np.where(cp.levels==oe)[0][0] fmt[cp.levels[trueeffect_index]] = "Estimated Effect" # Label every other level using strings plt.clabel(cp,[cp.levels[trueeffect_index]],inline=True, fmt=fmt) plt.colorbar(cp) elif self.plotmethod=="colormesh": cp = plt.pcolormesh(self.kappa_y, self.kappa_t, results_matrix, shading="nearest") plt.colorbar(cp, ticks=contour_levels) ax.yaxis.set_ticks(self.kappa_t) ax.xaxis.set_ticks(self.kappa_y) plt.xticks(rotation=45) ax.set_title('Effect of Unobserved Common Cause') ax.set_ylabel('Value of Linear Constant on Treatment') ax.set_xlabel('Value of Linear Constant on Outcome') plt.show() return refute elif isinstance(self.kappa_t, (list, np.ndarray)): outcomes = np.random.rand(len(self.kappa_t)) orig_data = copy.deepcopy(self._data) for i in range(0,len(self.kappa_t)): new_data = self.include_confounders_effect(orig_data, self.kappa_t[i], self.kappa_y) new_estimator = CausalEstimator.get_estimator_object(new_data, self._target_estimand, self._estimate) new_effect = new_estimator.estimate_effect() refute = CausalRefutation(self._estimate.value, new_effect.value, refutation_type="Refute: Add an Unobserved Common Cause") self.logger.debug(refute) outcomes[i] = refute.new_effect # Populate the results refute.new_effect_array = outcomes refute.new_effect = (np.min(outcomes), np.max(outcomes)) refute.add_refuter(self) if self.plotmethod is None: return refute import matplotlib import matplotlib.pyplot as plt fig = plt.figure(figsize=(6,5)) left, bottom, width, height = 0.1, 0.1, 0.8, 0.8 ax = fig.add_axes([left, bottom, width, height]) plt.plot(self.kappa_t, outcomes) plt.axhline(self._estimate.value, linestyle='--',color="gray") ax.set_title('Effect of Unobserved Common Cause') ax.set_xlabel('Value of Linear Constant on Treatment') ax.set_ylabel('Estimated Effect after adding the common cause') plt.show() return refute elif isinstance(self.kappa_y, (list, np.ndarray)): outcomes = np.random.rand(len(self.kappa_y)) orig_data = copy.deepcopy(self._data) for i in range(0, len(self.kappa_y)): new_data = self.include_confounders_effect(orig_data, self.kappa_t, self.kappa_y[i]) new_estimator = CausalEstimator.get_estimator_object(new_data, self._target_estimand, self._estimate) new_effect = new_estimator.estimate_effect() refute = CausalRefutation(self._estimate.value, new_effect.value, refutation_type="Refute: Add an Unobserved Common Cause") self.logger.debug(refute) outcomes[i] = refute.new_effect # Populate the results refute.new_effect_array = outcomes refute.new_effect = (np.min(outcomes), np.max(outcomes)) refute.add_refuter(self) if self.plotmethod is None: return refute import matplotlib import matplotlib.pyplot as plt fig = plt.figure(figsize=(6,5)) left, bottom, width, height = 0.1, 0.1, 0.8, 0.8 ax = fig.add_axes([left, bottom, width, height]) plt.plot(self.kappa_y, outcomes) plt.axhline(self._estimate.value, linestyle='--',color="gray") ax.set_title('Effect of Unobserved Common Cause') ax.set_xlabel('Value of Linear Constant on Outcome') ax.set_ylabel('Estimated Effect after adding the common cause') plt.show() return refute def include_confounders_effect(self, new_data, kappa_t, kappa_y): """ This function deals with the change in the value of the data due to the effect of the unobserved confounder. In the case of a binary flip, we flip only if the random number is greater than the threshold set. In the case of a linear effect, we use the variable as the linear regression constant. :param new_data: pandas.DataFrame: The data to be changed due to the effects of the unobserved confounder. :param kappa_t: numpy.float64: The value of the threshold for binary_flip or the value of the regression coefficient for linear effect. :param kappa_y: numpy.float64: The value of the threshold for binary_flip or the value of the regression coefficient for linear effect. :return: pandas.DataFrame: The DataFrame that includes the effects of the unobserved confounder. """ num_rows = self._data.shape[0] stdnorm = scipy.stats.norm() w_random = stdnorm.rvs(num_rows) if self.effect_on_t == "binary_flip": alpha = 2*kappa_t-1 if kappa_t >=0.5 else 1-2*kappa_t interval = stdnorm.interval(alpha) rel_interval = interval[0] if kappa_t >=0.5 else interval[1] new_data.loc[rel_interval <= w_random, self._treatment_name ] = 1- new_data.loc[rel_interval <= w_random, self._treatment_name] for tname in self._treatment_name: if pd.api.types.is_bool_dtype(self._data[tname]): new_data = new_data.astype({tname: 'bool'}, copy=False) elif self.effect_on_t == "linear": confounder_t_effect = kappa_t * w_random # By default, we add the effect of simulated confounder for treatment. # But subtract it from outcome to create a negative correlation # assuming that the original confounder's effect was positive on both. # This is to remove the effect of the original confounder. new_data[self._treatment_name] = new_data[self._treatment_name].values + np.ndarray(shape=(num_rows,1), buffer=confounder_t_effect) else: raise NotImplementedError("'" + self.effect_on_t + "' method not supported for confounders' effect on treatment") if self.effect_on_y == "binary_flip": alpha = 2*kappa_y-1 if kappa_y >=0.5 else 1-2*kappa_y interval = stdnorm.interval(alpha) rel_interval = interval[0] if kappa_y >=0.5 else interval[1] new_data.loc[rel_interval <= w_random, self._outcome_name ] = 1- new_data.loc[rel_interval <= w_random, self._outcome_name] for yname in self._outcome_name: if pd.api.types.is_bool_dtype(self._data[yname]): new_data = new_data.astype({yname: 'bool'}, copy=False) elif self.effect_on_y == "linear": confounder_y_effect = (-1) * kappa_y * w_random # By default, we add the effect of simulated confounder for treatment. # But subtract it from outcome to create a negative correlation # assuming that the original confounder's effect was positive on both. # This is to remove the effect of the original confounder. new_data[self._outcome_name] = new_data[self._outcome_name].values + np.ndarray(shape=(num_rows,1), buffer=confounder_y_effect) else: raise NotImplementedError("'" + self.effect_on_y+ "' method not supported for confounders' effect on outcome") return new_data def include_simulated_confounder(self, convergence_threshold = 0.1, c_star_max = 1000): ''' This function simulates an unobserved confounder based on the data using the following steps: 1. It calculates the "residuals" from the treatment and outcome model i.) The outcome model has outcome as the dependent variable and all the observed variables including treatment as independent variables ii.) The treatment model has treatment as the dependent variable and all the observed variables as independent variables. 2. U is an intermediate random variable drawn from the normal distribution with the weighted average of residuals as mean and a unit variance U ~ N(c1*d_y + c2*d_t, 1) where *d_y and d_t are residuals from the treatment and outcome model *c1 and c2 are coefficients to the residuals 3. The final U, which is the simulated unobserved confounder is obtained by debiasing the intermediate variable U by residualising it with X Choosing the coefficients c1 and c2: The coefficients are chosen based on these basic assumptions: 1. There is a hyperbolic relationship satisfying c1*c2 = c_star 2. c_star is chosen from a range of possible values based on the correlation of the obtained simulated variable with outcome and treatment. 3. The product of correlations with treatment and outcome should be at a minimum distance to the maximum correlations with treatment and outcome in any of the observed confounders 4. The ratio of the weights should be such that they maintain the ratio of the maximum possible observed coefficients within some confidence interval :param c_star_max: The maximum possible value for the hyperbolic curve on which the coefficients to the residuals lie. It defaults to 1000 in the code if not specified by the user. :type int :param convergence_threshold: The threshold to check the plateauing of the correlation while selecting a c_star. It defaults to 0.1 in the code if not specified by the user :type float :returns: The simulated values of the unobserved confounder based on the data :type pandas.core.series.Series ''' #Obtaining the list of observed variables required_variables = True observed_variables = self.choose_variables(required_variables) observed_variables_with_treatment_and_outcome = observed_variables + self._treatment_name + self._outcome_name #Taking a subset of the dataframe that has only observed variables self._data = self._data[observed_variables_with_treatment_and_outcome] #Residuals from the outcome model obtained by fitting a linear model y = self._data[self._outcome_name[0]] observed_variables_with_treatment = observed_variables + self._treatment_name X = self._data[observed_variables_with_treatment] model = sm.OLS(y,X.astype('float')) results = model.fit() residuals_y = y - results.fittedvalues d_y = list(pd.Series(residuals_y)) #Residuals from the treatment model obtained by fitting a linear model t = self._data[self._treatment_name[0]].astype('int64') X = self._data[observed_variables] model = sm.OLS(t,X) results = model.fit() residuals_t = t - results.fittedvalues d_t = list(pd.Series(residuals_t)) #Initialising product_cor_metric_observed with a really low value as finding maximum product_cor_metric_observed = -10000000000 for i in observed_variables: current_obs_confounder = self._data[i] outcome_values = self._data[self._outcome_name[0]] correlation_y = current_obs_confounder.corr(outcome_values) treatment_values = t correlation_t = current_obs_confounder.corr(treatment_values) product_cor_metric_current = correlation_y*correlation_t if product_cor_metric_current>=product_cor_metric_observed: product_cor_metric_observed = product_cor_metric_current correlation_t_observed = correlation_t correlation_y_observed = correlation_y #The user has an option to give the the effect_strength_on_y and effect_strength_on_t which can be then used instead of maximum correlation with treatment and outcome in the observed variables as it specifies the desired effect. if self.kappa_t is not None: correlation_t_observed = self.kappa_t if self.kappa_y is not None: correlation_y_observed = self.kappa_y #Choosing a c_star based on the data. #The correlations stop increasing upon increasing c_star after a certain value, that is it plateaus and we choose the value of c_star to be the value it plateaus. correlation_y_list = [] correlation_t_list = [] product_cor_metric_simulated_list = [] x_list = [] step = int(c_star_max/10) for i in range(0, int(c_star_max), step): c1 = math.sqrt(i) c2 = c1 final_U = self.generate_confounder_from_residuals(c1, c2, d_y, d_t, X) current_simulated_confounder = final_U outcome_values = self._data[self._outcome_name[0]] correlation_y = current_simulated_confounder.corr(outcome_values) correlation_y_list.append(correlation_y) treatment_values = t correlation_t = current_simulated_confounder.corr(treatment_values) correlation_t_list.append(correlation_t) product_cor_metric_simulated = correlation_y*correlation_t product_cor_metric_simulated_list.append(product_cor_metric_simulated) x_list.append(i) index = 1 while index<len(correlation_y_list): if (correlation_y_list[index]-correlation_y_list[index-1])<=convergence_threshold: c_star = x_list[index] break index = index+1 #Choosing c1 and c2 based on the hyperbolic relationship once c_star is chosen by going over various combinations of c1 and c2 values and choosing the combination which #which maintains the minimum distance between the product of correlations of the simulated variable and the product of maximum correlations of one of the observed variables # and additionally checks if the ratio of the weights are such that they maintain the ratio of the maximum possible observed coefficients within some confidence interval #c1_final and c2_final are initialised to the values on the hyperbolic curve such that c1_final = c2_final and c1_final*c2_final = c_star c1_final = math.sqrt(c_star) c2_final = math.sqrt(c_star) #initialising min_distance_between_product_cor_metrics to be a value greater than 1 min_distance_between_product_cor_metrics = 1.5 i = 0.05 threshold = c_star/0.05 while i<=threshold: c2 = i c1 = c_star/c2 final_U = self.generate_confounder_from_residuals(c1, c2, d_y, d_t, X) current_simulated_confounder = final_U outcome_values = self._data[self._outcome_name[0]] correlation_y = current_simulated_confounder.corr(outcome_values) treatment_values = t correlation_t = current_simulated_confounder.corr(treatment_values) product_cor_metric_simulated = correlation_y*correlation_t if min_distance_between_product_cor_metrics>=abs(product_cor_metric_simulated - product_cor_metric_observed): min_distance_between_product_cor_metrics = abs(product_cor_metric_simulated - product_cor_metric_observed) additional_condition = (correlation_y_observed/correlation_t_observed) if ((c1/c2) <= (additional_condition + 0.3*additional_condition)) and ((c1/c2) >= (additional_condition - 0.3*additional_condition)): #choose minimum positive value c1_final = c1 c2_final = c2 i = i*1.5 '''#closed form solution print("c_star_max before closed form", c_star_max) if max_correlation_with_t == -1000: c2 = 0 c1 = c_star_max else: additional_condition = abs(max_correlation_with_y/max_correlation_with_t) print("additional_condition", additional_condition) c2 = math.sqrt(c_star_max/additional_condition) c1 = c_star_max/c2''' final_U = self.generate_confounder_from_residuals(c1_final, c2_final, d_y, d_t, X) return final_U def generate_confounder_from_residuals(self, c1, c2, d_y, d_t, X): ''' This function takes the residuals from the treatment and outcome model and their coefficients and simulates the intermediate random variable U by taking the row wise normal distribution corresponding to each residual value and then debiasing the intermediate variable to get the final variable. :param c1: coefficient to the residual from the outcome model :type float :param c2: coefficient to the residual from the treatment model :type float :param d_y: residuals from the outcome model :type list :param d_t: residuals from the treatment model :type list :returns: The simulated values of the unobserved confounder based on the data :type pandas.core.series.Series ''' U = [] for j in range(len(d_t)): simulated_variable_mean = c1*d_y[j]+c2*d_t[j] simulated_variable_stddev = 1 U.append(np.random.normal(simulated_variable_mean, simulated_variable_stddev, 1)) U = np.array(U) model = sm.OLS(U,X) results = model.fit() U = U.reshape(-1, ) final_U = U - results.fittedvalues.values final_U = pd.Series(U) return final_U

import copy import logging import numpy as np import pandas as pd import scipy.stats from tqdm.auto import tqdm import math import statsmodels.api as sm from sklearn.preprocessing import StandardScaler from sklearn.linear_model import LogisticRegression from dowhy.causal_refuter import CausalRefutation from dowhy.causal_refuter import CausalRefuter from dowhy.causal_estimator import CausalEstimator from dowhy.causal_refuters.linear_sensitivity_analyzer import LinearSensitivityAnalyzer from dowhy.causal_estimators.linear_regression_estimator import LinearRegressionEstimator class AddUnobservedCommonCause(CausalRefuter): """Add an unobserved confounder for refutation. Supports additional parameters that can be specified in the refute_estimate() method. - 'confounders_effect_on_treatment': how the simulated confounder affects the value of treatment. This can be linear (for continuous treatment) or binary_flip (for binary treatment) - 'confounders_effect_on_outcome': how the simulated confounder affects the value of outcome. This can be linear (for continuous outcome) or binary_flip (for binary outcome) - 'effect_strength_on_treatment': parameter for the strength of the effect of simulated confounder on treatment. For linear effect, it is the regression coeffient. For binary_flip, it is the probability that simulated confounder's effect flips the value of treatment from 0 to 1 (or vice-versa). - 'effect_strength_on_outcome': parameter for the strength of the effect of simulated confounder on outcome. For linear effect, it is the regression coeffient. For binary_flip, it is the probability that simulated confounder's effect flips the value of outcome from 0 to 1 (or vice-versa). TODO: Needs an interpretation module """ def __init__(self, *args, **kwargs): """ Initialize the parameters required for the refuter. If effect_strength_on_treatment or effect_strength_on_outcome is not given, it is calculated automatically as a range between the minimum and maximum effect strength of observed confounders on treatment and outcome respectively. :param confounders_effect_on_treatment: str : The type of effect on the treatment due to the unobserved confounder. Possible values are ['binary_flip', 'linear'] :param confounders_effect_on_outcome: str : The type of effect on the outcome due to the unobserved confounder. Possible values are ['binary_flip', 'linear'] :param effect_strength_on_treatment: float, numpy.ndarray: This refers to the strength of the confounder on treatment. For a linear effect, it behaves like the regression coeffecient. For a binary flip it is the probability with which it can invert the value of the treatment. :param effect_strength_on_outcome: float, numpy.ndarray: This refers to the strength of the confounder on outcome. For a linear effect, it behaves like the regression coefficient. For a binary flip, it is the probability with which it can invert the value of the outcome. :param effect_fraction_on_treatment: float: If effect_strength_on_treatment is not provided, this parameter decides the effect strength of the simulated confounder as a fraction of the effect strength of observed confounders on treatment. Defaults to 1. :param effect_fraction_on_outcome: float: If effect_strength_on_outcome is not provided, this parameter decides the effect strength of the simulated confounder as a fraction of the effect strength of observed confounders on outcome. Defaults to 1. :param plotmethod: string: Type of plot to be shown. If None, no plot is generated. This parameter is used only only when more than one treatment confounder effect values or outcome confounder effect values are provided. Default is "colormesh". Supported values are "contour", "colormesh" when more than one value is provided for both confounder effect value parameters; "line" when provided for only one of them. :param simulated_method_name: method type to add unobserved common cause. "linear-partial-R2" for linear sensitivity analysis :param percent_change_estimate: It is the percentage of reduction of treatment estimate that could alter the results (default = 1) if percent_change_estimate = 1, the robustness value describes the strength of association of confounders with treatment and outcome in order to reduce the estimate by 100% i.e bring it down to 0. :param confounder_increases_estimate: True implies that confounder increases the absolute value of estimate and vice versa. (Default = False) :param benchmark_common_causes: names of variables for bounding strength of confounders :param significance_level: confidence interval for statistical inference(default = 0.05) :param null_hypothesis_effect: assumed effect under the null hypothesis :param plot_estimate: Generate contour plot for estimate while performing sensitivity analysis. (default = True). To override the setting, set plot_estimate = False. """ super().__init__(*args, **kwargs) self.effect_on_t = kwargs["confounders_effect_on_treatment"] if "confounders_effect_on_treatment" in kwargs else "binary_flip" self.effect_on_y = kwargs["confounders_effect_on_outcome"] if "confounders_effect_on_outcome" in kwargs else "linear" self.kappa_t = kwargs["effect_strength_on_treatment"] if "effect_strength_on_treatment" in kwargs else None self.kappa_y = kwargs["effect_strength_on_outcome"] if "effect_strength_on_outcome" in kwargs else None self.frac_strength_treatment = kwargs["effect_fraction_on_treatment"] if "effect_fraction_on_treatment" in kwargs else 1 self.frac_strength_outcome = kwargs["effect_fraction_on_outcome"] if "effect_fraction_on_outcome" in kwargs else 1 self.simulated_method_name = kwargs["simulated_method_name"] if "simulated_method_name" in kwargs else "linear_based" self.plotmethod = kwargs['plotmethod'] if "plotmethod" in kwargs else "colormesh" self.percent_change_estimate = kwargs["percent_change_estimate"] if 'percent_change_estimate' in kwargs else 1.0 self.significance_level = kwargs["significance_level"] if "significance_level" in kwargs else 0.05 self.confounder_increases_estimate = kwargs["confounder_increases_estimate"] if "confounder_increases_estimate" in kwargs else False self.benchmark_common_causes = kwargs["benchmark_common_causes"] if "benchmark_common_causes" in kwargs else None self.null_hypothesis_effect = kwargs["null_hypothesis_effect"] if "null_hypothesis_effect" in kwargs else 0 self.plot_estimate = kwargs["plot_estimate"] if "plot_estimate" in kwargs else True self.logger = logging.getLogger(__name__) def infer_default_kappa_t(self, len_kappa_t = 10): """ Infer default effect strength of simulated confounder on treatment. """ observed_common_causes_names = self._target_estimand.get_backdoor_variables() if len(observed_common_causes_names)>0: observed_common_causes = self._data[observed_common_causes_names] observed_common_causes = pd.get_dummies(observed_common_causes, drop_first=True) else: raise ValueError("There needs to be at least one common cause to" + "automatically compute the default value of kappa_t."+ " Provide a value for kappa_t") t = self._data[self._treatment_name] # Standardizing the data observed_common_causes = StandardScaler().fit_transform(observed_common_causes) if self.effect_on_t == "binary_flip": # Fit a model containing all confounders and compare predictions # using all features compared to all features except a given # confounder. tmodel = LogisticRegression().fit(observed_common_causes, t) tpred = tmodel.predict(observed_common_causes).astype(int) flips = [] for i in range(observed_common_causes.shape[1]): oldval = np.copy(observed_common_causes[:, i]) observed_common_causes[:,i] = 0 tcap = tmodel.predict(observed_common_causes).astype(int) observed_common_causes[:,i] = oldval flips.append(np.sum(abs(tcap-tpred))/tpred.shape[0]) min_coeff, max_coeff = min(flips), max(flips) elif self.effect_on_t == "linear": # Estimating the regression coefficient from standardized features to t corrcoef_var_t = np.corrcoef(observed_common_causes, t, rowvar=False)[-1, :-1] std_dev_t = np.std(t)[0] max_coeff = max(corrcoef_var_t) * std_dev_t min_coeff = min(corrcoef_var_t) * std_dev_t else: raise NotImplementedError("'" + self.effect_on_t + "' method not supported for confounders' effect on treatment") min_coeff, max_coeff = self._compute_min_max_coeff(min_coeff, max_coeff, self.frac_strength_treatment) # By default, return a plot with 10 points # consider 10 values of the effect of the unobserved confounder step = (max_coeff - min_coeff)/len_kappa_t self.logger.info("(Min, Max) kappa_t for observed common causes, ({0}, {1})".format( min_coeff, max_coeff)) if np.equal(max_coeff, min_coeff): return max_coeff else: return np.arange(min_coeff, max_coeff, step) def _compute_min_max_coeff(self, min_coeff, max_coeff, effect_strength_fraction): max_coeff = effect_strength_fraction * max_coeff min_coeff = effect_strength_fraction * min_coeff return min_coeff, max_coeff def infer_default_kappa_y(self, len_kappa_y = 10): """ Infer default effect strength of simulated confounder on treatment. """ observed_common_causes_names = self._target_estimand.get_backdoor_variables() if len(observed_common_causes_names)>0: observed_common_causes = self._data[observed_common_causes_names] observed_common_causes = pd.get_dummies(observed_common_causes, drop_first=True) else: raise ValueError("There needs to be at least one common cause to" + "automatically compute the default value of kappa_y."+ " Provide a value for kappa_y") y = self._data[self._outcome_name] # Standardizing the data observed_common_causes = StandardScaler().fit_transform(observed_common_causes) if self.effect_on_y == "binary_flip": # Fit a model containing all confounders and compare predictions # using all features compared to all features except a given # confounder. ymodel = LogisticRegression().fit(observed_common_causes, y) ypred = ymodel.predict(observed_common_causes).astype(int) flips = [] for i in range(observed_common_causes.shape[1]): oldval = np.copy(observed_common_causes[:, i]) observed_common_causes[:,i] = 0 ycap = ymodel.predict(observed_common_causes).astype(int) observed_common_causes[:,i] = oldval flips.append(np.sum(abs(ycap-ypred))/ypred.shape[0]) min_coeff, max_coeff = min(flips), max(flips) elif self.effect_on_y == "linear": corrcoef_var_y = np.corrcoef(observed_common_causes, y, rowvar=False)[-1, :-1] std_dev_y = np.std(y)[0] max_coeff = max(corrcoef_var_y) * std_dev_y min_coeff = min(corrcoef_var_y) * std_dev_y else: raise NotImplementedError("'" + self.effect_on_y + "' method not supported for confounders' effect on outcome") min_coeff, max_coeff = self._compute_min_max_coeff(min_coeff, max_coeff, self.frac_strength_outcome) # By default, return a plot with 10 points # consider 10 values of the effect of the unobserved confounder step = (max_coeff - min_coeff)/len_kappa_y self.logger.info("(Min, Max) kappa_y for observed common causes, ({0}, {1})".format( min_coeff, max_coeff)) if np.equal(max_coeff, min_coeff): return max_coeff else: return np.arange(min_coeff, max_coeff, step) def refute_estimate(self, show_progress_bar=False): """ This function attempts to add an unobserved common cause to the outcome and the treatment. At present, we have implemented the behavior for one dimensional behaviors for continuous and binary variables. This function can either take single valued inputs or a range of inputs. The function then looks at the data type of the input and then decides on the course of action. :return: CausalRefuter: An object that contains the estimated effect and a new effect and the name of the refutation used. """ if self.simulated_method_name == "linear-partial-R2": if not(isinstance(self._estimate.estimator, LinearRegressionEstimator)): raise NotImplementedError("Currently only LinearRegressionEstimator is supported for Sensitivity Analysis") if(len(self._estimate.estimator._effect_modifier_names) > 0): raise NotImplementedError("The current implementation does not support effect modifiers") if(self.frac_strength_outcome == 1): self.frac_strength_outcome = self.frac_strength_treatment analyzer = LinearSensitivityAnalyzer(estimator = self._estimate.estimator, data = self._data, treatment_name = self._treatment_name, percent_change_estimate = self.percent_change_estimate, significance_level = self.significance_level, benchmark_common_causes= self.benchmark_common_causes, null_hypothesis_effect = self.null_hypothesis_effect, frac_strength_treatment = self.frac_strength_treatment, frac_strength_outcome = self.frac_strength_outcome, common_causes_order = self._estimate.estimator._observed_common_causes.columns) analyzer.check_sensitivity(plot = self.plot_estimate) return analyzer if self.kappa_t is None: self.kappa_t = self.infer_default_kappa_t() if self.kappa_y is None: self.kappa_y = self.infer_default_kappa_y() if not isinstance(self.kappa_t, (list, np.ndarray)) and not isinstance(self.kappa_y, (list,np.ndarray)): # Deal with single value inputs new_data = copy.deepcopy(self._data) new_data = self.include_confounders_effect(new_data, self.kappa_t, self.kappa_y) new_estimator = CausalEstimator.get_estimator_object(new_data, self._target_estimand, self._estimate) new_effect = new_estimator.estimate_effect() refute = CausalRefutation(self._estimate.value, new_effect.value, refutation_type="Refute: Add an Unobserved Common Cause") refute.new_effect_array = np.array(new_effect.value) refute.new_effect = new_effect.value refute.add_refuter(self) return refute else: # Deal with multiple value inputs if isinstance(self.kappa_t, (list, np.ndarray)) and isinstance(self.kappa_y, (list, np.ndarray)): # Deal with range inputs # Get a 2D matrix of values #x,y = np.meshgrid(self.kappa_t, self.kappa_y) # x,y are both MxN results_matrix = np.random.rand(len(self.kappa_t),len(self.kappa_y)) # Matrix to hold all the results of NxM orig_data = copy.deepcopy(self._data) for i in tqdm(range(len(self.kappa_t)), colour=CausalRefuter.PROGRESS_BAR_COLOR, disable = not show_progress_bar, desc="Refuting Estimates: "): for j in range(len(self.kappa_y)): new_data = self.include_confounders_effect(orig_data, self.kappa_t[i], self.kappa_y[j]) new_estimator = CausalEstimator.get_estimator_object(new_data, self._target_estimand, self._estimate) new_effect = new_estimator.estimate_effect() refute = CausalRefutation(self._estimate.value, new_effect.value, refutation_type="Refute: Add an Unobserved Common Cause") results_matrix[i][j] = refute.new_effect # Populate the results refute.new_effect_array = results_matrix refute.new_effect = (np.min(results_matrix), np.max(results_matrix)) # Store the values into the refute object refute.add_refuter(self) if self.plotmethod is None: return refute import matplotlib import matplotlib.pyplot as plt fig = plt.figure(figsize=(6,5)) left, bottom, width, height = 0.1, 0.1, 0.8, 0.8 ax = fig.add_axes([left, bottom, width, height]) oe = self._estimate.value contour_levels = [oe/4.0, oe/2.0, (3.0/4)*oe, oe] contour_levels.extend([0, np.min(results_matrix), np.max(results_matrix)]) if self.plotmethod=="contour": cp = plt.contourf(self.kappa_y, self.kappa_t, results_matrix, levels=sorted(contour_levels)) # Adding a label on the contour line for the original estimate fmt = {} trueeffect_index = np.where(cp.levels==oe)[0][0] fmt[cp.levels[trueeffect_index]] = "Estimated Effect" # Label every other level using strings plt.clabel(cp,[cp.levels[trueeffect_index]],inline=True, fmt=fmt) plt.colorbar(cp) elif self.plotmethod=="colormesh": cp = plt.pcolormesh(self.kappa_y, self.kappa_t, results_matrix, shading="nearest") plt.colorbar(cp, ticks=contour_levels) ax.yaxis.set_ticks(self.kappa_t) ax.xaxis.set_ticks(self.kappa_y) plt.xticks(rotation=45) ax.set_title('Effect of Unobserved Common Cause') ax.set_ylabel('Value of Linear Constant on Treatment') ax.set_xlabel('Value of Linear Constant on Outcome') plt.show() return refute elif isinstance(self.kappa_t, (list, np.ndarray)): outcomes = np.random.rand(len(self.kappa_t)) orig_data = copy.deepcopy(self._data) for i in tqdm(range(0,len(self.kappa_t)), colour=CausalRefuter.PROGRESS_BAR_COLOR, disable = not show_progress_bar, desc="Refuting Estimates: "): new_data = self.include_confounders_effect(orig_data, self.kappa_t[i], self.kappa_y) new_estimator = CausalEstimator.get_estimator_object(new_data, self._target_estimand, self._estimate) new_effect = new_estimator.estimate_effect() refute = CausalRefutation(self._estimate.value, new_effect.value, refutation_type="Refute: Add an Unobserved Common Cause") self.logger.debug(refute) outcomes[i] = refute.new_effect # Populate the results refute.new_effect_array = outcomes refute.new_effect = (np.min(outcomes), np.max(outcomes)) refute.add_refuter(self) if self.plotmethod is None: return refute import matplotlib import matplotlib.pyplot as plt fig = plt.figure(figsize=(6,5)) left, bottom, width, height = 0.1, 0.1, 0.8, 0.8 ax = fig.add_axes([left, bottom, width, height]) plt.plot(self.kappa_t, outcomes) plt.axhline(self._estimate.value, linestyle='--',color="gray") ax.set_title('Effect of Unobserved Common Cause') ax.set_xlabel('Value of Linear Constant on Treatment') ax.set_ylabel('Estimated Effect after adding the common cause') plt.show() return refute elif isinstance(self.kappa_y, (list, np.ndarray)): outcomes = np.random.rand(len(self.kappa_y)) orig_data = copy.deepcopy(self._data) for i in tqdm(range(0,len(self.kappa_y)), colour=CausalRefuter.PROGRESS_BAR_COLOR, disable = not show_progress_bar, desc="Refuting Estimates: "): new_data = self.include_confounders_effect(orig_data, self.kappa_t, self.kappa_y[i]) new_estimator = CausalEstimator.get_estimator_object(new_data, self._target_estimand, self._estimate) new_effect = new_estimator.estimate_effect() refute = CausalRefutation(self._estimate.value, new_effect.value, refutation_type="Refute: Add an Unobserved Common Cause") self.logger.debug(refute) outcomes[i] = refute.new_effect # Populate the results refute.new_effect_array = outcomes refute.new_effect = (np.min(outcomes), np.max(outcomes)) refute.add_refuter(self) if self.plotmethod is None: return refute import matplotlib import matplotlib.pyplot as plt fig = plt.figure(figsize=(6,5)) left, bottom, width, height = 0.1, 0.1, 0.8, 0.8 ax = fig.add_axes([left, bottom, width, height]) plt.plot(self.kappa_y, outcomes) plt.axhline(self._estimate.value, linestyle='--',color="gray") ax.set_title('Effect of Unobserved Common Cause') ax.set_xlabel('Value of Linear Constant on Outcome') ax.set_ylabel('Estimated Effect after adding the common cause') plt.show() return refute def include_confounders_effect(self, new_data, kappa_t, kappa_y): """ This function deals with the change in the value of the data due to the effect of the unobserved confounder. In the case of a binary flip, we flip only if the random number is greater than the threshold set. In the case of a linear effect, we use the variable as the linear regression constant. :param new_data: pandas.DataFrame: The data to be changed due to the effects of the unobserved confounder. :param kappa_t: numpy.float64: The value of the threshold for binary_flip or the value of the regression coefficient for linear effect. :param kappa_y: numpy.float64: The value of the threshold for binary_flip or the value of the regression coefficient for linear effect. :return: pandas.DataFrame: The DataFrame that includes the effects of the unobserved confounder. """ num_rows = self._data.shape[0] stdnorm = scipy.stats.norm() w_random = stdnorm.rvs(num_rows) if self.effect_on_t == "binary_flip": alpha = 2*kappa_t-1 if kappa_t >=0.5 else 1-2*kappa_t interval = stdnorm.interval(alpha) rel_interval = interval[0] if kappa_t >=0.5 else interval[1] new_data.loc[rel_interval <= w_random, self._treatment_name ] = 1- new_data.loc[rel_interval <= w_random, self._treatment_name] for tname in self._treatment_name: if pd.api.types.is_bool_dtype(self._data[tname]): new_data = new_data.astype({tname: 'bool'}, copy=False) elif self.effect_on_t == "linear": confounder_t_effect = kappa_t * w_random # By default, we add the effect of simulated confounder for treatment. # But subtract it from outcome to create a negative correlation # assuming that the original confounder's effect was positive on both. # This is to remove the effect of the original confounder. new_data[self._treatment_name] = new_data[self._treatment_name].values + np.ndarray(shape=(num_rows,1), buffer=confounder_t_effect) else: raise NotImplementedError("'" + self.effect_on_t + "' method not supported for confounders' effect on treatment") if self.effect_on_y == "binary_flip": alpha = 2*kappa_y-1 if kappa_y >=0.5 else 1-2*kappa_y interval = stdnorm.interval(alpha) rel_interval = interval[0] if kappa_y >=0.5 else interval[1] new_data.loc[rel_interval <= w_random, self._outcome_name ] = 1- new_data.loc[rel_interval <= w_random, self._outcome_name] for yname in self._outcome_name: if pd.api.types.is_bool_dtype(self._data[yname]): new_data = new_data.astype({yname: 'bool'}, copy=False) elif self.effect_on_y == "linear": confounder_y_effect = (-1) * kappa_y * w_random # By default, we add the effect of simulated confounder for treatment. # But subtract it from outcome to create a negative correlation # assuming that the original confounder's effect was positive on both. # This is to remove the effect of the original confounder. new_data[self._outcome_name] = new_data[self._outcome_name].values + np.ndarray(shape=(num_rows,1), buffer=confounder_y_effect) else: raise NotImplementedError("'" + self.effect_on_y+ "' method not supported for confounders' effect on outcome") return new_data def include_simulated_confounder(self, convergence_threshold = 0.1, c_star_max = 1000): ''' This function simulates an unobserved confounder based on the data using the following steps: 1. It calculates the "residuals" from the treatment and outcome model i.) The outcome model has outcome as the dependent variable and all the observed variables including treatment as independent variables ii.) The treatment model has treatment as the dependent variable and all the observed variables as independent variables. 2. U is an intermediate random variable drawn from the normal distribution with the weighted average of residuals as mean and a unit variance U ~ N(c1*d_y + c2*d_t, 1) where *d_y and d_t are residuals from the treatment and outcome model *c1 and c2 are coefficients to the residuals 3. The final U, which is the simulated unobserved confounder is obtained by debiasing the intermediate variable U by residualising it with X Choosing the coefficients c1 and c2: The coefficients are chosen based on these basic assumptions: 1. There is a hyperbolic relationship satisfying c1*c2 = c_star 2. c_star is chosen from a range of possible values based on the correlation of the obtained simulated variable with outcome and treatment. 3. The product of correlations with treatment and outcome should be at a minimum distance to the maximum correlations with treatment and outcome in any of the observed confounders 4. The ratio of the weights should be such that they maintain the ratio of the maximum possible observed coefficients within some confidence interval :param c_star_max: The maximum possible value for the hyperbolic curve on which the coefficients to the residuals lie. It defaults to 1000 in the code if not specified by the user. :type int :param convergence_threshold: The threshold to check the plateauing of the correlation while selecting a c_star. It defaults to 0.1 in the code if not specified by the user :type float :returns: The simulated values of the unobserved confounder based on the data :type pandas.core.series.Series ''' #Obtaining the list of observed variables required_variables = True observed_variables = self.choose_variables(required_variables) observed_variables_with_treatment_and_outcome = observed_variables + self._treatment_name + self._outcome_name #Taking a subset of the dataframe that has only observed variables self._data = self._data[observed_variables_with_treatment_and_outcome] #Residuals from the outcome model obtained by fitting a linear model y = self._data[self._outcome_name[0]] observed_variables_with_treatment = observed_variables + self._treatment_name X = self._data[observed_variables_with_treatment] model = sm.OLS(y,X.astype('float')) results = model.fit() residuals_y = y - results.fittedvalues d_y = list(pd.Series(residuals_y)) #Residuals from the treatment model obtained by fitting a linear model t = self._data[self._treatment_name[0]].astype('int64') X = self._data[observed_variables] model = sm.OLS(t,X) results = model.fit() residuals_t = t - results.fittedvalues d_t = list(pd.Series(residuals_t)) #Initialising product_cor_metric_observed with a really low value as finding maximum product_cor_metric_observed = -10000000000 for i in observed_variables: current_obs_confounder = self._data[i] outcome_values = self._data[self._outcome_name[0]] correlation_y = current_obs_confounder.corr(outcome_values) treatment_values = t correlation_t = current_obs_confounder.corr(treatment_values) product_cor_metric_current = correlation_y*correlation_t if product_cor_metric_current>=product_cor_metric_observed: product_cor_metric_observed = product_cor_metric_current correlation_t_observed = correlation_t correlation_y_observed = correlation_y #The user has an option to give the the effect_strength_on_y and effect_strength_on_t which can be then used instead of maximum correlation with treatment and outcome in the observed variables as it specifies the desired effect. if self.kappa_t is not None: correlation_t_observed = self.kappa_t if self.kappa_y is not None: correlation_y_observed = self.kappa_y #Choosing a c_star based on the data. #The correlations stop increasing upon increasing c_star after a certain value, that is it plateaus and we choose the value of c_star to be the value it plateaus. correlation_y_list = [] correlation_t_list = [] product_cor_metric_simulated_list = [] x_list = [] step = int(c_star_max/10) for i in range(0, int(c_star_max), step): c1 = math.sqrt(i) c2 = c1 final_U = self.generate_confounder_from_residuals(c1, c2, d_y, d_t, X) current_simulated_confounder = final_U outcome_values = self._data[self._outcome_name[0]] correlation_y = current_simulated_confounder.corr(outcome_values) correlation_y_list.append(correlation_y) treatment_values = t correlation_t = current_simulated_confounder.corr(treatment_values) correlation_t_list.append(correlation_t) product_cor_metric_simulated = correlation_y*correlation_t product_cor_metric_simulated_list.append(product_cor_metric_simulated) x_list.append(i) index = 1 while index<len(correlation_y_list): if (correlation_y_list[index]-correlation_y_list[index-1])<=convergence_threshold: c_star = x_list[index] break index = index+1 #Choosing c1 and c2 based on the hyperbolic relationship once c_star is chosen by going over various combinations of c1 and c2 values and choosing the combination which #which maintains the minimum distance between the product of correlations of the simulated variable and the product of maximum correlations of one of the observed variables # and additionally checks if the ratio of the weights are such that they maintain the ratio of the maximum possible observed coefficients within some confidence interval #c1_final and c2_final are initialised to the values on the hyperbolic curve such that c1_final = c2_final and c1_final*c2_final = c_star c1_final = math.sqrt(c_star) c2_final = math.sqrt(c_star) #initialising min_distance_between_product_cor_metrics to be a value greater than 1 min_distance_between_product_cor_metrics = 1.5 i = 0.05 threshold = c_star/0.05 while i<=threshold: c2 = i c1 = c_star/c2 final_U = self.generate_confounder_from_residuals(c1, c2, d_y, d_t, X) current_simulated_confounder = final_U outcome_values = self._data[self._outcome_name[0]] correlation_y = current_simulated_confounder.corr(outcome_values) treatment_values = t correlation_t = current_simulated_confounder.corr(treatment_values) product_cor_metric_simulated = correlation_y*correlation_t if min_distance_between_product_cor_metrics>=abs(product_cor_metric_simulated - product_cor_metric_observed): min_distance_between_product_cor_metrics = abs(product_cor_metric_simulated - product_cor_metric_observed) additional_condition = (correlation_y_observed/correlation_t_observed) if ((c1/c2) <= (additional_condition + 0.3*additional_condition)) and ((c1/c2) >= (additional_condition - 0.3*additional_condition)): #choose minimum positive value c1_final = c1 c2_final = c2 i = i*1.5 '''#closed form solution print("c_star_max before closed form", c_star_max) if max_correlation_with_t == -1000: c2 = 0 c1 = c_star_max else: additional_condition = abs(max_correlation_with_y/max_correlation_with_t) print("additional_condition", additional_condition) c2 = math.sqrt(c_star_max/additional_condition) c1 = c_star_max/c2''' final_U = self.generate_confounder_from_residuals(c1_final, c2_final, d_y, d_t, X) return final_U def generate_confounder_from_residuals(self, c1, c2, d_y, d_t, X): ''' This function takes the residuals from the treatment and outcome model and their coefficients and simulates the intermediate random variable U by taking the row wise normal distribution corresponding to each residual value and then debiasing the intermediate variable to get the final variable. :param c1: coefficient to the residual from the outcome model :type float :param c2: coefficient to the residual from the treatment model :type float :param d_y: residuals from the outcome model :type list :param d_t: residuals from the treatment model :type list :returns: The simulated values of the unobserved confounder based on the data :type pandas.core.series.Series ''' U = [] for j in range(len(d_t)): simulated_variable_mean = c1*d_y[j]+c2*d_t[j] simulated_variable_stddev = 1 U.append(np.random.normal(simulated_variable_mean, simulated_variable_stddev, 1)) U = np.array(U) model = sm.OLS(U,X) results = model.fit() U = U.reshape(-1, ) final_U = U - results.fittedvalues.values final_U = pd.Series(U) return final_U

yemaedahrav

a38a03f8b2daa0627833821e92c1b9117925e331

f94638633ef23064c69c261c324cc4739d036ac0

we need tqdm.notebook only if user is running the code in a notebook. Otherwise we need tqdm. better to use tqdm.auto. see this example: https://github.com/tqdm/tqdm/pull/1218

amit-sharma

py-why/dowhy

fixed warnings and progrss bar improvements

Fixed the warnings arising in propensity score estimators and added optional progress bars for refuters Signed-off-by: Amey Varhade <ameyvarhade@gmail.com>

2022-07-20 18:03:07+00:00

2022-08-19 03:36:42+00:00

dowhy/causal_refuters/data_subset_refuter.py

import numpy as np import logging from joblib import Parallel, delayed from dowhy.causal_refuter import CausalRefuter, CausalRefutation from dowhy.causal_estimator import CausalEstimator class DataSubsetRefuter(CausalRefuter): """Refute an estimate by rerunning it on a random subset of the original data. Supports additional parameters that can be specified in the refute_estimate() method. For joblib-related parameters (n_jobs, verbose), please refer to the joblib documentation for more details (https://joblib.readthedocs.io/en/latest/generated/joblib.Parallel.html). :param subset_fraction: Fraction of the data to be used for re-estimation, which is ``DataSubsetRefuter.DEFAULT_SUBSET_FRACTION`` by default. :type subset_fraction: float, optional :param num_simulations: The number of simulations to be run, which is ``CausalRefuter.DEFAULT_NUM_SIMULATIONS`` by default :type num_simulations: int, optional :param random_state: The seed value to be added if we wish to repeat the same random behavior. If we with to repeat the same behavior we push the same seed in the psuedo-random generator :type random_state: int, RandomState, optional :param n_jobs: The maximum number of concurrently running jobs. If -1 all CPUs are used. If 1 is given, no parallel computing code is used at all (this is the default). :type n_jobs: int, optional :param verbose: The verbosity level: if non zero, progress messages are printed. Above 50, the output is sent to stdout. The frequency of the messages increases with the verbosity level. If it more than 10, all iterations are reported. The default is 0. :type verbose: int, optional """ # The default subset of the data to be used DEFAULT_SUBSET_FRACTION = 0.8 def __init__(self, *args, **kwargs): super().__init__(*args, **kwargs) self._subset_fraction = kwargs.pop("subset_fraction", 0.8) self._num_simulations = kwargs.pop("num_simulations", CausalRefuter.DEFAULT_NUM_SIMULATIONS ) self._random_state = kwargs.pop("random_state",None) self.logger = logging.getLogger(__name__) def refute_estimate(self): sample_estimates = np.zeros(self._num_simulations) self.logger.info("Refutation over {} simulated datasets of size {} each" .format(self._subset_fraction ,self._subset_fraction*len(self._data.index) ) ) def refute_once(): if self._random_state is None: new_data = self._data.sample(frac=self._subset_fraction) else: new_data = self._data.sample(frac=self._subset_fraction, random_state=self._random_state) new_estimator = CausalEstimator.get_estimator_object(new_data, self._target_estimand, self._estimate) new_effect = new_estimator.estimate_effect() return new_effect.value # Run refutation in parallel sample_estimates = Parallel( n_jobs=self._n_jobs, verbose=self._verbose )(delayed(refute_once)() for _ in range(self._num_simulations)) sample_estimates = np.array(sample_estimates) refute = CausalRefutation( self._estimate.value, np.mean(sample_estimates), refutation_type="Refute: Use a subset of data" ) # We want to see if the estimate falls in the same distribution as the one generated by the refuter # Ideally that should be the case as choosing a subset should not have a significant effect on the ability # of the treatment to affect the outcome refute.add_significance_test_results( self.test_significance(self._estimate, sample_estimates) ) refute.add_refuter(self) return refute

import numpy as np import logging from joblib import Parallel, delayed from tqdm.auto import tqdm from dowhy.causal_refuter import CausalRefuter, CausalRefutation from dowhy.causal_estimator import CausalEstimator class DataSubsetRefuter(CausalRefuter): """Refute an estimate by rerunning it on a random subset of the original data. Supports additional parameters that can be specified in the refute_estimate() method. For joblib-related parameters (n_jobs, verbose), please refer to the joblib documentation for more details (https://joblib.readthedocs.io/en/latest/generated/joblib.Parallel.html). :param subset_fraction: Fraction of the data to be used for re-estimation, which is ``DataSubsetRefuter.DEFAULT_SUBSET_FRACTION`` by default. :type subset_fraction: float, optional :param num_simulations: The number of simulations to be run, which is ``CausalRefuter.DEFAULT_NUM_SIMULATIONS`` by default :type num_simulations: int, optional :param random_state: The seed value to be added if we wish to repeat the same random behavior. If we with to repeat the same behavior we push the same seed in the psuedo-random generator :type random_state: int, RandomState, optional :param n_jobs: The maximum number of concurrently running jobs. If -1 all CPUs are used. If 1 is given, no parallel computing code is used at all (this is the default). :type n_jobs: int, optional :param verbose: The verbosity level: if non zero, progress messages are printed. Above 50, the output is sent to stdout. The frequency of the messages increases with the verbosity level. If it more than 10, all iterations are reported. The default is 0. :type verbose: int, optional """ # The default subset of the data to be used DEFAULT_SUBSET_FRACTION = 0.8 def __init__(self, *args, **kwargs): super().__init__(*args, **kwargs) self._subset_fraction = kwargs.pop("subset_fraction", 0.8) self._num_simulations = kwargs.pop("num_simulations", CausalRefuter.DEFAULT_NUM_SIMULATIONS ) self._random_state = kwargs.pop("random_state",None) self.logger = logging.getLogger(__name__) def refute_estimate(self, show_progress_bar=False): sample_estimates = np.zeros(self._num_simulations) self.logger.info("Refutation over {} simulated datasets of size {} each" .format(self._subset_fraction ,self._subset_fraction*len(self._data.index) ) ) def refute_once(): if self._random_state is None: new_data = self._data.sample(frac=self._subset_fraction) else: new_data = self._data.sample(frac=self._subset_fraction, random_state=self._random_state) new_estimator = CausalEstimator.get_estimator_object(new_data, self._target_estimand, self._estimate) new_effect = new_estimator.estimate_effect() return new_effect.value # Run refutation in parallel sample_estimates = Parallel( n_jobs=self._n_jobs, verbose=self._verbose )(delayed(refute_once)() for _ in tqdm(range(self._num_simulations), colour=CausalRefuter.PROGRESS_BAR_COLOR, disable = not show_progress_bar, desc="Refuting Estimates: ")) sample_estimates = np.array(sample_estimates) refute = CausalRefutation( self._estimate.value, np.mean(sample_estimates), refutation_type="Refute: Use a subset of data" ) # We want to see if the estimate falls in the same distribution as the one generated by the refuter # Ideally that should be the case as choosing a subset should not have a significant effect on the ability # of the treatment to affect the outcome refute.add_significance_test_results( self.test_significance(self._estimate, sample_estimates) ) refute.add_refuter(self) return refute

yemaedahrav

a38a03f8b2daa0627833821e92c1b9117925e331

f94638633ef23064c69c261c324cc4739d036ac0

better to define "green" as a static variable inside causalrefuter class. and then call it here as CausalRefuter.Progress_Bar_Color

amit-sharma

py-why/dowhy

Small correction in estimate_ftest_pvalue

The error for the model without inputs should be based on the difference of the observed values to the mean in the training data set. However, the mean of the test set was used instead.

2022-07-19 22:11:02+00:00

2022-08-16 13:11:57+00:00

dowhy/gcm/stats.py

"""Functions in this module should be considered experimental, meaning there might be breaking API changes in the future. """ from typing import Union, List, Optional, Callable import numpy as np from numpy.matlib import repmat from scipy import stats from sklearn.linear_model import LinearRegression from dowhy.gcm.constant import EPS from dowhy.gcm.util.general import shape_into_2d def quantile_based_fwer(p_values: Union[np.ndarray, List[float]], p_values_scaling: Optional[np.ndarray] = None, quantile: float = 0.5) -> float: """Applies a quantile based family wise error rate (FWER) control to the given p-values. This is based on the approach described in: Meinshausen, N., Meier, L. and Buehlmann, P. (2009). p-values for high-dimensional regression. J. Amer. Statist. Assoc.104 1671–1681 :param p_values: A list or array of p-values. :param p_values_scaling: An optional list of scaling factors for each p-value. :param quantile: The quantile used for the p-value adjustment. By default, this is the median (0.5). :return: The p-value that lies on the quantile threshold. Note that this is the quantile based on scaled values p_values / quantile. """ if quantile <= 0 or abs(quantile - 1) >= 1: raise ValueError("The given quantile is %f, but it needs to be on (0, 1]!" % quantile) p_values = np.array(p_values) if p_values_scaling is None: p_values_scaling = np.ones(p_values.shape[0]) if p_values.shape != p_values_scaling.shape: raise ValueError("The p-value scaling array needs to have the same dimension as the given p-values.") p_values_scaling = p_values_scaling[~np.isnan(p_values)] p_values = p_values[~np.isnan(p_values)] p_values = p_values * p_values_scaling p_values[p_values > 1] = 1.0 if p_values.shape[0] == 1: return float(p_values[0]) else: return float(min(1.0, np.quantile(p_values / quantile, quantile))) def marginal_expectation(prediction_method: Callable[[np.ndarray], np.ndarray], feature_samples: np.ndarray, baseline_samples: np.ndarray, baseline_feature_indices: List[int], return_averaged_results: bool = True, feature_perturbation: str = 'randomize_columns_jointly', max_batch_size: int = -1) -> np.ndarray: """ Estimates the marginal expectation for samples in baseline_noise_samples when randomizing features that are not part of baseline_feature_indices. This is, this function estimates y^i = E[Y | do(x^i_s)] := \\int_x_s' E[Y | x^i_s, x_s'] p(x_s') d x_s', where x^i_s is the i-th sample from baseline_noise_samples, s denotes the baseline_feature_indices and x_s' ~ X_s' denotes the randomized features that are not in s. For an approximation of the integral, the given prediction_method is evaluated multiple times for the same x^i_s, but different x_s' ~ X_s'. :param prediction_method: Prediction method of interest. This should expect a numpy array as input for making predictions. :param feature_samples: Samples from the joint distribution. These are used for randomizing the features that are not in baseline_feature_indices. :param baseline_samples: Samples for which the marginal expectation should be estimated. :param baseline_feature_indices: Column indices of the features in s. These values for these features are remain constant when estimating the expectation. :param return_averaged_results: If set to True, the expectation over all evaluated samples for the i-th baseline_noise_samples is returned. If set to False, all corresponding results for the i-th sample are returned. :param feature_perturbation: Type of feature permutation: 'randomize_columns_independently': Each feature not in s is randomly permuted separately. 'randomize_columns_jointly': All features not in s are jointly permuted. Note that this still represents an interventional distribution. :param max_batch_size: Maximum batch size for a estimating the predictions. This has a significant influence on the overall memory usage. If set to -1, all samples are used in one batch. :return: If return_averaged_results is False, a numpy array where the i-th entry belongs to the marginal expectation of x^i_s when randomizing the remaining features. If return_averaged_results is True, a two dimensional numpy array where the i-th entry contains all predictions for x^i_s when randomizing the remaining features. """ feature_samples, baseline_samples = shape_into_2d(feature_samples, baseline_samples) batch_size = baseline_samples.shape[0] if max_batch_size == -1 else max_batch_size result = [np.nan] * baseline_samples.shape[0] # Make copy to avoid manipulating the original matrix. feature_samples = np.array(feature_samples) features_to_randomize = np.delete(np.arange(0, feature_samples.shape[1]), baseline_feature_indices) if feature_perturbation == 'randomize_columns_independently': feature_samples = permute_features(feature_samples, features_to_randomize, False) elif feature_perturbation == 'randomize_columns_jointly': feature_samples = permute_features(feature_samples, features_to_randomize, True) else: raise ValueError("Unknown argument %s as feature_perturbation type!" % feature_perturbation) # The given prediction method has to be evaluated multiple times on a large amount of different inputs. Typically, # the batch evaluation of a prediction model on multiple inputs at the same time is significantly faster # than evaluating it on single simples in a for-loop. To make use of this, we try to evaluate as many samples as # possible in one batch call of the prediction method. However, this also requires a lot of memory for many samples. # To overcome potential memory issues, multiple batch calls are performed, each with at most batch_size many # samples. The number of samples that are evaluated is normally # baseline_noise_samples.shape[0] * feature_samples.shape[0]. Here, we reduce it to # batch_size * feature_samples.shape[0]. If the batch_size would be set 1, then each baseline_noise_samples is # evaluated one by one in a for-loop. inputs = repmat(feature_samples, batch_size, 1) for offset in range(0, baseline_samples.shape[0], batch_size): # Each batch consist of at most batch_size * feature_samples.shape[0] many samples. If there are multiple # batches, the offset indicates the index of the current baseline_noise_samples that has not been evaluated yet. if offset + batch_size > baseline_samples.shape[0]: # If the batch size would be larger than the remaining amount of samples, it is reduced to only include the # remaining baseline_noise_samples. adjusted_batch_size = baseline_samples.shape[0] - offset inputs = inputs[:adjusted_batch_size * feature_samples.shape[0]] else: adjusted_batch_size = batch_size for index in range(adjusted_batch_size): # The inputs consist of batch_size many copies of feature_samples. Here, we set the columns of the features # in baseline_feature_indices to their respective values in baseline_noise_samples. inputs[index * feature_samples.shape[0]:(index + 1) * feature_samples.shape[0], baseline_feature_indices] = baseline_samples[offset + index, baseline_feature_indices] # After creating the (potentially large) input data matrix, we can evaluate the prediction method. predictions = np.array(prediction_method(inputs)) for index in range(adjusted_batch_size): # Here, offset + index now indicates the sample index in baseline_noise_samples. if return_averaged_results: # This would average all prediction results obtained for the 'offset + index'-th sample in # baseline_noise_samples. This is, y^(offset + index) = E[Y | do(x^(offset + index)_s)]. result[offset + index] = np.mean(predictions[index * feature_samples.shape[0]: (index + 1) * feature_samples.shape[0]], axis=0) else: # This would return all prediction results obtained for the 'offset + index'-th sample in # baseline_noise_samples, i.e. the results are not averaged. result[offset + index] = predictions[index * feature_samples.shape[0]: (index + 1) * feature_samples.shape[0]] return np.array(result) def permute_features(feature_samples: np.ndarray, features_to_permute: Union[List[int], np.ndarray], randomize_features_jointly: bool) -> np.ndarray: # Making copy to ensure that the original object is not modified. feature_samples = np.array(feature_samples) if randomize_features_jointly: # Permute samples jointly. This still represents an interventional distribution. feature_samples[:, features_to_permute] \ = feature_samples[np.random.choice(feature_samples.shape[0], feature_samples.shape[0], replace=False)][:, features_to_permute] else: # Permute samples independently. for feature in features_to_permute: np.random.shuffle(feature_samples[:, feature]) return feature_samples def estimate_ftest_pvalue(X_training_a: np.ndarray, X_training_b: np.ndarray, Y_training: np.ndarray, X_test_a: np.ndarray, X_test_b: np.ndarray, Y_test: np.ndarray) -> float: """Estimates the p-value for the null hypothesis that the same regression error with less parameters can be achieved. This is, a linear model trained on a data set A with d number of features has the same performance (in terms of squared error) relative to the number of features as a model trained on a data set B with k number features, where k < d. Here, both data sets need to have the same target values. A small p-value would indicate that the model performances are significantly different. Note that all given test samples are utilized in the f-test. See https://en.wikipedia.org/wiki/F-test#Regression_problems for more details. :param X_training_a: Input training samples for model A. :param X_training_b: Input training samples for model B. These samples should have less features than samples in X_training_a. :param Y_training: Target training values. :param X_test_a: Test samples for model A. :param X_test_b: Test samples for model B. :param Y_test: Test values. :return: A p-value on [0, 1]. """ X_training_a, X_test_a = shape_into_2d(X_training_a, X_test_a) if X_training_b.size > 0: X_training_b, X_test_b = shape_into_2d(X_training_b, X_test_b) else: X_training_b = X_training_b.reshape(0, 0) X_test_b = X_test_b.reshape(0, 0) if X_training_a.shape[1] <= X_training_b.shape[1]: raise ValueError("The data X_training_a should have more dimensions (model parameters) than the data " "X_training_b!") ssr_a = np.sum( (Y_test - LinearRegression().fit(X_training_a, Y_training).predict(X_test_a)) ** 2) if X_training_b.shape[1] > 0: ssr_b = np.sum( (Y_test - LinearRegression().fit(X_training_b, Y_training).predict(X_test_b)) ** 2) else: ssr_b = np.sum((Y_test - np.mean(Y_test)) ** 2) dof_diff_1 = (X_test_a.shape[1] - X_test_b.shape[1]) # p1 - p2 dof_diff_2 = (X_test_a.shape[0] - X_test_a.shape[1] - 1) # n - p2 (parameters include intercept) f_statistic = (ssr_b - ssr_a) / dof_diff_1 * dof_diff_2 if ssr_a < EPS: ssr_a = 0 if ssr_b < EPS: ssr_b = 0 if ssr_a == 0 and ssr_b == 0: f_statistic = 0 elif ssr_a != 0: f_statistic /= ssr_a return stats.f.sf(f_statistic, dof_diff_1, dof_diff_2)

"""Functions in this module should be considered experimental, meaning there might be breaking API changes in the future. """ from typing import Union, List, Optional, Callable import numpy as np from numpy.matlib import repmat from scipy import stats from sklearn.linear_model import LinearRegression from dowhy.gcm.constant import EPS from dowhy.gcm.util.general import shape_into_2d def quantile_based_fwer(p_values: Union[np.ndarray, List[float]], p_values_scaling: Optional[np.ndarray] = None, quantile: float = 0.5) -> float: """Applies a quantile based family wise error rate (FWER) control to the given p-values. This is based on the approach described in: Meinshausen, N., Meier, L. and Buehlmann, P. (2009). p-values for high-dimensional regression. J. Amer. Statist. Assoc.104 1671–1681 :param p_values: A list or array of p-values. :param p_values_scaling: An optional list of scaling factors for each p-value. :param quantile: The quantile used for the p-value adjustment. By default, this is the median (0.5). :return: The p-value that lies on the quantile threshold. Note that this is the quantile based on scaled values p_values / quantile. """ if quantile <= 0 or abs(quantile - 1) >= 1: raise ValueError("The given quantile is %f, but it needs to be on (0, 1]!" % quantile) p_values = np.array(p_values) if p_values_scaling is None: p_values_scaling = np.ones(p_values.shape[0]) if p_values.shape != p_values_scaling.shape: raise ValueError("The p-value scaling array needs to have the same dimension as the given p-values.") p_values_scaling = p_values_scaling[~np.isnan(p_values)] p_values = p_values[~np.isnan(p_values)] p_values = p_values * p_values_scaling p_values[p_values > 1] = 1.0 if p_values.shape[0] == 1: return float(p_values[0]) else: return float(min(1.0, np.quantile(p_values / quantile, quantile))) def marginal_expectation(prediction_method: Callable[[np.ndarray], np.ndarray], feature_samples: np.ndarray, baseline_samples: np.ndarray, baseline_feature_indices: List[int], return_averaged_results: bool = True, feature_perturbation: str = 'randomize_columns_jointly', max_batch_size: int = -1) -> np.ndarray: """ Estimates the marginal expectation for samples in baseline_noise_samples when randomizing features that are not part of baseline_feature_indices. This is, this function estimates y^i = E[Y | do(x^i_s)] := \\int_x_s' E[Y | x^i_s, x_s'] p(x_s') d x_s', where x^i_s is the i-th sample from baseline_noise_samples, s denotes the baseline_feature_indices and x_s' ~ X_s' denotes the randomized features that are not in s. For an approximation of the integral, the given prediction_method is evaluated multiple times for the same x^i_s, but different x_s' ~ X_s'. :param prediction_method: Prediction method of interest. This should expect a numpy array as input for making predictions. :param feature_samples: Samples from the joint distribution. These are used for randomizing the features that are not in baseline_feature_indices. :param baseline_samples: Samples for which the marginal expectation should be estimated. :param baseline_feature_indices: Column indices of the features in s. These values for these features are remain constant when estimating the expectation. :param return_averaged_results: If set to True, the expectation over all evaluated samples for the i-th baseline_noise_samples is returned. If set to False, all corresponding results for the i-th sample are returned. :param feature_perturbation: Type of feature permutation: 'randomize_columns_independently': Each feature not in s is randomly permuted separately. 'randomize_columns_jointly': All features not in s are jointly permuted. Note that this still represents an interventional distribution. :param max_batch_size: Maximum batch size for a estimating the predictions. This has a significant influence on the overall memory usage. If set to -1, all samples are used in one batch. :return: If return_averaged_results is False, a numpy array where the i-th entry belongs to the marginal expectation of x^i_s when randomizing the remaining features. If return_averaged_results is True, a two dimensional numpy array where the i-th entry contains all predictions for x^i_s when randomizing the remaining features. """ feature_samples, baseline_samples = shape_into_2d(feature_samples, baseline_samples) batch_size = baseline_samples.shape[0] if max_batch_size == -1 else max_batch_size result = [np.nan] * baseline_samples.shape[0] # Make copy to avoid manipulating the original matrix. feature_samples = np.array(feature_samples) features_to_randomize = np.delete(np.arange(0, feature_samples.shape[1]), baseline_feature_indices) if feature_perturbation == 'randomize_columns_independently': feature_samples = permute_features(feature_samples, features_to_randomize, False) elif feature_perturbation == 'randomize_columns_jointly': feature_samples = permute_features(feature_samples, features_to_randomize, True) else: raise ValueError("Unknown argument %s as feature_perturbation type!" % feature_perturbation) # The given prediction method has to be evaluated multiple times on a large amount of different inputs. Typically, # the batch evaluation of a prediction model on multiple inputs at the same time is significantly faster # than evaluating it on single simples in a for-loop. To make use of this, we try to evaluate as many samples as # possible in one batch call of the prediction method. However, this also requires a lot of memory for many samples. # To overcome potential memory issues, multiple batch calls are performed, each with at most batch_size many # samples. The number of samples that are evaluated is normally # baseline_noise_samples.shape[0] * feature_samples.shape[0]. Here, we reduce it to # batch_size * feature_samples.shape[0]. If the batch_size would be set 1, then each baseline_noise_samples is # evaluated one by one in a for-loop. inputs = repmat(feature_samples, batch_size, 1) for offset in range(0, baseline_samples.shape[0], batch_size): # Each batch consist of at most batch_size * feature_samples.shape[0] many samples. If there are multiple # batches, the offset indicates the index of the current baseline_noise_samples that has not been evaluated yet. if offset + batch_size > baseline_samples.shape[0]: # If the batch size would be larger than the remaining amount of samples, it is reduced to only include the # remaining baseline_noise_samples. adjusted_batch_size = baseline_samples.shape[0] - offset inputs = inputs[:adjusted_batch_size * feature_samples.shape[0]] else: adjusted_batch_size = batch_size for index in range(adjusted_batch_size): # The inputs consist of batch_size many copies of feature_samples. Here, we set the columns of the features # in baseline_feature_indices to their respective values in baseline_noise_samples. inputs[index * feature_samples.shape[0]:(index + 1) * feature_samples.shape[0], baseline_feature_indices] = baseline_samples[offset + index, baseline_feature_indices] # After creating the (potentially large) input data matrix, we can evaluate the prediction method. predictions = np.array(prediction_method(inputs)) for index in range(adjusted_batch_size): # Here, offset + index now indicates the sample index in baseline_noise_samples. if return_averaged_results: # This would average all prediction results obtained for the 'offset + index'-th sample in # baseline_noise_samples. This is, y^(offset + index) = E[Y | do(x^(offset + index)_s)]. result[offset + index] = np.mean(predictions[index * feature_samples.shape[0]: (index + 1) * feature_samples.shape[0]], axis=0) else: # This would return all prediction results obtained for the 'offset + index'-th sample in # baseline_noise_samples, i.e. the results are not averaged. result[offset + index] = predictions[index * feature_samples.shape[0]: (index + 1) * feature_samples.shape[0]] return np.array(result) def permute_features(feature_samples: np.ndarray, features_to_permute: Union[List[int], np.ndarray], randomize_features_jointly: bool) -> np.ndarray: # Making copy to ensure that the original object is not modified. feature_samples = np.array(feature_samples) if randomize_features_jointly: # Permute samples jointly. This still represents an interventional distribution. feature_samples[:, features_to_permute] \ = feature_samples[np.random.choice(feature_samples.shape[0], feature_samples.shape[0], replace=False)][:, features_to_permute] else: # Permute samples independently. for feature in features_to_permute: np.random.shuffle(feature_samples[:, feature]) return feature_samples def estimate_ftest_pvalue(X_training_a: np.ndarray, X_training_b: np.ndarray, Y_training: np.ndarray, X_test_a: np.ndarray, X_test_b: np.ndarray, Y_test: np.ndarray) -> float: """Estimates the p-value for the null hypothesis that the same regression error with less parameters can be achieved. This is, a linear model trained on a data set A with d number of features has the same performance (in terms of squared error) relative to the number of features as a model trained on a data set B with k number features, where k < d. Here, both data sets need to have the same target values. A small p-value would indicate that the model performances are significantly different. Note that all given test samples are utilized in the f-test. See https://en.wikipedia.org/wiki/F-test#Regression_problems for more details. :param X_training_a: Input training samples for model A. :param X_training_b: Input training samples for model B. These samples should have less features than samples in X_training_a. :param Y_training: Target training values. :param X_test_a: Test samples for model A. :param X_test_b: Test samples for model B. :param Y_test: Test values. :return: A p-value on [0, 1]. """ X_training_a, X_test_a = shape_into_2d(X_training_a, X_test_a) if X_training_b.size > 0: X_training_b, X_test_b = shape_into_2d(X_training_b, X_test_b) else: X_training_b = X_training_b.reshape(0, 0) X_test_b = X_test_b.reshape(0, 0) if X_training_a.shape[1] <= X_training_b.shape[1]: raise ValueError("The data X_training_a should have more dimensions (model parameters) than the data " "X_training_b!") ssr_a = np.sum( (Y_test - LinearRegression().fit(X_training_a, Y_training).predict(X_test_a)) ** 2) if X_training_b.shape[1] > 0: ssr_b = np.sum( (Y_test - LinearRegression().fit(X_training_b, Y_training).predict(X_test_b)) ** 2) else: ssr_b = np.sum((Y_test - np.mean(Y_training)) ** 2) dof_diff_1 = (X_test_a.shape[1] - X_test_b.shape[1]) # p1 - p2 dof_diff_2 = (X_test_a.shape[0] - X_test_a.shape[1] - 1) # n - p2 (parameters include intercept) f_statistic = (ssr_b - ssr_a) / dof_diff_1 * dof_diff_2 if ssr_a < EPS: ssr_a = 0 if ssr_b < EPS: ssr_b = 0 if ssr_a == 0 and ssr_b == 0: f_statistic = 0 elif ssr_a != 0: f_statistic /= ssr_a return stats.f.sf(f_statistic, dof_diff_1, dof_diff_2)

bloebp

2b4832a91e7ab54d31b116d19958fddecc2c8510

fe22abab886c5aea768b8474295999a71d914be9

But this is not the error of the model (without inputs) though. Why does this make sense? Can you also point to any articles where this is advocated or advised?

kailashbuki

py-why/dowhy

Small correction in estimate_ftest_pvalue

The error for the model without inputs should be based on the difference of the observed values to the mean in the training data set. However, the mean of the test set was used instead.

2022-07-19 22:11:02+00:00

2022-08-16 13:11:57+00:00

dowhy/gcm/stats.py

"""Functions in this module should be considered experimental, meaning there might be breaking API changes in the future. """ from typing import Union, List, Optional, Callable import numpy as np from numpy.matlib import repmat from scipy import stats from sklearn.linear_model import LinearRegression from dowhy.gcm.constant import EPS from dowhy.gcm.util.general import shape_into_2d def quantile_based_fwer(p_values: Union[np.ndarray, List[float]], p_values_scaling: Optional[np.ndarray] = None, quantile: float = 0.5) -> float: """Applies a quantile based family wise error rate (FWER) control to the given p-values. This is based on the approach described in: Meinshausen, N., Meier, L. and Buehlmann, P. (2009). p-values for high-dimensional regression. J. Amer. Statist. Assoc.104 1671–1681 :param p_values: A list or array of p-values. :param p_values_scaling: An optional list of scaling factors for each p-value. :param quantile: The quantile used for the p-value adjustment. By default, this is the median (0.5). :return: The p-value that lies on the quantile threshold. Note that this is the quantile based on scaled values p_values / quantile. """ if quantile <= 0 or abs(quantile - 1) >= 1: raise ValueError("The given quantile is %f, but it needs to be on (0, 1]!" % quantile) p_values = np.array(p_values) if p_values_scaling is None: p_values_scaling = np.ones(p_values.shape[0]) if p_values.shape != p_values_scaling.shape: raise ValueError("The p-value scaling array needs to have the same dimension as the given p-values.") p_values_scaling = p_values_scaling[~np.isnan(p_values)] p_values = p_values[~np.isnan(p_values)] p_values = p_values * p_values_scaling p_values[p_values > 1] = 1.0 if p_values.shape[0] == 1: return float(p_values[0]) else: return float(min(1.0, np.quantile(p_values / quantile, quantile))) def marginal_expectation(prediction_method: Callable[[np.ndarray], np.ndarray], feature_samples: np.ndarray, baseline_samples: np.ndarray, baseline_feature_indices: List[int], return_averaged_results: bool = True, feature_perturbation: str = 'randomize_columns_jointly', max_batch_size: int = -1) -> np.ndarray: """ Estimates the marginal expectation for samples in baseline_noise_samples when randomizing features that are not part of baseline_feature_indices. This is, this function estimates y^i = E[Y | do(x^i_s)] := \\int_x_s' E[Y | x^i_s, x_s'] p(x_s') d x_s', where x^i_s is the i-th sample from baseline_noise_samples, s denotes the baseline_feature_indices and x_s' ~ X_s' denotes the randomized features that are not in s. For an approximation of the integral, the given prediction_method is evaluated multiple times for the same x^i_s, but different x_s' ~ X_s'. :param prediction_method: Prediction method of interest. This should expect a numpy array as input for making predictions. :param feature_samples: Samples from the joint distribution. These are used for randomizing the features that are not in baseline_feature_indices. :param baseline_samples: Samples for which the marginal expectation should be estimated. :param baseline_feature_indices: Column indices of the features in s. These values for these features are remain constant when estimating the expectation. :param return_averaged_results: If set to True, the expectation over all evaluated samples for the i-th baseline_noise_samples is returned. If set to False, all corresponding results for the i-th sample are returned. :param feature_perturbation: Type of feature permutation: 'randomize_columns_independently': Each feature not in s is randomly permuted separately. 'randomize_columns_jointly': All features not in s are jointly permuted. Note that this still represents an interventional distribution. :param max_batch_size: Maximum batch size for a estimating the predictions. This has a significant influence on the overall memory usage. If set to -1, all samples are used in one batch. :return: If return_averaged_results is False, a numpy array where the i-th entry belongs to the marginal expectation of x^i_s when randomizing the remaining features. If return_averaged_results is True, a two dimensional numpy array where the i-th entry contains all predictions for x^i_s when randomizing the remaining features. """ feature_samples, baseline_samples = shape_into_2d(feature_samples, baseline_samples) batch_size = baseline_samples.shape[0] if max_batch_size == -1 else max_batch_size result = [np.nan] * baseline_samples.shape[0] # Make copy to avoid manipulating the original matrix. feature_samples = np.array(feature_samples) features_to_randomize = np.delete(np.arange(0, feature_samples.shape[1]), baseline_feature_indices) if feature_perturbation == 'randomize_columns_independently': feature_samples = permute_features(feature_samples, features_to_randomize, False) elif feature_perturbation == 'randomize_columns_jointly': feature_samples = permute_features(feature_samples, features_to_randomize, True) else: raise ValueError("Unknown argument %s as feature_perturbation type!" % feature_perturbation) # The given prediction method has to be evaluated multiple times on a large amount of different inputs. Typically, # the batch evaluation of a prediction model on multiple inputs at the same time is significantly faster # than evaluating it on single simples in a for-loop. To make use of this, we try to evaluate as many samples as # possible in one batch call of the prediction method. However, this also requires a lot of memory for many samples. # To overcome potential memory issues, multiple batch calls are performed, each with at most batch_size many # samples. The number of samples that are evaluated is normally # baseline_noise_samples.shape[0] * feature_samples.shape[0]. Here, we reduce it to # batch_size * feature_samples.shape[0]. If the batch_size would be set 1, then each baseline_noise_samples is # evaluated one by one in a for-loop. inputs = repmat(feature_samples, batch_size, 1) for offset in range(0, baseline_samples.shape[0], batch_size): # Each batch consist of at most batch_size * feature_samples.shape[0] many samples. If there are multiple # batches, the offset indicates the index of the current baseline_noise_samples that has not been evaluated yet. if offset + batch_size > baseline_samples.shape[0]: # If the batch size would be larger than the remaining amount of samples, it is reduced to only include the # remaining baseline_noise_samples. adjusted_batch_size = baseline_samples.shape[0] - offset inputs = inputs[:adjusted_batch_size * feature_samples.shape[0]] else: adjusted_batch_size = batch_size for index in range(adjusted_batch_size): # The inputs consist of batch_size many copies of feature_samples. Here, we set the columns of the features # in baseline_feature_indices to their respective values in baseline_noise_samples. inputs[index * feature_samples.shape[0]:(index + 1) * feature_samples.shape[0], baseline_feature_indices] = baseline_samples[offset + index, baseline_feature_indices] # After creating the (potentially large) input data matrix, we can evaluate the prediction method. predictions = np.array(prediction_method(inputs)) for index in range(adjusted_batch_size): # Here, offset + index now indicates the sample index in baseline_noise_samples. if return_averaged_results: # This would average all prediction results obtained for the 'offset + index'-th sample in # baseline_noise_samples. This is, y^(offset + index) = E[Y | do(x^(offset + index)_s)]. result[offset + index] = np.mean(predictions[index * feature_samples.shape[0]: (index + 1) * feature_samples.shape[0]], axis=0) else: # This would return all prediction results obtained for the 'offset + index'-th sample in # baseline_noise_samples, i.e. the results are not averaged. result[offset + index] = predictions[index * feature_samples.shape[0]: (index + 1) * feature_samples.shape[0]] return np.array(result) def permute_features(feature_samples: np.ndarray, features_to_permute: Union[List[int], np.ndarray], randomize_features_jointly: bool) -> np.ndarray: # Making copy to ensure that the original object is not modified. feature_samples = np.array(feature_samples) if randomize_features_jointly: # Permute samples jointly. This still represents an interventional distribution. feature_samples[:, features_to_permute] \ = feature_samples[np.random.choice(feature_samples.shape[0], feature_samples.shape[0], replace=False)][:, features_to_permute] else: # Permute samples independently. for feature in features_to_permute: np.random.shuffle(feature_samples[:, feature]) return feature_samples def estimate_ftest_pvalue(X_training_a: np.ndarray, X_training_b: np.ndarray, Y_training: np.ndarray, X_test_a: np.ndarray, X_test_b: np.ndarray, Y_test: np.ndarray) -> float: """Estimates the p-value for the null hypothesis that the same regression error with less parameters can be achieved. This is, a linear model trained on a data set A with d number of features has the same performance (in terms of squared error) relative to the number of features as a model trained on a data set B with k number features, where k < d. Here, both data sets need to have the same target values. A small p-value would indicate that the model performances are significantly different. Note that all given test samples are utilized in the f-test. See https://en.wikipedia.org/wiki/F-test#Regression_problems for more details. :param X_training_a: Input training samples for model A. :param X_training_b: Input training samples for model B. These samples should have less features than samples in X_training_a. :param Y_training: Target training values. :param X_test_a: Test samples for model A. :param X_test_b: Test samples for model B. :param Y_test: Test values. :return: A p-value on [0, 1]. """ X_training_a, X_test_a = shape_into_2d(X_training_a, X_test_a) if X_training_b.size > 0: X_training_b, X_test_b = shape_into_2d(X_training_b, X_test_b) else: X_training_b = X_training_b.reshape(0, 0) X_test_b = X_test_b.reshape(0, 0) if X_training_a.shape[1] <= X_training_b.shape[1]: raise ValueError("The data X_training_a should have more dimensions (model parameters) than the data " "X_training_b!") ssr_a = np.sum( (Y_test - LinearRegression().fit(X_training_a, Y_training).predict(X_test_a)) ** 2) if X_training_b.shape[1] > 0: ssr_b = np.sum( (Y_test - LinearRegression().fit(X_training_b, Y_training).predict(X_test_b)) ** 2) else: ssr_b = np.sum((Y_test - np.mean(Y_test)) ** 2) dof_diff_1 = (X_test_a.shape[1] - X_test_b.shape[1]) # p1 - p2 dof_diff_2 = (X_test_a.shape[0] - X_test_a.shape[1] - 1) # n - p2 (parameters include intercept) f_statistic = (ssr_b - ssr_a) / dof_diff_1 * dof_diff_2 if ssr_a < EPS: ssr_a = 0 if ssr_b < EPS: ssr_b = 0 if ssr_a == 0 and ssr_b == 0: f_statistic = 0 elif ssr_a != 0: f_statistic /= ssr_a return stats.f.sf(f_statistic, dof_diff_1, dof_diff_2)

"""Functions in this module should be considered experimental, meaning there might be breaking API changes in the future. """ from typing import Union, List, Optional, Callable import numpy as np from numpy.matlib import repmat from scipy import stats from sklearn.linear_model import LinearRegression from dowhy.gcm.constant import EPS from dowhy.gcm.util.general import shape_into_2d def quantile_based_fwer(p_values: Union[np.ndarray, List[float]], p_values_scaling: Optional[np.ndarray] = None, quantile: float = 0.5) -> float: """Applies a quantile based family wise error rate (FWER) control to the given p-values. This is based on the approach described in: Meinshausen, N., Meier, L. and Buehlmann, P. (2009). p-values for high-dimensional regression. J. Amer. Statist. Assoc.104 1671–1681 :param p_values: A list or array of p-values. :param p_values_scaling: An optional list of scaling factors for each p-value. :param quantile: The quantile used for the p-value adjustment. By default, this is the median (0.5). :return: The p-value that lies on the quantile threshold. Note that this is the quantile based on scaled values p_values / quantile. """ if quantile <= 0 or abs(quantile - 1) >= 1: raise ValueError("The given quantile is %f, but it needs to be on (0, 1]!" % quantile) p_values = np.array(p_values) if p_values_scaling is None: p_values_scaling = np.ones(p_values.shape[0]) if p_values.shape != p_values_scaling.shape: raise ValueError("The p-value scaling array needs to have the same dimension as the given p-values.") p_values_scaling = p_values_scaling[~np.isnan(p_values)] p_values = p_values[~np.isnan(p_values)] p_values = p_values * p_values_scaling p_values[p_values > 1] = 1.0 if p_values.shape[0] == 1: return float(p_values[0]) else: return float(min(1.0, np.quantile(p_values / quantile, quantile))) def marginal_expectation(prediction_method: Callable[[np.ndarray], np.ndarray], feature_samples: np.ndarray, baseline_samples: np.ndarray, baseline_feature_indices: List[int], return_averaged_results: bool = True, feature_perturbation: str = 'randomize_columns_jointly', max_batch_size: int = -1) -> np.ndarray: """ Estimates the marginal expectation for samples in baseline_noise_samples when randomizing features that are not part of baseline_feature_indices. This is, this function estimates y^i = E[Y | do(x^i_s)] := \\int_x_s' E[Y | x^i_s, x_s'] p(x_s') d x_s', where x^i_s is the i-th sample from baseline_noise_samples, s denotes the baseline_feature_indices and x_s' ~ X_s' denotes the randomized features that are not in s. For an approximation of the integral, the given prediction_method is evaluated multiple times for the same x^i_s, but different x_s' ~ X_s'. :param prediction_method: Prediction method of interest. This should expect a numpy array as input for making predictions. :param feature_samples: Samples from the joint distribution. These are used for randomizing the features that are not in baseline_feature_indices. :param baseline_samples: Samples for which the marginal expectation should be estimated. :param baseline_feature_indices: Column indices of the features in s. These values for these features are remain constant when estimating the expectation. :param return_averaged_results: If set to True, the expectation over all evaluated samples for the i-th baseline_noise_samples is returned. If set to False, all corresponding results for the i-th sample are returned. :param feature_perturbation: Type of feature permutation: 'randomize_columns_independently': Each feature not in s is randomly permuted separately. 'randomize_columns_jointly': All features not in s are jointly permuted. Note that this still represents an interventional distribution. :param max_batch_size: Maximum batch size for a estimating the predictions. This has a significant influence on the overall memory usage. If set to -1, all samples are used in one batch. :return: If return_averaged_results is False, a numpy array where the i-th entry belongs to the marginal expectation of x^i_s when randomizing the remaining features. If return_averaged_results is True, a two dimensional numpy array where the i-th entry contains all predictions for x^i_s when randomizing the remaining features. """ feature_samples, baseline_samples = shape_into_2d(feature_samples, baseline_samples) batch_size = baseline_samples.shape[0] if max_batch_size == -1 else max_batch_size result = [np.nan] * baseline_samples.shape[0] # Make copy to avoid manipulating the original matrix. feature_samples = np.array(feature_samples) features_to_randomize = np.delete(np.arange(0, feature_samples.shape[1]), baseline_feature_indices) if feature_perturbation == 'randomize_columns_independently': feature_samples = permute_features(feature_samples, features_to_randomize, False) elif feature_perturbation == 'randomize_columns_jointly': feature_samples = permute_features(feature_samples, features_to_randomize, True) else: raise ValueError("Unknown argument %s as feature_perturbation type!" % feature_perturbation) # The given prediction method has to be evaluated multiple times on a large amount of different inputs. Typically, # the batch evaluation of a prediction model on multiple inputs at the same time is significantly faster # than evaluating it on single simples in a for-loop. To make use of this, we try to evaluate as many samples as # possible in one batch call of the prediction method. However, this also requires a lot of memory for many samples. # To overcome potential memory issues, multiple batch calls are performed, each with at most batch_size many # samples. The number of samples that are evaluated is normally # baseline_noise_samples.shape[0] * feature_samples.shape[0]. Here, we reduce it to # batch_size * feature_samples.shape[0]. If the batch_size would be set 1, then each baseline_noise_samples is # evaluated one by one in a for-loop. inputs = repmat(feature_samples, batch_size, 1) for offset in range(0, baseline_samples.shape[0], batch_size): # Each batch consist of at most batch_size * feature_samples.shape[0] many samples. If there are multiple # batches, the offset indicates the index of the current baseline_noise_samples that has not been evaluated yet. if offset + batch_size > baseline_samples.shape[0]: # If the batch size would be larger than the remaining amount of samples, it is reduced to only include the # remaining baseline_noise_samples. adjusted_batch_size = baseline_samples.shape[0] - offset inputs = inputs[:adjusted_batch_size * feature_samples.shape[0]] else: adjusted_batch_size = batch_size for index in range(adjusted_batch_size): # The inputs consist of batch_size many copies of feature_samples. Here, we set the columns of the features # in baseline_feature_indices to their respective values in baseline_noise_samples. inputs[index * feature_samples.shape[0]:(index + 1) * feature_samples.shape[0], baseline_feature_indices] = baseline_samples[offset + index, baseline_feature_indices] # After creating the (potentially large) input data matrix, we can evaluate the prediction method. predictions = np.array(prediction_method(inputs)) for index in range(adjusted_batch_size): # Here, offset + index now indicates the sample index in baseline_noise_samples. if return_averaged_results: # This would average all prediction results obtained for the 'offset + index'-th sample in # baseline_noise_samples. This is, y^(offset + index) = E[Y | do(x^(offset + index)_s)]. result[offset + index] = np.mean(predictions[index * feature_samples.shape[0]: (index + 1) * feature_samples.shape[0]], axis=0) else: # This would return all prediction results obtained for the 'offset + index'-th sample in # baseline_noise_samples, i.e. the results are not averaged. result[offset + index] = predictions[index * feature_samples.shape[0]: (index + 1) * feature_samples.shape[0]] return np.array(result) def permute_features(feature_samples: np.ndarray, features_to_permute: Union[List[int], np.ndarray], randomize_features_jointly: bool) -> np.ndarray: # Making copy to ensure that the original object is not modified. feature_samples = np.array(feature_samples) if randomize_features_jointly: # Permute samples jointly. This still represents an interventional distribution. feature_samples[:, features_to_permute] \ = feature_samples[np.random.choice(feature_samples.shape[0], feature_samples.shape[0], replace=False)][:, features_to_permute] else: # Permute samples independently. for feature in features_to_permute: np.random.shuffle(feature_samples[:, feature]) return feature_samples def estimate_ftest_pvalue(X_training_a: np.ndarray, X_training_b: np.ndarray, Y_training: np.ndarray, X_test_a: np.ndarray, X_test_b: np.ndarray, Y_test: np.ndarray) -> float: """Estimates the p-value for the null hypothesis that the same regression error with less parameters can be achieved. This is, a linear model trained on a data set A with d number of features has the same performance (in terms of squared error) relative to the number of features as a model trained on a data set B with k number features, where k < d. Here, both data sets need to have the same target values. A small p-value would indicate that the model performances are significantly different. Note that all given test samples are utilized in the f-test. See https://en.wikipedia.org/wiki/F-test#Regression_problems for more details. :param X_training_a: Input training samples for model A. :param X_training_b: Input training samples for model B. These samples should have less features than samples in X_training_a. :param Y_training: Target training values. :param X_test_a: Test samples for model A. :param X_test_b: Test samples for model B. :param Y_test: Test values. :return: A p-value on [0, 1]. """ X_training_a, X_test_a = shape_into_2d(X_training_a, X_test_a) if X_training_b.size > 0: X_training_b, X_test_b = shape_into_2d(X_training_b, X_test_b) else: X_training_b = X_training_b.reshape(0, 0) X_test_b = X_test_b.reshape(0, 0) if X_training_a.shape[1] <= X_training_b.shape[1]: raise ValueError("The data X_training_a should have more dimensions (model parameters) than the data " "X_training_b!") ssr_a = np.sum( (Y_test - LinearRegression().fit(X_training_a, Y_training).predict(X_test_a)) ** 2) if X_training_b.shape[1] > 0: ssr_b = np.sum( (Y_test - LinearRegression().fit(X_training_b, Y_training).predict(X_test_b)) ** 2) else: ssr_b = np.sum((Y_test - np.mean(Y_training)) ** 2) dof_diff_1 = (X_test_a.shape[1] - X_test_b.shape[1]) # p1 - p2 dof_diff_2 = (X_test_a.shape[0] - X_test_a.shape[1] - 1) # n - p2 (parameters include intercept) f_statistic = (ssr_b - ssr_a) / dof_diff_1 * dof_diff_2 if ssr_a < EPS: ssr_a = 0 if ssr_b < EPS: ssr_b = 0 if ssr_a == 0 and ssr_b == 0: f_statistic = 0 elif ssr_a != 0: f_statistic /= ssr_a return stats.f.sf(f_statistic, dof_diff_1, dof_diff_2)

bloebp

2b4832a91e7ab54d31b116d19958fddecc2c8510

fe22abab886c5aea768b8474295999a71d914be9

This else condition is the scenario where we don't have input features, i.e. empty conditioning set. Then we have: ```E[Y | {}] = E[Y]```. Here, ```Y``` is based on ```Y_training```. Therefore, the prediction model we are looking at here is ```f({}) = E[Y | {}] = E[Y]``` and, thus, the sum of squared error in the test data is ```sum_i (y_i - f({}))**2 = sum_i (y_i - E[Y])**2```

bloebp

py-why/dowhy

Auto generate documentation

This PR introduces a GitHub action to auto-generate versioned documentation and publish it to py-why.github.io/dowhy. To facilitate automatically generating documentation on every commit to master, this PR introduces multiple things (separated by commits): - It introduces [versioneer](https://github.com/python-versioneer/python-versioneer), a convenient tool to use git tags for versioning. Otherwise, keeping a master version of the docs separate from the latest release version is difficult: master would always list the latest version in its `VERSION` file, such as e.g. `0.7.1` and then documentation for master branch would still say v0.7.1 and easily confused with the real v0.7.1 documentation. Versioneer is also used by NumPy and Pandas. - It introduces [sphinx_multiversion](https://holzhaus.github.io/sphinx-multiversion/master/index.html), a Sphinx extension to generate multiple versions of the documentation based on different branches and tags of the git repo. To be precise, it uses a [slightly changed version of it](https://github.com/Holzhaus/sphinx-multiversion/compare/master...petergtz:sphinx-multiversion:override-version-with-refname), which uses the git refname for the version, not falling back to a hard-coded value in `conf.py`. For now, I'm hosting [this variant in my own GitHub account](https://github.com/petergtz/sphinx-multiversion/tree/override-version-with-refname), but my plan is to open a PR to upstream and introduce this as a new feature. - It introduce a new `generate_docs.sh` script as a replacement for the `Makefile`. This script invokes sphinx_multiversion instead of vanilla sphinx and it also creates an `index.html` which automatically redirects to the latest stable version of the documentation. - It introduces a GitHub action workflow that builds the versioned documentation and publishes it. This action is based on the container image [pego/dowhy-examples-notebooks-deps](https://hub.docker.com/repository/docker/pego/dowhy-examples-notebooks-deps) which is automatically built from [this Dockerfile](https://github.com/petergtz/dowhy-examples-notebooks-deps-dockerfile/blob/main/Dockerfile), which makes sure all necessary R dependencies are available. Instead of this additional Docker image, we could have installed all necessary dependencies in each run of the documentation build workflow, but that is both a waste of resources and also increasing the build time immensely. I suggest we move this repo into PyWhy and eventually create a docker hub account for PyWhy, or alternatively push the image into GitHub's own registry. - Finally, it makes the `str_to_dot` function more robust towards slightly changing inputs which is probably due to slight changes in graphviz libraries, which introduced additional whitespace in graph descriptions. **Notes:** - An example of this specific GitHub action in action can be found at: https://github.com/petergtz/dowhy/actions/workflows/build-and-publish-docs.yml - An example of the versioned documentation can be found at: https://petergtz.github.io/dowhy - `versioneer.py` and `dowhy/_version.py` do not have to be reviewed. Versioneer generates these files when invoking its install script.

2022-07-19 20:38:04+00:00

2022-07-28 10:10:47+00:00

setup.py

"""A setuptools based setup module for dowhy. Adapted from: https://packaging.python.org/en/latest/distributing.html https://github.com/pypa/sampleproject """ from setuptools import setup, find_packages from codecs import open from os import path import versioneer here = path.abspath(path.dirname(__file__)) # Get the long description from the README file with open(path.join(here, 'README.rst'), encoding='utf-8') as f: long_description = f.read() # Get the required packages with open(path.join(here, 'requirements.txt'), encoding='utf-8') as f: install_requires = f.read().splitlines() # Plotting packages are optional to install extras = ["plotting"] extras_require = dict() for e in extras: req_file = "requirements-{0}.txt".format(e) with open(req_file) as f: extras_require[e] = [line.strip() for line in f] setup( name='dowhy', version=versioneer.get_version(), cmdclass=versioneer.get_cmdclass(), description='DoWhy is a Python library for causal inference that supports explicit modeling and testing of causal assumptions.', # Required license='MIT', long_description=long_description, url='https://github.com/microsoft/dowhy', # Optional download_url='https://github.com/microsoft/dowhy/archive/v0.8.tar.gz', author='Amit Sharma, Emre Kiciman', classifiers=[ # Optional 'Development Status :: 4 - Beta', 'License :: OSI Approved :: MIT License', 'Programming Language :: Python :: 3.6', 'Programming Language :: Python :: 3.7', 'Programming Language :: Python :: 3.8', 'Programming Language :: Python :: 3.9', ], keywords='causality machine-learning causal-inference statistics graphical-model', packages=find_packages(exclude=['docs', 'tests']), python_requires='>=3.6', install_requires=install_requires, extras_require=extras_require, include_package_data=True, package_data={'dowhy':['VERSION']} )

"""A setuptools based setup module for dowhy. Adapted from: https://packaging.python.org/en/latest/distributing.html https://github.com/pypa/sampleproject """ from setuptools import setup, find_packages from codecs import open from os import path import versioneer here = path.abspath(path.dirname(__file__)) # Get the long description from the README file with open(path.join(here, 'README.rst'), encoding='utf-8') as f: long_description = f.read() # Get the required packages with open(path.join(here, 'requirements.txt'), encoding='utf-8') as f: install_requires = f.read().splitlines() # Plotting packages are optional to install extras = ["plotting"] extras_require = dict() for e in extras: req_file = "requirements-{0}.txt".format(e) with open(req_file) as f: extras_require[e] = [line.strip() for line in f] setup( name='dowhy', version=versioneer.get_version(), cmdclass=versioneer.get_cmdclass(), description='DoWhy is a Python library for causal inference that supports explicit modeling and testing of causal assumptions.', # Required license='MIT', long_description=long_description, url='https://github.com/microsoft/dowhy', # Optional download_url='https://github.com/microsoft/dowhy/archive/v0.8.tar.gz', author='Amit Sharma, Emre Kiciman', classifiers=[ # Optional 'Development Status :: 4 - Beta', 'License :: OSI Approved :: MIT License', 'Programming Language :: Python :: 3.6', 'Programming Language :: Python :: 3.7', 'Programming Language :: Python :: 3.8', 'Programming Language :: Python :: 3.9', ], keywords='causality machine-learning causal-inference statistics graphical-model', packages=find_packages(exclude=['docs', 'tests']), python_requires='>=3.6', install_requires=install_requires, extras_require=extras_require, include_package_data=True, package_data={'dowhy':['VERSION']} )

petergtz

570bc06baddc7c29b233e6afbb156f58ae9ae200

9a025a2003d754aa9749e8569b72dc566a17c3c2

This is cool. A few questions: 1. for a new release, where do we specify the new release version so that versioneer fills this correctly? 2. for an update to the master docs, I'm guessing no change is needed in the version?

amit-sharma

py-why/dowhy

Auto generate documentation

This PR introduces a GitHub action to auto-generate versioned documentation and publish it to py-why.github.io/dowhy. To facilitate automatically generating documentation on every commit to master, this PR introduces multiple things (separated by commits): - It introduces [versioneer](https://github.com/python-versioneer/python-versioneer), a convenient tool to use git tags for versioning. Otherwise, keeping a master version of the docs separate from the latest release version is difficult: master would always list the latest version in its `VERSION` file, such as e.g. `0.7.1` and then documentation for master branch would still say v0.7.1 and easily confused with the real v0.7.1 documentation. Versioneer is also used by NumPy and Pandas. - It introduces [sphinx_multiversion](https://holzhaus.github.io/sphinx-multiversion/master/index.html), a Sphinx extension to generate multiple versions of the documentation based on different branches and tags of the git repo. To be precise, it uses a [slightly changed version of it](https://github.com/Holzhaus/sphinx-multiversion/compare/master...petergtz:sphinx-multiversion:override-version-with-refname), which uses the git refname for the version, not falling back to a hard-coded value in `conf.py`. For now, I'm hosting [this variant in my own GitHub account](https://github.com/petergtz/sphinx-multiversion/tree/override-version-with-refname), but my plan is to open a PR to upstream and introduce this as a new feature. - It introduce a new `generate_docs.sh` script as a replacement for the `Makefile`. This script invokes sphinx_multiversion instead of vanilla sphinx and it also creates an `index.html` which automatically redirects to the latest stable version of the documentation. - It introduces a GitHub action workflow that builds the versioned documentation and publishes it. This action is based on the container image [pego/dowhy-examples-notebooks-deps](https://hub.docker.com/repository/docker/pego/dowhy-examples-notebooks-deps) which is automatically built from [this Dockerfile](https://github.com/petergtz/dowhy-examples-notebooks-deps-dockerfile/blob/main/Dockerfile), which makes sure all necessary R dependencies are available. Instead of this additional Docker image, we could have installed all necessary dependencies in each run of the documentation build workflow, but that is both a waste of resources and also increasing the build time immensely. I suggest we move this repo into PyWhy and eventually create a docker hub account for PyWhy, or alternatively push the image into GitHub's own registry. - Finally, it makes the `str_to_dot` function more robust towards slightly changing inputs which is probably due to slight changes in graphviz libraries, which introduced additional whitespace in graph descriptions. **Notes:** - An example of this specific GitHub action in action can be found at: https://github.com/petergtz/dowhy/actions/workflows/build-and-publish-docs.yml - An example of the versioned documentation can be found at: https://petergtz.github.io/dowhy - `versioneer.py` and `dowhy/_version.py` do not have to be reviewed. Versioneer generates these files when invoking its install script.

2022-07-19 20:38:04+00:00

2022-07-28 10:10:47+00:00

setup.py

"""A setuptools based setup module for dowhy. Adapted from: https://packaging.python.org/en/latest/distributing.html https://github.com/pypa/sampleproject """ from setuptools import setup, find_packages from codecs import open from os import path import versioneer here = path.abspath(path.dirname(__file__)) # Get the long description from the README file with open(path.join(here, 'README.rst'), encoding='utf-8') as f: long_description = f.read() # Get the required packages with open(path.join(here, 'requirements.txt'), encoding='utf-8') as f: install_requires = f.read().splitlines() # Plotting packages are optional to install extras = ["plotting"] extras_require = dict() for e in extras: req_file = "requirements-{0}.txt".format(e) with open(req_file) as f: extras_require[e] = [line.strip() for line in f] setup( name='dowhy', version=versioneer.get_version(), cmdclass=versioneer.get_cmdclass(), description='DoWhy is a Python library for causal inference that supports explicit modeling and testing of causal assumptions.', # Required license='MIT', long_description=long_description, url='https://github.com/microsoft/dowhy', # Optional download_url='https://github.com/microsoft/dowhy/archive/v0.8.tar.gz', author='Amit Sharma, Emre Kiciman', classifiers=[ # Optional 'Development Status :: 4 - Beta', 'License :: OSI Approved :: MIT License', 'Programming Language :: Python :: 3.6', 'Programming Language :: Python :: 3.7', 'Programming Language :: Python :: 3.8', 'Programming Language :: Python :: 3.9', ], keywords='causality machine-learning causal-inference statistics graphical-model', packages=find_packages(exclude=['docs', 'tests']), python_requires='>=3.6', install_requires=install_requires, extras_require=extras_require, include_package_data=True, package_data={'dowhy':['VERSION']} )

"""A setuptools based setup module for dowhy. Adapted from: https://packaging.python.org/en/latest/distributing.html https://github.com/pypa/sampleproject """ from setuptools import setup, find_packages from codecs import open from os import path import versioneer here = path.abspath(path.dirname(__file__)) # Get the long description from the README file with open(path.join(here, 'README.rst'), encoding='utf-8') as f: long_description = f.read() # Get the required packages with open(path.join(here, 'requirements.txt'), encoding='utf-8') as f: install_requires = f.read().splitlines() # Plotting packages are optional to install extras = ["plotting"] extras_require = dict() for e in extras: req_file = "requirements-{0}.txt".format(e) with open(req_file) as f: extras_require[e] = [line.strip() for line in f] setup( name='dowhy', version=versioneer.get_version(), cmdclass=versioneer.get_cmdclass(), description='DoWhy is a Python library for causal inference that supports explicit modeling and testing of causal assumptions.', # Required license='MIT', long_description=long_description, url='https://github.com/microsoft/dowhy', # Optional download_url='https://github.com/microsoft/dowhy/archive/v0.8.tar.gz', author='Amit Sharma, Emre Kiciman', classifiers=[ # Optional 'Development Status :: 4 - Beta', 'License :: OSI Approved :: MIT License', 'Programming Language :: Python :: 3.6', 'Programming Language :: Python :: 3.7', 'Programming Language :: Python :: 3.8', 'Programming Language :: Python :: 3.9', ], keywords='causality machine-learning causal-inference statistics graphical-model', packages=find_packages(exclude=['docs', 'tests']), python_requires='>=3.6', install_requires=install_requires, extras_require=extras_require, include_package_data=True, package_data={'dowhy':['VERSION']} )

petergtz

570bc06baddc7c29b233e6afbb156f58ae9ae200

9a025a2003d754aa9749e8569b72dc566a17c3c2

> 1. for a new release, where do we specify the new release version so that versioneer fills this correctly? You specify the version via `git tag` See https://github.com/python-versioneer/python-versioneer/blob/master/INSTALL.md#post-installation-usage, which says: > If you distribute your project through PyPI, then the release process should boil down to two steps: > > - 1: git tag 1.0 > - 2: python setup.py register sdist upload > 2. for an update to the master docs, I'm guessing no change is needed in the version? Correct. Pushing to `master`/`main` will modify the documentation, whereas the documentation for a specific release is frozen. It's important to realize that this gives us slightly less flexibility in terms of updating the docs for an already _released_ version. The only way I see how this could work is by creating a branch on the released-tagged commit and retagging a new commit with the same tag (basically moving the tag to another commit and forcing-pushing that change). It's a bit dirty, but would probably work. I'd prefer a more aggressive release frequency though.

petergtz

py-why/dowhy

Auto generate documentation

This PR introduces a GitHub action to auto-generate versioned documentation and publish it to py-why.github.io/dowhy. To facilitate automatically generating documentation on every commit to master, this PR introduces multiple things (separated by commits): - It introduces [versioneer](https://github.com/python-versioneer/python-versioneer), a convenient tool to use git tags for versioning. Otherwise, keeping a master version of the docs separate from the latest release version is difficult: master would always list the latest version in its `VERSION` file, such as e.g. `0.7.1` and then documentation for master branch would still say v0.7.1 and easily confused with the real v0.7.1 documentation. Versioneer is also used by NumPy and Pandas. - It introduces [sphinx_multiversion](https://holzhaus.github.io/sphinx-multiversion/master/index.html), a Sphinx extension to generate multiple versions of the documentation based on different branches and tags of the git repo. To be precise, it uses a [slightly changed version of it](https://github.com/Holzhaus/sphinx-multiversion/compare/master...petergtz:sphinx-multiversion:override-version-with-refname), which uses the git refname for the version, not falling back to a hard-coded value in `conf.py`. For now, I'm hosting [this variant in my own GitHub account](https://github.com/petergtz/sphinx-multiversion/tree/override-version-with-refname), but my plan is to open a PR to upstream and introduce this as a new feature. - It introduce a new `generate_docs.sh` script as a replacement for the `Makefile`. This script invokes sphinx_multiversion instead of vanilla sphinx and it also creates an `index.html` which automatically redirects to the latest stable version of the documentation. - It introduces a GitHub action workflow that builds the versioned documentation and publishes it. This action is based on the container image [pego/dowhy-examples-notebooks-deps](https://hub.docker.com/repository/docker/pego/dowhy-examples-notebooks-deps) which is automatically built from [this Dockerfile](https://github.com/petergtz/dowhy-examples-notebooks-deps-dockerfile/blob/main/Dockerfile), which makes sure all necessary R dependencies are available. Instead of this additional Docker image, we could have installed all necessary dependencies in each run of the documentation build workflow, but that is both a waste of resources and also increasing the build time immensely. I suggest we move this repo into PyWhy and eventually create a docker hub account for PyWhy, or alternatively push the image into GitHub's own registry. - Finally, it makes the `str_to_dot` function more robust towards slightly changing inputs which is probably due to slight changes in graphviz libraries, which introduced additional whitespace in graph descriptions. **Notes:** - An example of this specific GitHub action in action can be found at: https://github.com/petergtz/dowhy/actions/workflows/build-and-publish-docs.yml - An example of the versioned documentation can be found at: https://petergtz.github.io/dowhy - `versioneer.py` and `dowhy/_version.py` do not have to be reviewed. Versioneer generates these files when invoking its install script.

2022-07-19 20:38:04+00:00

2022-07-28 10:10:47+00:00

setup.py

"""A setuptools based setup module for dowhy. Adapted from: https://packaging.python.org/en/latest/distributing.html https://github.com/pypa/sampleproject """ from setuptools import setup, find_packages from codecs import open from os import path import versioneer here = path.abspath(path.dirname(__file__)) # Get the long description from the README file with open(path.join(here, 'README.rst'), encoding='utf-8') as f: long_description = f.read() # Get the required packages with open(path.join(here, 'requirements.txt'), encoding='utf-8') as f: install_requires = f.read().splitlines() # Plotting packages are optional to install extras = ["plotting"] extras_require = dict() for e in extras: req_file = "requirements-{0}.txt".format(e) with open(req_file) as f: extras_require[e] = [line.strip() for line in f] setup( name='dowhy', version=versioneer.get_version(), cmdclass=versioneer.get_cmdclass(), description='DoWhy is a Python library for causal inference that supports explicit modeling and testing of causal assumptions.', # Required license='MIT', long_description=long_description, url='https://github.com/microsoft/dowhy', # Optional download_url='https://github.com/microsoft/dowhy/archive/v0.8.tar.gz', author='Amit Sharma, Emre Kiciman', classifiers=[ # Optional 'Development Status :: 4 - Beta', 'License :: OSI Approved :: MIT License', 'Programming Language :: Python :: 3.6', 'Programming Language :: Python :: 3.7', 'Programming Language :: Python :: 3.8', 'Programming Language :: Python :: 3.9', ], keywords='causality machine-learning causal-inference statistics graphical-model', packages=find_packages(exclude=['docs', 'tests']), python_requires='>=3.6', install_requires=install_requires, extras_require=extras_require, include_package_data=True, package_data={'dowhy':['VERSION']} )

"""A setuptools based setup module for dowhy. Adapted from: https://packaging.python.org/en/latest/distributing.html https://github.com/pypa/sampleproject """ from setuptools import setup, find_packages from codecs import open from os import path import versioneer here = path.abspath(path.dirname(__file__)) # Get the long description from the README file with open(path.join(here, 'README.rst'), encoding='utf-8') as f: long_description = f.read() # Get the required packages with open(path.join(here, 'requirements.txt'), encoding='utf-8') as f: install_requires = f.read().splitlines() # Plotting packages are optional to install extras = ["plotting"] extras_require = dict() for e in extras: req_file = "requirements-{0}.txt".format(e) with open(req_file) as f: extras_require[e] = [line.strip() for line in f] setup( name='dowhy', version=versioneer.get_version(), cmdclass=versioneer.get_cmdclass(), description='DoWhy is a Python library for causal inference that supports explicit modeling and testing of causal assumptions.', # Required license='MIT', long_description=long_description, url='https://github.com/microsoft/dowhy', # Optional download_url='https://github.com/microsoft/dowhy/archive/v0.8.tar.gz', author='Amit Sharma, Emre Kiciman', classifiers=[ # Optional 'Development Status :: 4 - Beta', 'License :: OSI Approved :: MIT License', 'Programming Language :: Python :: 3.6', 'Programming Language :: Python :: 3.7', 'Programming Language :: Python :: 3.8', 'Programming Language :: Python :: 3.9', ], keywords='causality machine-learning causal-inference statistics graphical-model', packages=find_packages(exclude=['docs', 'tests']), python_requires='>=3.6', install_requires=install_requires, extras_require=extras_require, include_package_data=True, package_data={'dowhy':['VERSION']} )

petergtz

570bc06baddc7c29b233e6afbb156f58ae9ae200

9a025a2003d754aa9749e8569b72dc566a17c3c2

interesting, this automation will be useful. just to confirm: previously, I used to update the version manually in dowhy/version.py, and then create a release using the github UI (that created a tag and automatically [pypi publish workflow](https://github.com/py-why/dowhy/blob/main/.github/workflows/python-publish.yml)). Now, the steps will be: 1. create the release using the github UI (which also creates a tag) 2. let the pypi publish workflow run automatically. In this case, would versioneer automatically pick the latest version number? For older docs: As I mentioned on the other PR, I think it is okay to keep the docs only for v0.7 or v0.8 onwards. They are backwards-compatible and we can encourage people to update.

amit-sharma

py-why/dowhy

Auto generate documentation

This PR introduces a GitHub action to auto-generate versioned documentation and publish it to py-why.github.io/dowhy. To facilitate automatically generating documentation on every commit to master, this PR introduces multiple things (separated by commits): - It introduces [versioneer](https://github.com/python-versioneer/python-versioneer), a convenient tool to use git tags for versioning. Otherwise, keeping a master version of the docs separate from the latest release version is difficult: master would always list the latest version in its `VERSION` file, such as e.g. `0.7.1` and then documentation for master branch would still say v0.7.1 and easily confused with the real v0.7.1 documentation. Versioneer is also used by NumPy and Pandas. - It introduces [sphinx_multiversion](https://holzhaus.github.io/sphinx-multiversion/master/index.html), a Sphinx extension to generate multiple versions of the documentation based on different branches and tags of the git repo. To be precise, it uses a [slightly changed version of it](https://github.com/Holzhaus/sphinx-multiversion/compare/master...petergtz:sphinx-multiversion:override-version-with-refname), which uses the git refname for the version, not falling back to a hard-coded value in `conf.py`. For now, I'm hosting [this variant in my own GitHub account](https://github.com/petergtz/sphinx-multiversion/tree/override-version-with-refname), but my plan is to open a PR to upstream and introduce this as a new feature. - It introduce a new `generate_docs.sh` script as a replacement for the `Makefile`. This script invokes sphinx_multiversion instead of vanilla sphinx and it also creates an `index.html` which automatically redirects to the latest stable version of the documentation. - It introduces a GitHub action workflow that builds the versioned documentation and publishes it. This action is based on the container image [pego/dowhy-examples-notebooks-deps](https://hub.docker.com/repository/docker/pego/dowhy-examples-notebooks-deps) which is automatically built from [this Dockerfile](https://github.com/petergtz/dowhy-examples-notebooks-deps-dockerfile/blob/main/Dockerfile), which makes sure all necessary R dependencies are available. Instead of this additional Docker image, we could have installed all necessary dependencies in each run of the documentation build workflow, but that is both a waste of resources and also increasing the build time immensely. I suggest we move this repo into PyWhy and eventually create a docker hub account for PyWhy, or alternatively push the image into GitHub's own registry. - Finally, it makes the `str_to_dot` function more robust towards slightly changing inputs which is probably due to slight changes in graphviz libraries, which introduced additional whitespace in graph descriptions. **Notes:** - An example of this specific GitHub action in action can be found at: https://github.com/petergtz/dowhy/actions/workflows/build-and-publish-docs.yml - An example of the versioned documentation can be found at: https://petergtz.github.io/dowhy - `versioneer.py` and `dowhy/_version.py` do not have to be reviewed. Versioneer generates these files when invoking its install script.

2022-07-19 20:38:04+00:00

2022-07-28 10:10:47+00:00

setup.py

"""A setuptools based setup module for dowhy. Adapted from: https://packaging.python.org/en/latest/distributing.html https://github.com/pypa/sampleproject """ from setuptools import setup, find_packages from codecs import open from os import path import versioneer here = path.abspath(path.dirname(__file__)) # Get the long description from the README file with open(path.join(here, 'README.rst'), encoding='utf-8') as f: long_description = f.read() # Get the required packages with open(path.join(here, 'requirements.txt'), encoding='utf-8') as f: install_requires = f.read().splitlines() # Plotting packages are optional to install extras = ["plotting"] extras_require = dict() for e in extras: req_file = "requirements-{0}.txt".format(e) with open(req_file) as f: extras_require[e] = [line.strip() for line in f] setup( name='dowhy', version=versioneer.get_version(), cmdclass=versioneer.get_cmdclass(), description='DoWhy is a Python library for causal inference that supports explicit modeling and testing of causal assumptions.', # Required license='MIT', long_description=long_description, url='https://github.com/microsoft/dowhy', # Optional download_url='https://github.com/microsoft/dowhy/archive/v0.8.tar.gz', author='Amit Sharma, Emre Kiciman', classifiers=[ # Optional 'Development Status :: 4 - Beta', 'License :: OSI Approved :: MIT License', 'Programming Language :: Python :: 3.6', 'Programming Language :: Python :: 3.7', 'Programming Language :: Python :: 3.8', 'Programming Language :: Python :: 3.9', ], keywords='causality machine-learning causal-inference statistics graphical-model', packages=find_packages(exclude=['docs', 'tests']), python_requires='>=3.6', install_requires=install_requires, extras_require=extras_require, include_package_data=True, package_data={'dowhy':['VERSION']} )

"""A setuptools based setup module for dowhy. Adapted from: https://packaging.python.org/en/latest/distributing.html https://github.com/pypa/sampleproject """ from setuptools import setup, find_packages from codecs import open from os import path import versioneer here = path.abspath(path.dirname(__file__)) # Get the long description from the README file with open(path.join(here, 'README.rst'), encoding='utf-8') as f: long_description = f.read() # Get the required packages with open(path.join(here, 'requirements.txt'), encoding='utf-8') as f: install_requires = f.read().splitlines() # Plotting packages are optional to install extras = ["plotting"] extras_require = dict() for e in extras: req_file = "requirements-{0}.txt".format(e) with open(req_file) as f: extras_require[e] = [line.strip() for line in f] setup( name='dowhy', version=versioneer.get_version(), cmdclass=versioneer.get_cmdclass(), description='DoWhy is a Python library for causal inference that supports explicit modeling and testing of causal assumptions.', # Required license='MIT', long_description=long_description, url='https://github.com/microsoft/dowhy', # Optional download_url='https://github.com/microsoft/dowhy/archive/v0.8.tar.gz', author='Amit Sharma, Emre Kiciman', classifiers=[ # Optional 'Development Status :: 4 - Beta', 'License :: OSI Approved :: MIT License', 'Programming Language :: Python :: 3.6', 'Programming Language :: Python :: 3.7', 'Programming Language :: Python :: 3.8', 'Programming Language :: Python :: 3.9', ], keywords='causality machine-learning causal-inference statistics graphical-model', packages=find_packages(exclude=['docs', 'tests']), python_requires='>=3.6', install_requires=install_requires, extras_require=extras_require, include_package_data=True, package_data={'dowhy':['VERSION']} )

petergtz

570bc06baddc7c29b233e6afbb156f58ae9ae200

9a025a2003d754aa9749e8569b72dc566a17c3c2

> Now, the steps will be: > > 1. create the release using the github UI (which also creates a tag) > 2. let the pypi publish workflow run automatically. > > In this case, would versioneer automatically pick the latest version number? Yes. Internally, versioneer uses a specially parameterized `git describe` invocation to "heuristically" find the _latest release_ tag. And I assume when GitHub UI creates the version tag, it will have to push this tag and that push will also trigger the GitHub action to build and deploy the docs and then versioneer will pick this up. > For older docs: As I mentioned on the other PR, I think it is okay to keep the docs only for v0.7 or v0.8 onwards. They are backwards-compatible and we can encourage people to update. Makes sense.

petergtz

py-why/dowhy

Auto generate documentation

This PR introduces a GitHub action to auto-generate versioned documentation and publish it to py-why.github.io/dowhy. To facilitate automatically generating documentation on every commit to master, this PR introduces multiple things (separated by commits): - It introduces [versioneer](https://github.com/python-versioneer/python-versioneer), a convenient tool to use git tags for versioning. Otherwise, keeping a master version of the docs separate from the latest release version is difficult: master would always list the latest version in its `VERSION` file, such as e.g. `0.7.1` and then documentation for master branch would still say v0.7.1 and easily confused with the real v0.7.1 documentation. Versioneer is also used by NumPy and Pandas. - It introduces [sphinx_multiversion](https://holzhaus.github.io/sphinx-multiversion/master/index.html), a Sphinx extension to generate multiple versions of the documentation based on different branches and tags of the git repo. To be precise, it uses a [slightly changed version of it](https://github.com/Holzhaus/sphinx-multiversion/compare/master...petergtz:sphinx-multiversion:override-version-with-refname), which uses the git refname for the version, not falling back to a hard-coded value in `conf.py`. For now, I'm hosting [this variant in my own GitHub account](https://github.com/petergtz/sphinx-multiversion/tree/override-version-with-refname), but my plan is to open a PR to upstream and introduce this as a new feature. - It introduce a new `generate_docs.sh` script as a replacement for the `Makefile`. This script invokes sphinx_multiversion instead of vanilla sphinx and it also creates an `index.html` which automatically redirects to the latest stable version of the documentation. - It introduces a GitHub action workflow that builds the versioned documentation and publishes it. This action is based on the container image [pego/dowhy-examples-notebooks-deps](https://hub.docker.com/repository/docker/pego/dowhy-examples-notebooks-deps) which is automatically built from [this Dockerfile](https://github.com/petergtz/dowhy-examples-notebooks-deps-dockerfile/blob/main/Dockerfile), which makes sure all necessary R dependencies are available. Instead of this additional Docker image, we could have installed all necessary dependencies in each run of the documentation build workflow, but that is both a waste of resources and also increasing the build time immensely. I suggest we move this repo into PyWhy and eventually create a docker hub account for PyWhy, or alternatively push the image into GitHub's own registry. - Finally, it makes the `str_to_dot` function more robust towards slightly changing inputs which is probably due to slight changes in graphviz libraries, which introduced additional whitespace in graph descriptions. **Notes:** - An example of this specific GitHub action in action can be found at: https://github.com/petergtz/dowhy/actions/workflows/build-and-publish-docs.yml - An example of the versioned documentation can be found at: https://petergtz.github.io/dowhy - `versioneer.py` and `dowhy/_version.py` do not have to be reviewed. Versioneer generates these files when invoking its install script.

2022-07-19 20:38:04+00:00

2022-07-28 10:10:47+00:00

setup.py

"""A setuptools based setup module for dowhy. Adapted from: https://packaging.python.org/en/latest/distributing.html https://github.com/pypa/sampleproject """ from setuptools import setup, find_packages from codecs import open from os import path import versioneer here = path.abspath(path.dirname(__file__)) # Get the long description from the README file with open(path.join(here, 'README.rst'), encoding='utf-8') as f: long_description = f.read() # Get the required packages with open(path.join(here, 'requirements.txt'), encoding='utf-8') as f: install_requires = f.read().splitlines() # Plotting packages are optional to install extras = ["plotting"] extras_require = dict() for e in extras: req_file = "requirements-{0}.txt".format(e) with open(req_file) as f: extras_require[e] = [line.strip() for line in f] setup( name='dowhy', version=versioneer.get_version(), cmdclass=versioneer.get_cmdclass(), description='DoWhy is a Python library for causal inference that supports explicit modeling and testing of causal assumptions.', # Required license='MIT', long_description=long_description, url='https://github.com/microsoft/dowhy', # Optional download_url='https://github.com/microsoft/dowhy/archive/v0.8.tar.gz', author='Amit Sharma, Emre Kiciman', classifiers=[ # Optional 'Development Status :: 4 - Beta', 'License :: OSI Approved :: MIT License', 'Programming Language :: Python :: 3.6', 'Programming Language :: Python :: 3.7', 'Programming Language :: Python :: 3.8', 'Programming Language :: Python :: 3.9', ], keywords='causality machine-learning causal-inference statistics graphical-model', packages=find_packages(exclude=['docs', 'tests']), python_requires='>=3.6', install_requires=install_requires, extras_require=extras_require, include_package_data=True, package_data={'dowhy':['VERSION']} )

"""A setuptools based setup module for dowhy. Adapted from: https://packaging.python.org/en/latest/distributing.html https://github.com/pypa/sampleproject """ from setuptools import setup, find_packages from codecs import open from os import path import versioneer here = path.abspath(path.dirname(__file__)) # Get the long description from the README file with open(path.join(here, 'README.rst'), encoding='utf-8') as f: long_description = f.read() # Get the required packages with open(path.join(here, 'requirements.txt'), encoding='utf-8') as f: install_requires = f.read().splitlines() # Plotting packages are optional to install extras = ["plotting"] extras_require = dict() for e in extras: req_file = "requirements-{0}.txt".format(e) with open(req_file) as f: extras_require[e] = [line.strip() for line in f] setup( name='dowhy', version=versioneer.get_version(), cmdclass=versioneer.get_cmdclass(), description='DoWhy is a Python library for causal inference that supports explicit modeling and testing of causal assumptions.', # Required license='MIT', long_description=long_description, url='https://github.com/microsoft/dowhy', # Optional download_url='https://github.com/microsoft/dowhy/archive/v0.8.tar.gz', author='Amit Sharma, Emre Kiciman', classifiers=[ # Optional 'Development Status :: 4 - Beta', 'License :: OSI Approved :: MIT License', 'Programming Language :: Python :: 3.6', 'Programming Language :: Python :: 3.7', 'Programming Language :: Python :: 3.8', 'Programming Language :: Python :: 3.9', ], keywords='causality machine-learning causal-inference statistics graphical-model', packages=find_packages(exclude=['docs', 'tests']), python_requires='>=3.6', install_requires=install_requires, extras_require=extras_require, include_package_data=True, package_data={'dowhy':['VERSION']} )

petergtz

570bc06baddc7c29b233e6afbb156f58ae9ae200

9a025a2003d754aa9749e8569b72dc566a17c3c2

Oh, wait a second. Let me actually check the other workflows. To see how this would work. Sorry, I didn't realize PyPI publication also happens through a workflow.

petergtz

py-why/dowhy

Auto generate documentation

This PR introduces a GitHub action to auto-generate versioned documentation and publish it to py-why.github.io/dowhy. To facilitate automatically generating documentation on every commit to master, this PR introduces multiple things (separated by commits): - It introduces [versioneer](https://github.com/python-versioneer/python-versioneer), a convenient tool to use git tags for versioning. Otherwise, keeping a master version of the docs separate from the latest release version is difficult: master would always list the latest version in its `VERSION` file, such as e.g. `0.7.1` and then documentation for master branch would still say v0.7.1 and easily confused with the real v0.7.1 documentation. Versioneer is also used by NumPy and Pandas. - It introduces [sphinx_multiversion](https://holzhaus.github.io/sphinx-multiversion/master/index.html), a Sphinx extension to generate multiple versions of the documentation based on different branches and tags of the git repo. To be precise, it uses a [slightly changed version of it](https://github.com/Holzhaus/sphinx-multiversion/compare/master...petergtz:sphinx-multiversion:override-version-with-refname), which uses the git refname for the version, not falling back to a hard-coded value in `conf.py`. For now, I'm hosting [this variant in my own GitHub account](https://github.com/petergtz/sphinx-multiversion/tree/override-version-with-refname), but my plan is to open a PR to upstream and introduce this as a new feature. - It introduce a new `generate_docs.sh` script as a replacement for the `Makefile`. This script invokes sphinx_multiversion instead of vanilla sphinx and it also creates an `index.html` which automatically redirects to the latest stable version of the documentation. - It introduces a GitHub action workflow that builds the versioned documentation and publishes it. This action is based on the container image [pego/dowhy-examples-notebooks-deps](https://hub.docker.com/repository/docker/pego/dowhy-examples-notebooks-deps) which is automatically built from [this Dockerfile](https://github.com/petergtz/dowhy-examples-notebooks-deps-dockerfile/blob/main/Dockerfile), which makes sure all necessary R dependencies are available. Instead of this additional Docker image, we could have installed all necessary dependencies in each run of the documentation build workflow, but that is both a waste of resources and also increasing the build time immensely. I suggest we move this repo into PyWhy and eventually create a docker hub account for PyWhy, or alternatively push the image into GitHub's own registry. - Finally, it makes the `str_to_dot` function more robust towards slightly changing inputs which is probably due to slight changes in graphviz libraries, which introduced additional whitespace in graph descriptions. **Notes:** - An example of this specific GitHub action in action can be found at: https://github.com/petergtz/dowhy/actions/workflows/build-and-publish-docs.yml - An example of the versioned documentation can be found at: https://petergtz.github.io/dowhy - `versioneer.py` and `dowhy/_version.py` do not have to be reviewed. Versioneer generates these files when invoking its install script.

2022-07-19 20:38:04+00:00

2022-07-28 10:10:47+00:00

setup.py

"""A setuptools based setup module for dowhy. Adapted from: https://packaging.python.org/en/latest/distributing.html https://github.com/pypa/sampleproject """ from setuptools import setup, find_packages from codecs import open from os import path import versioneer here = path.abspath(path.dirname(__file__)) # Get the long description from the README file with open(path.join(here, 'README.rst'), encoding='utf-8') as f: long_description = f.read() # Get the required packages with open(path.join(here, 'requirements.txt'), encoding='utf-8') as f: install_requires = f.read().splitlines() # Plotting packages are optional to install extras = ["plotting"] extras_require = dict() for e in extras: req_file = "requirements-{0}.txt".format(e) with open(req_file) as f: extras_require[e] = [line.strip() for line in f] setup( name='dowhy', version=versioneer.get_version(), cmdclass=versioneer.get_cmdclass(), description='DoWhy is a Python library for causal inference that supports explicit modeling and testing of causal assumptions.', # Required license='MIT', long_description=long_description, url='https://github.com/microsoft/dowhy', # Optional download_url='https://github.com/microsoft/dowhy/archive/v0.8.tar.gz', author='Amit Sharma, Emre Kiciman', classifiers=[ # Optional 'Development Status :: 4 - Beta', 'License :: OSI Approved :: MIT License', 'Programming Language :: Python :: 3.6', 'Programming Language :: Python :: 3.7', 'Programming Language :: Python :: 3.8', 'Programming Language :: Python :: 3.9', ], keywords='causality machine-learning causal-inference statistics graphical-model', packages=find_packages(exclude=['docs', 'tests']), python_requires='>=3.6', install_requires=install_requires, extras_require=extras_require, include_package_data=True, package_data={'dowhy':['VERSION']} )

"""A setuptools based setup module for dowhy. Adapted from: https://packaging.python.org/en/latest/distributing.html https://github.com/pypa/sampleproject """ from setuptools import setup, find_packages from codecs import open from os import path import versioneer here = path.abspath(path.dirname(__file__)) # Get the long description from the README file with open(path.join(here, 'README.rst'), encoding='utf-8') as f: long_description = f.read() # Get the required packages with open(path.join(here, 'requirements.txt'), encoding='utf-8') as f: install_requires = f.read().splitlines() # Plotting packages are optional to install extras = ["plotting"] extras_require = dict() for e in extras: req_file = "requirements-{0}.txt".format(e) with open(req_file) as f: extras_require[e] = [line.strip() for line in f] setup( name='dowhy', version=versioneer.get_version(), cmdclass=versioneer.get_cmdclass(), description='DoWhy is a Python library for causal inference that supports explicit modeling and testing of causal assumptions.', # Required license='MIT', long_description=long_description, url='https://github.com/microsoft/dowhy', # Optional download_url='https://github.com/microsoft/dowhy/archive/v0.8.tar.gz', author='Amit Sharma, Emre Kiciman', classifiers=[ # Optional 'Development Status :: 4 - Beta', 'License :: OSI Approved :: MIT License', 'Programming Language :: Python :: 3.6', 'Programming Language :: Python :: 3.7', 'Programming Language :: Python :: 3.8', 'Programming Language :: Python :: 3.9', ], keywords='causality machine-learning causal-inference statistics graphical-model', packages=find_packages(exclude=['docs', 'tests']), python_requires='>=3.6', install_requires=install_requires, extras_require=extras_require, include_package_data=True, package_data={'dowhy':['VERSION']} )

petergtz

570bc06baddc7c29b233e6afbb156f58ae9ae200

9a025a2003d754aa9749e8569b72dc566a17c3c2

Okay, yes, this should work. The moment you use the GitHub UI to create the release and the git tag, it will push this tag and that will trigger the publish workflow which then just relies on the usual `python setup.py sdist bdist_wheel` call which uses versioneer to choose the current/latest version from the just-created git tag.

petergtz

py-why/dowhy

Algorithms for efficient adjustment (backdoor) sets

Implements the algorithms discussed [here](https://github.com/py-why/dowhy/issues/464). I added the new algorithms [here](https://github.com/py-why/dowhy/pull/549/files#diff-cb99b05726571b36d65d193004d3c854cbf055d86eadd94dc1ce81bc4ac7b4b4), and made a few (small I think) changes to the CausalIdentifier class. I added tests for the new identifier methods, essentially covering a number of graphs that appeared in our papers on these algorithms. This is still missing updates to the docs. I think feedback at this point would be super helpful :) I also have a few questions and comments: - Do the already implemented backdoor methods support multivariate treatments and/or outcomes? I ask this because the newly added algorithms are designed to work for univariate treatment and outcome only. - I'm currently raising a value error when no observable backdoor exists; is this how you handle this situation? I also raise value error when the (sufficient) conditions that we need to ensure the existence of an optimal efficient backdoor do not hold. - Computing the minimum cost efficient adjustment set of course requires the user passing the costs associated with nodes. This is done when calling the identify_ate_effect method. If no costs are passed, they are assume to be constant and equal to one, and hence the optimal minimum cost backdoor set is the optimal backdoor set of minimum cardinality. I wonder if the user should be warned about this, or putting it in the docs is enough. - The algorithms admit a set of conditional variables, that could be used to decide treatment (individualised treatment rules). This is also passed when calling the identify_ate_effect method, does that choice seem right? - The new files I created I passed through black to pass flake8, but I didn't do this with causal_identifier.py because there were pre-existing flake8 problems and I didn't want to make so many chances to the file at once.

2022-07-16 14:24:08+00:00

2022-08-08 04:09:13+00:00

dowhy/causal_identifier.py

import copy import itertools import logging import sympy as sp import sympy.stats as spstats import dowhy.utils.cli_helpers as cli from dowhy.utils.api import parse_state class CausalIdentifier: """Class that implements different identification methods. Currently supports backdoor and instrumental variable identification methods. The identification is based on the causal graph provided. """ NONPARAMETRIC_ATE="nonparametric-ate" NONPARAMETRIC_NDE="nonparametric-nde" NONPARAMETRIC_NIE="nonparametric-nie" MAX_BACKDOOR_ITERATIONS = 100000 # Backdoor method names BACKDOOR_DEFAULT="default" BACKDOOR_EXHAUSTIVE="exhaustive-search" BACKDOOR_MIN="minimal-adjustment" BACKDOOR_MAX="maximal-adjustment" METHOD_NAMES = {BACKDOOR_DEFAULT, BACKDOOR_EXHAUSTIVE, BACKDOOR_MIN, BACKDOOR_MAX} DEFAULT_BACKDOOR_METHOD = BACKDOOR_DEFAULT def __init__(self, graph, estimand_type, method_name = "default", proceed_when_unidentifiable=False): self._graph = graph self.estimand_type = estimand_type self.treatment_name = graph.treatment_name self.outcome_name = graph.outcome_name self.method_name = method_name self._proceed_when_unidentifiable = proceed_when_unidentifiable self.logger = logging.getLogger(__name__) def identify_effect(self, optimize_backdoor=False): """Main method that returns an identified estimand (if one exists). If estimand_type is non-parametric ATE, then uses backdoor, instrumental variable and frontdoor identification methods, to check if an identified estimand exists, based on the causal graph. :param self: instance of the CausalIdentifier class (or its subclass) :returns: target estimand, an instance of the IdentifiedEstimand class """ # First, check if there is a directed path from action to outcome if not self._graph.has_directed_path(self.treatment_name, self.outcome_name): self.logger.warn("No directed path from treatment to outcome. Causal Effect is zero.") return IdentifiedEstimand(self, treatment_variable=self.treatment_name, outcome_variable=self.outcome_name, no_directed_path=True) if self.estimand_type == CausalIdentifier.NONPARAMETRIC_ATE: return self.identify_ate_effect(optimize_backdoor=optimize_backdoor) elif self.estimand_type == CausalIdentifier.NONPARAMETRIC_NDE: return self.identify_nde_effect() elif self.estimand_type == CausalIdentifier.NONPARAMETRIC_NIE: return self.identify_nie_effect() else: raise ValueError("Estimand type is not supported. Use either {0}, {1}, or {2}.".format( CausalIdentifier.NONPARAMETRIC_ATE, CausalIdentifier.NONPARAMETRIC_NDE, CausalIdentifier.NONPARAMETRIC_NIE)) def identify_ate_effect(self, optimize_backdoor): estimands_dict = {} mediation_first_stage_confounders = None mediation_second_stage_confounders = None ### 1. BACKDOOR IDENTIFICATION # First, checking if there are any valid backdoor adjustment sets if optimize_backdoor == False: backdoor_sets = self.identify_backdoor(self.treatment_name, self.outcome_name) else: from dowhy.causal_identifiers.backdoor import Backdoor path = Backdoor(self._graph._graph, self.treatment_name, self.outcome_name) backdoor_sets = path.get_backdoor_vars() estimands_dict, backdoor_variables_dict = self.build_backdoor_estimands_dict( self.treatment_name, self.outcome_name, backdoor_sets, estimands_dict) # Setting default "backdoor" identification adjustment set default_backdoor_id = self.get_default_backdoor_set_id(backdoor_variables_dict) if len(backdoor_variables_dict) > 0: estimands_dict["backdoor"] = estimands_dict.get(str(default_backdoor_id), None) backdoor_variables_dict["backdoor"] = backdoor_variables_dict.get(str(default_backdoor_id), None) else: estimands_dict["backdoor"] = None ### 2. INSTRUMENTAL VARIABLE IDENTIFICATION # Now checking if there is also a valid iv estimand instrument_names = self._graph.get_instruments(self.treatment_name, self.outcome_name) self.logger.info("Instrumental variables for treatment and outcome:" + str(instrument_names)) if len(instrument_names) > 0: iv_estimand_expr = self.construct_iv_estimand( self.estimand_type, self._graph.treatment_name, self._graph.outcome_name, instrument_names ) self.logger.debug("Identified expression = " + str(iv_estimand_expr)) estimands_dict["iv"] = iv_estimand_expr else: estimands_dict["iv"] = None ### 3. FRONTDOOR IDENTIFICATION # Now checking if there is a valid frontdoor variable frontdoor_variables_names = self.identify_frontdoor() self.logger.info("Frontdoor variables for treatment and outcome:" + str(frontdoor_variables_names)) if len(frontdoor_variables_names) >0: frontdoor_estimand_expr = self.construct_frontdoor_estimand( self.estimand_type, self._graph.treatment_name, self._graph.outcome_name, frontdoor_variables_names ) self.logger.debug("Identified expression = " + str(frontdoor_estimand_expr)) estimands_dict["frontdoor"] = frontdoor_estimand_expr mediation_first_stage_confounders = self.identify_mediation_first_stage_confounders(self.treatment_name, frontdoor_variables_names) mediation_second_stage_confounders = self.identify_mediation_second_stage_confounders(frontdoor_variables_names, self.outcome_name) else: estimands_dict["frontdoor"] = None # Finally returning the estimand object estimand = IdentifiedEstimand( self, treatment_variable=self._graph.treatment_name, outcome_variable=self._graph.outcome_name, estimand_type=self.estimand_type, estimands=estimands_dict, backdoor_variables=backdoor_variables_dict, instrumental_variables=instrument_names, frontdoor_variables=frontdoor_variables_names, mediation_first_stage_confounders=mediation_first_stage_confounders, mediation_second_stage_confounders=mediation_second_stage_confounders, default_backdoor_id = default_backdoor_id ) return estimand def identify_nie_effect(self): estimands_dict = {} ### 1. FIRST DOING BACKDOOR IDENTIFICATION # First, checking if there are any valid backdoor adjustment sets backdoor_sets = self.identify_backdoor(self.treatment_name, self.outcome_name) estimands_dict, backdoor_variables_dict = self.build_backdoor_estimands_dict( self.treatment_name, self.outcome_name, backdoor_sets, estimands_dict) # Setting default "backdoor" identification adjustment set default_backdoor_id = self.get_default_backdoor_set_id(backdoor_variables_dict) backdoor_variables_dict["backdoor"] = backdoor_variables_dict.get(str(default_backdoor_id), None) ### 2. SECOND, CHECKING FOR MEDIATORS # Now checking if there are valid mediator variables estimands_dict = {} # Need to reinitialize this dictionary to avoid including the backdoor sets mediation_first_stage_confounders = None mediation_second_stage_confounders = None mediators_names = self.identify_mediation() self.logger.info("Mediators for treatment and outcome:" + str(mediators_names)) if len(mediators_names) >0: mediation_estimand_expr = self.construct_mediation_estimand( self.estimand_type, self._graph.treatment_name, self._graph.outcome_name, mediators_names ) self.logger.debug("Identified expression = " + str(mediation_estimand_expr)) estimands_dict["mediation"] = mediation_estimand_expr mediation_first_stage_confounders = self.identify_mediation_first_stage_confounders(self.treatment_name, mediators_names) mediation_second_stage_confounders = self.identify_mediation_second_stage_confounders(mediators_names, self.outcome_name) else: estimands_dict["mediation"] = None # Finally returning the estimand object estimand = IdentifiedEstimand( self, treatment_variable=self._graph.treatment_name, outcome_variable=self._graph.outcome_name, estimand_type=self.estimand_type, estimands=estimands_dict, backdoor_variables=backdoor_variables_dict, instrumental_variables=None, frontdoor_variables=None, mediator_variables=mediators_names, mediation_first_stage_confounders=mediation_first_stage_confounders, mediation_second_stage_confounders=mediation_second_stage_confounders, default_backdoor_id = None ) return estimand def identify_nde_effect(self): estimands_dict = {} ### 1. FIRST DOING BACKDOOR IDENTIFICATION # First, checking if there are any valid backdoor adjustment sets backdoor_sets = self.identify_backdoor(self.treatment_name, self.outcome_name) estimands_dict, backdoor_variables_dict = self.build_backdoor_estimands_dict( self.treatment_name, self.outcome_name, backdoor_sets, estimands_dict) # Setting default "backdoor" identification adjustment set default_backdoor_id = self.get_default_backdoor_set_id(backdoor_variables_dict) backdoor_variables_dict["backdoor"] = backdoor_variables_dict.get(str(default_backdoor_id), None) ### 2. SECOND, CHECKING FOR MEDIATORS # Now checking if there are valid mediator variables estimands_dict = {} mediation_first_stage_confounders = None mediation_second_stage_confounders = None mediators_names = self.identify_mediation() self.logger.info("Mediators for treatment and outcome:" + str(mediators_names)) if len(mediators_names) >0: mediation_estimand_expr = self.construct_mediation_estimand( self.estimand_type, self._graph.treatment_name, self._graph.outcome_name, mediators_names ) self.logger.debug("Identified expression = " + str(mediation_estimand_expr)) estimands_dict["mediation"] = mediation_estimand_expr mediation_first_stage_confounders = self.identify_mediation_first_stage_confounders(self.treatment_name, mediators_names) mediation_second_stage_confounders = self.identify_mediation_second_stage_confounders(mediators_names, self.outcome_name) else: estimands_dict["mediation"] = None # Finally returning the estimand object estimand = IdentifiedEstimand( self, treatment_variable=self._graph.treatment_name, outcome_variable=self._graph.outcome_name, estimand_type=self.estimand_type, estimands=estimands_dict, backdoor_variables=backdoor_variables_dict, instrumental_variables=None, frontdoor_variables=None, mediator_variables=mediators_names, mediation_first_stage_confounders=mediation_first_stage_confounders, mediation_second_stage_confounders=mediation_second_stage_confounders, default_backdoor_id = None ) return estimand def identify_backdoor(self, treatment_name, outcome_name, include_unobserved=False, dseparation_algo="default"): backdoor_sets = [] backdoor_paths = None bdoor_graph = None if dseparation_algo == "naive": backdoor_paths = self._graph.get_backdoor_paths(treatment_name, outcome_name) elif dseparation_algo == "default": bdoor_graph = self._graph.do_surgery(treatment_name, remove_outgoing_edges=True) else: raise ValueError(f"d-separation algorithm {dseparation_algo} is not supported") method_name = self.method_name if self.method_name != CausalIdentifier.BACKDOOR_DEFAULT else CausalIdentifier.DEFAULT_BACKDOOR_METHOD # First, checking if empty set is a valid backdoor set empty_set = set() check = self._graph.check_valid_backdoor_set(treatment_name, outcome_name, empty_set, backdoor_paths=backdoor_paths, new_graph=bdoor_graph, dseparation_algo=dseparation_algo) if check["is_dseparated"]: backdoor_sets.append({'backdoor_set':empty_set}) # If the method is `minimal-adjustment`, return the empty set right away. if method_name == CausalIdentifier.BACKDOOR_MIN: return backdoor_sets # Second, checking for all other sets of variables. If include_unobserved is false, then only observed variables are eligible. eligible_variables = self._graph.get_all_nodes(include_unobserved=include_unobserved) \ - set(treatment_name) \ - set(outcome_name) eligible_variables -= self._graph.get_descendants(treatment_name) # If var is d-separated from both treatment or outcome, it cannot # be a part of the backdoor set filt_eligible_variables = set() for var in eligible_variables: dsep_treat_var = self._graph.check_dseparation( treatment_name, parse_state(var), set()) dsep_outcome_var = self._graph.check_dseparation( outcome_name, parse_state(var), set()) if not dsep_outcome_var or not dsep_treat_var: filt_eligible_variables.add(var) if method_name in CausalIdentifier.METHOD_NAMES: backdoor_sets, found_valid_adjustment_set = self.find_valid_adjustment_sets( treatment_name, outcome_name, backdoor_paths, bdoor_graph, dseparation_algo, backdoor_sets, filt_eligible_variables, method_name=method_name, max_iterations= CausalIdentifier.MAX_BACKDOOR_ITERATIONS) if method_name == CausalIdentifier.BACKDOOR_DEFAULT and found_valid_adjustment_set: # repeat the above search with BACKDOOR_MIN backdoor_sets, _ = self.find_valid_adjustment_sets( treatment_name, outcome_name, backdoor_paths, bdoor_graph, dseparation_algo, backdoor_sets, filt_eligible_variables, method_name=CausalIdentifier.BACKDOOR_MIN, max_iterations= CausalIdentifier.MAX_BACKDOOR_ITERATIONS) else: raise ValueError(f"Identifier method {method_name} not supported. Try one of the following: {CausalIdentifier.METHOD_NAMES}") return backdoor_sets def find_valid_adjustment_sets(self, treatment_name, outcome_name, backdoor_paths, bdoor_graph, dseparation_algo, backdoor_sets, filt_eligible_variables, method_name, max_iterations): num_iterations = 0 found_valid_adjustment_set = False all_nodes_observed = self._graph.all_observed(self._graph.get_all_nodes()) # If `minimal-adjustment` method is specified, start the search from the set with minimum size. Otherwise, start from the largest. set_sizes = range(1, len(filt_eligible_variables) + 1, 1) if method_name == CausalIdentifier.BACKDOOR_MIN else range(len(filt_eligible_variables), 0, -1) for size_candidate_set in set_sizes: for candidate_set in itertools.combinations(filt_eligible_variables, size_candidate_set): check = self._graph.check_valid_backdoor_set(treatment_name, outcome_name, candidate_set, backdoor_paths=backdoor_paths, new_graph = bdoor_graph, dseparation_algo = dseparation_algo) self.logger.debug("Candidate backdoor set: {0}, is_dseparated: {1}".format(candidate_set, check["is_dseparated"])) if check["is_dseparated"]: backdoor_sets.append({'backdoor_set': candidate_set}) found_valid_adjustment_set = True num_iterations += 1 if method_name == CausalIdentifier.BACKDOOR_EXHAUSTIVE and num_iterations > max_iterations: self.logger.warning(f"Max number of iterations {max_iterations} reached.") break # If the backdoor method is `maximal-adjustment` or `minimal-adjustment`, return the first found adjustment set. if method_name in {CausalIdentifier.BACKDOOR_DEFAULT, CausalIdentifier.BACKDOOR_MAX, CausalIdentifier.BACKDOOR_MIN} and found_valid_adjustment_set: break # If all variables are observed, and the biggest eligible set # does not satisfy backdoor, then none of its subsets will. if method_name in {CausalIdentifier.BACKDOOR_DEFAULT, CausalIdentifier.BACKDOOR_MAX} and all_nodes_observed: break if num_iterations > max_iterations: self.logger.warning(f"Max number of iterations {max_iterations} reached. Could not find a valid backdoor set.") break return backdoor_sets, found_valid_adjustment_set def get_default_backdoor_set_id(self, backdoor_sets_dict): # Adding a None estimand if no backdoor set found if len(backdoor_sets_dict) == 0: return None # Default set contains minimum possible number of instrumental variables, to prevent lowering variance in the treatment variable. instrument_names = set(self._graph.get_instruments(self.treatment_name, self.outcome_name)) iv_count_dict = {key: len(set(bdoor_set).intersection(instrument_names)) for key, bdoor_set in backdoor_sets_dict.items()} min_iv_count = min(iv_count_dict.values()) min_iv_keys = {key for key, iv_count in iv_count_dict.items() if iv_count == min_iv_count} min_iv_backdoor_sets_dict = {key: backdoor_sets_dict[key] for key in min_iv_keys} # Default set is the one with the least number of adjustment variables (optimizing for efficiency) min_set_length = 1000000 default_key = None for key, bdoor_set in min_iv_backdoor_sets_dict.items(): if len(bdoor_set) < min_set_length: min_set_length = len(bdoor_set) default_key = key return default_key def build_backdoor_estimands_dict(self, treatment_name, outcome_name, backdoor_sets, estimands_dict, proceed_when_unidentifiable=None): """Build the final dict for backdoor sets by filtering unobserved variables if needed. """ backdoor_variables_dict = {} if proceed_when_unidentifiable is None: proceed_when_unidentifiable = self._proceed_when_unidentifiable is_identified = [ self._graph.all_observed(bset["backdoor_set"]) for bset in backdoor_sets ] if any(is_identified): self.logger.info("Causal effect can be identified.") backdoor_sets_arr = [list( bset["backdoor_set"]) for bset in backdoor_sets if self._graph.all_observed(bset["backdoor_set"]) ] else: # there is unobserved confounding self.logger.warning("Backdoor identification failed.") backdoor_sets_arr = [] for i in range(len(backdoor_sets_arr)): backdoor_estimand_expr = self.construct_backdoor_estimand( self.estimand_type, treatment_name, outcome_name, backdoor_sets_arr[i]) self.logger.debug("Identified expression = " + str(backdoor_estimand_expr)) estimands_dict["backdoor"+str(i+1)] = backdoor_estimand_expr backdoor_variables_dict["backdoor"+str(i+1)] = backdoor_sets_arr[i] return estimands_dict, backdoor_variables_dict def identify_frontdoor(self, dseparation_algo="default"): """ Find a valid frontdoor variable if it exists. Currently only supports a single variable frontdoor set. """ frontdoor_var = None frontdoor_paths = None fdoor_graph = None if dseparation_algo == "default": cond1_graph = self._graph.do_surgery(self.treatment_name, remove_incoming_edges=True) bdoor_graph1 = self._graph.do_surgery(self.treatment_name, remove_outgoing_edges=True) elif dseparation_algo == "naive": frontdoor_paths = self._graph.get_all_directed_paths(self.treatment_name, self.outcome_name) else: raise ValueError(f"d-separation algorithm {dseparation_algo} is not supported") eligible_variables = self._graph.get_descendants(self.treatment_name) \ - set(self.outcome_name) \ - set(self._graph.get_descendants(self.outcome_name)) # For simplicity, assuming a one-variable frontdoor set for candidate_var in eligible_variables: # Cond 1: All directed paths intercepted by candidate_var cond1 = self._graph.check_valid_frontdoor_set( self.treatment_name, self.outcome_name, parse_state(candidate_var), frontdoor_paths=frontdoor_paths, new_graph=cond1_graph, dseparation_algo=dseparation_algo) self.logger.debug("Candidate frontdoor set: {0}, is_dseparated: {1}".format(candidate_var, cond1)) if not cond1: continue # Cond 2: No confounding between treatment and candidate var cond2 = self._graph.check_valid_backdoor_set( self.treatment_name, parse_state(candidate_var), set(), backdoor_paths=None, new_graph= bdoor_graph1, dseparation_algo=dseparation_algo) if not cond2: continue # Cond 3: treatment blocks all confounding between candidate_var and outcome bdoor_graph2 = self._graph.do_surgery(candidate_var, remove_outgoing_edges=True) cond3 = self._graph.check_valid_backdoor_set( parse_state(candidate_var), self.outcome_name, self.treatment_name, backdoor_paths=None, new_graph= bdoor_graph2, dseparation_algo=dseparation_algo) is_valid_frontdoor = cond1 and cond2 and cond3 if is_valid_frontdoor: frontdoor_var = candidate_var break return parse_state(frontdoor_var) def identify_mediation(self): """ Find a valid mediator if it exists. Currently only supports a single variable mediator set. """ mediation_var = None mediation_paths = self._graph.get_all_directed_paths(self.treatment_name, self.outcome_name) eligible_variables = self._graph.get_descendants(self.treatment_name) \ - set(self.outcome_name) # For simplicity, assuming a one-variable mediation set for candidate_var in eligible_variables: is_valid_mediation = self._graph.check_valid_mediation_set(self.treatment_name, self.outcome_name, parse_state(candidate_var), mediation_paths=mediation_paths) self.logger.debug("Candidate mediation set: {0}, on_mediating_path: {1}".format(candidate_var, is_valid_mediation)) if is_valid_mediation: mediation_var = candidate_var break return parse_state(mediation_var) return None def identify_mediation_first_stage_confounders(self, treatment_name, mediators_names): # Create estimands dict as per the API for backdoor, but do not return it estimands_dict = {} backdoor_sets = self.identify_backdoor(treatment_name, mediators_names) estimands_dict, backdoor_variables_dict = self.build_backdoor_estimands_dict( treatment_name, mediators_names, backdoor_sets, estimands_dict, proceed_when_unidentifiable=True) # Setting default "backdoor" identification adjustment set default_backdoor_id = self.get_default_backdoor_set_id(backdoor_variables_dict) estimands_dict["backdoor"] = estimands_dict.get(str(default_backdoor_id), None) backdoor_variables_dict["backdoor"] = backdoor_variables_dict.get(str(default_backdoor_id), None) return backdoor_variables_dict def identify_mediation_second_stage_confounders(self, mediators_names, outcome_name): # Create estimands dict as per the API for backdoor, but do not return it estimands_dict = {} backdoor_sets = self.identify_backdoor(mediators_names, outcome_name) estimands_dict, backdoor_variables_dict = self.build_backdoor_estimands_dict( mediators_names, outcome_name, backdoor_sets, estimands_dict, proceed_when_unidentifiable=True) # Setting default "backdoor" identification adjustment set default_backdoor_id = self.get_default_backdoor_set_id(backdoor_variables_dict) estimands_dict["backdoor"] = estimands_dict.get(str(default_backdoor_id), None) backdoor_variables_dict["backdoor"] = backdoor_variables_dict.get(str(default_backdoor_id), None) return backdoor_variables_dict def construct_backdoor_estimand(self, estimand_type, treatment_name, outcome_name, common_causes): # TODO: outputs string for now, but ideally should do symbolic # expressions Mon 19 Feb 2018 04:54:17 PM DST # TODO Better support for multivariate treatments expr = None outcome_name = outcome_name[0] num_expr_str = outcome_name if len(common_causes)>0: num_expr_str += "|" + ",".join(common_causes) expr = "d(" + num_expr_str + ")/d" + ",".join(treatment_name) sym_mu = sp.Symbol("mu") sym_sigma = sp.Symbol("sigma", positive=True) sym_outcome = spstats.Normal(num_expr_str, sym_mu, sym_sigma) sym_treatment_symbols = [sp.Symbol(t) for t in treatment_name] sym_treatment = sp.Array(sym_treatment_symbols) sym_conditional_outcome = spstats.Expectation(sym_outcome) sym_effect = sp.Derivative(sym_conditional_outcome, sym_treatment) sym_assumptions = { 'Unconfoundedness': ( u"If U\N{RIGHTWARDS ARROW}{{{0}}} and U\N{RIGHTWARDS ARROW}{1}" " then P({1}|{0},{2},U) = P({1}|{0},{2})" ).format(",".join(treatment_name), outcome_name, ",".join(common_causes)) } estimand = { 'estimand': sym_effect, 'assumptions': sym_assumptions } return estimand def construct_iv_estimand(self, estimand_type, treatment_name, outcome_name, instrument_names): # TODO: support multivariate treatments better. expr = None outcome_name = outcome_name[0] sym_outcome = spstats.Normal(outcome_name, 0, 1) sym_treatment_symbols = [spstats.Normal(t, 0, 1) for t in treatment_name] sym_treatment = sp.Array(sym_treatment_symbols) sym_instrument_symbols = [sp.Symbol(inst) for inst in instrument_names] sym_instrument = sp.Array(sym_instrument_symbols) # ",".join(instrument_names)) sym_outcome_derivative = sp.Derivative(sym_outcome, sym_instrument) sym_treatment_derivative = sp.Derivative(sym_treatment, sym_instrument) sym_effect = spstats.Expectation(sym_outcome_derivative / sym_treatment_derivative) sym_assumptions = { "As-if-random": ( "If U\N{RIGHTWARDS ARROW}\N{RIGHTWARDS ARROW}{0} then " "\N{NOT SIGN}(U \N{RIGHTWARDS ARROW}\N{RIGHTWARDS ARROW}{{{1}}})" ).format(outcome_name, ",".join(instrument_names)), "Exclusion": ( u"If we remove {{{0}}}\N{RIGHTWARDS ARROW}{{{1}}}, then " u"\N{NOT SIGN}({{{0}}}\N{RIGHTWARDS ARROW}{2})" ).format(",".join(instrument_names), ",".join(treatment_name), outcome_name) } estimand = { 'estimand': sym_effect, 'assumptions': sym_assumptions } return estimand def construct_frontdoor_estimand(self, estimand_type, treatment_name, outcome_name, frontdoor_variables_names): # TODO: support multivariate treatments better. expr = None outcome_name = outcome_name[0] sym_outcome = spstats.Normal(outcome_name, 0, 1) sym_treatment_symbols = [spstats.Normal(t, 0, 1) for t in treatment_name] sym_treatment = sp.Array(sym_treatment_symbols) sym_frontdoor_symbols = [sp.Symbol(inst) for inst in frontdoor_variables_names] sym_frontdoor = sp.Array(sym_frontdoor_symbols) # ",".join(instrument_names)) sym_outcome_derivative = sp.Derivative(sym_outcome, sym_frontdoor) sym_treatment_derivative = sp.Derivative(sym_frontdoor, sym_treatment) sym_effect = spstats.Expectation(sym_treatment_derivative * sym_outcome_derivative) sym_assumptions = { "Full-mediation": ( "{2} intercepts (blocks) all directed paths from {0} to {1}." ).format(",".join(treatment_name), ",".join(outcome_name), ",".join(frontdoor_variables_names)), "First-stage-unconfoundedness": ( u"If U\N{RIGHTWARDS ARROW}{{{0}}} and U\N{RIGHTWARDS ARROW}{{{1}}}" " then P({1}|{0},U) = P({1}|{0})" ).format(",".join(treatment_name), ",".join(frontdoor_variables_names)), "Second-stage-unconfoundedness": ( u"If U\N{RIGHTWARDS ARROW}{{{2}}} and U\N{RIGHTWARDS ARROW}{1}" " then P({1}|{2}, {0}, U) = P({1}|{2}, {0})" ).format(",".join(treatment_name), outcome_name, ",".join(frontdoor_variables_names)) } estimand = { 'estimand': sym_effect, 'assumptions': sym_assumptions } return estimand def construct_mediation_estimand(self, estimand_type, treatment_name, outcome_name, mediators_names): # TODO: support multivariate treatments better. expr = None if estimand_type in (CausalIdentifier.NONPARAMETRIC_NDE, CausalIdentifier.NONPARAMETRIC_NIE): outcome_name = outcome_name[0] sym_outcome = spstats.Normal(outcome_name, 0, 1) sym_treatment_symbols = [spstats.Normal(t, 0, 1) for t in treatment_name] sym_treatment = sp.Array(sym_treatment_symbols) sym_mediators_symbols = [sp.Symbol(inst) for inst in mediators_names] sym_mediators = sp.Array(sym_mediators_symbols) sym_outcome_derivative = sp.Derivative(sym_outcome, sym_mediators) sym_treatment_derivative = sp.Derivative(sym_mediators, sym_treatment) # For direct effect num_expr_str = outcome_name if len(mediators_names)>0: num_expr_str += "|" + ",".join(mediators_names) sym_mu = sp.Symbol("mu") sym_sigma = sp.Symbol("sigma", positive=True) sym_conditional_outcome = spstats.Normal(num_expr_str, sym_mu, sym_sigma) sym_directeffect_derivative = sp.Derivative(sym_conditional_outcome, sym_treatment) if estimand_type == CausalIdentifier.NONPARAMETRIC_NIE: sym_effect = spstats.Expectation(sym_treatment_derivative * sym_outcome_derivative) elif estimand_type == CausalIdentifier.NONPARAMETRIC_NDE: sym_effect = spstats.Expectation(sym_directeffect_derivative) sym_assumptions = { "Mediation": ( "{2} intercepts (blocks) all directed paths from {0} to {1} except the path {{{0}}}\N{RIGHTWARDS ARROW}{{{1}}}." ).format(",".join(treatment_name), ",".join(outcome_name), ",".join(mediators_names)), "First-stage-unconfoundedness": ( u"If U\N{RIGHTWARDS ARROW}{{{0}}} and U\N{RIGHTWARDS ARROW}{{{1}}}" " then P({1}|{0},U) = P({1}|{0})" ).format(",".join(treatment_name), ",".join(mediators_names)), "Second-stage-unconfoundedness": ( u"If U\N{RIGHTWARDS ARROW}{{{2}}} and U\N{RIGHTWARDS ARROW}{1}" " then P({1}|{2}, {0}, U) = P({1}|{2}, {0})" ).format(",".join(treatment_name), outcome_name, ",".join(mediators_names)) } else: raise ValueError("Estimand type not supported. Supported estimand types are {0} or {1}'.".format( CausalIdentifier.NONPARAMETRIC_NDE, CausalIdentifier.NONPARAMETRIC_NIE)) estimand = { 'estimand': sym_effect, 'assumptions': sym_assumptions } return estimand class IdentifiedEstimand: """Class for storing a causal estimand, typically as a result of the identification step. """ def __init__(self, identifier, treatment_variable, outcome_variable, estimand_type=None, estimands=None, backdoor_variables=None, instrumental_variables=None, frontdoor_variables=None, mediator_variables=None, mediation_first_stage_confounders=None, mediation_second_stage_confounders=None, default_backdoor_id=None, identifier_method=None, no_directed_path=False): self.identifier = identifier self.treatment_variable = parse_state(treatment_variable) self.outcome_variable = parse_state(outcome_variable) self.backdoor_variables = backdoor_variables self.instrumental_variables = parse_state(instrumental_variables) self.frontdoor_variables = parse_state(frontdoor_variables) self.mediator_variables = parse_state(mediator_variables) self.mediation_first_stage_confounders=mediation_first_stage_confounders self.mediation_second_stage_confounders=mediation_second_stage_confounders self.estimand_type = estimand_type self.estimands = estimands self.default_backdoor_id = default_backdoor_id self.identifier_method = identifier_method self.no_directed_path = no_directed_path def set_identifier_method(self, identifier_name): self.identifier_method = identifier_name def get_backdoor_variables(self, key=None): """ Return a list containing the backdoor variables. If the calling estimator method is a backdoor method, return the backdoor variables corresponding to its target estimand. Otherwise, return the backdoor variables for the default backdoor estimand. """ if key is None: if self.identifier_method and self.identifier_method.startswith("backdoor"): return self.backdoor_variables[self.identifier_method] elif self.backdoor_variables is not None and len(self.backdoor_variables) > 0: return self.backdoor_variables[self.default_backdoor_id] else: return [] else: return self.backdoor_variables[key] def set_backdoor_variables(self, bdoor_variables_arr, key=None): if key is None: key = self.identifier_method self.backdoor_variables[key] = bdoor_variables_arr def get_frontdoor_variables(self): """Return a list containing the frontdoor variables (if present) """ return self.frontdoor_variables def get_mediator_variables(self): """Return a list containing the mediator variables (if present) """ return self.mediator_variables def get_instrumental_variables(self): """Return a list containing the instrumental variables (if present) """ return self.instrumental_variables def __deepcopy__(self, memo): return IdentifiedEstimand( self.identifier, # not deep copied copy.deepcopy(self.treatment_variable), copy.deepcopy(self.outcome_variable), estimand_type=copy.deepcopy(self.estimand_type), estimands=copy.deepcopy(self.estimands), backdoor_variables=copy.deepcopy(self.backdoor_variables), instrumental_variables=copy.deepcopy(self.instrumental_variables), frontdoor_variables=copy.deepcopy(self.frontdoor_variables), mediator_variables=copy.deepcopy(self.mediator_variables), default_backdoor_id=copy.deepcopy(self.default_backdoor_id), identifier_method=copy.deepcopy(self.identifier_method) ) def __str__(self, only_target_estimand=False, show_all_backdoor_sets=False): if self.no_directed_path: s = "No directed path from {0} to {1} in the causal graph.".format( self.treatment_variable, self.outcome_variable) s += "\nCausal effect is zero." return s s = "Estimand type: {0}\n".format(self.estimand_type) i = 1 has_valid_backdoor = sum("backdoor" in key for key in self.estimands.keys()) for k, v in self.estimands.items(): if show_all_backdoor_sets: # Do not show backdoor key unless it is the only backdoor set. if k == "backdoor" and has_valid_backdoor > 1: continue else: # Just show the default backdoor set if k.startswith("backdoor") and k != "backdoor": continue if only_target_estimand and k != self.identifier_method: continue s += "\n### Estimand : {0}\n".format(i) s += "Estimand name: {0}".format(k) if k == self.default_backdoor_id: s += " (Default)" s += "\n" if v is None: s += "No such variable(s) found!\n" else: sp_expr_str = sp.pretty(v["estimand"], use_unicode=True) s += "Estimand expression:\n{0}\n".format(sp_expr_str) j = 1 for ass_name, ass_str in v["assumptions"].items(): s += "Estimand assumption {0}, {1}: {2}\n".format(j, ass_name, ass_str) j += 1 i += 1 return s

import copy import itertools import logging import sympy as sp import sympy.stats as spstats import dowhy.utils.cli_helpers as cli from dowhy.causal_identifiers.efficient_backdoor import EfficientBackdoor from dowhy.utils.api import parse_state class CausalIdentifier: """Class that implements different identification methods. Currently supports backdoor and instrumental variable identification methods. The identification is based on the causal graph provided. """ NONPARAMETRIC_ATE = "nonparametric-ate" NONPARAMETRIC_NDE = "nonparametric-nde" NONPARAMETRIC_NIE = "nonparametric-nie" MAX_BACKDOOR_ITERATIONS = 100000 # Backdoor method names BACKDOOR_DEFAULT = "default" BACKDOOR_EXHAUSTIVE = "exhaustive-search" BACKDOOR_MIN = "minimal-adjustment" BACKDOOR_MAX = "maximal-adjustment" BACKDOOR_EFFICIENT = "efficient-adjustment" BACKDOOR_MIN_EFFICIENT = "efficient-minimal-adjustment" BACKDOOR_MINCOST_EFFICIENT = "efficient-mincost-adjustment" METHOD_NAMES = { BACKDOOR_DEFAULT, BACKDOOR_EXHAUSTIVE, BACKDOOR_MIN, BACKDOOR_MAX, BACKDOOR_EFFICIENT, BACKDOOR_MIN_EFFICIENT, BACKDOOR_MINCOST_EFFICIENT, } EFFICIENT_METHODS = { BACKDOOR_EFFICIENT, BACKDOOR_MIN_EFFICIENT, BACKDOOR_MINCOST_EFFICIENT, } DEFAULT_BACKDOOR_METHOD = BACKDOOR_DEFAULT def __init__( self, graph, estimand_type, method_name="default", proceed_when_unidentifiable=False, ): self._graph = graph self.estimand_type = estimand_type self.treatment_name = graph.treatment_name self.outcome_name = graph.outcome_name self.method_name = method_name self._proceed_when_unidentifiable = proceed_when_unidentifiable self.logger = logging.getLogger(__name__) def identify_effect( self, optimize_backdoor=False, costs=None, conditional_node_names=None ): """Main method that returns an identified estimand (if one exists). If estimand_type is non-parametric ATE, then uses backdoor, instrumental variable and frontdoor identification methods, to check if an identified estimand exists, based on the causal graph. :param self: instance of the CausalIdentifier class (or its subclass) :param optimize_backdoor: if True, uses an optimised algorithm to compute the backdoor sets :param costs: non-negative costs associated with variables in the graph. Only used for estimand_type='non-parametric-ate' and method_name='efficient-mincost-adjustment'. If no costs are provided by the user, and method_name='efficient-mincost-adjustment', costs are assumed to be equal to one for all variables in the graph. :param conditional_node_names: variables that are used to determine treatment. If none are provided, it is assumed that the intervention is static. :returns: target estimand, an instance of the IdentifiedEstimand class """ # First, check if there is a directed path from action to outcome if not self._graph.has_directed_path(self.treatment_name, self.outcome_name): self.logger.warn( "No directed path from treatment to outcome. Causal Effect is zero." ) return IdentifiedEstimand( self, treatment_variable=self.treatment_name, outcome_variable=self.outcome_name, no_directed_path=True, ) if self.estimand_type == CausalIdentifier.NONPARAMETRIC_ATE: return self.identify_ate_effect( optimize_backdoor=optimize_backdoor, costs=costs, conditional_node_names=conditional_node_names, ) elif self.estimand_type == CausalIdentifier.NONPARAMETRIC_NDE: return self.identify_nde_effect() elif self.estimand_type == CausalIdentifier.NONPARAMETRIC_NIE: return self.identify_nie_effect() else: raise ValueError( "Estimand type is not supported. Use either {0}, {1}, or {2}.".format( CausalIdentifier.NONPARAMETRIC_ATE, CausalIdentifier.NONPARAMETRIC_NDE, CausalIdentifier.NONPARAMETRIC_NIE, ) ) def identify_ate_effect( self, optimize_backdoor, costs=None, conditional_node_names=None ): estimands_dict = {} mediation_first_stage_confounders = None mediation_second_stage_confounders = None ### 1. BACKDOOR IDENTIFICATION # Pick algorithm to compute backdoor sets according to method chosen if self.method_name not in CausalIdentifier.EFFICIENT_METHODS: # First, checking if there are any valid backdoor adjustment sets if optimize_backdoor == False: backdoor_sets = self.identify_backdoor( self.treatment_name, self.outcome_name ) else: from dowhy.causal_identifiers.backdoor import Backdoor path = Backdoor( self._graph._graph, self.treatment_name, self.outcome_name ) backdoor_sets = path.get_backdoor_vars() elif self.method_name in CausalIdentifier.EFFICIENT_METHODS: backdoor_sets = self.identify_efficient_backdoor( costs=costs, conditional_node_names=conditional_node_names ) estimands_dict, backdoor_variables_dict = self.build_backdoor_estimands_dict( self.treatment_name, self.outcome_name, backdoor_sets, estimands_dict ) # Setting default "backdoor" identification adjustment set default_backdoor_id = self.get_default_backdoor_set_id(backdoor_variables_dict) if len(backdoor_variables_dict) > 0: estimands_dict["backdoor"] = estimands_dict.get( str(default_backdoor_id), None ) backdoor_variables_dict["backdoor"] = backdoor_variables_dict.get( str(default_backdoor_id), None ) else: estimands_dict["backdoor"] = None ### 2. INSTRUMENTAL VARIABLE IDENTIFICATION # Now checking if there is also a valid iv estimand instrument_names = self._graph.get_instruments( self.treatment_name, self.outcome_name ) self.logger.info( "Instrumental variables for treatment and outcome:" + str(instrument_names) ) if len(instrument_names) > 0: iv_estimand_expr = self.construct_iv_estimand( self.estimand_type, self._graph.treatment_name, self._graph.outcome_name, instrument_names, ) self.logger.debug("Identified expression = " + str(iv_estimand_expr)) estimands_dict["iv"] = iv_estimand_expr else: estimands_dict["iv"] = None ### 3. FRONTDOOR IDENTIFICATION # Now checking if there is a valid frontdoor variable frontdoor_variables_names = self.identify_frontdoor() self.logger.info( "Frontdoor variables for treatment and outcome:" + str(frontdoor_variables_names) ) if len(frontdoor_variables_names) > 0: frontdoor_estimand_expr = self.construct_frontdoor_estimand( self.estimand_type, self._graph.treatment_name, self._graph.outcome_name, frontdoor_variables_names, ) self.logger.debug("Identified expression = " + str(frontdoor_estimand_expr)) estimands_dict["frontdoor"] = frontdoor_estimand_expr mediation_first_stage_confounders = self.identify_mediation_first_stage_confounders( self.treatment_name, frontdoor_variables_names ) mediation_second_stage_confounders = self.identify_mediation_second_stage_confounders( frontdoor_variables_names, self.outcome_name ) else: estimands_dict["frontdoor"] = None # Finally returning the estimand object estimand = IdentifiedEstimand( self, treatment_variable=self._graph.treatment_name, outcome_variable=self._graph.outcome_name, estimand_type=self.estimand_type, estimands=estimands_dict, backdoor_variables=backdoor_variables_dict, instrumental_variables=instrument_names, frontdoor_variables=frontdoor_variables_names, mediation_first_stage_confounders=mediation_first_stage_confounders, mediation_second_stage_confounders=mediation_second_stage_confounders, default_backdoor_id=default_backdoor_id, ) return estimand def identify_nie_effect(self): estimands_dict = {} ### 1. FIRST DOING BACKDOOR IDENTIFICATION # First, checking if there are any valid backdoor adjustment sets backdoor_sets = self.identify_backdoor(self.treatment_name, self.outcome_name) estimands_dict, backdoor_variables_dict = self.build_backdoor_estimands_dict( self.treatment_name, self.outcome_name, backdoor_sets, estimands_dict ) # Setting default "backdoor" identification adjustment set default_backdoor_id = self.get_default_backdoor_set_id(backdoor_variables_dict) backdoor_variables_dict["backdoor"] = backdoor_variables_dict.get( str(default_backdoor_id), None ) ### 2. SECOND, CHECKING FOR MEDIATORS # Now checking if there are valid mediator variables estimands_dict = ( {} ) # Need to reinitialize this dictionary to avoid including the backdoor sets mediation_first_stage_confounders = None mediation_second_stage_confounders = None mediators_names = self.identify_mediation() self.logger.info("Mediators for treatment and outcome:" + str(mediators_names)) if len(mediators_names) > 0: mediation_estimand_expr = self.construct_mediation_estimand( self.estimand_type, self._graph.treatment_name, self._graph.outcome_name, mediators_names, ) self.logger.debug("Identified expression = " + str(mediation_estimand_expr)) estimands_dict["mediation"] = mediation_estimand_expr mediation_first_stage_confounders = self.identify_mediation_first_stage_confounders( self.treatment_name, mediators_names ) mediation_second_stage_confounders = self.identify_mediation_second_stage_confounders( mediators_names, self.outcome_name ) else: estimands_dict["mediation"] = None # Finally returning the estimand object estimand = IdentifiedEstimand( self, treatment_variable=self._graph.treatment_name, outcome_variable=self._graph.outcome_name, estimand_type=self.estimand_type, estimands=estimands_dict, backdoor_variables=backdoor_variables_dict, instrumental_variables=None, frontdoor_variables=None, mediator_variables=mediators_names, mediation_first_stage_confounders=mediation_first_stage_confounders, mediation_second_stage_confounders=mediation_second_stage_confounders, default_backdoor_id=None, ) return estimand def identify_nde_effect(self): estimands_dict = {} ### 1. FIRST DOING BACKDOOR IDENTIFICATION # First, checking if there are any valid backdoor adjustment sets backdoor_sets = self.identify_backdoor(self.treatment_name, self.outcome_name) estimands_dict, backdoor_variables_dict = self.build_backdoor_estimands_dict( self.treatment_name, self.outcome_name, backdoor_sets, estimands_dict ) # Setting default "backdoor" identification adjustment set default_backdoor_id = self.get_default_backdoor_set_id(backdoor_variables_dict) backdoor_variables_dict["backdoor"] = backdoor_variables_dict.get( str(default_backdoor_id), None ) ### 2. SECOND, CHECKING FOR MEDIATORS # Now checking if there are valid mediator variables estimands_dict = {} mediation_first_stage_confounders = None mediation_second_stage_confounders = None mediators_names = self.identify_mediation() self.logger.info("Mediators for treatment and outcome:" + str(mediators_names)) if len(mediators_names) > 0: mediation_estimand_expr = self.construct_mediation_estimand( self.estimand_type, self._graph.treatment_name, self._graph.outcome_name, mediators_names, ) self.logger.debug("Identified expression = " + str(mediation_estimand_expr)) estimands_dict["mediation"] = mediation_estimand_expr mediation_first_stage_confounders = self.identify_mediation_first_stage_confounders( self.treatment_name, mediators_names ) mediation_second_stage_confounders = self.identify_mediation_second_stage_confounders( mediators_names, self.outcome_name ) else: estimands_dict["mediation"] = None # Finally returning the estimand object estimand = IdentifiedEstimand( self, treatment_variable=self._graph.treatment_name, outcome_variable=self._graph.outcome_name, estimand_type=self.estimand_type, estimands=estimands_dict, backdoor_variables=backdoor_variables_dict, instrumental_variables=None, frontdoor_variables=None, mediator_variables=mediators_names, mediation_first_stage_confounders=mediation_first_stage_confounders, mediation_second_stage_confounders=mediation_second_stage_confounders, default_backdoor_id=None, ) return estimand def identify_backdoor( self, treatment_name, outcome_name, include_unobserved=False, dseparation_algo="default", ): backdoor_sets = [] backdoor_paths = None bdoor_graph = None if dseparation_algo == "naive": backdoor_paths = self._graph.get_backdoor_paths( treatment_name, outcome_name ) elif dseparation_algo == "default": bdoor_graph = self._graph.do_surgery( treatment_name, remove_outgoing_edges=True ) else: raise ValueError( f"d-separation algorithm {dseparation_algo} is not supported" ) method_name = ( self.method_name if self.method_name != CausalIdentifier.BACKDOOR_DEFAULT else CausalIdentifier.DEFAULT_BACKDOOR_METHOD ) # First, checking if empty set is a valid backdoor set empty_set = set() check = self._graph.check_valid_backdoor_set( treatment_name, outcome_name, empty_set, backdoor_paths=backdoor_paths, new_graph=bdoor_graph, dseparation_algo=dseparation_algo, ) if check["is_dseparated"]: backdoor_sets.append({"backdoor_set": empty_set}) # If the method is `minimal-adjustment`, return the empty set right away. if method_name == CausalIdentifier.BACKDOOR_MIN: return backdoor_sets # Second, checking for all other sets of variables. If include_unobserved is false, then only observed variables are eligible. eligible_variables = ( self._graph.get_all_nodes(include_unobserved=include_unobserved) - set(treatment_name) - set(outcome_name) ) eligible_variables -= self._graph.get_descendants(treatment_name) # If var is d-separated from both treatment or outcome, it cannot # be a part of the backdoor set filt_eligible_variables = set() for var in eligible_variables: dsep_treat_var = self._graph.check_dseparation( treatment_name, parse_state(var), set() ) dsep_outcome_var = self._graph.check_dseparation( outcome_name, parse_state(var), set() ) if not dsep_outcome_var or not dsep_treat_var: filt_eligible_variables.add(var) if method_name in CausalIdentifier.METHOD_NAMES: backdoor_sets, found_valid_adjustment_set = self.find_valid_adjustment_sets( treatment_name, outcome_name, backdoor_paths, bdoor_graph, dseparation_algo, backdoor_sets, filt_eligible_variables, method_name=method_name, max_iterations=CausalIdentifier.MAX_BACKDOOR_ITERATIONS, ) if ( method_name == CausalIdentifier.BACKDOOR_DEFAULT and found_valid_adjustment_set ): # repeat the above search with BACKDOOR_MIN backdoor_sets, _ = self.find_valid_adjustment_sets( treatment_name, outcome_name, backdoor_paths, bdoor_graph, dseparation_algo, backdoor_sets, filt_eligible_variables, method_name=CausalIdentifier.BACKDOOR_MIN, max_iterations=CausalIdentifier.MAX_BACKDOOR_ITERATIONS, ) else: raise ValueError( f"Identifier method {method_name} not supported. Try one of the following: {CausalIdentifier.METHOD_NAMES}" ) return backdoor_sets def identify_efficient_backdoor(self, costs=None, conditional_node_names=None): """Method implementing algorithms to compute efficient backdoor sets, as described in Rotnitzky and Smucler (2020), Smucler, Sapienza and Rotnitzky (2021) and Smucler and Rotnitzky (2022). For method_name='efficient-adjustment', computes an optimal backdoor set, that is, a backdoor set comprised of observable variables that yields non-parametric estimators of the interventional mean with the smallest asymptotic variance among those that are based on observable backdoor sets. This optimal backdoor set always exists when no variables are latent, and the algorithm is guaranteed to compute it in this case. Under a non-parametric graphical model with latent variables, such a backdoor set can fail to exist. When certain sufficient conditions under which it is known that such a backdoor set exists are not satisfied, an error is raised. For method_name='efficient-minimal-adjustment', computes an optimal minimal backdoor set, that is, a minimal backdoor set comprised of observable variables that yields non-parametric estimators of the interventional mean with the smallest asymptotic variance among those that are based on observable minimal backdoor sets. For method_name='efficient-mincost-adjustment', computes an optimal minimum cost backdoor set, that is, a minimum cost backdoor set comprised of observable variables that yields non-parametric estimators of the interventional mean with the smallest asymptotic variance among those that are based on observable minimum cost backdoor sets. The cost of a backdoor set is defined as the sum of the costs of the variables that comprise it. The various optimal backdoor sets computed by this method are not only optimal under non-parametric graphical models and non-parametric estimators of interventional mean, but also under linear graphical models and OLS estimators, per results in Henckel, Perkovic and Maathuis (2020). :param costs: a list with non-negative costs associated with variables in the graph. Only used for estimatand_type='non-parametric-ate' and method_name='efficient-mincost-adjustment'. If not costs are provided by the user, and method_name='efficient-mincost-adjustment', costs are assumed to be equal to one for all variables in the graph. The structure of the list should be of the form [(node, {"cost": x}) for node in nodes]. :param conditional_node_names: variables that are used to determine treatment. If none are provided, it is assumed that the intervention sets the treatment to a constant. :returns: backdoor_sets, a list of dictionaries, with each dictionary having as values a backdoor set. """ if costs is None and self.method_name == "efficient-mincost-adjustment": self.logger.warning( "No costs were passed, so they will be assumed to be constant and equal to 1." ) efficient_bd = EfficientBackdoor( graph=self._graph, conditional_node_names=conditional_node_names, costs=costs, ) if self.method_name == "efficient-adjustment": backdoor_set = efficient_bd.optimal_adj_set() backdoor_sets = [{"backdoor_set": tuple(backdoor_set)}] elif self.method_name == "efficient-minimal-adjustment": backdoor_set = efficient_bd.optimal_minimal_adj_set() backdoor_sets = [{"backdoor_set": tuple(backdoor_set)}] elif self.method_name == "efficient-mincost-adjustment": backdoor_set = efficient_bd.optimal_mincost_adj_set() backdoor_sets = [{"backdoor_set": tuple(backdoor_set)}] return backdoor_sets def find_valid_adjustment_sets( self, treatment_name, outcome_name, backdoor_paths, bdoor_graph, dseparation_algo, backdoor_sets, filt_eligible_variables, method_name, max_iterations, ): num_iterations = 0 found_valid_adjustment_set = False all_nodes_observed = self._graph.all_observed(self._graph.get_all_nodes()) # If `minimal-adjustment` method is specified, start the search from the set with minimum size. Otherwise, start from the largest. set_sizes = ( range(1, len(filt_eligible_variables) + 1, 1) if method_name == CausalIdentifier.BACKDOOR_MIN else range(len(filt_eligible_variables), 0, -1) ) for size_candidate_set in set_sizes: for candidate_set in itertools.combinations( filt_eligible_variables, size_candidate_set ): check = self._graph.check_valid_backdoor_set( treatment_name, outcome_name, candidate_set, backdoor_paths=backdoor_paths, new_graph=bdoor_graph, dseparation_algo=dseparation_algo, ) self.logger.debug( "Candidate backdoor set: {0}, is_dseparated: {1}".format( candidate_set, check["is_dseparated"] ) ) if check["is_dseparated"]: backdoor_sets.append({"backdoor_set": candidate_set}) found_valid_adjustment_set = True num_iterations += 1 if ( method_name == CausalIdentifier.BACKDOOR_EXHAUSTIVE and num_iterations > max_iterations ): self.logger.warning( f"Max number of iterations {max_iterations} reached." ) break # If the backdoor method is `maximal-adjustment` or `minimal-adjustment`, return the first found adjustment set. if ( method_name in { CausalIdentifier.BACKDOOR_DEFAULT, CausalIdentifier.BACKDOOR_MAX, CausalIdentifier.BACKDOOR_MIN, } and found_valid_adjustment_set ): break # If all variables are observed, and the biggest eligible set # does not satisfy backdoor, then none of its subsets will. if ( method_name in {CausalIdentifier.BACKDOOR_DEFAULT, CausalIdentifier.BACKDOOR_MAX} and all_nodes_observed ): break if num_iterations > max_iterations: self.logger.warning( f"Max number of iterations {max_iterations} reached. Could not find a valid backdoor set." ) break return backdoor_sets, found_valid_adjustment_set def get_default_backdoor_set_id(self, backdoor_sets_dict): # Adding a None estimand if no backdoor set found if len(backdoor_sets_dict) == 0: return None # Default set contains minimum possible number of instrumental variables, to prevent lowering variance in the treatment variable. instrument_names = set( self._graph.get_instruments(self.treatment_name, self.outcome_name) ) iv_count_dict = { key: len(set(bdoor_set).intersection(instrument_names)) for key, bdoor_set in backdoor_sets_dict.items() } min_iv_count = min(iv_count_dict.values()) min_iv_keys = { key for key, iv_count in iv_count_dict.items() if iv_count == min_iv_count } min_iv_backdoor_sets_dict = { key: backdoor_sets_dict[key] for key in min_iv_keys } # Default set is the one with the least number of adjustment variables (optimizing for efficiency) min_set_length = 1000000 default_key = None for key, bdoor_set in min_iv_backdoor_sets_dict.items(): if len(bdoor_set) < min_set_length: min_set_length = len(bdoor_set) default_key = key return default_key def build_backdoor_estimands_dict( self, treatment_name, outcome_name, backdoor_sets, estimands_dict, proceed_when_unidentifiable=None, ): """Build the final dict for backdoor sets by filtering unobserved variables if needed. """ backdoor_variables_dict = {} if proceed_when_unidentifiable is None: proceed_when_unidentifiable = self._proceed_when_unidentifiable is_identified = [ self._graph.all_observed(bset["backdoor_set"]) for bset in backdoor_sets ] if any(is_identified): self.logger.info("Causal effect can be identified.") backdoor_sets_arr = [ list(bset["backdoor_set"]) for bset in backdoor_sets if self._graph.all_observed(bset["backdoor_set"]) ] else: # there is unobserved confounding self.logger.warning("Backdoor identification failed.") backdoor_sets_arr = [] for i in range(len(backdoor_sets_arr)): backdoor_estimand_expr = self.construct_backdoor_estimand( self.estimand_type, treatment_name, outcome_name, backdoor_sets_arr[i] ) self.logger.debug("Identified expression = " + str(backdoor_estimand_expr)) estimands_dict["backdoor" + str(i + 1)] = backdoor_estimand_expr backdoor_variables_dict["backdoor" + str(i + 1)] = backdoor_sets_arr[i] return estimands_dict, backdoor_variables_dict def identify_frontdoor(self, dseparation_algo="default"): """ Find a valid frontdoor variable if it exists. Currently only supports a single variable frontdoor set. """ frontdoor_var = None frontdoor_paths = None fdoor_graph = None if dseparation_algo == "default": cond1_graph = self._graph.do_surgery( self.treatment_name, remove_incoming_edges=True ) bdoor_graph1 = self._graph.do_surgery( self.treatment_name, remove_outgoing_edges=True ) elif dseparation_algo == "naive": frontdoor_paths = self._graph.get_all_directed_paths( self.treatment_name, self.outcome_name ) else: raise ValueError( f"d-separation algorithm {dseparation_algo} is not supported" ) eligible_variables = ( self._graph.get_descendants(self.treatment_name) - set(self.outcome_name) - set(self._graph.get_descendants(self.outcome_name)) ) # For simplicity, assuming a one-variable frontdoor set for candidate_var in eligible_variables: # Cond 1: All directed paths intercepted by candidate_var cond1 = self._graph.check_valid_frontdoor_set( self.treatment_name, self.outcome_name, parse_state(candidate_var), frontdoor_paths=frontdoor_paths, new_graph=cond1_graph, dseparation_algo=dseparation_algo, ) self.logger.debug( "Candidate frontdoor set: {0}, is_dseparated: {1}".format( candidate_var, cond1 ) ) if not cond1: continue # Cond 2: No confounding between treatment and candidate var cond2 = self._graph.check_valid_backdoor_set( self.treatment_name, parse_state(candidate_var), set(), backdoor_paths=None, new_graph=bdoor_graph1, dseparation_algo=dseparation_algo, ) if not cond2: continue # Cond 3: treatment blocks all confounding between candidate_var and outcome bdoor_graph2 = self._graph.do_surgery( candidate_var, remove_outgoing_edges=True ) cond3 = self._graph.check_valid_backdoor_set( parse_state(candidate_var), self.outcome_name, self.treatment_name, backdoor_paths=None, new_graph=bdoor_graph2, dseparation_algo=dseparation_algo, ) is_valid_frontdoor = cond1 and cond2 and cond3 if is_valid_frontdoor: frontdoor_var = candidate_var break return parse_state(frontdoor_var) def identify_mediation(self): """ Find a valid mediator if it exists. Currently only supports a single variable mediator set. """ mediation_var = None mediation_paths = self._graph.get_all_directed_paths( self.treatment_name, self.outcome_name ) eligible_variables = self._graph.get_descendants(self.treatment_name) - set( self.outcome_name ) # For simplicity, assuming a one-variable mediation set for candidate_var in eligible_variables: is_valid_mediation = self._graph.check_valid_mediation_set( self.treatment_name, self.outcome_name, parse_state(candidate_var), mediation_paths=mediation_paths, ) self.logger.debug( "Candidate mediation set: {0}, on_mediating_path: {1}".format( candidate_var, is_valid_mediation ) ) if is_valid_mediation: mediation_var = candidate_var break return parse_state(mediation_var) return None def identify_mediation_first_stage_confounders( self, treatment_name, mediators_names ): # Create estimands dict as per the API for backdoor, but do not return it estimands_dict = {} backdoor_sets = self.identify_backdoor(treatment_name, mediators_names) estimands_dict, backdoor_variables_dict = self.build_backdoor_estimands_dict( treatment_name, mediators_names, backdoor_sets, estimands_dict, proceed_when_unidentifiable=True, ) # Setting default "backdoor" identification adjustment set default_backdoor_id = self.get_default_backdoor_set_id(backdoor_variables_dict) estimands_dict["backdoor"] = estimands_dict.get(str(default_backdoor_id), None) backdoor_variables_dict["backdoor"] = backdoor_variables_dict.get( str(default_backdoor_id), None ) return backdoor_variables_dict def identify_mediation_second_stage_confounders( self, mediators_names, outcome_name ): # Create estimands dict as per the API for backdoor, but do not return it estimands_dict = {} backdoor_sets = self.identify_backdoor(mediators_names, outcome_name) estimands_dict, backdoor_variables_dict = self.build_backdoor_estimands_dict( mediators_names, outcome_name, backdoor_sets, estimands_dict, proceed_when_unidentifiable=True, ) # Setting default "backdoor" identification adjustment set default_backdoor_id = self.get_default_backdoor_set_id(backdoor_variables_dict) estimands_dict["backdoor"] = estimands_dict.get(str(default_backdoor_id), None) backdoor_variables_dict["backdoor"] = backdoor_variables_dict.get( str(default_backdoor_id), None ) return backdoor_variables_dict def construct_backdoor_estimand( self, estimand_type, treatment_name, outcome_name, common_causes ): # TODO: outputs string for now, but ideally should do symbolic # expressions Mon 19 Feb 2018 04:54:17 PM DST # TODO Better support for multivariate treatments expr = None outcome_name = outcome_name[0] num_expr_str = outcome_name if len(common_causes) > 0: num_expr_str += "|" + ",".join(common_causes) expr = "d(" + num_expr_str + ")/d" + ",".join(treatment_name) sym_mu = sp.Symbol("mu") sym_sigma = sp.Symbol("sigma", positive=True) sym_outcome = spstats.Normal(num_expr_str, sym_mu, sym_sigma) sym_treatment_symbols = [sp.Symbol(t) for t in treatment_name] sym_treatment = sp.Array(sym_treatment_symbols) sym_conditional_outcome = spstats.Expectation(sym_outcome) sym_effect = sp.Derivative(sym_conditional_outcome, sym_treatment) sym_assumptions = { "Unconfoundedness": ( "If U\N{RIGHTWARDS ARROW}{{{0}}} and U\N{RIGHTWARDS ARROW}{1}" " then P({1}|{0},{2},U) = P({1}|{0},{2})" ).format(",".join(treatment_name), outcome_name, ",".join(common_causes)) } estimand = {"estimand": sym_effect, "assumptions": sym_assumptions} return estimand def construct_iv_estimand( self, estimand_type, treatment_name, outcome_name, instrument_names ): # TODO: support multivariate treatments better. expr = None outcome_name = outcome_name[0] sym_outcome = spstats.Normal(outcome_name, 0, 1) sym_treatment_symbols = [spstats.Normal(t, 0, 1) for t in treatment_name] sym_treatment = sp.Array(sym_treatment_symbols) sym_instrument_symbols = [sp.Symbol(inst) for inst in instrument_names] sym_instrument = sp.Array(sym_instrument_symbols) # ",".join(instrument_names)) sym_outcome_derivative = sp.Derivative(sym_outcome, sym_instrument) sym_treatment_derivative = sp.Derivative(sym_treatment, sym_instrument) sym_effect = spstats.Expectation( sym_outcome_derivative / sym_treatment_derivative ) sym_assumptions = { "As-if-random": ( "If U\N{RIGHTWARDS ARROW}\N{RIGHTWARDS ARROW}{0} then " "\N{NOT SIGN}(U \N{RIGHTWARDS ARROW}\N{RIGHTWARDS ARROW}{{{1}}})" ).format(outcome_name, ",".join(instrument_names)), "Exclusion": ( "If we remove {{{0}}}\N{RIGHTWARDS ARROW}{{{1}}}, then " "\N{NOT SIGN}({{{0}}}\N{RIGHTWARDS ARROW}{2})" ).format( ",".join(instrument_names), ",".join(treatment_name), outcome_name ), } estimand = {"estimand": sym_effect, "assumptions": sym_assumptions} return estimand def construct_frontdoor_estimand( self, estimand_type, treatment_name, outcome_name, frontdoor_variables_names ): # TODO: support multivariate treatments better. expr = None outcome_name = outcome_name[0] sym_outcome = spstats.Normal(outcome_name, 0, 1) sym_treatment_symbols = [spstats.Normal(t, 0, 1) for t in treatment_name] sym_treatment = sp.Array(sym_treatment_symbols) sym_frontdoor_symbols = [sp.Symbol(inst) for inst in frontdoor_variables_names] sym_frontdoor = sp.Array(sym_frontdoor_symbols) # ",".join(instrument_names)) sym_outcome_derivative = sp.Derivative(sym_outcome, sym_frontdoor) sym_treatment_derivative = sp.Derivative(sym_frontdoor, sym_treatment) sym_effect = spstats.Expectation( sym_treatment_derivative * sym_outcome_derivative ) sym_assumptions = { "Full-mediation": ( "{2} intercepts (blocks) all directed paths from {0} to {1}." ).format( ",".join(treatment_name), ",".join(outcome_name), ",".join(frontdoor_variables_names), ), "First-stage-unconfoundedness": ( "If U\N{RIGHTWARDS ARROW}{{{0}}} and U\N{RIGHTWARDS ARROW}{{{1}}}" " then P({1}|{0},U) = P({1}|{0})" ).format(",".join(treatment_name), ",".join(frontdoor_variables_names)), "Second-stage-unconfoundedness": ( "If U\N{RIGHTWARDS ARROW}{{{2}}} and U\N{RIGHTWARDS ARROW}{1}" " then P({1}|{2}, {0}, U) = P({1}|{2}, {0})" ).format( ",".join(treatment_name), outcome_name, ",".join(frontdoor_variables_names), ), } estimand = {"estimand": sym_effect, "assumptions": sym_assumptions} return estimand def construct_mediation_estimand( self, estimand_type, treatment_name, outcome_name, mediators_names ): # TODO: support multivariate treatments better. expr = None if estimand_type in ( CausalIdentifier.NONPARAMETRIC_NDE, CausalIdentifier.NONPARAMETRIC_NIE, ): outcome_name = outcome_name[0] sym_outcome = spstats.Normal(outcome_name, 0, 1) sym_treatment_symbols = [spstats.Normal(t, 0, 1) for t in treatment_name] sym_treatment = sp.Array(sym_treatment_symbols) sym_mediators_symbols = [sp.Symbol(inst) for inst in mediators_names] sym_mediators = sp.Array(sym_mediators_symbols) sym_outcome_derivative = sp.Derivative(sym_outcome, sym_mediators) sym_treatment_derivative = sp.Derivative(sym_mediators, sym_treatment) # For direct effect num_expr_str = outcome_name if len(mediators_names) > 0: num_expr_str += "|" + ",".join(mediators_names) sym_mu = sp.Symbol("mu") sym_sigma = sp.Symbol("sigma", positive=True) sym_conditional_outcome = spstats.Normal(num_expr_str, sym_mu, sym_sigma) sym_directeffect_derivative = sp.Derivative( sym_conditional_outcome, sym_treatment ) if estimand_type == CausalIdentifier.NONPARAMETRIC_NIE: sym_effect = spstats.Expectation( sym_treatment_derivative * sym_outcome_derivative ) elif estimand_type == CausalIdentifier.NONPARAMETRIC_NDE: sym_effect = spstats.Expectation(sym_directeffect_derivative) sym_assumptions = { "Mediation": ( "{2} intercepts (blocks) all directed paths from {0} to {1} except the path {{{0}}}\N{RIGHTWARDS ARROW}{{{1}}}." ).format( ",".join(treatment_name), ",".join(outcome_name), ",".join(mediators_names), ), "First-stage-unconfoundedness": ( "If U\N{RIGHTWARDS ARROW}{{{0}}} and U\N{RIGHTWARDS ARROW}{{{1}}}" " then P({1}|{0},U) = P({1}|{0})" ).format(",".join(treatment_name), ",".join(mediators_names)), "Second-stage-unconfoundedness": ( "If U\N{RIGHTWARDS ARROW}{{{2}}} and U\N{RIGHTWARDS ARROW}{1}" " then P({1}|{2}, {0}, U) = P({1}|{2}, {0})" ).format( ",".join(treatment_name), outcome_name, ",".join(mediators_names) ), } else: raise ValueError( "Estimand type not supported. Supported estimand types are {0} or {1}'.".format( CausalIdentifier.NONPARAMETRIC_NDE, CausalIdentifier.NONPARAMETRIC_NIE, ) ) estimand = {"estimand": sym_effect, "assumptions": sym_assumptions} return estimand class IdentifiedEstimand: """Class for storing a causal estimand, typically as a result of the identification step. """ def __init__( self, identifier, treatment_variable, outcome_variable, estimand_type=None, estimands=None, backdoor_variables=None, instrumental_variables=None, frontdoor_variables=None, mediator_variables=None, mediation_first_stage_confounders=None, mediation_second_stage_confounders=None, default_backdoor_id=None, identifier_method=None, no_directed_path=False, ): self.identifier = identifier self.treatment_variable = parse_state(treatment_variable) self.outcome_variable = parse_state(outcome_variable) self.backdoor_variables = backdoor_variables self.instrumental_variables = parse_state(instrumental_variables) self.frontdoor_variables = parse_state(frontdoor_variables) self.mediator_variables = parse_state(mediator_variables) self.mediation_first_stage_confounders = mediation_first_stage_confounders self.mediation_second_stage_confounders = mediation_second_stage_confounders self.estimand_type = estimand_type self.estimands = estimands self.default_backdoor_id = default_backdoor_id self.identifier_method = identifier_method self.no_directed_path = no_directed_path def set_identifier_method(self, identifier_name): self.identifier_method = identifier_name def get_backdoor_variables(self, key=None): """ Return a list containing the backdoor variables. If the calling estimator method is a backdoor method, return the backdoor variables corresponding to its target estimand. Otherwise, return the backdoor variables for the default backdoor estimand. """ if key is None: if self.identifier_method and self.identifier_method.startswith("backdoor"): return self.backdoor_variables[self.identifier_method] elif ( self.backdoor_variables is not None and len(self.backdoor_variables) > 0 ): return self.backdoor_variables[self.default_backdoor_id] else: return [] else: return self.backdoor_variables[key] def set_backdoor_variables(self, bdoor_variables_arr, key=None): if key is None: key = self.identifier_method self.backdoor_variables[key] = bdoor_variables_arr def get_frontdoor_variables(self): """Return a list containing the frontdoor variables (if present) """ return self.frontdoor_variables def get_mediator_variables(self): """Return a list containing the mediator variables (if present) """ return self.mediator_variables def get_instrumental_variables(self): """Return a list containing the instrumental variables (if present) """ return self.instrumental_variables def __deepcopy__(self, memo): return IdentifiedEstimand( self.identifier, # not deep copied copy.deepcopy(self.treatment_variable), copy.deepcopy(self.outcome_variable), estimand_type=copy.deepcopy(self.estimand_type), estimands=copy.deepcopy(self.estimands), backdoor_variables=copy.deepcopy(self.backdoor_variables), instrumental_variables=copy.deepcopy(self.instrumental_variables), frontdoor_variables=copy.deepcopy(self.frontdoor_variables), mediator_variables=copy.deepcopy(self.mediator_variables), default_backdoor_id=copy.deepcopy(self.default_backdoor_id), identifier_method=copy.deepcopy(self.identifier_method), ) def __str__(self, only_target_estimand=False, show_all_backdoor_sets=False): if self.no_directed_path: s = "No directed path from {0} to {1} in the causal graph.".format( self.treatment_variable, self.outcome_variable ) s += "\nCausal effect is zero." return s s = "Estimand type: {0}\n".format(self.estimand_type) i = 1 has_valid_backdoor = sum("backdoor" in key for key in self.estimands.keys()) for k, v in self.estimands.items(): if show_all_backdoor_sets: # Do not show backdoor key unless it is the only backdoor set. if k == "backdoor" and has_valid_backdoor > 1: continue else: # Just show the default backdoor set if k.startswith("backdoor") and k != "backdoor": continue if only_target_estimand and k != self.identifier_method: continue s += "\n### Estimand : {0}\n".format(i) s += "Estimand name: {0}".format(k) if k == self.default_backdoor_id: s += " (Default)" s += "\n" if v is None: s += "No such variable(s) found!\n" else: sp_expr_str = sp.pretty(v["estimand"], use_unicode=True) s += "Estimand expression:\n{0}\n".format(sp_expr_str) j = 1 for ass_name, ass_str in v["assumptions"].items(): s += "Estimand assumption {0}, {1}: {2}\n".format( j, ass_name, ass_str ) j += 1 i += 1 return s

esmucler

77f7064c85b3de740b5beefb0ad7067ffdb024fd

824f5532c0644812867bb018bf22585f2466960c

I'm curious---what are these conditional_node_names graphically? are they parents of the treatment only?

amit-sharma

py-why/dowhy

Algorithms for efficient adjustment (backdoor) sets

Implements the algorithms discussed [here](https://github.com/py-why/dowhy/issues/464). I added the new algorithms [here](https://github.com/py-why/dowhy/pull/549/files#diff-cb99b05726571b36d65d193004d3c854cbf055d86eadd94dc1ce81bc4ac7b4b4), and made a few (small I think) changes to the CausalIdentifier class. I added tests for the new identifier methods, essentially covering a number of graphs that appeared in our papers on these algorithms. This is still missing updates to the docs. I think feedback at this point would be super helpful :) I also have a few questions and comments: - Do the already implemented backdoor methods support multivariate treatments and/or outcomes? I ask this because the newly added algorithms are designed to work for univariate treatment and outcome only. - I'm currently raising a value error when no observable backdoor exists; is this how you handle this situation? I also raise value error when the (sufficient) conditions that we need to ensure the existence of an optimal efficient backdoor do not hold. - Computing the minimum cost efficient adjustment set of course requires the user passing the costs associated with nodes. This is done when calling the identify_ate_effect method. If no costs are passed, they are assume to be constant and equal to one, and hence the optimal minimum cost backdoor set is the optimal backdoor set of minimum cardinality. I wonder if the user should be warned about this, or putting it in the docs is enough. - The algorithms admit a set of conditional variables, that could be used to decide treatment (individualised treatment rules). This is also passed when calling the identify_ate_effect method, does that choice seem right? - The new files I created I passed through black to pass flake8, but I didn't do this with causal_identifier.py because there were pre-existing flake8 problems and I didn't want to make so many chances to the file at once.

2022-07-16 14:24:08+00:00

2022-08-08 04:09:13+00:00

dowhy/causal_identifier.py

import copy import itertools import logging import sympy as sp import sympy.stats as spstats import dowhy.utils.cli_helpers as cli from dowhy.utils.api import parse_state class CausalIdentifier: """Class that implements different identification methods. Currently supports backdoor and instrumental variable identification methods. The identification is based on the causal graph provided. """ NONPARAMETRIC_ATE="nonparametric-ate" NONPARAMETRIC_NDE="nonparametric-nde" NONPARAMETRIC_NIE="nonparametric-nie" MAX_BACKDOOR_ITERATIONS = 100000 # Backdoor method names BACKDOOR_DEFAULT="default" BACKDOOR_EXHAUSTIVE="exhaustive-search" BACKDOOR_MIN="minimal-adjustment" BACKDOOR_MAX="maximal-adjustment" METHOD_NAMES = {BACKDOOR_DEFAULT, BACKDOOR_EXHAUSTIVE, BACKDOOR_MIN, BACKDOOR_MAX} DEFAULT_BACKDOOR_METHOD = BACKDOOR_DEFAULT def __init__(self, graph, estimand_type, method_name = "default", proceed_when_unidentifiable=False): self._graph = graph self.estimand_type = estimand_type self.treatment_name = graph.treatment_name self.outcome_name = graph.outcome_name self.method_name = method_name self._proceed_when_unidentifiable = proceed_when_unidentifiable self.logger = logging.getLogger(__name__) def identify_effect(self, optimize_backdoor=False): """Main method that returns an identified estimand (if one exists). If estimand_type is non-parametric ATE, then uses backdoor, instrumental variable and frontdoor identification methods, to check if an identified estimand exists, based on the causal graph. :param self: instance of the CausalIdentifier class (or its subclass) :returns: target estimand, an instance of the IdentifiedEstimand class """ # First, check if there is a directed path from action to outcome if not self._graph.has_directed_path(self.treatment_name, self.outcome_name): self.logger.warn("No directed path from treatment to outcome. Causal Effect is zero.") return IdentifiedEstimand(self, treatment_variable=self.treatment_name, outcome_variable=self.outcome_name, no_directed_path=True) if self.estimand_type == CausalIdentifier.NONPARAMETRIC_ATE: return self.identify_ate_effect(optimize_backdoor=optimize_backdoor) elif self.estimand_type == CausalIdentifier.NONPARAMETRIC_NDE: return self.identify_nde_effect() elif self.estimand_type == CausalIdentifier.NONPARAMETRIC_NIE: return self.identify_nie_effect() else: raise ValueError("Estimand type is not supported. Use either {0}, {1}, or {2}.".format( CausalIdentifier.NONPARAMETRIC_ATE, CausalIdentifier.NONPARAMETRIC_NDE, CausalIdentifier.NONPARAMETRIC_NIE)) def identify_ate_effect(self, optimize_backdoor): estimands_dict = {} mediation_first_stage_confounders = None mediation_second_stage_confounders = None ### 1. BACKDOOR IDENTIFICATION # First, checking if there are any valid backdoor adjustment sets if optimize_backdoor == False: backdoor_sets = self.identify_backdoor(self.treatment_name, self.outcome_name) else: from dowhy.causal_identifiers.backdoor import Backdoor path = Backdoor(self._graph._graph, self.treatment_name, self.outcome_name) backdoor_sets = path.get_backdoor_vars() estimands_dict, backdoor_variables_dict = self.build_backdoor_estimands_dict( self.treatment_name, self.outcome_name, backdoor_sets, estimands_dict) # Setting default "backdoor" identification adjustment set default_backdoor_id = self.get_default_backdoor_set_id(backdoor_variables_dict) if len(backdoor_variables_dict) > 0: estimands_dict["backdoor"] = estimands_dict.get(str(default_backdoor_id), None) backdoor_variables_dict["backdoor"] = backdoor_variables_dict.get(str(default_backdoor_id), None) else: estimands_dict["backdoor"] = None ### 2. INSTRUMENTAL VARIABLE IDENTIFICATION # Now checking if there is also a valid iv estimand instrument_names = self._graph.get_instruments(self.treatment_name, self.outcome_name) self.logger.info("Instrumental variables for treatment and outcome:" + str(instrument_names)) if len(instrument_names) > 0: iv_estimand_expr = self.construct_iv_estimand( self.estimand_type, self._graph.treatment_name, self._graph.outcome_name, instrument_names ) self.logger.debug("Identified expression = " + str(iv_estimand_expr)) estimands_dict["iv"] = iv_estimand_expr else: estimands_dict["iv"] = None ### 3. FRONTDOOR IDENTIFICATION # Now checking if there is a valid frontdoor variable frontdoor_variables_names = self.identify_frontdoor() self.logger.info("Frontdoor variables for treatment and outcome:" + str(frontdoor_variables_names)) if len(frontdoor_variables_names) >0: frontdoor_estimand_expr = self.construct_frontdoor_estimand( self.estimand_type, self._graph.treatment_name, self._graph.outcome_name, frontdoor_variables_names ) self.logger.debug("Identified expression = " + str(frontdoor_estimand_expr)) estimands_dict["frontdoor"] = frontdoor_estimand_expr mediation_first_stage_confounders = self.identify_mediation_first_stage_confounders(self.treatment_name, frontdoor_variables_names) mediation_second_stage_confounders = self.identify_mediation_second_stage_confounders(frontdoor_variables_names, self.outcome_name) else: estimands_dict["frontdoor"] = None # Finally returning the estimand object estimand = IdentifiedEstimand( self, treatment_variable=self._graph.treatment_name, outcome_variable=self._graph.outcome_name, estimand_type=self.estimand_type, estimands=estimands_dict, backdoor_variables=backdoor_variables_dict, instrumental_variables=instrument_names, frontdoor_variables=frontdoor_variables_names, mediation_first_stage_confounders=mediation_first_stage_confounders, mediation_second_stage_confounders=mediation_second_stage_confounders, default_backdoor_id = default_backdoor_id ) return estimand def identify_nie_effect(self): estimands_dict = {} ### 1. FIRST DOING BACKDOOR IDENTIFICATION # First, checking if there are any valid backdoor adjustment sets backdoor_sets = self.identify_backdoor(self.treatment_name, self.outcome_name) estimands_dict, backdoor_variables_dict = self.build_backdoor_estimands_dict( self.treatment_name, self.outcome_name, backdoor_sets, estimands_dict) # Setting default "backdoor" identification adjustment set default_backdoor_id = self.get_default_backdoor_set_id(backdoor_variables_dict) backdoor_variables_dict["backdoor"] = backdoor_variables_dict.get(str(default_backdoor_id), None) ### 2. SECOND, CHECKING FOR MEDIATORS # Now checking if there are valid mediator variables estimands_dict = {} # Need to reinitialize this dictionary to avoid including the backdoor sets mediation_first_stage_confounders = None mediation_second_stage_confounders = None mediators_names = self.identify_mediation() self.logger.info("Mediators for treatment and outcome:" + str(mediators_names)) if len(mediators_names) >0: mediation_estimand_expr = self.construct_mediation_estimand( self.estimand_type, self._graph.treatment_name, self._graph.outcome_name, mediators_names ) self.logger.debug("Identified expression = " + str(mediation_estimand_expr)) estimands_dict["mediation"] = mediation_estimand_expr mediation_first_stage_confounders = self.identify_mediation_first_stage_confounders(self.treatment_name, mediators_names) mediation_second_stage_confounders = self.identify_mediation_second_stage_confounders(mediators_names, self.outcome_name) else: estimands_dict["mediation"] = None # Finally returning the estimand object estimand = IdentifiedEstimand( self, treatment_variable=self._graph.treatment_name, outcome_variable=self._graph.outcome_name, estimand_type=self.estimand_type, estimands=estimands_dict, backdoor_variables=backdoor_variables_dict, instrumental_variables=None, frontdoor_variables=None, mediator_variables=mediators_names, mediation_first_stage_confounders=mediation_first_stage_confounders, mediation_second_stage_confounders=mediation_second_stage_confounders, default_backdoor_id = None ) return estimand def identify_nde_effect(self): estimands_dict = {} ### 1. FIRST DOING BACKDOOR IDENTIFICATION # First, checking if there are any valid backdoor adjustment sets backdoor_sets = self.identify_backdoor(self.treatment_name, self.outcome_name) estimands_dict, backdoor_variables_dict = self.build_backdoor_estimands_dict( self.treatment_name, self.outcome_name, backdoor_sets, estimands_dict) # Setting default "backdoor" identification adjustment set default_backdoor_id = self.get_default_backdoor_set_id(backdoor_variables_dict) backdoor_variables_dict["backdoor"] = backdoor_variables_dict.get(str(default_backdoor_id), None) ### 2. SECOND, CHECKING FOR MEDIATORS # Now checking if there are valid mediator variables estimands_dict = {} mediation_first_stage_confounders = None mediation_second_stage_confounders = None mediators_names = self.identify_mediation() self.logger.info("Mediators for treatment and outcome:" + str(mediators_names)) if len(mediators_names) >0: mediation_estimand_expr = self.construct_mediation_estimand( self.estimand_type, self._graph.treatment_name, self._graph.outcome_name, mediators_names ) self.logger.debug("Identified expression = " + str(mediation_estimand_expr)) estimands_dict["mediation"] = mediation_estimand_expr mediation_first_stage_confounders = self.identify_mediation_first_stage_confounders(self.treatment_name, mediators_names) mediation_second_stage_confounders = self.identify_mediation_second_stage_confounders(mediators_names, self.outcome_name) else: estimands_dict["mediation"] = None # Finally returning the estimand object estimand = IdentifiedEstimand( self, treatment_variable=self._graph.treatment_name, outcome_variable=self._graph.outcome_name, estimand_type=self.estimand_type, estimands=estimands_dict, backdoor_variables=backdoor_variables_dict, instrumental_variables=None, frontdoor_variables=None, mediator_variables=mediators_names, mediation_first_stage_confounders=mediation_first_stage_confounders, mediation_second_stage_confounders=mediation_second_stage_confounders, default_backdoor_id = None ) return estimand def identify_backdoor(self, treatment_name, outcome_name, include_unobserved=False, dseparation_algo="default"): backdoor_sets = [] backdoor_paths = None bdoor_graph = None if dseparation_algo == "naive": backdoor_paths = self._graph.get_backdoor_paths(treatment_name, outcome_name) elif dseparation_algo == "default": bdoor_graph = self._graph.do_surgery(treatment_name, remove_outgoing_edges=True) else: raise ValueError(f"d-separation algorithm {dseparation_algo} is not supported") method_name = self.method_name if self.method_name != CausalIdentifier.BACKDOOR_DEFAULT else CausalIdentifier.DEFAULT_BACKDOOR_METHOD # First, checking if empty set is a valid backdoor set empty_set = set() check = self._graph.check_valid_backdoor_set(treatment_name, outcome_name, empty_set, backdoor_paths=backdoor_paths, new_graph=bdoor_graph, dseparation_algo=dseparation_algo) if check["is_dseparated"]: backdoor_sets.append({'backdoor_set':empty_set}) # If the method is `minimal-adjustment`, return the empty set right away. if method_name == CausalIdentifier.BACKDOOR_MIN: return backdoor_sets # Second, checking for all other sets of variables. If include_unobserved is false, then only observed variables are eligible. eligible_variables = self._graph.get_all_nodes(include_unobserved=include_unobserved) \ - set(treatment_name) \ - set(outcome_name) eligible_variables -= self._graph.get_descendants(treatment_name) # If var is d-separated from both treatment or outcome, it cannot # be a part of the backdoor set filt_eligible_variables = set() for var in eligible_variables: dsep_treat_var = self._graph.check_dseparation( treatment_name, parse_state(var), set()) dsep_outcome_var = self._graph.check_dseparation( outcome_name, parse_state(var), set()) if not dsep_outcome_var or not dsep_treat_var: filt_eligible_variables.add(var) if method_name in CausalIdentifier.METHOD_NAMES: backdoor_sets, found_valid_adjustment_set = self.find_valid_adjustment_sets( treatment_name, outcome_name, backdoor_paths, bdoor_graph, dseparation_algo, backdoor_sets, filt_eligible_variables, method_name=method_name, max_iterations= CausalIdentifier.MAX_BACKDOOR_ITERATIONS) if method_name == CausalIdentifier.BACKDOOR_DEFAULT and found_valid_adjustment_set: # repeat the above search with BACKDOOR_MIN backdoor_sets, _ = self.find_valid_adjustment_sets( treatment_name, outcome_name, backdoor_paths, bdoor_graph, dseparation_algo, backdoor_sets, filt_eligible_variables, method_name=CausalIdentifier.BACKDOOR_MIN, max_iterations= CausalIdentifier.MAX_BACKDOOR_ITERATIONS) else: raise ValueError(f"Identifier method {method_name} not supported. Try one of the following: {CausalIdentifier.METHOD_NAMES}") return backdoor_sets def find_valid_adjustment_sets(self, treatment_name, outcome_name, backdoor_paths, bdoor_graph, dseparation_algo, backdoor_sets, filt_eligible_variables, method_name, max_iterations): num_iterations = 0 found_valid_adjustment_set = False all_nodes_observed = self._graph.all_observed(self._graph.get_all_nodes()) # If `minimal-adjustment` method is specified, start the search from the set with minimum size. Otherwise, start from the largest. set_sizes = range(1, len(filt_eligible_variables) + 1, 1) if method_name == CausalIdentifier.BACKDOOR_MIN else range(len(filt_eligible_variables), 0, -1) for size_candidate_set in set_sizes: for candidate_set in itertools.combinations(filt_eligible_variables, size_candidate_set): check = self._graph.check_valid_backdoor_set(treatment_name, outcome_name, candidate_set, backdoor_paths=backdoor_paths, new_graph = bdoor_graph, dseparation_algo = dseparation_algo) self.logger.debug("Candidate backdoor set: {0}, is_dseparated: {1}".format(candidate_set, check["is_dseparated"])) if check["is_dseparated"]: backdoor_sets.append({'backdoor_set': candidate_set}) found_valid_adjustment_set = True num_iterations += 1 if method_name == CausalIdentifier.BACKDOOR_EXHAUSTIVE and num_iterations > max_iterations: self.logger.warning(f"Max number of iterations {max_iterations} reached.") break # If the backdoor method is `maximal-adjustment` or `minimal-adjustment`, return the first found adjustment set. if method_name in {CausalIdentifier.BACKDOOR_DEFAULT, CausalIdentifier.BACKDOOR_MAX, CausalIdentifier.BACKDOOR_MIN} and found_valid_adjustment_set: break # If all variables are observed, and the biggest eligible set # does not satisfy backdoor, then none of its subsets will. if method_name in {CausalIdentifier.BACKDOOR_DEFAULT, CausalIdentifier.BACKDOOR_MAX} and all_nodes_observed: break if num_iterations > max_iterations: self.logger.warning(f"Max number of iterations {max_iterations} reached. Could not find a valid backdoor set.") break return backdoor_sets, found_valid_adjustment_set def get_default_backdoor_set_id(self, backdoor_sets_dict): # Adding a None estimand if no backdoor set found if len(backdoor_sets_dict) == 0: return None # Default set contains minimum possible number of instrumental variables, to prevent lowering variance in the treatment variable. instrument_names = set(self._graph.get_instruments(self.treatment_name, self.outcome_name)) iv_count_dict = {key: len(set(bdoor_set).intersection(instrument_names)) for key, bdoor_set in backdoor_sets_dict.items()} min_iv_count = min(iv_count_dict.values()) min_iv_keys = {key for key, iv_count in iv_count_dict.items() if iv_count == min_iv_count} min_iv_backdoor_sets_dict = {key: backdoor_sets_dict[key] for key in min_iv_keys} # Default set is the one with the least number of adjustment variables (optimizing for efficiency) min_set_length = 1000000 default_key = None for key, bdoor_set in min_iv_backdoor_sets_dict.items(): if len(bdoor_set) < min_set_length: min_set_length = len(bdoor_set) default_key = key return default_key def build_backdoor_estimands_dict(self, treatment_name, outcome_name, backdoor_sets, estimands_dict, proceed_when_unidentifiable=None): """Build the final dict for backdoor sets by filtering unobserved variables if needed. """ backdoor_variables_dict = {} if proceed_when_unidentifiable is None: proceed_when_unidentifiable = self._proceed_when_unidentifiable is_identified = [ self._graph.all_observed(bset["backdoor_set"]) for bset in backdoor_sets ] if any(is_identified): self.logger.info("Causal effect can be identified.") backdoor_sets_arr = [list( bset["backdoor_set"]) for bset in backdoor_sets if self._graph.all_observed(bset["backdoor_set"]) ] else: # there is unobserved confounding self.logger.warning("Backdoor identification failed.") backdoor_sets_arr = [] for i in range(len(backdoor_sets_arr)): backdoor_estimand_expr = self.construct_backdoor_estimand( self.estimand_type, treatment_name, outcome_name, backdoor_sets_arr[i]) self.logger.debug("Identified expression = " + str(backdoor_estimand_expr)) estimands_dict["backdoor"+str(i+1)] = backdoor_estimand_expr backdoor_variables_dict["backdoor"+str(i+1)] = backdoor_sets_arr[i] return estimands_dict, backdoor_variables_dict def identify_frontdoor(self, dseparation_algo="default"): """ Find a valid frontdoor variable if it exists. Currently only supports a single variable frontdoor set. """ frontdoor_var = None frontdoor_paths = None fdoor_graph = None if dseparation_algo == "default": cond1_graph = self._graph.do_surgery(self.treatment_name, remove_incoming_edges=True) bdoor_graph1 = self._graph.do_surgery(self.treatment_name, remove_outgoing_edges=True) elif dseparation_algo == "naive": frontdoor_paths = self._graph.get_all_directed_paths(self.treatment_name, self.outcome_name) else: raise ValueError(f"d-separation algorithm {dseparation_algo} is not supported") eligible_variables = self._graph.get_descendants(self.treatment_name) \ - set(self.outcome_name) \ - set(self._graph.get_descendants(self.outcome_name)) # For simplicity, assuming a one-variable frontdoor set for candidate_var in eligible_variables: # Cond 1: All directed paths intercepted by candidate_var cond1 = self._graph.check_valid_frontdoor_set( self.treatment_name, self.outcome_name, parse_state(candidate_var), frontdoor_paths=frontdoor_paths, new_graph=cond1_graph, dseparation_algo=dseparation_algo) self.logger.debug("Candidate frontdoor set: {0}, is_dseparated: {1}".format(candidate_var, cond1)) if not cond1: continue # Cond 2: No confounding between treatment and candidate var cond2 = self._graph.check_valid_backdoor_set( self.treatment_name, parse_state(candidate_var), set(), backdoor_paths=None, new_graph= bdoor_graph1, dseparation_algo=dseparation_algo) if not cond2: continue # Cond 3: treatment blocks all confounding between candidate_var and outcome bdoor_graph2 = self._graph.do_surgery(candidate_var, remove_outgoing_edges=True) cond3 = self._graph.check_valid_backdoor_set( parse_state(candidate_var), self.outcome_name, self.treatment_name, backdoor_paths=None, new_graph= bdoor_graph2, dseparation_algo=dseparation_algo) is_valid_frontdoor = cond1 and cond2 and cond3 if is_valid_frontdoor: frontdoor_var = candidate_var break return parse_state(frontdoor_var) def identify_mediation(self): """ Find a valid mediator if it exists. Currently only supports a single variable mediator set. """ mediation_var = None mediation_paths = self._graph.get_all_directed_paths(self.treatment_name, self.outcome_name) eligible_variables = self._graph.get_descendants(self.treatment_name) \ - set(self.outcome_name) # For simplicity, assuming a one-variable mediation set for candidate_var in eligible_variables: is_valid_mediation = self._graph.check_valid_mediation_set(self.treatment_name, self.outcome_name, parse_state(candidate_var), mediation_paths=mediation_paths) self.logger.debug("Candidate mediation set: {0}, on_mediating_path: {1}".format(candidate_var, is_valid_mediation)) if is_valid_mediation: mediation_var = candidate_var break return parse_state(mediation_var) return None def identify_mediation_first_stage_confounders(self, treatment_name, mediators_names): # Create estimands dict as per the API for backdoor, but do not return it estimands_dict = {} backdoor_sets = self.identify_backdoor(treatment_name, mediators_names) estimands_dict, backdoor_variables_dict = self.build_backdoor_estimands_dict( treatment_name, mediators_names, backdoor_sets, estimands_dict, proceed_when_unidentifiable=True) # Setting default "backdoor" identification adjustment set default_backdoor_id = self.get_default_backdoor_set_id(backdoor_variables_dict) estimands_dict["backdoor"] = estimands_dict.get(str(default_backdoor_id), None) backdoor_variables_dict["backdoor"] = backdoor_variables_dict.get(str(default_backdoor_id), None) return backdoor_variables_dict def identify_mediation_second_stage_confounders(self, mediators_names, outcome_name): # Create estimands dict as per the API for backdoor, but do not return it estimands_dict = {} backdoor_sets = self.identify_backdoor(mediators_names, outcome_name) estimands_dict, backdoor_variables_dict = self.build_backdoor_estimands_dict( mediators_names, outcome_name, backdoor_sets, estimands_dict, proceed_when_unidentifiable=True) # Setting default "backdoor" identification adjustment set default_backdoor_id = self.get_default_backdoor_set_id(backdoor_variables_dict) estimands_dict["backdoor"] = estimands_dict.get(str(default_backdoor_id), None) backdoor_variables_dict["backdoor"] = backdoor_variables_dict.get(str(default_backdoor_id), None) return backdoor_variables_dict def construct_backdoor_estimand(self, estimand_type, treatment_name, outcome_name, common_causes): # TODO: outputs string for now, but ideally should do symbolic # expressions Mon 19 Feb 2018 04:54:17 PM DST # TODO Better support for multivariate treatments expr = None outcome_name = outcome_name[0] num_expr_str = outcome_name if len(common_causes)>0: num_expr_str += "|" + ",".join(common_causes) expr = "d(" + num_expr_str + ")/d" + ",".join(treatment_name) sym_mu = sp.Symbol("mu") sym_sigma = sp.Symbol("sigma", positive=True) sym_outcome = spstats.Normal(num_expr_str, sym_mu, sym_sigma) sym_treatment_symbols = [sp.Symbol(t) for t in treatment_name] sym_treatment = sp.Array(sym_treatment_symbols) sym_conditional_outcome = spstats.Expectation(sym_outcome) sym_effect = sp.Derivative(sym_conditional_outcome, sym_treatment) sym_assumptions = { 'Unconfoundedness': ( u"If U\N{RIGHTWARDS ARROW}{{{0}}} and U\N{RIGHTWARDS ARROW}{1}" " then P({1}|{0},{2},U) = P({1}|{0},{2})" ).format(",".join(treatment_name), outcome_name, ",".join(common_causes)) } estimand = { 'estimand': sym_effect, 'assumptions': sym_assumptions } return estimand def construct_iv_estimand(self, estimand_type, treatment_name, outcome_name, instrument_names): # TODO: support multivariate treatments better. expr = None outcome_name = outcome_name[0] sym_outcome = spstats.Normal(outcome_name, 0, 1) sym_treatment_symbols = [spstats.Normal(t, 0, 1) for t in treatment_name] sym_treatment = sp.Array(sym_treatment_symbols) sym_instrument_symbols = [sp.Symbol(inst) for inst in instrument_names] sym_instrument = sp.Array(sym_instrument_symbols) # ",".join(instrument_names)) sym_outcome_derivative = sp.Derivative(sym_outcome, sym_instrument) sym_treatment_derivative = sp.Derivative(sym_treatment, sym_instrument) sym_effect = spstats.Expectation(sym_outcome_derivative / sym_treatment_derivative) sym_assumptions = { "As-if-random": ( "If U\N{RIGHTWARDS ARROW}\N{RIGHTWARDS ARROW}{0} then " "\N{NOT SIGN}(U \N{RIGHTWARDS ARROW}\N{RIGHTWARDS ARROW}{{{1}}})" ).format(outcome_name, ",".join(instrument_names)), "Exclusion": ( u"If we remove {{{0}}}\N{RIGHTWARDS ARROW}{{{1}}}, then " u"\N{NOT SIGN}({{{0}}}\N{RIGHTWARDS ARROW}{2})" ).format(",".join(instrument_names), ",".join(treatment_name), outcome_name) } estimand = { 'estimand': sym_effect, 'assumptions': sym_assumptions } return estimand def construct_frontdoor_estimand(self, estimand_type, treatment_name, outcome_name, frontdoor_variables_names): # TODO: support multivariate treatments better. expr = None outcome_name = outcome_name[0] sym_outcome = spstats.Normal(outcome_name, 0, 1) sym_treatment_symbols = [spstats.Normal(t, 0, 1) for t in treatment_name] sym_treatment = sp.Array(sym_treatment_symbols) sym_frontdoor_symbols = [sp.Symbol(inst) for inst in frontdoor_variables_names] sym_frontdoor = sp.Array(sym_frontdoor_symbols) # ",".join(instrument_names)) sym_outcome_derivative = sp.Derivative(sym_outcome, sym_frontdoor) sym_treatment_derivative = sp.Derivative(sym_frontdoor, sym_treatment) sym_effect = spstats.Expectation(sym_treatment_derivative * sym_outcome_derivative) sym_assumptions = { "Full-mediation": ( "{2} intercepts (blocks) all directed paths from {0} to {1}." ).format(",".join(treatment_name), ",".join(outcome_name), ",".join(frontdoor_variables_names)), "First-stage-unconfoundedness": ( u"If U\N{RIGHTWARDS ARROW}{{{0}}} and U\N{RIGHTWARDS ARROW}{{{1}}}" " then P({1}|{0},U) = P({1}|{0})" ).format(",".join(treatment_name), ",".join(frontdoor_variables_names)), "Second-stage-unconfoundedness": ( u"If U\N{RIGHTWARDS ARROW}{{{2}}} and U\N{RIGHTWARDS ARROW}{1}" " then P({1}|{2}, {0}, U) = P({1}|{2}, {0})" ).format(",".join(treatment_name), outcome_name, ",".join(frontdoor_variables_names)) } estimand = { 'estimand': sym_effect, 'assumptions': sym_assumptions } return estimand def construct_mediation_estimand(self, estimand_type, treatment_name, outcome_name, mediators_names): # TODO: support multivariate treatments better. expr = None if estimand_type in (CausalIdentifier.NONPARAMETRIC_NDE, CausalIdentifier.NONPARAMETRIC_NIE): outcome_name = outcome_name[0] sym_outcome = spstats.Normal(outcome_name, 0, 1) sym_treatment_symbols = [spstats.Normal(t, 0, 1) for t in treatment_name] sym_treatment = sp.Array(sym_treatment_symbols) sym_mediators_symbols = [sp.Symbol(inst) for inst in mediators_names] sym_mediators = sp.Array(sym_mediators_symbols) sym_outcome_derivative = sp.Derivative(sym_outcome, sym_mediators) sym_treatment_derivative = sp.Derivative(sym_mediators, sym_treatment) # For direct effect num_expr_str = outcome_name if len(mediators_names)>0: num_expr_str += "|" + ",".join(mediators_names) sym_mu = sp.Symbol("mu") sym_sigma = sp.Symbol("sigma", positive=True) sym_conditional_outcome = spstats.Normal(num_expr_str, sym_mu, sym_sigma) sym_directeffect_derivative = sp.Derivative(sym_conditional_outcome, sym_treatment) if estimand_type == CausalIdentifier.NONPARAMETRIC_NIE: sym_effect = spstats.Expectation(sym_treatment_derivative * sym_outcome_derivative) elif estimand_type == CausalIdentifier.NONPARAMETRIC_NDE: sym_effect = spstats.Expectation(sym_directeffect_derivative) sym_assumptions = { "Mediation": ( "{2} intercepts (blocks) all directed paths from {0} to {1} except the path {{{0}}}\N{RIGHTWARDS ARROW}{{{1}}}." ).format(",".join(treatment_name), ",".join(outcome_name), ",".join(mediators_names)), "First-stage-unconfoundedness": ( u"If U\N{RIGHTWARDS ARROW}{{{0}}} and U\N{RIGHTWARDS ARROW}{{{1}}}" " then P({1}|{0},U) = P({1}|{0})" ).format(",".join(treatment_name), ",".join(mediators_names)), "Second-stage-unconfoundedness": ( u"If U\N{RIGHTWARDS ARROW}{{{2}}} and U\N{RIGHTWARDS ARROW}{1}" " then P({1}|{2}, {0}, U) = P({1}|{2}, {0})" ).format(",".join(treatment_name), outcome_name, ",".join(mediators_names)) } else: raise ValueError("Estimand type not supported. Supported estimand types are {0} or {1}'.".format( CausalIdentifier.NONPARAMETRIC_NDE, CausalIdentifier.NONPARAMETRIC_NIE)) estimand = { 'estimand': sym_effect, 'assumptions': sym_assumptions } return estimand class IdentifiedEstimand: """Class for storing a causal estimand, typically as a result of the identification step. """ def __init__(self, identifier, treatment_variable, outcome_variable, estimand_type=None, estimands=None, backdoor_variables=None, instrumental_variables=None, frontdoor_variables=None, mediator_variables=None, mediation_first_stage_confounders=None, mediation_second_stage_confounders=None, default_backdoor_id=None, identifier_method=None, no_directed_path=False): self.identifier = identifier self.treatment_variable = parse_state(treatment_variable) self.outcome_variable = parse_state(outcome_variable) self.backdoor_variables = backdoor_variables self.instrumental_variables = parse_state(instrumental_variables) self.frontdoor_variables = parse_state(frontdoor_variables) self.mediator_variables = parse_state(mediator_variables) self.mediation_first_stage_confounders=mediation_first_stage_confounders self.mediation_second_stage_confounders=mediation_second_stage_confounders self.estimand_type = estimand_type self.estimands = estimands self.default_backdoor_id = default_backdoor_id self.identifier_method = identifier_method self.no_directed_path = no_directed_path def set_identifier_method(self, identifier_name): self.identifier_method = identifier_name def get_backdoor_variables(self, key=None): """ Return a list containing the backdoor variables. If the calling estimator method is a backdoor method, return the backdoor variables corresponding to its target estimand. Otherwise, return the backdoor variables for the default backdoor estimand. """ if key is None: if self.identifier_method and self.identifier_method.startswith("backdoor"): return self.backdoor_variables[self.identifier_method] elif self.backdoor_variables is not None and len(self.backdoor_variables) > 0: return self.backdoor_variables[self.default_backdoor_id] else: return [] else: return self.backdoor_variables[key] def set_backdoor_variables(self, bdoor_variables_arr, key=None): if key is None: key = self.identifier_method self.backdoor_variables[key] = bdoor_variables_arr def get_frontdoor_variables(self): """Return a list containing the frontdoor variables (if present) """ return self.frontdoor_variables def get_mediator_variables(self): """Return a list containing the mediator variables (if present) """ return self.mediator_variables def get_instrumental_variables(self): """Return a list containing the instrumental variables (if present) """ return self.instrumental_variables def __deepcopy__(self, memo): return IdentifiedEstimand( self.identifier, # not deep copied copy.deepcopy(self.treatment_variable), copy.deepcopy(self.outcome_variable), estimand_type=copy.deepcopy(self.estimand_type), estimands=copy.deepcopy(self.estimands), backdoor_variables=copy.deepcopy(self.backdoor_variables), instrumental_variables=copy.deepcopy(self.instrumental_variables), frontdoor_variables=copy.deepcopy(self.frontdoor_variables), mediator_variables=copy.deepcopy(self.mediator_variables), default_backdoor_id=copy.deepcopy(self.default_backdoor_id), identifier_method=copy.deepcopy(self.identifier_method) ) def __str__(self, only_target_estimand=False, show_all_backdoor_sets=False): if self.no_directed_path: s = "No directed path from {0} to {1} in the causal graph.".format( self.treatment_variable, self.outcome_variable) s += "\nCausal effect is zero." return s s = "Estimand type: {0}\n".format(self.estimand_type) i = 1 has_valid_backdoor = sum("backdoor" in key for key in self.estimands.keys()) for k, v in self.estimands.items(): if show_all_backdoor_sets: # Do not show backdoor key unless it is the only backdoor set. if k == "backdoor" and has_valid_backdoor > 1: continue else: # Just show the default backdoor set if k.startswith("backdoor") and k != "backdoor": continue if only_target_estimand and k != self.identifier_method: continue s += "\n### Estimand : {0}\n".format(i) s += "Estimand name: {0}".format(k) if k == self.default_backdoor_id: s += " (Default)" s += "\n" if v is None: s += "No such variable(s) found!\n" else: sp_expr_str = sp.pretty(v["estimand"], use_unicode=True) s += "Estimand expression:\n{0}\n".format(sp_expr_str) j = 1 for ass_name, ass_str in v["assumptions"].items(): s += "Estimand assumption {0}, {1}: {2}\n".format(j, ass_name, ass_str) j += 1 i += 1 return s

import copy import itertools import logging import sympy as sp import sympy.stats as spstats import dowhy.utils.cli_helpers as cli from dowhy.causal_identifiers.efficient_backdoor import EfficientBackdoor from dowhy.utils.api import parse_state class CausalIdentifier: """Class that implements different identification methods. Currently supports backdoor and instrumental variable identification methods. The identification is based on the causal graph provided. """ NONPARAMETRIC_ATE = "nonparametric-ate" NONPARAMETRIC_NDE = "nonparametric-nde" NONPARAMETRIC_NIE = "nonparametric-nie" MAX_BACKDOOR_ITERATIONS = 100000 # Backdoor method names BACKDOOR_DEFAULT = "default" BACKDOOR_EXHAUSTIVE = "exhaustive-search" BACKDOOR_MIN = "minimal-adjustment" BACKDOOR_MAX = "maximal-adjustment" BACKDOOR_EFFICIENT = "efficient-adjustment" BACKDOOR_MIN_EFFICIENT = "efficient-minimal-adjustment" BACKDOOR_MINCOST_EFFICIENT = "efficient-mincost-adjustment" METHOD_NAMES = { BACKDOOR_DEFAULT, BACKDOOR_EXHAUSTIVE, BACKDOOR_MIN, BACKDOOR_MAX, BACKDOOR_EFFICIENT, BACKDOOR_MIN_EFFICIENT, BACKDOOR_MINCOST_EFFICIENT, } EFFICIENT_METHODS = { BACKDOOR_EFFICIENT, BACKDOOR_MIN_EFFICIENT, BACKDOOR_MINCOST_EFFICIENT, } DEFAULT_BACKDOOR_METHOD = BACKDOOR_DEFAULT def __init__( self, graph, estimand_type, method_name="default", proceed_when_unidentifiable=False, ): self._graph = graph self.estimand_type = estimand_type self.treatment_name = graph.treatment_name self.outcome_name = graph.outcome_name self.method_name = method_name self._proceed_when_unidentifiable = proceed_when_unidentifiable self.logger = logging.getLogger(__name__) def identify_effect( self, optimize_backdoor=False, costs=None, conditional_node_names=None ): """Main method that returns an identified estimand (if one exists). If estimand_type is non-parametric ATE, then uses backdoor, instrumental variable and frontdoor identification methods, to check if an identified estimand exists, based on the causal graph. :param self: instance of the CausalIdentifier class (or its subclass) :param optimize_backdoor: if True, uses an optimised algorithm to compute the backdoor sets :param costs: non-negative costs associated with variables in the graph. Only used for estimand_type='non-parametric-ate' and method_name='efficient-mincost-adjustment'. If no costs are provided by the user, and method_name='efficient-mincost-adjustment', costs are assumed to be equal to one for all variables in the graph. :param conditional_node_names: variables that are used to determine treatment. If none are provided, it is assumed that the intervention is static. :returns: target estimand, an instance of the IdentifiedEstimand class """ # First, check if there is a directed path from action to outcome if not self._graph.has_directed_path(self.treatment_name, self.outcome_name): self.logger.warn( "No directed path from treatment to outcome. Causal Effect is zero." ) return IdentifiedEstimand( self, treatment_variable=self.treatment_name, outcome_variable=self.outcome_name, no_directed_path=True, ) if self.estimand_type == CausalIdentifier.NONPARAMETRIC_ATE: return self.identify_ate_effect( optimize_backdoor=optimize_backdoor, costs=costs, conditional_node_names=conditional_node_names, ) elif self.estimand_type == CausalIdentifier.NONPARAMETRIC_NDE: return self.identify_nde_effect() elif self.estimand_type == CausalIdentifier.NONPARAMETRIC_NIE: return self.identify_nie_effect() else: raise ValueError( "Estimand type is not supported. Use either {0}, {1}, or {2}.".format( CausalIdentifier.NONPARAMETRIC_ATE, CausalIdentifier.NONPARAMETRIC_NDE, CausalIdentifier.NONPARAMETRIC_NIE, ) ) def identify_ate_effect( self, optimize_backdoor, costs=None, conditional_node_names=None ): estimands_dict = {} mediation_first_stage_confounders = None mediation_second_stage_confounders = None ### 1. BACKDOOR IDENTIFICATION # Pick algorithm to compute backdoor sets according to method chosen if self.method_name not in CausalIdentifier.EFFICIENT_METHODS: # First, checking if there are any valid backdoor adjustment sets if optimize_backdoor == False: backdoor_sets = self.identify_backdoor( self.treatment_name, self.outcome_name ) else: from dowhy.causal_identifiers.backdoor import Backdoor path = Backdoor( self._graph._graph, self.treatment_name, self.outcome_name ) backdoor_sets = path.get_backdoor_vars() elif self.method_name in CausalIdentifier.EFFICIENT_METHODS: backdoor_sets = self.identify_efficient_backdoor( costs=costs, conditional_node_names=conditional_node_names ) estimands_dict, backdoor_variables_dict = self.build_backdoor_estimands_dict( self.treatment_name, self.outcome_name, backdoor_sets, estimands_dict ) # Setting default "backdoor" identification adjustment set default_backdoor_id = self.get_default_backdoor_set_id(backdoor_variables_dict) if len(backdoor_variables_dict) > 0: estimands_dict["backdoor"] = estimands_dict.get( str(default_backdoor_id), None ) backdoor_variables_dict["backdoor"] = backdoor_variables_dict.get( str(default_backdoor_id), None ) else: estimands_dict["backdoor"] = None ### 2. INSTRUMENTAL VARIABLE IDENTIFICATION # Now checking if there is also a valid iv estimand instrument_names = self._graph.get_instruments( self.treatment_name, self.outcome_name ) self.logger.info( "Instrumental variables for treatment and outcome:" + str(instrument_names) ) if len(instrument_names) > 0: iv_estimand_expr = self.construct_iv_estimand( self.estimand_type, self._graph.treatment_name, self._graph.outcome_name, instrument_names, ) self.logger.debug("Identified expression = " + str(iv_estimand_expr)) estimands_dict["iv"] = iv_estimand_expr else: estimands_dict["iv"] = None ### 3. FRONTDOOR IDENTIFICATION # Now checking if there is a valid frontdoor variable frontdoor_variables_names = self.identify_frontdoor() self.logger.info( "Frontdoor variables for treatment and outcome:" + str(frontdoor_variables_names) ) if len(frontdoor_variables_names) > 0: frontdoor_estimand_expr = self.construct_frontdoor_estimand( self.estimand_type, self._graph.treatment_name, self._graph.outcome_name, frontdoor_variables_names, ) self.logger.debug("Identified expression = " + str(frontdoor_estimand_expr)) estimands_dict["frontdoor"] = frontdoor_estimand_expr mediation_first_stage_confounders = self.identify_mediation_first_stage_confounders( self.treatment_name, frontdoor_variables_names ) mediation_second_stage_confounders = self.identify_mediation_second_stage_confounders( frontdoor_variables_names, self.outcome_name ) else: estimands_dict["frontdoor"] = None # Finally returning the estimand object estimand = IdentifiedEstimand( self, treatment_variable=self._graph.treatment_name, outcome_variable=self._graph.outcome_name, estimand_type=self.estimand_type, estimands=estimands_dict, backdoor_variables=backdoor_variables_dict, instrumental_variables=instrument_names, frontdoor_variables=frontdoor_variables_names, mediation_first_stage_confounders=mediation_first_stage_confounders, mediation_second_stage_confounders=mediation_second_stage_confounders, default_backdoor_id=default_backdoor_id, ) return estimand def identify_nie_effect(self): estimands_dict = {} ### 1. FIRST DOING BACKDOOR IDENTIFICATION # First, checking if there are any valid backdoor adjustment sets backdoor_sets = self.identify_backdoor(self.treatment_name, self.outcome_name) estimands_dict, backdoor_variables_dict = self.build_backdoor_estimands_dict( self.treatment_name, self.outcome_name, backdoor_sets, estimands_dict ) # Setting default "backdoor" identification adjustment set default_backdoor_id = self.get_default_backdoor_set_id(backdoor_variables_dict) backdoor_variables_dict["backdoor"] = backdoor_variables_dict.get( str(default_backdoor_id), None ) ### 2. SECOND, CHECKING FOR MEDIATORS # Now checking if there are valid mediator variables estimands_dict = ( {} ) # Need to reinitialize this dictionary to avoid including the backdoor sets mediation_first_stage_confounders = None mediation_second_stage_confounders = None mediators_names = self.identify_mediation() self.logger.info("Mediators for treatment and outcome:" + str(mediators_names)) if len(mediators_names) > 0: mediation_estimand_expr = self.construct_mediation_estimand( self.estimand_type, self._graph.treatment_name, self._graph.outcome_name, mediators_names, ) self.logger.debug("Identified expression = " + str(mediation_estimand_expr)) estimands_dict["mediation"] = mediation_estimand_expr mediation_first_stage_confounders = self.identify_mediation_first_stage_confounders( self.treatment_name, mediators_names ) mediation_second_stage_confounders = self.identify_mediation_second_stage_confounders( mediators_names, self.outcome_name ) else: estimands_dict["mediation"] = None # Finally returning the estimand object estimand = IdentifiedEstimand( self, treatment_variable=self._graph.treatment_name, outcome_variable=self._graph.outcome_name, estimand_type=self.estimand_type, estimands=estimands_dict, backdoor_variables=backdoor_variables_dict, instrumental_variables=None, frontdoor_variables=None, mediator_variables=mediators_names, mediation_first_stage_confounders=mediation_first_stage_confounders, mediation_second_stage_confounders=mediation_second_stage_confounders, default_backdoor_id=None, ) return estimand def identify_nde_effect(self): estimands_dict = {} ### 1. FIRST DOING BACKDOOR IDENTIFICATION # First, checking if there are any valid backdoor adjustment sets backdoor_sets = self.identify_backdoor(self.treatment_name, self.outcome_name) estimands_dict, backdoor_variables_dict = self.build_backdoor_estimands_dict( self.treatment_name, self.outcome_name, backdoor_sets, estimands_dict ) # Setting default "backdoor" identification adjustment set default_backdoor_id = self.get_default_backdoor_set_id(backdoor_variables_dict) backdoor_variables_dict["backdoor"] = backdoor_variables_dict.get( str(default_backdoor_id), None ) ### 2. SECOND, CHECKING FOR MEDIATORS # Now checking if there are valid mediator variables estimands_dict = {} mediation_first_stage_confounders = None mediation_second_stage_confounders = None mediators_names = self.identify_mediation() self.logger.info("Mediators for treatment and outcome:" + str(mediators_names)) if len(mediators_names) > 0: mediation_estimand_expr = self.construct_mediation_estimand( self.estimand_type, self._graph.treatment_name, self._graph.outcome_name, mediators_names, ) self.logger.debug("Identified expression = " + str(mediation_estimand_expr)) estimands_dict["mediation"] = mediation_estimand_expr mediation_first_stage_confounders = self.identify_mediation_first_stage_confounders( self.treatment_name, mediators_names ) mediation_second_stage_confounders = self.identify_mediation_second_stage_confounders( mediators_names, self.outcome_name ) else: estimands_dict["mediation"] = None # Finally returning the estimand object estimand = IdentifiedEstimand( self, treatment_variable=self._graph.treatment_name, outcome_variable=self._graph.outcome_name, estimand_type=self.estimand_type, estimands=estimands_dict, backdoor_variables=backdoor_variables_dict, instrumental_variables=None, frontdoor_variables=None, mediator_variables=mediators_names, mediation_first_stage_confounders=mediation_first_stage_confounders, mediation_second_stage_confounders=mediation_second_stage_confounders, default_backdoor_id=None, ) return estimand def identify_backdoor( self, treatment_name, outcome_name, include_unobserved=False, dseparation_algo="default", ): backdoor_sets = [] backdoor_paths = None bdoor_graph = None if dseparation_algo == "naive": backdoor_paths = self._graph.get_backdoor_paths( treatment_name, outcome_name ) elif dseparation_algo == "default": bdoor_graph = self._graph.do_surgery( treatment_name, remove_outgoing_edges=True ) else: raise ValueError( f"d-separation algorithm {dseparation_algo} is not supported" ) method_name = ( self.method_name if self.method_name != CausalIdentifier.BACKDOOR_DEFAULT else CausalIdentifier.DEFAULT_BACKDOOR_METHOD ) # First, checking if empty set is a valid backdoor set empty_set = set() check = self._graph.check_valid_backdoor_set( treatment_name, outcome_name, empty_set, backdoor_paths=backdoor_paths, new_graph=bdoor_graph, dseparation_algo=dseparation_algo, ) if check["is_dseparated"]: backdoor_sets.append({"backdoor_set": empty_set}) # If the method is `minimal-adjustment`, return the empty set right away. if method_name == CausalIdentifier.BACKDOOR_MIN: return backdoor_sets # Second, checking for all other sets of variables. If include_unobserved is false, then only observed variables are eligible. eligible_variables = ( self._graph.get_all_nodes(include_unobserved=include_unobserved) - set(treatment_name) - set(outcome_name) ) eligible_variables -= self._graph.get_descendants(treatment_name) # If var is d-separated from both treatment or outcome, it cannot # be a part of the backdoor set filt_eligible_variables = set() for var in eligible_variables: dsep_treat_var = self._graph.check_dseparation( treatment_name, parse_state(var), set() ) dsep_outcome_var = self._graph.check_dseparation( outcome_name, parse_state(var), set() ) if not dsep_outcome_var or not dsep_treat_var: filt_eligible_variables.add(var) if method_name in CausalIdentifier.METHOD_NAMES: backdoor_sets, found_valid_adjustment_set = self.find_valid_adjustment_sets( treatment_name, outcome_name, backdoor_paths, bdoor_graph, dseparation_algo, backdoor_sets, filt_eligible_variables, method_name=method_name, max_iterations=CausalIdentifier.MAX_BACKDOOR_ITERATIONS, ) if ( method_name == CausalIdentifier.BACKDOOR_DEFAULT and found_valid_adjustment_set ): # repeat the above search with BACKDOOR_MIN backdoor_sets, _ = self.find_valid_adjustment_sets( treatment_name, outcome_name, backdoor_paths, bdoor_graph, dseparation_algo, backdoor_sets, filt_eligible_variables, method_name=CausalIdentifier.BACKDOOR_MIN, max_iterations=CausalIdentifier.MAX_BACKDOOR_ITERATIONS, ) else: raise ValueError( f"Identifier method {method_name} not supported. Try one of the following: {CausalIdentifier.METHOD_NAMES}" ) return backdoor_sets def identify_efficient_backdoor(self, costs=None, conditional_node_names=None): """Method implementing algorithms to compute efficient backdoor sets, as described in Rotnitzky and Smucler (2020), Smucler, Sapienza and Rotnitzky (2021) and Smucler and Rotnitzky (2022). For method_name='efficient-adjustment', computes an optimal backdoor set, that is, a backdoor set comprised of observable variables that yields non-parametric estimators of the interventional mean with the smallest asymptotic variance among those that are based on observable backdoor sets. This optimal backdoor set always exists when no variables are latent, and the algorithm is guaranteed to compute it in this case. Under a non-parametric graphical model with latent variables, such a backdoor set can fail to exist. When certain sufficient conditions under which it is known that such a backdoor set exists are not satisfied, an error is raised. For method_name='efficient-minimal-adjustment', computes an optimal minimal backdoor set, that is, a minimal backdoor set comprised of observable variables that yields non-parametric estimators of the interventional mean with the smallest asymptotic variance among those that are based on observable minimal backdoor sets. For method_name='efficient-mincost-adjustment', computes an optimal minimum cost backdoor set, that is, a minimum cost backdoor set comprised of observable variables that yields non-parametric estimators of the interventional mean with the smallest asymptotic variance among those that are based on observable minimum cost backdoor sets. The cost of a backdoor set is defined as the sum of the costs of the variables that comprise it. The various optimal backdoor sets computed by this method are not only optimal under non-parametric graphical models and non-parametric estimators of interventional mean, but also under linear graphical models and OLS estimators, per results in Henckel, Perkovic and Maathuis (2020). :param costs: a list with non-negative costs associated with variables in the graph. Only used for estimatand_type='non-parametric-ate' and method_name='efficient-mincost-adjustment'. If not costs are provided by the user, and method_name='efficient-mincost-adjustment', costs are assumed to be equal to one for all variables in the graph. The structure of the list should be of the form [(node, {"cost": x}) for node in nodes]. :param conditional_node_names: variables that are used to determine treatment. If none are provided, it is assumed that the intervention sets the treatment to a constant. :returns: backdoor_sets, a list of dictionaries, with each dictionary having as values a backdoor set. """ if costs is None and self.method_name == "efficient-mincost-adjustment": self.logger.warning( "No costs were passed, so they will be assumed to be constant and equal to 1." ) efficient_bd = EfficientBackdoor( graph=self._graph, conditional_node_names=conditional_node_names, costs=costs, ) if self.method_name == "efficient-adjustment": backdoor_set = efficient_bd.optimal_adj_set() backdoor_sets = [{"backdoor_set": tuple(backdoor_set)}] elif self.method_name == "efficient-minimal-adjustment": backdoor_set = efficient_bd.optimal_minimal_adj_set() backdoor_sets = [{"backdoor_set": tuple(backdoor_set)}] elif self.method_name == "efficient-mincost-adjustment": backdoor_set = efficient_bd.optimal_mincost_adj_set() backdoor_sets = [{"backdoor_set": tuple(backdoor_set)}] return backdoor_sets def find_valid_adjustment_sets( self, treatment_name, outcome_name, backdoor_paths, bdoor_graph, dseparation_algo, backdoor_sets, filt_eligible_variables, method_name, max_iterations, ): num_iterations = 0 found_valid_adjustment_set = False all_nodes_observed = self._graph.all_observed(self._graph.get_all_nodes()) # If `minimal-adjustment` method is specified, start the search from the set with minimum size. Otherwise, start from the largest. set_sizes = ( range(1, len(filt_eligible_variables) + 1, 1) if method_name == CausalIdentifier.BACKDOOR_MIN else range(len(filt_eligible_variables), 0, -1) ) for size_candidate_set in set_sizes: for candidate_set in itertools.combinations( filt_eligible_variables, size_candidate_set ): check = self._graph.check_valid_backdoor_set( treatment_name, outcome_name, candidate_set, backdoor_paths=backdoor_paths, new_graph=bdoor_graph, dseparation_algo=dseparation_algo, ) self.logger.debug( "Candidate backdoor set: {0}, is_dseparated: {1}".format( candidate_set, check["is_dseparated"] ) ) if check["is_dseparated"]: backdoor_sets.append({"backdoor_set": candidate_set}) found_valid_adjustment_set = True num_iterations += 1 if ( method_name == CausalIdentifier.BACKDOOR_EXHAUSTIVE and num_iterations > max_iterations ): self.logger.warning( f"Max number of iterations {max_iterations} reached." ) break # If the backdoor method is `maximal-adjustment` or `minimal-adjustment`, return the first found adjustment set. if ( method_name in { CausalIdentifier.BACKDOOR_DEFAULT, CausalIdentifier.BACKDOOR_MAX, CausalIdentifier.BACKDOOR_MIN, } and found_valid_adjustment_set ): break # If all variables are observed, and the biggest eligible set # does not satisfy backdoor, then none of its subsets will. if ( method_name in {CausalIdentifier.BACKDOOR_DEFAULT, CausalIdentifier.BACKDOOR_MAX} and all_nodes_observed ): break if num_iterations > max_iterations: self.logger.warning( f"Max number of iterations {max_iterations} reached. Could not find a valid backdoor set." ) break return backdoor_sets, found_valid_adjustment_set def get_default_backdoor_set_id(self, backdoor_sets_dict): # Adding a None estimand if no backdoor set found if len(backdoor_sets_dict) == 0: return None # Default set contains minimum possible number of instrumental variables, to prevent lowering variance in the treatment variable. instrument_names = set( self._graph.get_instruments(self.treatment_name, self.outcome_name) ) iv_count_dict = { key: len(set(bdoor_set).intersection(instrument_names)) for key, bdoor_set in backdoor_sets_dict.items() } min_iv_count = min(iv_count_dict.values()) min_iv_keys = { key for key, iv_count in iv_count_dict.items() if iv_count == min_iv_count } min_iv_backdoor_sets_dict = { key: backdoor_sets_dict[key] for key in min_iv_keys } # Default set is the one with the least number of adjustment variables (optimizing for efficiency) min_set_length = 1000000 default_key = None for key, bdoor_set in min_iv_backdoor_sets_dict.items(): if len(bdoor_set) < min_set_length: min_set_length = len(bdoor_set) default_key = key return default_key def build_backdoor_estimands_dict( self, treatment_name, outcome_name, backdoor_sets, estimands_dict, proceed_when_unidentifiable=None, ): """Build the final dict for backdoor sets by filtering unobserved variables if needed. """ backdoor_variables_dict = {} if proceed_when_unidentifiable is None: proceed_when_unidentifiable = self._proceed_when_unidentifiable is_identified = [ self._graph.all_observed(bset["backdoor_set"]) for bset in backdoor_sets ] if any(is_identified): self.logger.info("Causal effect can be identified.") backdoor_sets_arr = [ list(bset["backdoor_set"]) for bset in backdoor_sets if self._graph.all_observed(bset["backdoor_set"]) ] else: # there is unobserved confounding self.logger.warning("Backdoor identification failed.") backdoor_sets_arr = [] for i in range(len(backdoor_sets_arr)): backdoor_estimand_expr = self.construct_backdoor_estimand( self.estimand_type, treatment_name, outcome_name, backdoor_sets_arr[i] ) self.logger.debug("Identified expression = " + str(backdoor_estimand_expr)) estimands_dict["backdoor" + str(i + 1)] = backdoor_estimand_expr backdoor_variables_dict["backdoor" + str(i + 1)] = backdoor_sets_arr[i] return estimands_dict, backdoor_variables_dict def identify_frontdoor(self, dseparation_algo="default"): """ Find a valid frontdoor variable if it exists. Currently only supports a single variable frontdoor set. """ frontdoor_var = None frontdoor_paths = None fdoor_graph = None if dseparation_algo == "default": cond1_graph = self._graph.do_surgery( self.treatment_name, remove_incoming_edges=True ) bdoor_graph1 = self._graph.do_surgery( self.treatment_name, remove_outgoing_edges=True ) elif dseparation_algo == "naive": frontdoor_paths = self._graph.get_all_directed_paths( self.treatment_name, self.outcome_name ) else: raise ValueError( f"d-separation algorithm {dseparation_algo} is not supported" ) eligible_variables = ( self._graph.get_descendants(self.treatment_name) - set(self.outcome_name) - set(self._graph.get_descendants(self.outcome_name)) ) # For simplicity, assuming a one-variable frontdoor set for candidate_var in eligible_variables: # Cond 1: All directed paths intercepted by candidate_var cond1 = self._graph.check_valid_frontdoor_set( self.treatment_name, self.outcome_name, parse_state(candidate_var), frontdoor_paths=frontdoor_paths, new_graph=cond1_graph, dseparation_algo=dseparation_algo, ) self.logger.debug( "Candidate frontdoor set: {0}, is_dseparated: {1}".format( candidate_var, cond1 ) ) if not cond1: continue # Cond 2: No confounding between treatment and candidate var cond2 = self._graph.check_valid_backdoor_set( self.treatment_name, parse_state(candidate_var), set(), backdoor_paths=None, new_graph=bdoor_graph1, dseparation_algo=dseparation_algo, ) if not cond2: continue # Cond 3: treatment blocks all confounding between candidate_var and outcome bdoor_graph2 = self._graph.do_surgery( candidate_var, remove_outgoing_edges=True ) cond3 = self._graph.check_valid_backdoor_set( parse_state(candidate_var), self.outcome_name, self.treatment_name, backdoor_paths=None, new_graph=bdoor_graph2, dseparation_algo=dseparation_algo, ) is_valid_frontdoor = cond1 and cond2 and cond3 if is_valid_frontdoor: frontdoor_var = candidate_var break return parse_state(frontdoor_var) def identify_mediation(self): """ Find a valid mediator if it exists. Currently only supports a single variable mediator set. """ mediation_var = None mediation_paths = self._graph.get_all_directed_paths( self.treatment_name, self.outcome_name ) eligible_variables = self._graph.get_descendants(self.treatment_name) - set( self.outcome_name ) # For simplicity, assuming a one-variable mediation set for candidate_var in eligible_variables: is_valid_mediation = self._graph.check_valid_mediation_set( self.treatment_name, self.outcome_name, parse_state(candidate_var), mediation_paths=mediation_paths, ) self.logger.debug( "Candidate mediation set: {0}, on_mediating_path: {1}".format( candidate_var, is_valid_mediation ) ) if is_valid_mediation: mediation_var = candidate_var break return parse_state(mediation_var) return None def identify_mediation_first_stage_confounders( self, treatment_name, mediators_names ): # Create estimands dict as per the API for backdoor, but do not return it estimands_dict = {} backdoor_sets = self.identify_backdoor(treatment_name, mediators_names) estimands_dict, backdoor_variables_dict = self.build_backdoor_estimands_dict( treatment_name, mediators_names, backdoor_sets, estimands_dict, proceed_when_unidentifiable=True, ) # Setting default "backdoor" identification adjustment set default_backdoor_id = self.get_default_backdoor_set_id(backdoor_variables_dict) estimands_dict["backdoor"] = estimands_dict.get(str(default_backdoor_id), None) backdoor_variables_dict["backdoor"] = backdoor_variables_dict.get( str(default_backdoor_id), None ) return backdoor_variables_dict def identify_mediation_second_stage_confounders( self, mediators_names, outcome_name ): # Create estimands dict as per the API for backdoor, but do not return it estimands_dict = {} backdoor_sets = self.identify_backdoor(mediators_names, outcome_name) estimands_dict, backdoor_variables_dict = self.build_backdoor_estimands_dict( mediators_names, outcome_name, backdoor_sets, estimands_dict, proceed_when_unidentifiable=True, ) # Setting default "backdoor" identification adjustment set default_backdoor_id = self.get_default_backdoor_set_id(backdoor_variables_dict) estimands_dict["backdoor"] = estimands_dict.get(str(default_backdoor_id), None) backdoor_variables_dict["backdoor"] = backdoor_variables_dict.get( str(default_backdoor_id), None ) return backdoor_variables_dict def construct_backdoor_estimand( self, estimand_type, treatment_name, outcome_name, common_causes ): # TODO: outputs string for now, but ideally should do symbolic # expressions Mon 19 Feb 2018 04:54:17 PM DST # TODO Better support for multivariate treatments expr = None outcome_name = outcome_name[0] num_expr_str = outcome_name if len(common_causes) > 0: num_expr_str += "|" + ",".join(common_causes) expr = "d(" + num_expr_str + ")/d" + ",".join(treatment_name) sym_mu = sp.Symbol("mu") sym_sigma = sp.Symbol("sigma", positive=True) sym_outcome = spstats.Normal(num_expr_str, sym_mu, sym_sigma) sym_treatment_symbols = [sp.Symbol(t) for t in treatment_name] sym_treatment = sp.Array(sym_treatment_symbols) sym_conditional_outcome = spstats.Expectation(sym_outcome) sym_effect = sp.Derivative(sym_conditional_outcome, sym_treatment) sym_assumptions = { "Unconfoundedness": ( "If U\N{RIGHTWARDS ARROW}{{{0}}} and U\N{RIGHTWARDS ARROW}{1}" " then P({1}|{0},{2},U) = P({1}|{0},{2})" ).format(",".join(treatment_name), outcome_name, ",".join(common_causes)) } estimand = {"estimand": sym_effect, "assumptions": sym_assumptions} return estimand def construct_iv_estimand( self, estimand_type, treatment_name, outcome_name, instrument_names ): # TODO: support multivariate treatments better. expr = None outcome_name = outcome_name[0] sym_outcome = spstats.Normal(outcome_name, 0, 1) sym_treatment_symbols = [spstats.Normal(t, 0, 1) for t in treatment_name] sym_treatment = sp.Array(sym_treatment_symbols) sym_instrument_symbols = [sp.Symbol(inst) for inst in instrument_names] sym_instrument = sp.Array(sym_instrument_symbols) # ",".join(instrument_names)) sym_outcome_derivative = sp.Derivative(sym_outcome, sym_instrument) sym_treatment_derivative = sp.Derivative(sym_treatment, sym_instrument) sym_effect = spstats.Expectation( sym_outcome_derivative / sym_treatment_derivative ) sym_assumptions = { "As-if-random": ( "If U\N{RIGHTWARDS ARROW}\N{RIGHTWARDS ARROW}{0} then " "\N{NOT SIGN}(U \N{RIGHTWARDS ARROW}\N{RIGHTWARDS ARROW}{{{1}}})" ).format(outcome_name, ",".join(instrument_names)), "Exclusion": ( "If we remove {{{0}}}\N{RIGHTWARDS ARROW}{{{1}}}, then " "\N{NOT SIGN}({{{0}}}\N{RIGHTWARDS ARROW}{2})" ).format( ",".join(instrument_names), ",".join(treatment_name), outcome_name ), } estimand = {"estimand": sym_effect, "assumptions": sym_assumptions} return estimand def construct_frontdoor_estimand( self, estimand_type, treatment_name, outcome_name, frontdoor_variables_names ): # TODO: support multivariate treatments better. expr = None outcome_name = outcome_name[0] sym_outcome = spstats.Normal(outcome_name, 0, 1) sym_treatment_symbols = [spstats.Normal(t, 0, 1) for t in treatment_name] sym_treatment = sp.Array(sym_treatment_symbols) sym_frontdoor_symbols = [sp.Symbol(inst) for inst in frontdoor_variables_names] sym_frontdoor = sp.Array(sym_frontdoor_symbols) # ",".join(instrument_names)) sym_outcome_derivative = sp.Derivative(sym_outcome, sym_frontdoor) sym_treatment_derivative = sp.Derivative(sym_frontdoor, sym_treatment) sym_effect = spstats.Expectation( sym_treatment_derivative * sym_outcome_derivative ) sym_assumptions = { "Full-mediation": ( "{2} intercepts (blocks) all directed paths from {0} to {1}." ).format( ",".join(treatment_name), ",".join(outcome_name), ",".join(frontdoor_variables_names), ), "First-stage-unconfoundedness": ( "If U\N{RIGHTWARDS ARROW}{{{0}}} and U\N{RIGHTWARDS ARROW}{{{1}}}" " then P({1}|{0},U) = P({1}|{0})" ).format(",".join(treatment_name), ",".join(frontdoor_variables_names)), "Second-stage-unconfoundedness": ( "If U\N{RIGHTWARDS ARROW}{{{2}}} and U\N{RIGHTWARDS ARROW}{1}" " then P({1}|{2}, {0}, U) = P({1}|{2}, {0})" ).format( ",".join(treatment_name), outcome_name, ",".join(frontdoor_variables_names), ), } estimand = {"estimand": sym_effect, "assumptions": sym_assumptions} return estimand def construct_mediation_estimand( self, estimand_type, treatment_name, outcome_name, mediators_names ): # TODO: support multivariate treatments better. expr = None if estimand_type in ( CausalIdentifier.NONPARAMETRIC_NDE, CausalIdentifier.NONPARAMETRIC_NIE, ): outcome_name = outcome_name[0] sym_outcome = spstats.Normal(outcome_name, 0, 1) sym_treatment_symbols = [spstats.Normal(t, 0, 1) for t in treatment_name] sym_treatment = sp.Array(sym_treatment_symbols) sym_mediators_symbols = [sp.Symbol(inst) for inst in mediators_names] sym_mediators = sp.Array(sym_mediators_symbols) sym_outcome_derivative = sp.Derivative(sym_outcome, sym_mediators) sym_treatment_derivative = sp.Derivative(sym_mediators, sym_treatment) # For direct effect num_expr_str = outcome_name if len(mediators_names) > 0: num_expr_str += "|" + ",".join(mediators_names) sym_mu = sp.Symbol("mu") sym_sigma = sp.Symbol("sigma", positive=True) sym_conditional_outcome = spstats.Normal(num_expr_str, sym_mu, sym_sigma) sym_directeffect_derivative = sp.Derivative( sym_conditional_outcome, sym_treatment ) if estimand_type == CausalIdentifier.NONPARAMETRIC_NIE: sym_effect = spstats.Expectation( sym_treatment_derivative * sym_outcome_derivative ) elif estimand_type == CausalIdentifier.NONPARAMETRIC_NDE: sym_effect = spstats.Expectation(sym_directeffect_derivative) sym_assumptions = { "Mediation": ( "{2} intercepts (blocks) all directed paths from {0} to {1} except the path {{{0}}}\N{RIGHTWARDS ARROW}{{{1}}}." ).format( ",".join(treatment_name), ",".join(outcome_name), ",".join(mediators_names), ), "First-stage-unconfoundedness": ( "If U\N{RIGHTWARDS ARROW}{{{0}}} and U\N{RIGHTWARDS ARROW}{{{1}}}" " then P({1}|{0},U) = P({1}|{0})" ).format(",".join(treatment_name), ",".join(mediators_names)), "Second-stage-unconfoundedness": ( "If U\N{RIGHTWARDS ARROW}{{{2}}} and U\N{RIGHTWARDS ARROW}{1}" " then P({1}|{2}, {0}, U) = P({1}|{2}, {0})" ).format( ",".join(treatment_name), outcome_name, ",".join(mediators_names) ), } else: raise ValueError( "Estimand type not supported. Supported estimand types are {0} or {1}'.".format( CausalIdentifier.NONPARAMETRIC_NDE, CausalIdentifier.NONPARAMETRIC_NIE, ) ) estimand = {"estimand": sym_effect, "assumptions": sym_assumptions} return estimand class IdentifiedEstimand: """Class for storing a causal estimand, typically as a result of the identification step. """ def __init__( self, identifier, treatment_variable, outcome_variable, estimand_type=None, estimands=None, backdoor_variables=None, instrumental_variables=None, frontdoor_variables=None, mediator_variables=None, mediation_first_stage_confounders=None, mediation_second_stage_confounders=None, default_backdoor_id=None, identifier_method=None, no_directed_path=False, ): self.identifier = identifier self.treatment_variable = parse_state(treatment_variable) self.outcome_variable = parse_state(outcome_variable) self.backdoor_variables = backdoor_variables self.instrumental_variables = parse_state(instrumental_variables) self.frontdoor_variables = parse_state(frontdoor_variables) self.mediator_variables = parse_state(mediator_variables) self.mediation_first_stage_confounders = mediation_first_stage_confounders self.mediation_second_stage_confounders = mediation_second_stage_confounders self.estimand_type = estimand_type self.estimands = estimands self.default_backdoor_id = default_backdoor_id self.identifier_method = identifier_method self.no_directed_path = no_directed_path def set_identifier_method(self, identifier_name): self.identifier_method = identifier_name def get_backdoor_variables(self, key=None): """ Return a list containing the backdoor variables. If the calling estimator method is a backdoor method, return the backdoor variables corresponding to its target estimand. Otherwise, return the backdoor variables for the default backdoor estimand. """ if key is None: if self.identifier_method and self.identifier_method.startswith("backdoor"): return self.backdoor_variables[self.identifier_method] elif ( self.backdoor_variables is not None and len(self.backdoor_variables) > 0 ): return self.backdoor_variables[self.default_backdoor_id] else: return [] else: return self.backdoor_variables[key] def set_backdoor_variables(self, bdoor_variables_arr, key=None): if key is None: key = self.identifier_method self.backdoor_variables[key] = bdoor_variables_arr def get_frontdoor_variables(self): """Return a list containing the frontdoor variables (if present) """ return self.frontdoor_variables def get_mediator_variables(self): """Return a list containing the mediator variables (if present) """ return self.mediator_variables def get_instrumental_variables(self): """Return a list containing the instrumental variables (if present) """ return self.instrumental_variables def __deepcopy__(self, memo): return IdentifiedEstimand( self.identifier, # not deep copied copy.deepcopy(self.treatment_variable), copy.deepcopy(self.outcome_variable), estimand_type=copy.deepcopy(self.estimand_type), estimands=copy.deepcopy(self.estimands), backdoor_variables=copy.deepcopy(self.backdoor_variables), instrumental_variables=copy.deepcopy(self.instrumental_variables), frontdoor_variables=copy.deepcopy(self.frontdoor_variables), mediator_variables=copy.deepcopy(self.mediator_variables), default_backdoor_id=copy.deepcopy(self.default_backdoor_id), identifier_method=copy.deepcopy(self.identifier_method), ) def __str__(self, only_target_estimand=False, show_all_backdoor_sets=False): if self.no_directed_path: s = "No directed path from {0} to {1} in the causal graph.".format( self.treatment_variable, self.outcome_variable ) s += "\nCausal effect is zero." return s s = "Estimand type: {0}\n".format(self.estimand_type) i = 1 has_valid_backdoor = sum("backdoor" in key for key in self.estimands.keys()) for k, v in self.estimands.items(): if show_all_backdoor_sets: # Do not show backdoor key unless it is the only backdoor set. if k == "backdoor" and has_valid_backdoor > 1: continue else: # Just show the default backdoor set if k.startswith("backdoor") and k != "backdoor": continue if only_target_estimand and k != self.identifier_method: continue s += "\n### Estimand : {0}\n".format(i) s += "Estimand name: {0}".format(k) if k == self.default_backdoor_id: s += " (Default)" s += "\n" if v is None: s += "No such variable(s) found!\n" else: sp_expr_str = sp.pretty(v["estimand"], use_unicode=True) s += "Estimand expression:\n{0}\n".format(sp_expr_str) j = 1 for ass_name, ass_str in v["assumptions"].items(): s += "Estimand assumption {0}, {1}: {2}\n".format( j, ass_name, ass_str ) j += 1 i += 1 return s

esmucler

77f7064c85b3de740b5beefb0ad7067ffdb024fd

824f5532c0644812867bb018bf22585f2466960c

See my answer in the [comment](https://github.com/py-why/dowhy/pull/549#issuecomment-1188730376) below

esmucler

py-why/dowhy

Adding Non Linear Sensitivity Analysis

This PR implements the non-parametric sensitivity analysis from Chernozhukov et al. https://arxiv.org/abs/2112.13398 It implements two sensitivity analyzers: 1. For Partial Linear DGPs and estimators like LinearDML 2. For general non-parametric DGPs and estimators like KernelDML. The notebook in this PR provides an introduction on how the sensitivity bounds are calculated for the partial linear case. For the general nonparametric DGPs, we need to estimate a special function called the Reisz representer. For binary treatment, it is exactly the difference in outcome weighted by propensity score. So we provide two options to learn the Reisz representer, 1) plugin_reisz that uses the propensity score; and 2) general estimator that uses a custom loss function. These two are in the file reisz.py. Briefly, the sensitivity bounds depend on two parameters that denote the effect of the unobserved confounder on treatment and outcome. That's why we use the same API as for the `add_unobserved_common_cause` method and add this sensitivity analysis as a possible simulation method="non-parametric-partial-R2". The format of the plots is identical to those from the "linear-partial-r2" simulation method that is already implemented. We provide two modes for the user. 1) User specifies the effect strength parameters themselves, as a range of values. 2) User benchmarks the effect strength parameters as a multiple of the same parameters for the observed common causes. Signed-off-by: anusha <anushaagarwal2000.com>

2022-06-20 14:37:11+00:00

2022-09-16 03:57:26+00:00

dowhy/causal_refuters/add_unobserved_common_cause.py

import copy import logging import math import numpy as np import pandas as pd import scipy.stats import statsmodels.api as sm from sklearn.linear_model import LogisticRegression from sklearn.preprocessing import StandardScaler from tqdm.auto import tqdm from dowhy.causal_estimator import CausalEstimator from dowhy.causal_estimators.linear_regression_estimator import LinearRegressionEstimator from dowhy.causal_refuter import CausalRefutation, CausalRefuter from dowhy.causal_refuters.linear_sensitivity_analyzer import LinearSensitivityAnalyzer class AddUnobservedCommonCause(CausalRefuter): """Add an unobserved confounder for refutation. Supports additional parameters that can be specified in the refute_estimate() method. - 'confounders_effect_on_treatment': how the simulated confounder affects the value of treatment. This can be linear (for continuous treatment) or binary_flip (for binary treatment) - 'confounders_effect_on_outcome': how the simulated confounder affects the value of outcome. This can be linear (for continuous outcome) or binary_flip (for binary outcome) - 'effect_strength_on_treatment': parameter for the strength of the effect of simulated confounder on treatment. For linear effect, it is the regression coeffient. For binary_flip, it is the probability that simulated confounder's effect flips the value of treatment from 0 to 1 (or vice-versa). - 'effect_strength_on_outcome': parameter for the strength of the effect of simulated confounder on outcome. For linear effect, it is the regression coeffient. For binary_flip, it is the probability that simulated confounder's effect flips the value of outcome from 0 to 1 (or vice-versa). TODO: Needs an interpretation module """ def __init__(self, *args, **kwargs): """ Initialize the parameters required for the refuter. If effect_strength_on_treatment or effect_strength_on_outcome is not given, it is calculated automatically as a range between the minimum and maximum effect strength of observed confounders on treatment and outcome respectively. :param confounders_effect_on_treatment: str : The type of effect on the treatment due to the unobserved confounder. Possible values are ['binary_flip', 'linear'] :param confounders_effect_on_outcome: str : The type of effect on the outcome due to the unobserved confounder. Possible values are ['binary_flip', 'linear'] :param effect_strength_on_treatment: float, numpy.ndarray: This refers to the strength of the confounder on treatment. For a linear effect, it behaves like the regression coeffecient. For a binary flip it is the probability with which it can invert the value of the treatment. :param effect_strength_on_outcome: float, numpy.ndarray: This refers to the strength of the confounder on outcome. For a linear effect, it behaves like the regression coefficient. For a binary flip, it is the probability with which it can invert the value of the outcome. :param effect_fraction_on_treatment: float: If effect_strength_on_treatment is not provided, this parameter decides the effect strength of the simulated confounder as a fraction of the effect strength of observed confounders on treatment. Defaults to 1. :param effect_fraction_on_outcome: float: If effect_strength_on_outcome is not provided, this parameter decides the effect strength of the simulated confounder as a fraction of the effect strength of observed confounders on outcome. Defaults to 1. :param plotmethod: string: Type of plot to be shown. If None, no plot is generated. This parameter is used only only when more than one treatment confounder effect values or outcome confounder effect values are provided. Default is "colormesh". Supported values are "contour", "colormesh" when more than one value is provided for both confounder effect value parameters; "line" when provided for only one of them. :param simulated_method_name: method type to add unobserved common cause. "linear-partial-R2" for linear sensitivity analysis :param percent_change_estimate: It is the percentage of reduction of treatment estimate that could alter the results (default = 1) if percent_change_estimate = 1, the robustness value describes the strength of association of confounders with treatment and outcome in order to reduce the estimate by 100% i.e bring it down to 0. :param confounder_increases_estimate: True implies that confounder increases the absolute value of estimate and vice versa. (Default = False) :param benchmark_common_causes: names of variables for bounding strength of confounders :param significance_level: confidence interval for statistical inference(default = 0.05) :param null_hypothesis_effect: assumed effect under the null hypothesis :param plot_estimate: Generate contour plot for estimate while performing sensitivity analysis. (default = True). To override the setting, set plot_estimate = False. """ super().__init__(*args, **kwargs) self.effect_on_t = ( kwargs["confounders_effect_on_treatment"] if "confounders_effect_on_treatment" in kwargs else "binary_flip" ) self.effect_on_y = ( kwargs["confounders_effect_on_outcome"] if "confounders_effect_on_outcome" in kwargs else "linear" ) self.kappa_t = kwargs["effect_strength_on_treatment"] if "effect_strength_on_treatment" in kwargs else None self.kappa_y = kwargs["effect_strength_on_outcome"] if "effect_strength_on_outcome" in kwargs else None self.frac_strength_treatment = ( kwargs["effect_fraction_on_treatment"] if "effect_fraction_on_treatment" in kwargs else 1 ) self.frac_strength_outcome = ( kwargs["effect_fraction_on_outcome"] if "effect_fraction_on_outcome" in kwargs else 1 ) self.simulated_method_name = ( kwargs["simulated_method_name"] if "simulated_method_name" in kwargs else "linear_based" ) self.plotmethod = kwargs["plotmethod"] if "plotmethod" in kwargs else "colormesh" self.percent_change_estimate = kwargs["percent_change_estimate"] if "percent_change_estimate" in kwargs else 1.0 self.significance_level = kwargs["significance_level"] if "significance_level" in kwargs else 0.05 self.confounder_increases_estimate = ( kwargs["confounder_increases_estimate"] if "confounder_increases_estimate" in kwargs else False ) self.benchmark_common_causes = ( kwargs["benchmark_common_causes"] if "benchmark_common_causes" in kwargs else None ) self.null_hypothesis_effect = kwargs["null_hypothesis_effect"] if "null_hypothesis_effect" in kwargs else 0 self.plot_estimate = kwargs["plot_estimate"] if "plot_estimate" in kwargs else True self.logger = logging.getLogger(__name__) def infer_default_kappa_t(self, len_kappa_t=10): """Infer default effect strength of simulated confounder on treatment.""" observed_common_causes_names = self._target_estimand.get_backdoor_variables() if len(observed_common_causes_names) > 0: observed_common_causes = self._data[observed_common_causes_names] observed_common_causes = pd.get_dummies(observed_common_causes, drop_first=True) else: raise ValueError( "There needs to be at least one common cause to" + "automatically compute the default value of kappa_t." + " Provide a value for kappa_t" ) t = self._data[self._treatment_name] # Standardizing the data observed_common_causes = StandardScaler().fit_transform(observed_common_causes) if self.effect_on_t == "binary_flip": # Fit a model containing all confounders and compare predictions # using all features compared to all features except a given # confounder. tmodel = LogisticRegression().fit(observed_common_causes, t) tpred = tmodel.predict(observed_common_causes).astype(int) flips = [] for i in range(observed_common_causes.shape[1]): oldval = np.copy(observed_common_causes[:, i]) observed_common_causes[:, i] = 0 tcap = tmodel.predict(observed_common_causes).astype(int) observed_common_causes[:, i] = oldval flips.append(np.sum(abs(tcap - tpred)) / tpred.shape[0]) min_coeff, max_coeff = min(flips), max(flips) elif self.effect_on_t == "linear": # Estimating the regression coefficient from standardized features to t corrcoef_var_t = np.corrcoef(observed_common_causes, t, rowvar=False)[-1, :-1] std_dev_t = np.std(t)[0] max_coeff = max(corrcoef_var_t) * std_dev_t min_coeff = min(corrcoef_var_t) * std_dev_t else: raise NotImplementedError( "'" + self.effect_on_t + "' method not supported for confounders' effect on treatment" ) min_coeff, max_coeff = self._compute_min_max_coeff(min_coeff, max_coeff, self.frac_strength_treatment) # By default, return a plot with 10 points # consider 10 values of the effect of the unobserved confounder step = (max_coeff - min_coeff) / len_kappa_t self.logger.info("(Min, Max) kappa_t for observed common causes, ({0}, {1})".format(min_coeff, max_coeff)) if np.equal(max_coeff, min_coeff): return max_coeff else: return np.arange(min_coeff, max_coeff, step) def _compute_min_max_coeff(self, min_coeff, max_coeff, effect_strength_fraction): max_coeff = effect_strength_fraction * max_coeff min_coeff = effect_strength_fraction * min_coeff return min_coeff, max_coeff def infer_default_kappa_y(self, len_kappa_y=10): """Infer default effect strength of simulated confounder on treatment.""" observed_common_causes_names = self._target_estimand.get_backdoor_variables() if len(observed_common_causes_names) > 0: observed_common_causes = self._data[observed_common_causes_names] observed_common_causes = pd.get_dummies(observed_common_causes, drop_first=True) else: raise ValueError( "There needs to be at least one common cause to" + "automatically compute the default value of kappa_y." + " Provide a value for kappa_y" ) y = self._data[self._outcome_name] # Standardizing the data observed_common_causes = StandardScaler().fit_transform(observed_common_causes) if self.effect_on_y == "binary_flip": # Fit a model containing all confounders and compare predictions # using all features compared to all features except a given # confounder. ymodel = LogisticRegression().fit(observed_common_causes, y) ypred = ymodel.predict(observed_common_causes).astype(int) flips = [] for i in range(observed_common_causes.shape[1]): oldval = np.copy(observed_common_causes[:, i]) observed_common_causes[:, i] = 0 ycap = ymodel.predict(observed_common_causes).astype(int) observed_common_causes[:, i] = oldval flips.append(np.sum(abs(ycap - ypred)) / ypred.shape[0]) min_coeff, max_coeff = min(flips), max(flips) elif self.effect_on_y == "linear": corrcoef_var_y = np.corrcoef(observed_common_causes, y, rowvar=False)[-1, :-1] std_dev_y = np.std(y)[0] max_coeff = max(corrcoef_var_y) * std_dev_y min_coeff = min(corrcoef_var_y) * std_dev_y else: raise NotImplementedError( "'" + self.effect_on_y + "' method not supported for confounders' effect on outcome" ) min_coeff, max_coeff = self._compute_min_max_coeff(min_coeff, max_coeff, self.frac_strength_outcome) # By default, return a plot with 10 points # consider 10 values of the effect of the unobserved confounder step = (max_coeff - min_coeff) / len_kappa_y self.logger.info("(Min, Max) kappa_y for observed common causes, ({0}, {1})".format(min_coeff, max_coeff)) if np.equal(max_coeff, min_coeff): return max_coeff else: return np.arange(min_coeff, max_coeff, step) def refute_estimate(self, show_progress_bar=False): """ This function attempts to add an unobserved common cause to the outcome and the treatment. At present, we have implemented the behavior for one dimensional behaviors for continuous and binary variables. This function can either take single valued inputs or a range of inputs. The function then looks at the data type of the input and then decides on the course of action. :return: CausalRefuter: An object that contains the estimated effect and a new effect and the name of the refutation used. """ if self.simulated_method_name == "linear-partial-R2": if not (isinstance(self._estimate.estimator, LinearRegressionEstimator)): raise NotImplementedError( "Currently only LinearRegressionEstimator is supported for Sensitivity Analysis" ) if len(self._estimate.estimator._effect_modifier_names) > 0: raise NotImplementedError("The current implementation does not support effect modifiers") if self.frac_strength_outcome == 1: self.frac_strength_outcome = self.frac_strength_treatment analyzer = LinearSensitivityAnalyzer( estimator=self._estimate.estimator, data=self._data, treatment_name=self._treatment_name, percent_change_estimate=self.percent_change_estimate, significance_level=self.significance_level, benchmark_common_causes=self.benchmark_common_causes, null_hypothesis_effect=self.null_hypothesis_effect, frac_strength_treatment=self.frac_strength_treatment, frac_strength_outcome=self.frac_strength_outcome, common_causes_order=self._estimate.estimator._observed_common_causes.columns, ) analyzer.check_sensitivity(plot=self.plot_estimate) return analyzer if self.kappa_t is None: self.kappa_t = self.infer_default_kappa_t() if self.kappa_y is None: self.kappa_y = self.infer_default_kappa_y() if not isinstance(self.kappa_t, (list, np.ndarray)) and not isinstance( self.kappa_y, (list, np.ndarray) ): # Deal with single value inputs new_data = copy.deepcopy(self._data) new_data = self.include_confounders_effect(new_data, self.kappa_t, self.kappa_y) new_estimator = CausalEstimator.get_estimator_object(new_data, self._target_estimand, self._estimate) new_effect = new_estimator.estimate_effect() refute = CausalRefutation( self._estimate.value, new_effect.value, refutation_type="Refute: Add an Unobserved Common Cause" ) refute.new_effect_array = np.array(new_effect.value) refute.new_effect = new_effect.value refute.add_refuter(self) return refute else: # Deal with multiple value inputs if isinstance(self.kappa_t, (list, np.ndarray)) and isinstance( self.kappa_y, (list, np.ndarray) ): # Deal with range inputs # Get a 2D matrix of values # x,y = np.meshgrid(self.kappa_t, self.kappa_y) # x,y are both MxN results_matrix = np.random.rand( len(self.kappa_t), len(self.kappa_y) ) # Matrix to hold all the results of NxM orig_data = copy.deepcopy(self._data) for i in tqdm( range(len(self.kappa_t)), colour=CausalRefuter.PROGRESS_BAR_COLOR, disable=not show_progress_bar, desc="Refuting Estimates: ", ): for j in range(len(self.kappa_y)): new_data = self.include_confounders_effect(orig_data, self.kappa_t[i], self.kappa_y[j]) new_estimator = CausalEstimator.get_estimator_object( new_data, self._target_estimand, self._estimate ) new_effect = new_estimator.estimate_effect() refute = CausalRefutation( self._estimate.value, new_effect.value, refutation_type="Refute: Add an Unobserved Common Cause", ) results_matrix[i][j] = refute.new_effect # Populate the results refute.new_effect_array = results_matrix refute.new_effect = (np.min(results_matrix), np.max(results_matrix)) # Store the values into the refute object refute.add_refuter(self) if self.plotmethod is None: return refute import matplotlib import matplotlib.pyplot as plt fig = plt.figure(figsize=(6, 5)) left, bottom, width, height = 0.1, 0.1, 0.8, 0.8 ax = fig.add_axes([left, bottom, width, height]) oe = self._estimate.value contour_levels = [oe / 4.0, oe / 2.0, (3.0 / 4) * oe, oe] contour_levels.extend([0, np.min(results_matrix), np.max(results_matrix)]) if self.plotmethod == "contour": cp = plt.contourf(self.kappa_y, self.kappa_t, results_matrix, levels=sorted(contour_levels)) # Adding a label on the contour line for the original estimate fmt = {} trueeffect_index = np.where(cp.levels == oe)[0][0] fmt[cp.levels[trueeffect_index]] = "Estimated Effect" # Label every other level using strings plt.clabel(cp, [cp.levels[trueeffect_index]], inline=True, fmt=fmt) plt.colorbar(cp) elif self.plotmethod == "colormesh": cp = plt.pcolormesh(self.kappa_y, self.kappa_t, results_matrix, shading="nearest") plt.colorbar(cp, ticks=contour_levels) ax.yaxis.set_ticks(self.kappa_t) ax.xaxis.set_ticks(self.kappa_y) plt.xticks(rotation=45) ax.set_title("Effect of Unobserved Common Cause") ax.set_ylabel("Value of Linear Constant on Treatment") ax.set_xlabel("Value of Linear Constant on Outcome") plt.show() return refute elif isinstance(self.kappa_t, (list, np.ndarray)): outcomes = np.random.rand(len(self.kappa_t)) orig_data = copy.deepcopy(self._data) for i in tqdm( range(0, len(self.kappa_t)), colour=CausalRefuter.PROGRESS_BAR_COLOR, disable=not show_progress_bar, desc="Refuting Estimates: ", ): new_data = self.include_confounders_effect(orig_data, self.kappa_t[i], self.kappa_y) new_estimator = CausalEstimator.get_estimator_object( new_data, self._target_estimand, self._estimate ) new_effect = new_estimator.estimate_effect() refute = CausalRefutation( self._estimate.value, new_effect.value, refutation_type="Refute: Add an Unobserved Common Cause" ) self.logger.debug(refute) outcomes[i] = refute.new_effect # Populate the results refute.new_effect_array = outcomes refute.new_effect = (np.min(outcomes), np.max(outcomes)) refute.add_refuter(self) if self.plotmethod is None: return refute import matplotlib import matplotlib.pyplot as plt fig = plt.figure(figsize=(6, 5)) left, bottom, width, height = 0.1, 0.1, 0.8, 0.8 ax = fig.add_axes([left, bottom, width, height]) plt.plot(self.kappa_t, outcomes) plt.axhline(self._estimate.value, linestyle="--", color="gray") ax.set_title("Effect of Unobserved Common Cause") ax.set_xlabel("Value of Linear Constant on Treatment") ax.set_ylabel("Estimated Effect after adding the common cause") plt.show() return refute elif isinstance(self.kappa_y, (list, np.ndarray)): outcomes = np.random.rand(len(self.kappa_y)) orig_data = copy.deepcopy(self._data) for i in tqdm( range(0, len(self.kappa_y)), colour=CausalRefuter.PROGRESS_BAR_COLOR, disable=not show_progress_bar, desc="Refuting Estimates: ", ): new_data = self.include_confounders_effect(orig_data, self.kappa_t, self.kappa_y[i]) new_estimator = CausalEstimator.get_estimator_object( new_data, self._target_estimand, self._estimate ) new_effect = new_estimator.estimate_effect() refute = CausalRefutation( self._estimate.value, new_effect.value, refutation_type="Refute: Add an Unobserved Common Cause" ) self.logger.debug(refute) outcomes[i] = refute.new_effect # Populate the results refute.new_effect_array = outcomes refute.new_effect = (np.min(outcomes), np.max(outcomes)) refute.add_refuter(self) if self.plotmethod is None: return refute import matplotlib import matplotlib.pyplot as plt fig = plt.figure(figsize=(6, 5)) left, bottom, width, height = 0.1, 0.1, 0.8, 0.8 ax = fig.add_axes([left, bottom, width, height]) plt.plot(self.kappa_y, outcomes) plt.axhline(self._estimate.value, linestyle="--", color="gray") ax.set_title("Effect of Unobserved Common Cause") ax.set_xlabel("Value of Linear Constant on Outcome") ax.set_ylabel("Estimated Effect after adding the common cause") plt.show() return refute def include_confounders_effect(self, new_data, kappa_t, kappa_y): """ This function deals with the change in the value of the data due to the effect of the unobserved confounder. In the case of a binary flip, we flip only if the random number is greater than the threshold set. In the case of a linear effect, we use the variable as the linear regression constant. :param new_data: pandas.DataFrame: The data to be changed due to the effects of the unobserved confounder. :param kappa_t: numpy.float64: The value of the threshold for binary_flip or the value of the regression coefficient for linear effect. :param kappa_y: numpy.float64: The value of the threshold for binary_flip or the value of the regression coefficient for linear effect. :return: pandas.DataFrame: The DataFrame that includes the effects of the unobserved confounder. """ num_rows = self._data.shape[0] stdnorm = scipy.stats.norm() w_random = stdnorm.rvs(num_rows) if self.effect_on_t == "binary_flip": alpha = 2 * kappa_t - 1 if kappa_t >= 0.5 else 1 - 2 * kappa_t interval = stdnorm.interval(alpha) rel_interval = interval[0] if kappa_t >= 0.5 else interval[1] new_data.loc[rel_interval <= w_random, self._treatment_name] = ( 1 - new_data.loc[rel_interval <= w_random, self._treatment_name] ) for tname in self._treatment_name: if pd.api.types.is_bool_dtype(self._data[tname]): new_data = new_data.astype({tname: "bool"}, copy=False) elif self.effect_on_t == "linear": confounder_t_effect = kappa_t * w_random # By default, we add the effect of simulated confounder for treatment. # But subtract it from outcome to create a negative correlation # assuming that the original confounder's effect was positive on both. # This is to remove the effect of the original confounder. new_data[self._treatment_name] = new_data[self._treatment_name].values + np.ndarray( shape=(num_rows, 1), buffer=confounder_t_effect ) else: raise NotImplementedError( "'" + self.effect_on_t + "' method not supported for confounders' effect on treatment" ) if self.effect_on_y == "binary_flip": alpha = 2 * kappa_y - 1 if kappa_y >= 0.5 else 1 - 2 * kappa_y interval = stdnorm.interval(alpha) rel_interval = interval[0] if kappa_y >= 0.5 else interval[1] new_data.loc[rel_interval <= w_random, self._outcome_name] = ( 1 - new_data.loc[rel_interval <= w_random, self._outcome_name] ) for yname in self._outcome_name: if pd.api.types.is_bool_dtype(self._data[yname]): new_data = new_data.astype({yname: "bool"}, copy=False) elif self.effect_on_y == "linear": confounder_y_effect = (-1) * kappa_y * w_random # By default, we add the effect of simulated confounder for treatment. # But subtract it from outcome to create a negative correlation # assuming that the original confounder's effect was positive on both. # This is to remove the effect of the original confounder. new_data[self._outcome_name] = new_data[self._outcome_name].values + np.ndarray( shape=(num_rows, 1), buffer=confounder_y_effect ) else: raise NotImplementedError( "'" + self.effect_on_y + "' method not supported for confounders' effect on outcome" ) return new_data def include_simulated_confounder(self, convergence_threshold=0.1, c_star_max=1000): """ This function simulates an unobserved confounder based on the data using the following steps: 1. It calculates the "residuals" from the treatment and outcome model i.) The outcome model has outcome as the dependent variable and all the observed variables including treatment as independent variables ii.) The treatment model has treatment as the dependent variable and all the observed variables as independent variables. 2. U is an intermediate random variable drawn from the normal distribution with the weighted average of residuals as mean and a unit variance U ~ N(c1*d_y + c2*d_t, 1) where *d_y and d_t are residuals from the treatment and outcome model *c1 and c2 are coefficients to the residuals 3. The final U, which is the simulated unobserved confounder is obtained by debiasing the intermediate variable U by residualising it with X Choosing the coefficients c1 and c2: The coefficients are chosen based on these basic assumptions: 1. There is a hyperbolic relationship satisfying c1*c2 = c_star 2. c_star is chosen from a range of possible values based on the correlation of the obtained simulated variable with outcome and treatment. 3. The product of correlations with treatment and outcome should be at a minimum distance to the maximum correlations with treatment and outcome in any of the observed confounders 4. The ratio of the weights should be such that they maintain the ratio of the maximum possible observed coefficients within some confidence interval :param c_star_max: The maximum possible value for the hyperbolic curve on which the coefficients to the residuals lie. It defaults to 1000 in the code if not specified by the user. :type int :param convergence_threshold: The threshold to check the plateauing of the correlation while selecting a c_star. It defaults to 0.1 in the code if not specified by the user :type float :returns: The simulated values of the unobserved confounder based on the data :type pandas.core.series.Series """ # Obtaining the list of observed variables required_variables = True observed_variables = self.choose_variables(required_variables) observed_variables_with_treatment_and_outcome = observed_variables + self._treatment_name + self._outcome_name # Taking a subset of the dataframe that has only observed variables self._data = self._data[observed_variables_with_treatment_and_outcome] # Residuals from the outcome model obtained by fitting a linear model y = self._data[self._outcome_name[0]] observed_variables_with_treatment = observed_variables + self._treatment_name X = self._data[observed_variables_with_treatment] model = sm.OLS(y, X.astype("float")) results = model.fit() residuals_y = y - results.fittedvalues d_y = list(pd.Series(residuals_y)) # Residuals from the treatment model obtained by fitting a linear model t = self._data[self._treatment_name[0]].astype("int64") X = self._data[observed_variables] model = sm.OLS(t, X) results = model.fit() residuals_t = t - results.fittedvalues d_t = list(pd.Series(residuals_t)) # Initialising product_cor_metric_observed with a really low value as finding maximum product_cor_metric_observed = -10000000000 for i in observed_variables: current_obs_confounder = self._data[i] outcome_values = self._data[self._outcome_name[0]] correlation_y = current_obs_confounder.corr(outcome_values) treatment_values = t correlation_t = current_obs_confounder.corr(treatment_values) product_cor_metric_current = correlation_y * correlation_t if product_cor_metric_current >= product_cor_metric_observed: product_cor_metric_observed = product_cor_metric_current correlation_t_observed = correlation_t correlation_y_observed = correlation_y # The user has an option to give the the effect_strength_on_y and effect_strength_on_t which can be then used instead of maximum correlation with treatment and outcome in the observed variables as it specifies the desired effect. if self.kappa_t is not None: correlation_t_observed = self.kappa_t if self.kappa_y is not None: correlation_y_observed = self.kappa_y # Choosing a c_star based on the data. # The correlations stop increasing upon increasing c_star after a certain value, that is it plateaus and we choose the value of c_star to be the value it plateaus. correlation_y_list = [] correlation_t_list = [] product_cor_metric_simulated_list = [] x_list = [] step = int(c_star_max / 10) for i in range(0, int(c_star_max), step): c1 = math.sqrt(i) c2 = c1 final_U = self.generate_confounder_from_residuals(c1, c2, d_y, d_t, X) current_simulated_confounder = final_U outcome_values = self._data[self._outcome_name[0]] correlation_y = current_simulated_confounder.corr(outcome_values) correlation_y_list.append(correlation_y) treatment_values = t correlation_t = current_simulated_confounder.corr(treatment_values) correlation_t_list.append(correlation_t) product_cor_metric_simulated = correlation_y * correlation_t product_cor_metric_simulated_list.append(product_cor_metric_simulated) x_list.append(i) index = 1 while index < len(correlation_y_list): if (correlation_y_list[index] - correlation_y_list[index - 1]) <= convergence_threshold: c_star = x_list[index] break index = index + 1 # Choosing c1 and c2 based on the hyperbolic relationship once c_star is chosen by going over various combinations of c1 and c2 values and choosing the combination which # which maintains the minimum distance between the product of correlations of the simulated variable and the product of maximum correlations of one of the observed variables # and additionally checks if the ratio of the weights are such that they maintain the ratio of the maximum possible observed coefficients within some confidence interval # c1_final and c2_final are initialised to the values on the hyperbolic curve such that c1_final = c2_final and c1_final*c2_final = c_star c1_final = math.sqrt(c_star) c2_final = math.sqrt(c_star) # initialising min_distance_between_product_cor_metrics to be a value greater than 1 min_distance_between_product_cor_metrics = 1.5 i = 0.05 threshold = c_star / 0.05 while i <= threshold: c2 = i c1 = c_star / c2 final_U = self.generate_confounder_from_residuals(c1, c2, d_y, d_t, X) current_simulated_confounder = final_U outcome_values = self._data[self._outcome_name[0]] correlation_y = current_simulated_confounder.corr(outcome_values) treatment_values = t correlation_t = current_simulated_confounder.corr(treatment_values) product_cor_metric_simulated = correlation_y * correlation_t if min_distance_between_product_cor_metrics >= abs( product_cor_metric_simulated - product_cor_metric_observed ): min_distance_between_product_cor_metrics = abs( product_cor_metric_simulated - product_cor_metric_observed ) additional_condition = correlation_y_observed / correlation_t_observed if ((c1 / c2) <= (additional_condition + 0.3 * additional_condition)) and ( (c1 / c2) >= (additional_condition - 0.3 * additional_condition) ): # choose minimum positive value c1_final = c1 c2_final = c2 i = i * 1.5 """#closed form solution print("c_star_max before closed form", c_star_max) if max_correlation_with_t == -1000: c2 = 0 c1 = c_star_max else: additional_condition = abs(max_correlation_with_y/max_correlation_with_t) print("additional_condition", additional_condition) c2 = math.sqrt(c_star_max/additional_condition) c1 = c_star_max/c2""" final_U = self.generate_confounder_from_residuals(c1_final, c2_final, d_y, d_t, X) return final_U def generate_confounder_from_residuals(self, c1, c2, d_y, d_t, X): """ This function takes the residuals from the treatment and outcome model and their coefficients and simulates the intermediate random variable U by taking the row wise normal distribution corresponding to each residual value and then debiasing the intermediate variable to get the final variable. :param c1: coefficient to the residual from the outcome model :type float :param c2: coefficient to the residual from the treatment model :type float :param d_y: residuals from the outcome model :type list :param d_t: residuals from the treatment model :type list :returns: The simulated values of the unobserved confounder based on the data :type pandas.core.series.Series """ U = [] for j in range(len(d_t)): simulated_variable_mean = c1 * d_y[j] + c2 * d_t[j] simulated_variable_stddev = 1 U.append(np.random.normal(simulated_variable_mean, simulated_variable_stddev, 1)) U = np.array(U) model = sm.OLS(U, X) results = model.fit() U = U.reshape( -1, ) final_U = U - results.fittedvalues.values final_U = pd.Series(U) return final_U

import copy import logging import math import numpy as np import pandas as pd import scipy.stats import statsmodels.api as sm from sklearn.linear_model import LogisticRegression from sklearn.preprocessing import StandardScaler from tqdm.auto import tqdm import dowhy.causal_estimators.econml from dowhy.causal_estimator import CausalEstimator from dowhy.causal_estimators.linear_regression_estimator import LinearRegressionEstimator from dowhy.causal_refuter import CausalRefutation, CausalRefuter from dowhy.causal_refuters.linear_sensitivity_analyzer import LinearSensitivityAnalyzer from dowhy.causal_refuters.non_parametric_sensitivity_analyzer import NonParametricSensitivityAnalyzer from dowhy.causal_refuters.partial_linear_sensitivity_analyzer import PartialLinearSensitivityAnalyzer class AddUnobservedCommonCause(CausalRefuter): """Add an unobserved confounder for refutation. AddUnobservedCommonCause class supports three methods: 1) Simulation of an unobserved confounder 2) Linear partial R2 : Sensitivity Analysis for linear models. 3) Non-Parametric partial R2 based : Sensitivity Analyis for non-parametric models. Supports additional parameters that can be specified in the refute_estimate() method. """ def __init__(self, *args, **kwargs): """ Initialize the parameters required for the refuter. For direct_simulation, if effect_strength_on_treatment or effect_strength_on_outcome is not given, it is calculated automatically as a range between the minimum and maximum effect strength of observed confounders on treatment and outcome respectively. :param simulation_method: The method to use for simulating effect of unobserved confounder. Possible values are ["direct-simulation", "linear-partial-R2", "non-parametric-partial-R2"]. :param confounders_effect_on_treatment: str : The type of effect on the treatment due to the unobserved confounder. Possible values are ['binary_flip', 'linear'] :param confounders_effect_on_outcome: str : The type of effect on the outcome due to the unobserved confounder. Possible values are ['binary_flip', 'linear'] :param effect_strength_on_treatment: float, numpy.ndarray: [Used when simulation_method="direct-simulation"] Strength of the confounder's effect on treatment. When confounders_effect_on_treatment is linear, it is the regression coefficient. When the confounders_effect_on_treatment is binary flip, it is the probability with which effect of unobserved confounder can invert the value of the treatment. :param effect_strength_on_outcome: float, numpy.ndarray: Strength of the confounder's effect on outcome. Its interpretation depends on confounders_effect_on_outcome and the simulation_method. When simulation_method is direct-simulation, for a linear effect it behaves like the regression coefficient and for a binary flip, it is the probability with which it can invert the value of the outcome. :param partial_r2_confounder_treatment: float, numpy.ndarray: [Used when simulation_method is linear-partial-R2 or non-parametric-partial-R2] Partial R2 of the unobserved confounder wrt the treatment conditioned on the observed confounders. Only in the case of general non-parametric-partial-R2, it is the fraction of variance in the reisz representer that is explained by the unobserved confounder; specifically (1-r), where r is the ratio of variance of reisz representer, alpha^2, based on observed confounders and that based on all confounders. :param partial_r2_confounder_outcome: float, numpy.ndarray: [Used when simulation_method is linear-partial-R2 or non-parametric-partial-R2] Partial R2 of the unobserved confounder wrt the outcome conditioned on the treatment and observed confounders. :param frac_strength_treatment: float: This parameter decides the effect strength of the simulated confounder as a fraction of the effect strength of observed confounders on treatment. Defaults to 1. :param frac_strength_outcome: float: This parameter decides the effect strength of the simulated confounder as a fraction of the effect strength of observed confounders on outcome. Defaults to 1. :param plotmethod: string: Type of plot to be shown. If None, no plot is generated. This parameter is used only only when more than one treatment confounder effect values or outcome confounder effect values are provided. Default is "colormesh". Supported values are "contour", "colormesh" when more than one value is provided for both confounder effect value parameters; "line" when provided for only one of them. :param percent_change_estimate: It is the percentage of reduction of treatment estimate that could alter the results (default = 1). if percent_change_estimate = 1, the robustness value describes the strength of association of confounders with treatment and outcome in order to reduce the estimate by 100% i.e bring it down to 0. (relevant only for Linear Sensitivity Analysis, ignore for rest) :param confounder_increases_estimate: True implies that confounder increases the absolute value of estimate and vice versa. (Default = False). (relevant only for Linear Sensitivity Analysis, ignore for rest) :param benchmark_common_causes: names of variables for bounding strength of confounders. (relevant only for partial-r2 based simulation methods) :param significance_level: confidence interval for statistical inference(default = 0.05). (relevant only for partial-r2 based simulation methods) :param null_hypothesis_effect: assumed effect under the null hypothesis. (relevant only for linear-partial-R2, ignore for rest) :param plot_estimate: Generate contour plot for estimate while performing sensitivity analysis. (default = True). (relevant only for partial-r2 based simulation methods) :param num_splits: number of splits for cross validation. (default = 5). (relevant only for non-parametric-partial-R2 simulation method) :param shuffle_data : shuffle data or not before splitting into folds (default = False). (relevant only for non-parametric-partial-R2 simulation method) :param shuffle_random_seed: seed for randomly shuffling data. (relevant only for non-parametric-partial-R2 simulation method) :param alpha_s_estimator_param_list: list of dictionaries with parameters for finding alpha_s. (relevant only for non-parametric-partial-R2 simulation method) :param g_s_estimator_list: list of estimator objects for finding g_s. These objects should have fit() and predict() functions implemented. (relevant only for non-parametric-partial-R2 simulation method) :param g_s_estimator_param_list: list of dictionaries with parameters for tuning respective estimators in "g_s_estimator_list". The order of the dictionaries in the list should be consistent with the estimator objects order in "g_s_estimator_list". (relevant only for non-parametric-partial-R2 simulation method) """ super().__init__(*args, **kwargs) self.simulation_method = kwargs["simulation_method"] if "simulation_method" in kwargs else "direct-simulation" self.effect_on_t = ( kwargs["confounders_effect_on_treatment"] if "confounders_effect_on_treatment" in kwargs else "binary_flip" ) self.effect_on_y = ( kwargs["confounders_effect_on_outcome"] if "confounders_effect_on_outcome" in kwargs else "linear" ) if self.simulation_method == "direct-simulation": self.kappa_t = kwargs["effect_strength_on_treatment"] if "effect_strength_on_treatment" in kwargs else None self.kappa_y = kwargs["effect_strength_on_outcome"] if "effect_strength_on_outcome" in kwargs else None elif self.simulation_method in ["linear-partial-R2", "non-parametric-partial-R2"]: self.kappa_t = ( kwargs["partial_r2_confounder_treatment"] if "partial_r2_confounder_treatment" in kwargs else None ) self.kappa_y = ( kwargs["partial_r2_confounder_outcome"] if "partial_r2_confounder_outcome" in kwargs else None ) else: raise ValueError( "simulation method is not supported. Try direct-simulation, linear-partial-R2 or non-parametric-partial-R2" ) self.frac_strength_treatment = ( kwargs["effect_fraction_on_treatment"] if "effect_fraction_on_treatment" in kwargs else 1 ) self.frac_strength_outcome = ( kwargs["effect_fraction_on_outcome"] if "effect_fraction_on_outcome" in kwargs else 1 ) self.plotmethod = kwargs["plotmethod"] if "plotmethod" in kwargs else "colormesh" self.percent_change_estimate = kwargs["percent_change_estimate"] if "percent_change_estimate" in kwargs else 1.0 self.significance_level = kwargs["significance_level"] if "significance_level" in kwargs else 0.05 self.confounder_increases_estimate = ( kwargs["confounder_increases_estimate"] if "confounder_increases_estimate" in kwargs else False ) self.benchmark_common_causes = ( kwargs["benchmark_common_causes"] if "benchmark_common_causes" in kwargs else None ) self.null_hypothesis_effect = kwargs["null_hypothesis_effect"] if "null_hypothesis_effect" in kwargs else 0 self.plot_estimate = kwargs["plot_estimate"] if "plot_estimate" in kwargs else True self.num_splits = kwargs["num_splits"] if "num_splits" in kwargs else 5 self.shuffle_data = kwargs["shuffle_data"] if "shuffle_data" in kwargs else False self.shuffle_random_seed = kwargs["shuffle_random_seed"] if "shuffle_random_seed" in kwargs else None self.alpha_s_estimator_param_list = ( kwargs["alpha_s_estimator_param_list"] if "alpha_s_estimator_param_list" in kwargs else None ) self.alpha_s_estimator_list = kwargs["alpha_s_estimator_list"] if "alpha_s_estimator_list" in kwargs else None self.g_s_estimator_list = kwargs["g_s_estimator_list"] if "g_s_estimator_list" in kwargs else None self.g_s_estimator_param_list = ( kwargs["g_s_estimator_param_list"] if "g_s_estimator_param_list" in kwargs else None ) self.plugin_reisz = kwargs["plugin_reisz"] if "plugin_reisz" in kwargs else False self.logger = logging.getLogger(__name__) def infer_default_kappa_t(self, len_kappa_t=10): """Infer default effect strength of simulated confounder on treatment.""" observed_common_causes_names = self._target_estimand.get_backdoor_variables() if len(observed_common_causes_names) > 0: observed_common_causes = self._data[observed_common_causes_names] observed_common_causes = pd.get_dummies(observed_common_causes, drop_first=True) else: raise ValueError( "There needs to be at least one common cause to" + "automatically compute the default value of kappa_t." + " Provide a value for kappa_t" ) t = self._data[self._treatment_name] # Standardizing the data observed_common_causes = StandardScaler().fit_transform(observed_common_causes) if self.effect_on_t == "binary_flip": # Fit a model containing all confounders and compare predictions # using all features compared to all features except a given # confounder. tmodel = LogisticRegression().fit(observed_common_causes, t) tpred = tmodel.predict(observed_common_causes).astype(int) flips = [] for i in range(observed_common_causes.shape[1]): oldval = np.copy(observed_common_causes[:, i]) observed_common_causes[:, i] = 0 tcap = tmodel.predict(observed_common_causes).astype(int) observed_common_causes[:, i] = oldval flips.append(np.sum(abs(tcap - tpred)) / tpred.shape[0]) min_coeff, max_coeff = min(flips), max(flips) elif self.effect_on_t == "linear": # Estimating the regression coefficient from standardized features to t corrcoef_var_t = np.corrcoef(observed_common_causes, t, rowvar=False)[-1, :-1] std_dev_t = np.std(t)[0] max_coeff = max(corrcoef_var_t) * std_dev_t min_coeff = min(corrcoef_var_t) * std_dev_t else: raise NotImplementedError( "'" + self.effect_on_t + "' method not supported for confounders' effect on treatment" ) min_coeff, max_coeff = self._compute_min_max_coeff(min_coeff, max_coeff, self.frac_strength_treatment) # By default, return a plot with 10 points # consider 10 values of the effect of the unobserved confounder step = (max_coeff - min_coeff) / len_kappa_t self.logger.info("(Min, Max) kappa_t for observed common causes, ({0}, {1})".format(min_coeff, max_coeff)) if np.equal(max_coeff, min_coeff): return max_coeff else: return np.arange(min_coeff, max_coeff, step) def _compute_min_max_coeff(self, min_coeff, max_coeff, effect_strength_fraction): max_coeff = effect_strength_fraction * max_coeff min_coeff = effect_strength_fraction * min_coeff return min_coeff, max_coeff def infer_default_kappa_y(self, len_kappa_y=10): """Infer default effect strength of simulated confounder on treatment.""" observed_common_causes_names = self._target_estimand.get_backdoor_variables() if len(observed_common_causes_names) > 0: observed_common_causes = self._data[observed_common_causes_names] observed_common_causes = pd.get_dummies(observed_common_causes, drop_first=True) else: raise ValueError( "There needs to be at least one common cause to" + "automatically compute the default value of kappa_y." + " Provide a value for kappa_y" ) y = self._data[self._outcome_name] # Standardizing the data observed_common_causes = StandardScaler().fit_transform(observed_common_causes) if self.effect_on_y == "binary_flip": # Fit a model containing all confounders and compare predictions # using all features compared to all features except a given # confounder. ymodel = LogisticRegression().fit(observed_common_causes, y) ypred = ymodel.predict(observed_common_causes).astype(int) flips = [] for i in range(observed_common_causes.shape[1]): oldval = np.copy(observed_common_causes[:, i]) observed_common_causes[:, i] = 0 ycap = ymodel.predict(observed_common_causes).astype(int) observed_common_causes[:, i] = oldval flips.append(np.sum(abs(ycap - ypred)) / ypred.shape[0]) min_coeff, max_coeff = min(flips), max(flips) elif self.effect_on_y == "linear": corrcoef_var_y = np.corrcoef(observed_common_causes, y, rowvar=False)[-1, :-1] std_dev_y = np.std(y)[0] max_coeff = max(corrcoef_var_y) * std_dev_y min_coeff = min(corrcoef_var_y) * std_dev_y else: raise NotImplementedError( "'" + self.effect_on_y + "' method not supported for confounders' effect on outcome" ) min_coeff, max_coeff = self._compute_min_max_coeff(min_coeff, max_coeff, self.frac_strength_outcome) # By default, return a plot with 10 points # consider 10 values of the effect of the unobserved confounder step = (max_coeff - min_coeff) / len_kappa_y self.logger.info("(Min, Max) kappa_y for observed common causes, ({0}, {1})".format(min_coeff, max_coeff)) if np.equal(max_coeff, min_coeff): return max_coeff else: return np.arange(min_coeff, max_coeff, step) def refute_estimate(self, show_progress_bar=False): """ This function attempts to add an unobserved common cause to the outcome and the treatment. At present, we have implemented the behavior for one dimensional behaviors for continuous and binary variables. This function can either take single valued inputs or a range of inputs. The function then looks at the data type of the input and then decides on the course of action. :return: CausalRefuter: An object that contains the estimated effect and a new effect and the name of the refutation used. """ if self.simulation_method == "linear-partial-R2": if not (isinstance(self._estimate.estimator, LinearRegressionEstimator)): raise NotImplementedError( "Currently only LinearRegressionEstimator is supported for Sensitivity Analysis" ) if len(self._estimate.estimator._effect_modifier_names) > 0: raise NotImplementedError("The current implementation does not support effect modifiers") if self.frac_strength_outcome == 1: self.frac_strength_outcome = self.frac_strength_treatment analyzer = LinearSensitivityAnalyzer( estimator=self._estimate.estimator, data=self._data, treatment_name=self._treatment_name, percent_change_estimate=self.percent_change_estimate, significance_level=self.significance_level, benchmark_common_causes=self.benchmark_common_causes, null_hypothesis_effect=self.null_hypothesis_effect, frac_strength_treatment=self.frac_strength_treatment, frac_strength_outcome=self.frac_strength_outcome, common_causes_order=self._estimate.estimator._observed_common_causes.columns, ) analyzer.check_sensitivity(plot=self.plot_estimate) return analyzer if self.simulation_method == "non-parametric-partial-R2": # If the estimator used is LinearDML, partially linear sensitivity analysis will be automatically chosen if isinstance(self._estimate.estimator, dowhy.causal_estimators.econml.Econml): if self._estimate.estimator._econml_methodname == "econml.dml.LinearDML": analyzer = PartialLinearSensitivityAnalyzer( estimator=self._estimate._estimator_object, observed_common_causes=self._estimate.estimator._observed_common_causes, treatment=self._estimate.estimator._treatment, outcome=self._estimate.estimator._outcome, alpha_s_estimator_param_list=self.alpha_s_estimator_param_list, g_s_estimator_list=self.g_s_estimator_list, g_s_estimator_param_list=self.g_s_estimator_param_list, effect_strength_treatment=self.kappa_t, effect_strength_outcome=self.kappa_y, benchmark_common_causes=self.benchmark_common_causes, frac_strength_treatment=self.frac_strength_treatment, frac_strength_outcome=self.frac_strength_outcome, ) analyzer.check_sensitivity(plot=self.plot_estimate) return analyzer analyzer = NonParametricSensitivityAnalyzer( estimator=self._estimate.estimator, observed_common_causes=self._estimate.estimator._observed_common_causes, treatment=self._estimate.estimator._treatment, outcome=self._estimate.estimator._outcome, alpha_s_estimator_list=self.alpha_s_estimator_list, alpha_s_estimator_param_list=self.alpha_s_estimator_param_list, g_s_estimator_list=self.g_s_estimator_list, g_s_estimator_param_list=self.g_s_estimator_param_list, effect_strength_treatment=self.kappa_t, effect_strength_outcome=self.kappa_y, benchmark_common_causes=self.benchmark_common_causes, frac_strength_treatment=self.frac_strength_treatment, frac_strength_outcome=self.frac_strength_outcome, theta_s=self._estimate.value, plugin_reisz=self.plugin_reisz, ) analyzer.check_sensitivity(plot=self.plot_estimate) return analyzer if self.kappa_t is None: self.kappa_t = self.infer_default_kappa_t() if self.kappa_y is None: self.kappa_y = self.infer_default_kappa_y() if not isinstance(self.kappa_t, (list, np.ndarray)) and not isinstance( self.kappa_y, (list, np.ndarray) ): # Deal with single value inputs new_data = copy.deepcopy(self._data) new_data = self.include_confounders_effect(new_data, self.kappa_t, self.kappa_y) new_estimator = CausalEstimator.get_estimator_object(new_data, self._target_estimand, self._estimate) new_effect = new_estimator.estimate_effect() refute = CausalRefutation( self._estimate.value, new_effect.value, refutation_type="Refute: Add an Unobserved Common Cause" ) refute.new_effect_array = np.array(new_effect.value) refute.new_effect = new_effect.value refute.add_refuter(self) return refute else: # Deal with multiple value inputs if isinstance(self.kappa_t, (list, np.ndarray)) and isinstance( self.kappa_y, (list, np.ndarray) ): # Deal with range inputs # Get a 2D matrix of values # x,y = np.meshgrid(self.kappa_t, self.kappa_y) # x,y are both MxN results_matrix = np.random.rand( len(self.kappa_t), len(self.kappa_y) ) # Matrix to hold all the results of NxM orig_data = copy.deepcopy(self._data) for i in tqdm( range(len(self.kappa_t)), colour=CausalRefuter.PROGRESS_BAR_COLOR, disable=not show_progress_bar, desc="Refuting Estimates: ", ): for j in range(len(self.kappa_y)): new_data = self.include_confounders_effect(orig_data, self.kappa_t[i], self.kappa_y[j]) new_estimator = CausalEstimator.get_estimator_object( new_data, self._target_estimand, self._estimate ) new_effect = new_estimator.estimate_effect() refute = CausalRefutation( self._estimate.value, new_effect.value, refutation_type="Refute: Add an Unobserved Common Cause", ) results_matrix[i][j] = refute.new_effect # Populate the results refute.new_effect_array = results_matrix refute.new_effect = (np.min(results_matrix), np.max(results_matrix)) # Store the values into the refute object refute.add_refuter(self) if self.plotmethod is None: return refute import matplotlib import matplotlib.pyplot as plt fig = plt.figure(figsize=(6, 5)) left, bottom, width, height = 0.1, 0.1, 0.8, 0.8 ax = fig.add_axes([left, bottom, width, height]) oe = self._estimate.value contour_levels = [oe / 4.0, oe / 2.0, (3.0 / 4) * oe, oe] contour_levels.extend([0, np.min(results_matrix), np.max(results_matrix)]) if self.plotmethod == "contour": cp = plt.contourf(self.kappa_y, self.kappa_t, results_matrix, levels=sorted(contour_levels)) # Adding a label on the contour line for the original estimate fmt = {} trueeffect_index = np.where(cp.levels == oe)[0][0] fmt[cp.levels[trueeffect_index]] = "Estimated Effect" # Label every other level using strings plt.clabel(cp, [cp.levels[trueeffect_index]], inline=True, fmt=fmt) plt.colorbar(cp) elif self.plotmethod == "colormesh": cp = plt.pcolormesh(self.kappa_y, self.kappa_t, results_matrix, shading="nearest") plt.colorbar(cp, ticks=contour_levels) ax.yaxis.set_ticks(self.kappa_t) ax.xaxis.set_ticks(self.kappa_y) plt.xticks(rotation=45) ax.set_title("Effect of Unobserved Common Cause") ax.set_ylabel("Value of Linear Constant on Treatment") ax.set_xlabel("Value of Linear Constant on Outcome") plt.show() return refute elif isinstance(self.kappa_t, (list, np.ndarray)): outcomes = np.random.rand(len(self.kappa_t)) orig_data = copy.deepcopy(self._data) for i in tqdm( range(0, len(self.kappa_t)), colour=CausalRefuter.PROGRESS_BAR_COLOR, disable=not show_progress_bar, desc="Refuting Estimates: ", ): new_data = self.include_confounders_effect(orig_data, self.kappa_t[i], self.kappa_y) new_estimator = CausalEstimator.get_estimator_object( new_data, self._target_estimand, self._estimate ) new_effect = new_estimator.estimate_effect() refute = CausalRefutation( self._estimate.value, new_effect.value, refutation_type="Refute: Add an Unobserved Common Cause" ) self.logger.debug(refute) outcomes[i] = refute.new_effect # Populate the results refute.new_effect_array = outcomes refute.new_effect = (np.min(outcomes), np.max(outcomes)) refute.add_refuter(self) if self.plotmethod is None: return refute import matplotlib import matplotlib.pyplot as plt fig = plt.figure(figsize=(6, 5)) left, bottom, width, height = 0.1, 0.1, 0.8, 0.8 ax = fig.add_axes([left, bottom, width, height]) plt.plot(self.kappa_t, outcomes) plt.axhline(self._estimate.value, linestyle="--", color="gray") ax.set_title("Effect of Unobserved Common Cause") ax.set_xlabel("Value of Linear Constant on Treatment") ax.set_ylabel("Estimated Effect after adding the common cause") plt.show() return refute elif isinstance(self.kappa_y, (list, np.ndarray)): outcomes = np.random.rand(len(self.kappa_y)) orig_data = copy.deepcopy(self._data) for i in tqdm( range(0, len(self.kappa_y)), colour=CausalRefuter.PROGRESS_BAR_COLOR, disable=not show_progress_bar, desc="Refuting Estimates: ", ): new_data = self.include_confounders_effect(orig_data, self.kappa_t, self.kappa_y[i]) new_estimator = CausalEstimator.get_estimator_object( new_data, self._target_estimand, self._estimate ) new_effect = new_estimator.estimate_effect() refute = CausalRefutation( self._estimate.value, new_effect.value, refutation_type="Refute: Add an Unobserved Common Cause" ) self.logger.debug(refute) outcomes[i] = refute.new_effect # Populate the results refute.new_effect_array = outcomes refute.new_effect = (np.min(outcomes), np.max(outcomes)) refute.add_refuter(self) if self.plotmethod is None: return refute import matplotlib import matplotlib.pyplot as plt fig = plt.figure(figsize=(6, 5)) left, bottom, width, height = 0.1, 0.1, 0.8, 0.8 ax = fig.add_axes([left, bottom, width, height]) plt.plot(self.kappa_y, outcomes) plt.axhline(self._estimate.value, linestyle="--", color="gray") ax.set_title("Effect of Unobserved Common Cause") ax.set_xlabel("Value of Linear Constant on Outcome") ax.set_ylabel("Estimated Effect after adding the common cause") plt.show() return refute def include_confounders_effect(self, new_data, kappa_t, kappa_y): """ This function deals with the change in the value of the data due to the effect of the unobserved confounder. In the case of a binary flip, we flip only if the random number is greater than the threshold set. In the case of a linear effect, we use the variable as the linear regression constant. :param new_data: pandas.DataFrame: The data to be changed due to the effects of the unobserved confounder. :param kappa_t: numpy.float64: The value of the threshold for binary_flip or the value of the regression coefficient for linear effect. :param kappa_y: numpy.float64: The value of the threshold for binary_flip or the value of the regression coefficient for linear effect. :return: pandas.DataFrame: The DataFrame that includes the effects of the unobserved confounder. """ num_rows = self._data.shape[0] stdnorm = scipy.stats.norm() w_random = stdnorm.rvs(num_rows) if self.effect_on_t == "binary_flip": alpha = 2 * kappa_t - 1 if kappa_t >= 0.5 else 1 - 2 * kappa_t interval = stdnorm.interval(alpha) rel_interval = interval[0] if kappa_t >= 0.5 else interval[1] new_data.loc[rel_interval <= w_random, self._treatment_name] = ( 1 - new_data.loc[rel_interval <= w_random, self._treatment_name] ) for tname in self._treatment_name: if pd.api.types.is_bool_dtype(self._data[tname]): new_data = new_data.astype({tname: "bool"}, copy=False) elif self.effect_on_t == "linear": confounder_t_effect = kappa_t * w_random # By default, we add the effect of simulated confounder for treatment. # But subtract it from outcome to create a negative correlation # assuming that the original confounder's effect was positive on both. # This is to remove the effect of the original confounder. new_data[self._treatment_name] = new_data[self._treatment_name].values + np.ndarray( shape=(num_rows, 1), buffer=confounder_t_effect ) else: raise NotImplementedError( "'" + self.effect_on_t + "' method not supported for confounders' effect on treatment" ) if self.effect_on_y == "binary_flip": alpha = 2 * kappa_y - 1 if kappa_y >= 0.5 else 1 - 2 * kappa_y interval = stdnorm.interval(alpha) rel_interval = interval[0] if kappa_y >= 0.5 else interval[1] new_data.loc[rel_interval <= w_random, self._outcome_name] = ( 1 - new_data.loc[rel_interval <= w_random, self._outcome_name] ) for yname in self._outcome_name: if pd.api.types.is_bool_dtype(self._data[yname]): new_data = new_data.astype({yname: "bool"}, copy=False) elif self.effect_on_y == "linear": confounder_y_effect = (-1) * kappa_y * w_random # By default, we add the effect of simulated confounder for treatment. # But subtract it from outcome to create a negative correlation # assuming that the original confounder's effect was positive on both. # This is to remove the effect of the original confounder. new_data[self._outcome_name] = new_data[self._outcome_name].values + np.ndarray( shape=(num_rows, 1), buffer=confounder_y_effect ) else: raise NotImplementedError( "'" + self.effect_on_y + "' method not supported for confounders' effect on outcome" ) return new_data def include_simulated_confounder(self, convergence_threshold=0.1, c_star_max=1000): """ This function simulates an unobserved confounder based on the data using the following steps: 1. It calculates the "residuals" from the treatment and outcome model i.) The outcome model has outcome as the dependent variable and all the observed variables including treatment as independent variables ii.) The treatment model has treatment as the dependent variable and all the observed variables as independent variables. 2. U is an intermediate random variable drawn from the normal distribution with the weighted average of residuals as mean and a unit variance U ~ N(c1*d_y + c2*d_t, 1) where *d_y and d_t are residuals from the treatment and outcome model *c1 and c2 are coefficients to the residuals 3. The final U, which is the simulated unobserved confounder is obtained by debiasing the intermediate variable U by residualising it with X Choosing the coefficients c1 and c2: The coefficients are chosen based on these basic assumptions: 1. There is a hyperbolic relationship satisfying c1*c2 = c_star 2. c_star is chosen from a range of possible values based on the correlation of the obtained simulated variable with outcome and treatment. 3. The product of correlations with treatment and outcome should be at a minimum distance to the maximum correlations with treatment and outcome in any of the observed confounders 4. The ratio of the weights should be such that they maintain the ratio of the maximum possible observed coefficients within some confidence interval :param c_star_max: The maximum possible value for the hyperbolic curve on which the coefficients to the residuals lie. It defaults to 1000 in the code if not specified by the user. :type int :param convergence_threshold: The threshold to check the plateauing of the correlation while selecting a c_star. It defaults to 0.1 in the code if not specified by the user :type float :returns: The simulated values of the unobserved confounder based on the data :type pandas.core.series.Series """ # Obtaining the list of observed variables required_variables = True observed_variables = self.choose_variables(required_variables) observed_variables_with_treatment_and_outcome = observed_variables + self._treatment_name + self._outcome_name # Taking a subset of the dataframe that has only observed variables self._data = self._data[observed_variables_with_treatment_and_outcome] # Residuals from the outcome model obtained by fitting a linear model y = self._data[self._outcome_name[0]] observed_variables_with_treatment = observed_variables + self._treatment_name X = self._data[observed_variables_with_treatment] model = sm.OLS(y, X.astype("float")) results = model.fit() residuals_y = y - results.fittedvalues d_y = list(pd.Series(residuals_y)) # Residuals from the treatment model obtained by fitting a linear model t = self._data[self._treatment_name[0]].astype("int64") X = self._data[observed_variables] model = sm.OLS(t, X) results = model.fit() residuals_t = t - results.fittedvalues d_t = list(pd.Series(residuals_t)) # Initialising product_cor_metric_observed with a really low value as finding maximum product_cor_metric_observed = -10000000000 for i in observed_variables: current_obs_confounder = self._data[i] outcome_values = self._data[self._outcome_name[0]] correlation_y = current_obs_confounder.corr(outcome_values) treatment_values = t correlation_t = current_obs_confounder.corr(treatment_values) product_cor_metric_current = correlation_y * correlation_t if product_cor_metric_current >= product_cor_metric_observed: product_cor_metric_observed = product_cor_metric_current correlation_t_observed = correlation_t correlation_y_observed = correlation_y # The user has an option to give the the effect_strength_on_y and effect_strength_on_t which can be then used instead of maximum correlation with treatment and outcome in the observed variables as it specifies the desired effect. if self.kappa_t is not None: correlation_t_observed = self.kappa_t if self.kappa_y is not None: correlation_y_observed = self.kappa_y # Choosing a c_star based on the data. # The correlations stop increasing upon increasing c_star after a certain value, that is it plateaus and we choose the value of c_star to be the value it plateaus. correlation_y_list = [] correlation_t_list = [] product_cor_metric_simulated_list = [] x_list = [] step = int(c_star_max / 10) for i in range(0, int(c_star_max), step): c1 = math.sqrt(i) c2 = c1 final_U = self.generate_confounder_from_residuals(c1, c2, d_y, d_t, X) current_simulated_confounder = final_U outcome_values = self._data[self._outcome_name[0]] correlation_y = current_simulated_confounder.corr(outcome_values) correlation_y_list.append(correlation_y) treatment_values = t correlation_t = current_simulated_confounder.corr(treatment_values) correlation_t_list.append(correlation_t) product_cor_metric_simulated = correlation_y * correlation_t product_cor_metric_simulated_list.append(product_cor_metric_simulated) x_list.append(i) index = 1 while index < len(correlation_y_list): if (correlation_y_list[index] - correlation_y_list[index - 1]) <= convergence_threshold: c_star = x_list[index] break index = index + 1 # Choosing c1 and c2 based on the hyperbolic relationship once c_star is chosen by going over various combinations of c1 and c2 values and choosing the combination which # which maintains the minimum distance between the product of correlations of the simulated variable and the product of maximum correlations of one of the observed variables # and additionally checks if the ratio of the weights are such that they maintain the ratio of the maximum possible observed coefficients within some confidence interval # c1_final and c2_final are initialised to the values on the hyperbolic curve such that c1_final = c2_final and c1_final*c2_final = c_star c1_final = math.sqrt(c_star) c2_final = math.sqrt(c_star) # initialising min_distance_between_product_cor_metrics to be a value greater than 1 min_distance_between_product_cor_metrics = 1.5 i = 0.05 threshold = c_star / 0.05 while i <= threshold: c2 = i c1 = c_star / c2 final_U = self.generate_confounder_from_residuals(c1, c2, d_y, d_t, X) current_simulated_confounder = final_U outcome_values = self._data[self._outcome_name[0]] correlation_y = current_simulated_confounder.corr(outcome_values) treatment_values = t correlation_t = current_simulated_confounder.corr(treatment_values) product_cor_metric_simulated = correlation_y * correlation_t if min_distance_between_product_cor_metrics >= abs( product_cor_metric_simulated - product_cor_metric_observed ): min_distance_between_product_cor_metrics = abs( product_cor_metric_simulated - product_cor_metric_observed ) additional_condition = correlation_y_observed / correlation_t_observed if ((c1 / c2) <= (additional_condition + 0.3 * additional_condition)) and ( (c1 / c2) >= (additional_condition - 0.3 * additional_condition) ): # choose minimum positive value c1_final = c1 c2_final = c2 i = i * 1.5 """#closed form solution print("c_star_max before closed form", c_star_max) if max_correlation_with_t == -1000: c2 = 0 c1 = c_star_max else: additional_condition = abs(max_correlation_with_y/max_correlation_with_t) print("additional_condition", additional_condition) c2 = math.sqrt(c_star_max/additional_condition) c1 = c_star_max/c2""" final_U = self.generate_confounder_from_residuals(c1_final, c2_final, d_y, d_t, X) return final_U def generate_confounder_from_residuals(self, c1, c2, d_y, d_t, X): """ This function takes the residuals from the treatment and outcome model and their coefficients and simulates the intermediate random variable U by taking the row wise normal distribution corresponding to each residual value and then debiasing the intermediate variable to get the final variable. :param c1: coefficient to the residual from the outcome model :type float :param c2: coefficient to the residual from the treatment model :type float :param d_y: residuals from the outcome model :type list :param d_t: residuals from the treatment model :type list :returns: The simulated values of the unobserved confounder based on the data :type pandas.core.series.Series """ U = [] for j in range(len(d_t)): simulated_variable_mean = c1 * d_y[j] + c2 * d_t[j] simulated_variable_stddev = 1 U.append(np.random.normal(simulated_variable_mean, simulated_variable_stddev, 1)) U = np.array(U) model = sm.OLS(U, X) results = model.fit() U = U.reshape( -1, ) final_U = U - results.fittedvalues.values final_U = pd.Series(U) return final_U

anusha0409

81841c697bd5e80ecf9e731432305f6186666f1f

bb446c333f2256074304b0dec9cb5628d284b542

this is very nice, you can add the description of g, g_s, alpha etc to the notebook also

amit-sharma

py-why/dowhy

Adding Non Linear Sensitivity Analysis

This PR implements the non-parametric sensitivity analysis from Chernozhukov et al. https://arxiv.org/abs/2112.13398 It implements two sensitivity analyzers: 1. For Partial Linear DGPs and estimators like LinearDML 2. For general non-parametric DGPs and estimators like KernelDML. The notebook in this PR provides an introduction on how the sensitivity bounds are calculated for the partial linear case. For the general nonparametric DGPs, we need to estimate a special function called the Reisz representer. For binary treatment, it is exactly the difference in outcome weighted by propensity score. So we provide two options to learn the Reisz representer, 1) plugin_reisz that uses the propensity score; and 2) general estimator that uses a custom loss function. These two are in the file reisz.py. Briefly, the sensitivity bounds depend on two parameters that denote the effect of the unobserved confounder on treatment and outcome. That's why we use the same API as for the `add_unobserved_common_cause` method and add this sensitivity analysis as a possible simulation method="non-parametric-partial-R2". The format of the plots is identical to those from the "linear-partial-r2" simulation method that is already implemented. We provide two modes for the user. 1) User specifies the effect strength parameters themselves, as a range of values. 2) User benchmarks the effect strength parameters as a multiple of the same parameters for the observed common causes. Signed-off-by: anusha <anushaagarwal2000.com>

2022-06-20 14:37:11+00:00

2022-09-16 03:57:26+00:00

dowhy/causal_refuters/add_unobserved_common_cause.py

import copy import logging import math import numpy as np import pandas as pd import scipy.stats import statsmodels.api as sm from sklearn.linear_model import LogisticRegression from sklearn.preprocessing import StandardScaler from tqdm.auto import tqdm from dowhy.causal_estimator import CausalEstimator from dowhy.causal_estimators.linear_regression_estimator import LinearRegressionEstimator from dowhy.causal_refuter import CausalRefutation, CausalRefuter from dowhy.causal_refuters.linear_sensitivity_analyzer import LinearSensitivityAnalyzer class AddUnobservedCommonCause(CausalRefuter): """Add an unobserved confounder for refutation. Supports additional parameters that can be specified in the refute_estimate() method. - 'confounders_effect_on_treatment': how the simulated confounder affects the value of treatment. This can be linear (for continuous treatment) or binary_flip (for binary treatment) - 'confounders_effect_on_outcome': how the simulated confounder affects the value of outcome. This can be linear (for continuous outcome) or binary_flip (for binary outcome) - 'effect_strength_on_treatment': parameter for the strength of the effect of simulated confounder on treatment. For linear effect, it is the regression coeffient. For binary_flip, it is the probability that simulated confounder's effect flips the value of treatment from 0 to 1 (or vice-versa). - 'effect_strength_on_outcome': parameter for the strength of the effect of simulated confounder on outcome. For linear effect, it is the regression coeffient. For binary_flip, it is the probability that simulated confounder's effect flips the value of outcome from 0 to 1 (or vice-versa). TODO: Needs an interpretation module """ def __init__(self, *args, **kwargs): """ Initialize the parameters required for the refuter. If effect_strength_on_treatment or effect_strength_on_outcome is not given, it is calculated automatically as a range between the minimum and maximum effect strength of observed confounders on treatment and outcome respectively. :param confounders_effect_on_treatment: str : The type of effect on the treatment due to the unobserved confounder. Possible values are ['binary_flip', 'linear'] :param confounders_effect_on_outcome: str : The type of effect on the outcome due to the unobserved confounder. Possible values are ['binary_flip', 'linear'] :param effect_strength_on_treatment: float, numpy.ndarray: This refers to the strength of the confounder on treatment. For a linear effect, it behaves like the regression coeffecient. For a binary flip it is the probability with which it can invert the value of the treatment. :param effect_strength_on_outcome: float, numpy.ndarray: This refers to the strength of the confounder on outcome. For a linear effect, it behaves like the regression coefficient. For a binary flip, it is the probability with which it can invert the value of the outcome. :param effect_fraction_on_treatment: float: If effect_strength_on_treatment is not provided, this parameter decides the effect strength of the simulated confounder as a fraction of the effect strength of observed confounders on treatment. Defaults to 1. :param effect_fraction_on_outcome: float: If effect_strength_on_outcome is not provided, this parameter decides the effect strength of the simulated confounder as a fraction of the effect strength of observed confounders on outcome. Defaults to 1. :param plotmethod: string: Type of plot to be shown. If None, no plot is generated. This parameter is used only only when more than one treatment confounder effect values or outcome confounder effect values are provided. Default is "colormesh". Supported values are "contour", "colormesh" when more than one value is provided for both confounder effect value parameters; "line" when provided for only one of them. :param simulated_method_name: method type to add unobserved common cause. "linear-partial-R2" for linear sensitivity analysis :param percent_change_estimate: It is the percentage of reduction of treatment estimate that could alter the results (default = 1) if percent_change_estimate = 1, the robustness value describes the strength of association of confounders with treatment and outcome in order to reduce the estimate by 100% i.e bring it down to 0. :param confounder_increases_estimate: True implies that confounder increases the absolute value of estimate and vice versa. (Default = False) :param benchmark_common_causes: names of variables for bounding strength of confounders :param significance_level: confidence interval for statistical inference(default = 0.05) :param null_hypothesis_effect: assumed effect under the null hypothesis :param plot_estimate: Generate contour plot for estimate while performing sensitivity analysis. (default = True). To override the setting, set plot_estimate = False. """ super().__init__(*args, **kwargs) self.effect_on_t = ( kwargs["confounders_effect_on_treatment"] if "confounders_effect_on_treatment" in kwargs else "binary_flip" ) self.effect_on_y = ( kwargs["confounders_effect_on_outcome"] if "confounders_effect_on_outcome" in kwargs else "linear" ) self.kappa_t = kwargs["effect_strength_on_treatment"] if "effect_strength_on_treatment" in kwargs else None self.kappa_y = kwargs["effect_strength_on_outcome"] if "effect_strength_on_outcome" in kwargs else None self.frac_strength_treatment = ( kwargs["effect_fraction_on_treatment"] if "effect_fraction_on_treatment" in kwargs else 1 ) self.frac_strength_outcome = ( kwargs["effect_fraction_on_outcome"] if "effect_fraction_on_outcome" in kwargs else 1 ) self.simulated_method_name = ( kwargs["simulated_method_name"] if "simulated_method_name" in kwargs else "linear_based" ) self.plotmethod = kwargs["plotmethod"] if "plotmethod" in kwargs else "colormesh" self.percent_change_estimate = kwargs["percent_change_estimate"] if "percent_change_estimate" in kwargs else 1.0 self.significance_level = kwargs["significance_level"] if "significance_level" in kwargs else 0.05 self.confounder_increases_estimate = ( kwargs["confounder_increases_estimate"] if "confounder_increases_estimate" in kwargs else False ) self.benchmark_common_causes = ( kwargs["benchmark_common_causes"] if "benchmark_common_causes" in kwargs else None ) self.null_hypothesis_effect = kwargs["null_hypothesis_effect"] if "null_hypothesis_effect" in kwargs else 0 self.plot_estimate = kwargs["plot_estimate"] if "plot_estimate" in kwargs else True self.logger = logging.getLogger(__name__) def infer_default_kappa_t(self, len_kappa_t=10): """Infer default effect strength of simulated confounder on treatment.""" observed_common_causes_names = self._target_estimand.get_backdoor_variables() if len(observed_common_causes_names) > 0: observed_common_causes = self._data[observed_common_causes_names] observed_common_causes = pd.get_dummies(observed_common_causes, drop_first=True) else: raise ValueError( "There needs to be at least one common cause to" + "automatically compute the default value of kappa_t." + " Provide a value for kappa_t" ) t = self._data[self._treatment_name] # Standardizing the data observed_common_causes = StandardScaler().fit_transform(observed_common_causes) if self.effect_on_t == "binary_flip": # Fit a model containing all confounders and compare predictions # using all features compared to all features except a given # confounder. tmodel = LogisticRegression().fit(observed_common_causes, t) tpred = tmodel.predict(observed_common_causes).astype(int) flips = [] for i in range(observed_common_causes.shape[1]): oldval = np.copy(observed_common_causes[:, i]) observed_common_causes[:, i] = 0 tcap = tmodel.predict(observed_common_causes).astype(int) observed_common_causes[:, i] = oldval flips.append(np.sum(abs(tcap - tpred)) / tpred.shape[0]) min_coeff, max_coeff = min(flips), max(flips) elif self.effect_on_t == "linear": # Estimating the regression coefficient from standardized features to t corrcoef_var_t = np.corrcoef(observed_common_causes, t, rowvar=False)[-1, :-1] std_dev_t = np.std(t)[0] max_coeff = max(corrcoef_var_t) * std_dev_t min_coeff = min(corrcoef_var_t) * std_dev_t else: raise NotImplementedError( "'" + self.effect_on_t + "' method not supported for confounders' effect on treatment" ) min_coeff, max_coeff = self._compute_min_max_coeff(min_coeff, max_coeff, self.frac_strength_treatment) # By default, return a plot with 10 points # consider 10 values of the effect of the unobserved confounder step = (max_coeff - min_coeff) / len_kappa_t self.logger.info("(Min, Max) kappa_t for observed common causes, ({0}, {1})".format(min_coeff, max_coeff)) if np.equal(max_coeff, min_coeff): return max_coeff else: return np.arange(min_coeff, max_coeff, step) def _compute_min_max_coeff(self, min_coeff, max_coeff, effect_strength_fraction): max_coeff = effect_strength_fraction * max_coeff min_coeff = effect_strength_fraction * min_coeff return min_coeff, max_coeff def infer_default_kappa_y(self, len_kappa_y=10): """Infer default effect strength of simulated confounder on treatment.""" observed_common_causes_names = self._target_estimand.get_backdoor_variables() if len(observed_common_causes_names) > 0: observed_common_causes = self._data[observed_common_causes_names] observed_common_causes = pd.get_dummies(observed_common_causes, drop_first=True) else: raise ValueError( "There needs to be at least one common cause to" + "automatically compute the default value of kappa_y." + " Provide a value for kappa_y" ) y = self._data[self._outcome_name] # Standardizing the data observed_common_causes = StandardScaler().fit_transform(observed_common_causes) if self.effect_on_y == "binary_flip": # Fit a model containing all confounders and compare predictions # using all features compared to all features except a given # confounder. ymodel = LogisticRegression().fit(observed_common_causes, y) ypred = ymodel.predict(observed_common_causes).astype(int) flips = [] for i in range(observed_common_causes.shape[1]): oldval = np.copy(observed_common_causes[:, i]) observed_common_causes[:, i] = 0 ycap = ymodel.predict(observed_common_causes).astype(int) observed_common_causes[:, i] = oldval flips.append(np.sum(abs(ycap - ypred)) / ypred.shape[0]) min_coeff, max_coeff = min(flips), max(flips) elif self.effect_on_y == "linear": corrcoef_var_y = np.corrcoef(observed_common_causes, y, rowvar=False)[-1, :-1] std_dev_y = np.std(y)[0] max_coeff = max(corrcoef_var_y) * std_dev_y min_coeff = min(corrcoef_var_y) * std_dev_y else: raise NotImplementedError( "'" + self.effect_on_y + "' method not supported for confounders' effect on outcome" ) min_coeff, max_coeff = self._compute_min_max_coeff(min_coeff, max_coeff, self.frac_strength_outcome) # By default, return a plot with 10 points # consider 10 values of the effect of the unobserved confounder step = (max_coeff - min_coeff) / len_kappa_y self.logger.info("(Min, Max) kappa_y for observed common causes, ({0}, {1})".format(min_coeff, max_coeff)) if np.equal(max_coeff, min_coeff): return max_coeff else: return np.arange(min_coeff, max_coeff, step) def refute_estimate(self, show_progress_bar=False): """ This function attempts to add an unobserved common cause to the outcome and the treatment. At present, we have implemented the behavior for one dimensional behaviors for continuous and binary variables. This function can either take single valued inputs or a range of inputs. The function then looks at the data type of the input and then decides on the course of action. :return: CausalRefuter: An object that contains the estimated effect and a new effect and the name of the refutation used. """ if self.simulated_method_name == "linear-partial-R2": if not (isinstance(self._estimate.estimator, LinearRegressionEstimator)): raise NotImplementedError( "Currently only LinearRegressionEstimator is supported for Sensitivity Analysis" ) if len(self._estimate.estimator._effect_modifier_names) > 0: raise NotImplementedError("The current implementation does not support effect modifiers") if self.frac_strength_outcome == 1: self.frac_strength_outcome = self.frac_strength_treatment analyzer = LinearSensitivityAnalyzer( estimator=self._estimate.estimator, data=self._data, treatment_name=self._treatment_name, percent_change_estimate=self.percent_change_estimate, significance_level=self.significance_level, benchmark_common_causes=self.benchmark_common_causes, null_hypothesis_effect=self.null_hypothesis_effect, frac_strength_treatment=self.frac_strength_treatment, frac_strength_outcome=self.frac_strength_outcome, common_causes_order=self._estimate.estimator._observed_common_causes.columns, ) analyzer.check_sensitivity(plot=self.plot_estimate) return analyzer if self.kappa_t is None: self.kappa_t = self.infer_default_kappa_t() if self.kappa_y is None: self.kappa_y = self.infer_default_kappa_y() if not isinstance(self.kappa_t, (list, np.ndarray)) and not isinstance( self.kappa_y, (list, np.ndarray) ): # Deal with single value inputs new_data = copy.deepcopy(self._data) new_data = self.include_confounders_effect(new_data, self.kappa_t, self.kappa_y) new_estimator = CausalEstimator.get_estimator_object(new_data, self._target_estimand, self._estimate) new_effect = new_estimator.estimate_effect() refute = CausalRefutation( self._estimate.value, new_effect.value, refutation_type="Refute: Add an Unobserved Common Cause" ) refute.new_effect_array = np.array(new_effect.value) refute.new_effect = new_effect.value refute.add_refuter(self) return refute else: # Deal with multiple value inputs if isinstance(self.kappa_t, (list, np.ndarray)) and isinstance( self.kappa_y, (list, np.ndarray) ): # Deal with range inputs # Get a 2D matrix of values # x,y = np.meshgrid(self.kappa_t, self.kappa_y) # x,y are both MxN results_matrix = np.random.rand( len(self.kappa_t), len(self.kappa_y) ) # Matrix to hold all the results of NxM orig_data = copy.deepcopy(self._data) for i in tqdm( range(len(self.kappa_t)), colour=CausalRefuter.PROGRESS_BAR_COLOR, disable=not show_progress_bar, desc="Refuting Estimates: ", ): for j in range(len(self.kappa_y)): new_data = self.include_confounders_effect(orig_data, self.kappa_t[i], self.kappa_y[j]) new_estimator = CausalEstimator.get_estimator_object( new_data, self._target_estimand, self._estimate ) new_effect = new_estimator.estimate_effect() refute = CausalRefutation( self._estimate.value, new_effect.value, refutation_type="Refute: Add an Unobserved Common Cause", ) results_matrix[i][j] = refute.new_effect # Populate the results refute.new_effect_array = results_matrix refute.new_effect = (np.min(results_matrix), np.max(results_matrix)) # Store the values into the refute object refute.add_refuter(self) if self.plotmethod is None: return refute import matplotlib import matplotlib.pyplot as plt fig = plt.figure(figsize=(6, 5)) left, bottom, width, height = 0.1, 0.1, 0.8, 0.8 ax = fig.add_axes([left, bottom, width, height]) oe = self._estimate.value contour_levels = [oe / 4.0, oe / 2.0, (3.0 / 4) * oe, oe] contour_levels.extend([0, np.min(results_matrix), np.max(results_matrix)]) if self.plotmethod == "contour": cp = plt.contourf(self.kappa_y, self.kappa_t, results_matrix, levels=sorted(contour_levels)) # Adding a label on the contour line for the original estimate fmt = {} trueeffect_index = np.where(cp.levels == oe)[0][0] fmt[cp.levels[trueeffect_index]] = "Estimated Effect" # Label every other level using strings plt.clabel(cp, [cp.levels[trueeffect_index]], inline=True, fmt=fmt) plt.colorbar(cp) elif self.plotmethod == "colormesh": cp = plt.pcolormesh(self.kappa_y, self.kappa_t, results_matrix, shading="nearest") plt.colorbar(cp, ticks=contour_levels) ax.yaxis.set_ticks(self.kappa_t) ax.xaxis.set_ticks(self.kappa_y) plt.xticks(rotation=45) ax.set_title("Effect of Unobserved Common Cause") ax.set_ylabel("Value of Linear Constant on Treatment") ax.set_xlabel("Value of Linear Constant on Outcome") plt.show() return refute elif isinstance(self.kappa_t, (list, np.ndarray)): outcomes = np.random.rand(len(self.kappa_t)) orig_data = copy.deepcopy(self._data) for i in tqdm( range(0, len(self.kappa_t)), colour=CausalRefuter.PROGRESS_BAR_COLOR, disable=not show_progress_bar, desc="Refuting Estimates: ", ): new_data = self.include_confounders_effect(orig_data, self.kappa_t[i], self.kappa_y) new_estimator = CausalEstimator.get_estimator_object( new_data, self._target_estimand, self._estimate ) new_effect = new_estimator.estimate_effect() refute = CausalRefutation( self._estimate.value, new_effect.value, refutation_type="Refute: Add an Unobserved Common Cause" ) self.logger.debug(refute) outcomes[i] = refute.new_effect # Populate the results refute.new_effect_array = outcomes refute.new_effect = (np.min(outcomes), np.max(outcomes)) refute.add_refuter(self) if self.plotmethod is None: return refute import matplotlib import matplotlib.pyplot as plt fig = plt.figure(figsize=(6, 5)) left, bottom, width, height = 0.1, 0.1, 0.8, 0.8 ax = fig.add_axes([left, bottom, width, height]) plt.plot(self.kappa_t, outcomes) plt.axhline(self._estimate.value, linestyle="--", color="gray") ax.set_title("Effect of Unobserved Common Cause") ax.set_xlabel("Value of Linear Constant on Treatment") ax.set_ylabel("Estimated Effect after adding the common cause") plt.show() return refute elif isinstance(self.kappa_y, (list, np.ndarray)): outcomes = np.random.rand(len(self.kappa_y)) orig_data = copy.deepcopy(self._data) for i in tqdm( range(0, len(self.kappa_y)), colour=CausalRefuter.PROGRESS_BAR_COLOR, disable=not show_progress_bar, desc="Refuting Estimates: ", ): new_data = self.include_confounders_effect(orig_data, self.kappa_t, self.kappa_y[i]) new_estimator = CausalEstimator.get_estimator_object( new_data, self._target_estimand, self._estimate ) new_effect = new_estimator.estimate_effect() refute = CausalRefutation( self._estimate.value, new_effect.value, refutation_type="Refute: Add an Unobserved Common Cause" ) self.logger.debug(refute) outcomes[i] = refute.new_effect # Populate the results refute.new_effect_array = outcomes refute.new_effect = (np.min(outcomes), np.max(outcomes)) refute.add_refuter(self) if self.plotmethod is None: return refute import matplotlib import matplotlib.pyplot as plt fig = plt.figure(figsize=(6, 5)) left, bottom, width, height = 0.1, 0.1, 0.8, 0.8 ax = fig.add_axes([left, bottom, width, height]) plt.plot(self.kappa_y, outcomes) plt.axhline(self._estimate.value, linestyle="--", color="gray") ax.set_title("Effect of Unobserved Common Cause") ax.set_xlabel("Value of Linear Constant on Outcome") ax.set_ylabel("Estimated Effect after adding the common cause") plt.show() return refute def include_confounders_effect(self, new_data, kappa_t, kappa_y): """ This function deals with the change in the value of the data due to the effect of the unobserved confounder. In the case of a binary flip, we flip only if the random number is greater than the threshold set. In the case of a linear effect, we use the variable as the linear regression constant. :param new_data: pandas.DataFrame: The data to be changed due to the effects of the unobserved confounder. :param kappa_t: numpy.float64: The value of the threshold for binary_flip or the value of the regression coefficient for linear effect. :param kappa_y: numpy.float64: The value of the threshold for binary_flip or the value of the regression coefficient for linear effect. :return: pandas.DataFrame: The DataFrame that includes the effects of the unobserved confounder. """ num_rows = self._data.shape[0] stdnorm = scipy.stats.norm() w_random = stdnorm.rvs(num_rows) if self.effect_on_t == "binary_flip": alpha = 2 * kappa_t - 1 if kappa_t >= 0.5 else 1 - 2 * kappa_t interval = stdnorm.interval(alpha) rel_interval = interval[0] if kappa_t >= 0.5 else interval[1] new_data.loc[rel_interval <= w_random, self._treatment_name] = ( 1 - new_data.loc[rel_interval <= w_random, self._treatment_name] ) for tname in self._treatment_name: if pd.api.types.is_bool_dtype(self._data[tname]): new_data = new_data.astype({tname: "bool"}, copy=False) elif self.effect_on_t == "linear": confounder_t_effect = kappa_t * w_random # By default, we add the effect of simulated confounder for treatment. # But subtract it from outcome to create a negative correlation # assuming that the original confounder's effect was positive on both. # This is to remove the effect of the original confounder. new_data[self._treatment_name] = new_data[self._treatment_name].values + np.ndarray( shape=(num_rows, 1), buffer=confounder_t_effect ) else: raise NotImplementedError( "'" + self.effect_on_t + "' method not supported for confounders' effect on treatment" ) if self.effect_on_y == "binary_flip": alpha = 2 * kappa_y - 1 if kappa_y >= 0.5 else 1 - 2 * kappa_y interval = stdnorm.interval(alpha) rel_interval = interval[0] if kappa_y >= 0.5 else interval[1] new_data.loc[rel_interval <= w_random, self._outcome_name] = ( 1 - new_data.loc[rel_interval <= w_random, self._outcome_name] ) for yname in self._outcome_name: if pd.api.types.is_bool_dtype(self._data[yname]): new_data = new_data.astype({yname: "bool"}, copy=False) elif self.effect_on_y == "linear": confounder_y_effect = (-1) * kappa_y * w_random # By default, we add the effect of simulated confounder for treatment. # But subtract it from outcome to create a negative correlation # assuming that the original confounder's effect was positive on both. # This is to remove the effect of the original confounder. new_data[self._outcome_name] = new_data[self._outcome_name].values + np.ndarray( shape=(num_rows, 1), buffer=confounder_y_effect ) else: raise NotImplementedError( "'" + self.effect_on_y + "' method not supported for confounders' effect on outcome" ) return new_data def include_simulated_confounder(self, convergence_threshold=0.1, c_star_max=1000): """ This function simulates an unobserved confounder based on the data using the following steps: 1. It calculates the "residuals" from the treatment and outcome model i.) The outcome model has outcome as the dependent variable and all the observed variables including treatment as independent variables ii.) The treatment model has treatment as the dependent variable and all the observed variables as independent variables. 2. U is an intermediate random variable drawn from the normal distribution with the weighted average of residuals as mean and a unit variance U ~ N(c1*d_y + c2*d_t, 1) where *d_y and d_t are residuals from the treatment and outcome model *c1 and c2 are coefficients to the residuals 3. The final U, which is the simulated unobserved confounder is obtained by debiasing the intermediate variable U by residualising it with X Choosing the coefficients c1 and c2: The coefficients are chosen based on these basic assumptions: 1. There is a hyperbolic relationship satisfying c1*c2 = c_star 2. c_star is chosen from a range of possible values based on the correlation of the obtained simulated variable with outcome and treatment. 3. The product of correlations with treatment and outcome should be at a minimum distance to the maximum correlations with treatment and outcome in any of the observed confounders 4. The ratio of the weights should be such that they maintain the ratio of the maximum possible observed coefficients within some confidence interval :param c_star_max: The maximum possible value for the hyperbolic curve on which the coefficients to the residuals lie. It defaults to 1000 in the code if not specified by the user. :type int :param convergence_threshold: The threshold to check the plateauing of the correlation while selecting a c_star. It defaults to 0.1 in the code if not specified by the user :type float :returns: The simulated values of the unobserved confounder based on the data :type pandas.core.series.Series """ # Obtaining the list of observed variables required_variables = True observed_variables = self.choose_variables(required_variables) observed_variables_with_treatment_and_outcome = observed_variables + self._treatment_name + self._outcome_name # Taking a subset of the dataframe that has only observed variables self._data = self._data[observed_variables_with_treatment_and_outcome] # Residuals from the outcome model obtained by fitting a linear model y = self._data[self._outcome_name[0]] observed_variables_with_treatment = observed_variables + self._treatment_name X = self._data[observed_variables_with_treatment] model = sm.OLS(y, X.astype("float")) results = model.fit() residuals_y = y - results.fittedvalues d_y = list(pd.Series(residuals_y)) # Residuals from the treatment model obtained by fitting a linear model t = self._data[self._treatment_name[0]].astype("int64") X = self._data[observed_variables] model = sm.OLS(t, X) results = model.fit() residuals_t = t - results.fittedvalues d_t = list(pd.Series(residuals_t)) # Initialising product_cor_metric_observed with a really low value as finding maximum product_cor_metric_observed = -10000000000 for i in observed_variables: current_obs_confounder = self._data[i] outcome_values = self._data[self._outcome_name[0]] correlation_y = current_obs_confounder.corr(outcome_values) treatment_values = t correlation_t = current_obs_confounder.corr(treatment_values) product_cor_metric_current = correlation_y * correlation_t if product_cor_metric_current >= product_cor_metric_observed: product_cor_metric_observed = product_cor_metric_current correlation_t_observed = correlation_t correlation_y_observed = correlation_y # The user has an option to give the the effect_strength_on_y and effect_strength_on_t which can be then used instead of maximum correlation with treatment and outcome in the observed variables as it specifies the desired effect. if self.kappa_t is not None: correlation_t_observed = self.kappa_t if self.kappa_y is not None: correlation_y_observed = self.kappa_y # Choosing a c_star based on the data. # The correlations stop increasing upon increasing c_star after a certain value, that is it plateaus and we choose the value of c_star to be the value it plateaus. correlation_y_list = [] correlation_t_list = [] product_cor_metric_simulated_list = [] x_list = [] step = int(c_star_max / 10) for i in range(0, int(c_star_max), step): c1 = math.sqrt(i) c2 = c1 final_U = self.generate_confounder_from_residuals(c1, c2, d_y, d_t, X) current_simulated_confounder = final_U outcome_values = self._data[self._outcome_name[0]] correlation_y = current_simulated_confounder.corr(outcome_values) correlation_y_list.append(correlation_y) treatment_values = t correlation_t = current_simulated_confounder.corr(treatment_values) correlation_t_list.append(correlation_t) product_cor_metric_simulated = correlation_y * correlation_t product_cor_metric_simulated_list.append(product_cor_metric_simulated) x_list.append(i) index = 1 while index < len(correlation_y_list): if (correlation_y_list[index] - correlation_y_list[index - 1]) <= convergence_threshold: c_star = x_list[index] break index = index + 1 # Choosing c1 and c2 based on the hyperbolic relationship once c_star is chosen by going over various combinations of c1 and c2 values and choosing the combination which # which maintains the minimum distance between the product of correlations of the simulated variable and the product of maximum correlations of one of the observed variables # and additionally checks if the ratio of the weights are such that they maintain the ratio of the maximum possible observed coefficients within some confidence interval # c1_final and c2_final are initialised to the values on the hyperbolic curve such that c1_final = c2_final and c1_final*c2_final = c_star c1_final = math.sqrt(c_star) c2_final = math.sqrt(c_star) # initialising min_distance_between_product_cor_metrics to be a value greater than 1 min_distance_between_product_cor_metrics = 1.5 i = 0.05 threshold = c_star / 0.05 while i <= threshold: c2 = i c1 = c_star / c2 final_U = self.generate_confounder_from_residuals(c1, c2, d_y, d_t, X) current_simulated_confounder = final_U outcome_values = self._data[self._outcome_name[0]] correlation_y = current_simulated_confounder.corr(outcome_values) treatment_values = t correlation_t = current_simulated_confounder.corr(treatment_values) product_cor_metric_simulated = correlation_y * correlation_t if min_distance_between_product_cor_metrics >= abs( product_cor_metric_simulated - product_cor_metric_observed ): min_distance_between_product_cor_metrics = abs( product_cor_metric_simulated - product_cor_metric_observed ) additional_condition = correlation_y_observed / correlation_t_observed if ((c1 / c2) <= (additional_condition + 0.3 * additional_condition)) and ( (c1 / c2) >= (additional_condition - 0.3 * additional_condition) ): # choose minimum positive value c1_final = c1 c2_final = c2 i = i * 1.5 """#closed form solution print("c_star_max before closed form", c_star_max) if max_correlation_with_t == -1000: c2 = 0 c1 = c_star_max else: additional_condition = abs(max_correlation_with_y/max_correlation_with_t) print("additional_condition", additional_condition) c2 = math.sqrt(c_star_max/additional_condition) c1 = c_star_max/c2""" final_U = self.generate_confounder_from_residuals(c1_final, c2_final, d_y, d_t, X) return final_U def generate_confounder_from_residuals(self, c1, c2, d_y, d_t, X): """ This function takes the residuals from the treatment and outcome model and their coefficients and simulates the intermediate random variable U by taking the row wise normal distribution corresponding to each residual value and then debiasing the intermediate variable to get the final variable. :param c1: coefficient to the residual from the outcome model :type float :param c2: coefficient to the residual from the treatment model :type float :param d_y: residuals from the outcome model :type list :param d_t: residuals from the treatment model :type list :returns: The simulated values of the unobserved confounder based on the data :type pandas.core.series.Series """ U = [] for j in range(len(d_t)): simulated_variable_mean = c1 * d_y[j] + c2 * d_t[j] simulated_variable_stddev = 1 U.append(np.random.normal(simulated_variable_mean, simulated_variable_stddev, 1)) U = np.array(U) model = sm.OLS(U, X) results = model.fit() U = U.reshape( -1, ) final_U = U - results.fittedvalues.values final_U = pd.Series(U) return final_U

import copy import logging import math import numpy as np import pandas as pd import scipy.stats import statsmodels.api as sm from sklearn.linear_model import LogisticRegression from sklearn.preprocessing import StandardScaler from tqdm.auto import tqdm import dowhy.causal_estimators.econml from dowhy.causal_estimator import CausalEstimator from dowhy.causal_estimators.linear_regression_estimator import LinearRegressionEstimator from dowhy.causal_refuter import CausalRefutation, CausalRefuter from dowhy.causal_refuters.linear_sensitivity_analyzer import LinearSensitivityAnalyzer from dowhy.causal_refuters.non_parametric_sensitivity_analyzer import NonParametricSensitivityAnalyzer from dowhy.causal_refuters.partial_linear_sensitivity_analyzer import PartialLinearSensitivityAnalyzer class AddUnobservedCommonCause(CausalRefuter): """Add an unobserved confounder for refutation. AddUnobservedCommonCause class supports three methods: 1) Simulation of an unobserved confounder 2) Linear partial R2 : Sensitivity Analysis for linear models. 3) Non-Parametric partial R2 based : Sensitivity Analyis for non-parametric models. Supports additional parameters that can be specified in the refute_estimate() method. """ def __init__(self, *args, **kwargs): """ Initialize the parameters required for the refuter. For direct_simulation, if effect_strength_on_treatment or effect_strength_on_outcome is not given, it is calculated automatically as a range between the minimum and maximum effect strength of observed confounders on treatment and outcome respectively. :param simulation_method: The method to use for simulating effect of unobserved confounder. Possible values are ["direct-simulation", "linear-partial-R2", "non-parametric-partial-R2"]. :param confounders_effect_on_treatment: str : The type of effect on the treatment due to the unobserved confounder. Possible values are ['binary_flip', 'linear'] :param confounders_effect_on_outcome: str : The type of effect on the outcome due to the unobserved confounder. Possible values are ['binary_flip', 'linear'] :param effect_strength_on_treatment: float, numpy.ndarray: [Used when simulation_method="direct-simulation"] Strength of the confounder's effect on treatment. When confounders_effect_on_treatment is linear, it is the regression coefficient. When the confounders_effect_on_treatment is binary flip, it is the probability with which effect of unobserved confounder can invert the value of the treatment. :param effect_strength_on_outcome: float, numpy.ndarray: Strength of the confounder's effect on outcome. Its interpretation depends on confounders_effect_on_outcome and the simulation_method. When simulation_method is direct-simulation, for a linear effect it behaves like the regression coefficient and for a binary flip, it is the probability with which it can invert the value of the outcome. :param partial_r2_confounder_treatment: float, numpy.ndarray: [Used when simulation_method is linear-partial-R2 or non-parametric-partial-R2] Partial R2 of the unobserved confounder wrt the treatment conditioned on the observed confounders. Only in the case of general non-parametric-partial-R2, it is the fraction of variance in the reisz representer that is explained by the unobserved confounder; specifically (1-r), where r is the ratio of variance of reisz representer, alpha^2, based on observed confounders and that based on all confounders. :param partial_r2_confounder_outcome: float, numpy.ndarray: [Used when simulation_method is linear-partial-R2 or non-parametric-partial-R2] Partial R2 of the unobserved confounder wrt the outcome conditioned on the treatment and observed confounders. :param frac_strength_treatment: float: This parameter decides the effect strength of the simulated confounder as a fraction of the effect strength of observed confounders on treatment. Defaults to 1. :param frac_strength_outcome: float: This parameter decides the effect strength of the simulated confounder as a fraction of the effect strength of observed confounders on outcome. Defaults to 1. :param plotmethod: string: Type of plot to be shown. If None, no plot is generated. This parameter is used only only when more than one treatment confounder effect values or outcome confounder effect values are provided. Default is "colormesh". Supported values are "contour", "colormesh" when more than one value is provided for both confounder effect value parameters; "line" when provided for only one of them. :param percent_change_estimate: It is the percentage of reduction of treatment estimate that could alter the results (default = 1). if percent_change_estimate = 1, the robustness value describes the strength of association of confounders with treatment and outcome in order to reduce the estimate by 100% i.e bring it down to 0. (relevant only for Linear Sensitivity Analysis, ignore for rest) :param confounder_increases_estimate: True implies that confounder increases the absolute value of estimate and vice versa. (Default = False). (relevant only for Linear Sensitivity Analysis, ignore for rest) :param benchmark_common_causes: names of variables for bounding strength of confounders. (relevant only for partial-r2 based simulation methods) :param significance_level: confidence interval for statistical inference(default = 0.05). (relevant only for partial-r2 based simulation methods) :param null_hypothesis_effect: assumed effect under the null hypothesis. (relevant only for linear-partial-R2, ignore for rest) :param plot_estimate: Generate contour plot for estimate while performing sensitivity analysis. (default = True). (relevant only for partial-r2 based simulation methods) :param num_splits: number of splits for cross validation. (default = 5). (relevant only for non-parametric-partial-R2 simulation method) :param shuffle_data : shuffle data or not before splitting into folds (default = False). (relevant only for non-parametric-partial-R2 simulation method) :param shuffle_random_seed: seed for randomly shuffling data. (relevant only for non-parametric-partial-R2 simulation method) :param alpha_s_estimator_param_list: list of dictionaries with parameters for finding alpha_s. (relevant only for non-parametric-partial-R2 simulation method) :param g_s_estimator_list: list of estimator objects for finding g_s. These objects should have fit() and predict() functions implemented. (relevant only for non-parametric-partial-R2 simulation method) :param g_s_estimator_param_list: list of dictionaries with parameters for tuning respective estimators in "g_s_estimator_list". The order of the dictionaries in the list should be consistent with the estimator objects order in "g_s_estimator_list". (relevant only for non-parametric-partial-R2 simulation method) """ super().__init__(*args, **kwargs) self.simulation_method = kwargs["simulation_method"] if "simulation_method" in kwargs else "direct-simulation" self.effect_on_t = ( kwargs["confounders_effect_on_treatment"] if "confounders_effect_on_treatment" in kwargs else "binary_flip" ) self.effect_on_y = ( kwargs["confounders_effect_on_outcome"] if "confounders_effect_on_outcome" in kwargs else "linear" ) if self.simulation_method == "direct-simulation": self.kappa_t = kwargs["effect_strength_on_treatment"] if "effect_strength_on_treatment" in kwargs else None self.kappa_y = kwargs["effect_strength_on_outcome"] if "effect_strength_on_outcome" in kwargs else None elif self.simulation_method in ["linear-partial-R2", "non-parametric-partial-R2"]: self.kappa_t = ( kwargs["partial_r2_confounder_treatment"] if "partial_r2_confounder_treatment" in kwargs else None ) self.kappa_y = ( kwargs["partial_r2_confounder_outcome"] if "partial_r2_confounder_outcome" in kwargs else None ) else: raise ValueError( "simulation method is not supported. Try direct-simulation, linear-partial-R2 or non-parametric-partial-R2" ) self.frac_strength_treatment = ( kwargs["effect_fraction_on_treatment"] if "effect_fraction_on_treatment" in kwargs else 1 ) self.frac_strength_outcome = ( kwargs["effect_fraction_on_outcome"] if "effect_fraction_on_outcome" in kwargs else 1 ) self.plotmethod = kwargs["plotmethod"] if "plotmethod" in kwargs else "colormesh" self.percent_change_estimate = kwargs["percent_change_estimate"] if "percent_change_estimate" in kwargs else 1.0 self.significance_level = kwargs["significance_level"] if "significance_level" in kwargs else 0.05 self.confounder_increases_estimate = ( kwargs["confounder_increases_estimate"] if "confounder_increases_estimate" in kwargs else False ) self.benchmark_common_causes = ( kwargs["benchmark_common_causes"] if "benchmark_common_causes" in kwargs else None ) self.null_hypothesis_effect = kwargs["null_hypothesis_effect"] if "null_hypothesis_effect" in kwargs else 0 self.plot_estimate = kwargs["plot_estimate"] if "plot_estimate" in kwargs else True self.num_splits = kwargs["num_splits"] if "num_splits" in kwargs else 5 self.shuffle_data = kwargs["shuffle_data"] if "shuffle_data" in kwargs else False self.shuffle_random_seed = kwargs["shuffle_random_seed"] if "shuffle_random_seed" in kwargs else None self.alpha_s_estimator_param_list = ( kwargs["alpha_s_estimator_param_list"] if "alpha_s_estimator_param_list" in kwargs else None ) self.alpha_s_estimator_list = kwargs["alpha_s_estimator_list"] if "alpha_s_estimator_list" in kwargs else None self.g_s_estimator_list = kwargs["g_s_estimator_list"] if "g_s_estimator_list" in kwargs else None self.g_s_estimator_param_list = ( kwargs["g_s_estimator_param_list"] if "g_s_estimator_param_list" in kwargs else None ) self.plugin_reisz = kwargs["plugin_reisz"] if "plugin_reisz" in kwargs else False self.logger = logging.getLogger(__name__) def infer_default_kappa_t(self, len_kappa_t=10): """Infer default effect strength of simulated confounder on treatment.""" observed_common_causes_names = self._target_estimand.get_backdoor_variables() if len(observed_common_causes_names) > 0: observed_common_causes = self._data[observed_common_causes_names] observed_common_causes = pd.get_dummies(observed_common_causes, drop_first=True) else: raise ValueError( "There needs to be at least one common cause to" + "automatically compute the default value of kappa_t." + " Provide a value for kappa_t" ) t = self._data[self._treatment_name] # Standardizing the data observed_common_causes = StandardScaler().fit_transform(observed_common_causes) if self.effect_on_t == "binary_flip": # Fit a model containing all confounders and compare predictions # using all features compared to all features except a given # confounder. tmodel = LogisticRegression().fit(observed_common_causes, t) tpred = tmodel.predict(observed_common_causes).astype(int) flips = [] for i in range(observed_common_causes.shape[1]): oldval = np.copy(observed_common_causes[:, i]) observed_common_causes[:, i] = 0 tcap = tmodel.predict(observed_common_causes).astype(int) observed_common_causes[:, i] = oldval flips.append(np.sum(abs(tcap - tpred)) / tpred.shape[0]) min_coeff, max_coeff = min(flips), max(flips) elif self.effect_on_t == "linear": # Estimating the regression coefficient from standardized features to t corrcoef_var_t = np.corrcoef(observed_common_causes, t, rowvar=False)[-1, :-1] std_dev_t = np.std(t)[0] max_coeff = max(corrcoef_var_t) * std_dev_t min_coeff = min(corrcoef_var_t) * std_dev_t else: raise NotImplementedError( "'" + self.effect_on_t + "' method not supported for confounders' effect on treatment" ) min_coeff, max_coeff = self._compute_min_max_coeff(min_coeff, max_coeff, self.frac_strength_treatment) # By default, return a plot with 10 points # consider 10 values of the effect of the unobserved confounder step = (max_coeff - min_coeff) / len_kappa_t self.logger.info("(Min, Max) kappa_t for observed common causes, ({0}, {1})".format(min_coeff, max_coeff)) if np.equal(max_coeff, min_coeff): return max_coeff else: return np.arange(min_coeff, max_coeff, step) def _compute_min_max_coeff(self, min_coeff, max_coeff, effect_strength_fraction): max_coeff = effect_strength_fraction * max_coeff min_coeff = effect_strength_fraction * min_coeff return min_coeff, max_coeff def infer_default_kappa_y(self, len_kappa_y=10): """Infer default effect strength of simulated confounder on treatment.""" observed_common_causes_names = self._target_estimand.get_backdoor_variables() if len(observed_common_causes_names) > 0: observed_common_causes = self._data[observed_common_causes_names] observed_common_causes = pd.get_dummies(observed_common_causes, drop_first=True) else: raise ValueError( "There needs to be at least one common cause to" + "automatically compute the default value of kappa_y." + " Provide a value for kappa_y" ) y = self._data[self._outcome_name] # Standardizing the data observed_common_causes = StandardScaler().fit_transform(observed_common_causes) if self.effect_on_y == "binary_flip": # Fit a model containing all confounders and compare predictions # using all features compared to all features except a given # confounder. ymodel = LogisticRegression().fit(observed_common_causes, y) ypred = ymodel.predict(observed_common_causes).astype(int) flips = [] for i in range(observed_common_causes.shape[1]): oldval = np.copy(observed_common_causes[:, i]) observed_common_causes[:, i] = 0 ycap = ymodel.predict(observed_common_causes).astype(int) observed_common_causes[:, i] = oldval flips.append(np.sum(abs(ycap - ypred)) / ypred.shape[0]) min_coeff, max_coeff = min(flips), max(flips) elif self.effect_on_y == "linear": corrcoef_var_y = np.corrcoef(observed_common_causes, y, rowvar=False)[-1, :-1] std_dev_y = np.std(y)[0] max_coeff = max(corrcoef_var_y) * std_dev_y min_coeff = min(corrcoef_var_y) * std_dev_y else: raise NotImplementedError( "'" + self.effect_on_y + "' method not supported for confounders' effect on outcome" ) min_coeff, max_coeff = self._compute_min_max_coeff(min_coeff, max_coeff, self.frac_strength_outcome) # By default, return a plot with 10 points # consider 10 values of the effect of the unobserved confounder step = (max_coeff - min_coeff) / len_kappa_y self.logger.info("(Min, Max) kappa_y for observed common causes, ({0}, {1})".format(min_coeff, max_coeff)) if np.equal(max_coeff, min_coeff): return max_coeff else: return np.arange(min_coeff, max_coeff, step) def refute_estimate(self, show_progress_bar=False): """ This function attempts to add an unobserved common cause to the outcome and the treatment. At present, we have implemented the behavior for one dimensional behaviors for continuous and binary variables. This function can either take single valued inputs or a range of inputs. The function then looks at the data type of the input and then decides on the course of action. :return: CausalRefuter: An object that contains the estimated effect and a new effect and the name of the refutation used. """ if self.simulation_method == "linear-partial-R2": if not (isinstance(self._estimate.estimator, LinearRegressionEstimator)): raise NotImplementedError( "Currently only LinearRegressionEstimator is supported for Sensitivity Analysis" ) if len(self._estimate.estimator._effect_modifier_names) > 0: raise NotImplementedError("The current implementation does not support effect modifiers") if self.frac_strength_outcome == 1: self.frac_strength_outcome = self.frac_strength_treatment analyzer = LinearSensitivityAnalyzer( estimator=self._estimate.estimator, data=self._data, treatment_name=self._treatment_name, percent_change_estimate=self.percent_change_estimate, significance_level=self.significance_level, benchmark_common_causes=self.benchmark_common_causes, null_hypothesis_effect=self.null_hypothesis_effect, frac_strength_treatment=self.frac_strength_treatment, frac_strength_outcome=self.frac_strength_outcome, common_causes_order=self._estimate.estimator._observed_common_causes.columns, ) analyzer.check_sensitivity(plot=self.plot_estimate) return analyzer if self.simulation_method == "non-parametric-partial-R2": # If the estimator used is LinearDML, partially linear sensitivity analysis will be automatically chosen if isinstance(self._estimate.estimator, dowhy.causal_estimators.econml.Econml): if self._estimate.estimator._econml_methodname == "econml.dml.LinearDML": analyzer = PartialLinearSensitivityAnalyzer( estimator=self._estimate._estimator_object, observed_common_causes=self._estimate.estimator._observed_common_causes, treatment=self._estimate.estimator._treatment, outcome=self._estimate.estimator._outcome, alpha_s_estimator_param_list=self.alpha_s_estimator_param_list, g_s_estimator_list=self.g_s_estimator_list, g_s_estimator_param_list=self.g_s_estimator_param_list, effect_strength_treatment=self.kappa_t, effect_strength_outcome=self.kappa_y, benchmark_common_causes=self.benchmark_common_causes, frac_strength_treatment=self.frac_strength_treatment, frac_strength_outcome=self.frac_strength_outcome, ) analyzer.check_sensitivity(plot=self.plot_estimate) return analyzer analyzer = NonParametricSensitivityAnalyzer( estimator=self._estimate.estimator, observed_common_causes=self._estimate.estimator._observed_common_causes, treatment=self._estimate.estimator._treatment, outcome=self._estimate.estimator._outcome, alpha_s_estimator_list=self.alpha_s_estimator_list, alpha_s_estimator_param_list=self.alpha_s_estimator_param_list, g_s_estimator_list=self.g_s_estimator_list, g_s_estimator_param_list=self.g_s_estimator_param_list, effect_strength_treatment=self.kappa_t, effect_strength_outcome=self.kappa_y, benchmark_common_causes=self.benchmark_common_causes, frac_strength_treatment=self.frac_strength_treatment, frac_strength_outcome=self.frac_strength_outcome, theta_s=self._estimate.value, plugin_reisz=self.plugin_reisz, ) analyzer.check_sensitivity(plot=self.plot_estimate) return analyzer if self.kappa_t is None: self.kappa_t = self.infer_default_kappa_t() if self.kappa_y is None: self.kappa_y = self.infer_default_kappa_y() if not isinstance(self.kappa_t, (list, np.ndarray)) and not isinstance( self.kappa_y, (list, np.ndarray) ): # Deal with single value inputs new_data = copy.deepcopy(self._data) new_data = self.include_confounders_effect(new_data, self.kappa_t, self.kappa_y) new_estimator = CausalEstimator.get_estimator_object(new_data, self._target_estimand, self._estimate) new_effect = new_estimator.estimate_effect() refute = CausalRefutation( self._estimate.value, new_effect.value, refutation_type="Refute: Add an Unobserved Common Cause" ) refute.new_effect_array = np.array(new_effect.value) refute.new_effect = new_effect.value refute.add_refuter(self) return refute else: # Deal with multiple value inputs if isinstance(self.kappa_t, (list, np.ndarray)) and isinstance( self.kappa_y, (list, np.ndarray) ): # Deal with range inputs # Get a 2D matrix of values # x,y = np.meshgrid(self.kappa_t, self.kappa_y) # x,y are both MxN results_matrix = np.random.rand( len(self.kappa_t), len(self.kappa_y) ) # Matrix to hold all the results of NxM orig_data = copy.deepcopy(self._data) for i in tqdm( range(len(self.kappa_t)), colour=CausalRefuter.PROGRESS_BAR_COLOR, disable=not show_progress_bar, desc="Refuting Estimates: ", ): for j in range(len(self.kappa_y)): new_data = self.include_confounders_effect(orig_data, self.kappa_t[i], self.kappa_y[j]) new_estimator = CausalEstimator.get_estimator_object( new_data, self._target_estimand, self._estimate ) new_effect = new_estimator.estimate_effect() refute = CausalRefutation( self._estimate.value, new_effect.value, refutation_type="Refute: Add an Unobserved Common Cause", ) results_matrix[i][j] = refute.new_effect # Populate the results refute.new_effect_array = results_matrix refute.new_effect = (np.min(results_matrix), np.max(results_matrix)) # Store the values into the refute object refute.add_refuter(self) if self.plotmethod is None: return refute import matplotlib import matplotlib.pyplot as plt fig = plt.figure(figsize=(6, 5)) left, bottom, width, height = 0.1, 0.1, 0.8, 0.8 ax = fig.add_axes([left, bottom, width, height]) oe = self._estimate.value contour_levels = [oe / 4.0, oe / 2.0, (3.0 / 4) * oe, oe] contour_levels.extend([0, np.min(results_matrix), np.max(results_matrix)]) if self.plotmethod == "contour": cp = plt.contourf(self.kappa_y, self.kappa_t, results_matrix, levels=sorted(contour_levels)) # Adding a label on the contour line for the original estimate fmt = {} trueeffect_index = np.where(cp.levels == oe)[0][0] fmt[cp.levels[trueeffect_index]] = "Estimated Effect" # Label every other level using strings plt.clabel(cp, [cp.levels[trueeffect_index]], inline=True, fmt=fmt) plt.colorbar(cp) elif self.plotmethod == "colormesh": cp = plt.pcolormesh(self.kappa_y, self.kappa_t, results_matrix, shading="nearest") plt.colorbar(cp, ticks=contour_levels) ax.yaxis.set_ticks(self.kappa_t) ax.xaxis.set_ticks(self.kappa_y) plt.xticks(rotation=45) ax.set_title("Effect of Unobserved Common Cause") ax.set_ylabel("Value of Linear Constant on Treatment") ax.set_xlabel("Value of Linear Constant on Outcome") plt.show() return refute elif isinstance(self.kappa_t, (list, np.ndarray)): outcomes = np.random.rand(len(self.kappa_t)) orig_data = copy.deepcopy(self._data) for i in tqdm( range(0, len(self.kappa_t)), colour=CausalRefuter.PROGRESS_BAR_COLOR, disable=not show_progress_bar, desc="Refuting Estimates: ", ): new_data = self.include_confounders_effect(orig_data, self.kappa_t[i], self.kappa_y) new_estimator = CausalEstimator.get_estimator_object( new_data, self._target_estimand, self._estimate ) new_effect = new_estimator.estimate_effect() refute = CausalRefutation( self._estimate.value, new_effect.value, refutation_type="Refute: Add an Unobserved Common Cause" ) self.logger.debug(refute) outcomes[i] = refute.new_effect # Populate the results refute.new_effect_array = outcomes refute.new_effect = (np.min(outcomes), np.max(outcomes)) refute.add_refuter(self) if self.plotmethod is None: return refute import matplotlib import matplotlib.pyplot as plt fig = plt.figure(figsize=(6, 5)) left, bottom, width, height = 0.1, 0.1, 0.8, 0.8 ax = fig.add_axes([left, bottom, width, height]) plt.plot(self.kappa_t, outcomes) plt.axhline(self._estimate.value, linestyle="--", color="gray") ax.set_title("Effect of Unobserved Common Cause") ax.set_xlabel("Value of Linear Constant on Treatment") ax.set_ylabel("Estimated Effect after adding the common cause") plt.show() return refute elif isinstance(self.kappa_y, (list, np.ndarray)): outcomes = np.random.rand(len(self.kappa_y)) orig_data = copy.deepcopy(self._data) for i in tqdm( range(0, len(self.kappa_y)), colour=CausalRefuter.PROGRESS_BAR_COLOR, disable=not show_progress_bar, desc="Refuting Estimates: ", ): new_data = self.include_confounders_effect(orig_data, self.kappa_t, self.kappa_y[i]) new_estimator = CausalEstimator.get_estimator_object( new_data, self._target_estimand, self._estimate ) new_effect = new_estimator.estimate_effect() refute = CausalRefutation( self._estimate.value, new_effect.value, refutation_type="Refute: Add an Unobserved Common Cause" ) self.logger.debug(refute) outcomes[i] = refute.new_effect # Populate the results refute.new_effect_array = outcomes refute.new_effect = (np.min(outcomes), np.max(outcomes)) refute.add_refuter(self) if self.plotmethod is None: return refute import matplotlib import matplotlib.pyplot as plt fig = plt.figure(figsize=(6, 5)) left, bottom, width, height = 0.1, 0.1, 0.8, 0.8 ax = fig.add_axes([left, bottom, width, height]) plt.plot(self.kappa_y, outcomes) plt.axhline(self._estimate.value, linestyle="--", color="gray") ax.set_title("Effect of Unobserved Common Cause") ax.set_xlabel("Value of Linear Constant on Outcome") ax.set_ylabel("Estimated Effect after adding the common cause") plt.show() return refute def include_confounders_effect(self, new_data, kappa_t, kappa_y): """ This function deals with the change in the value of the data due to the effect of the unobserved confounder. In the case of a binary flip, we flip only if the random number is greater than the threshold set. In the case of a linear effect, we use the variable as the linear regression constant. :param new_data: pandas.DataFrame: The data to be changed due to the effects of the unobserved confounder. :param kappa_t: numpy.float64: The value of the threshold for binary_flip or the value of the regression coefficient for linear effect. :param kappa_y: numpy.float64: The value of the threshold for binary_flip or the value of the regression coefficient for linear effect. :return: pandas.DataFrame: The DataFrame that includes the effects of the unobserved confounder. """ num_rows = self._data.shape[0] stdnorm = scipy.stats.norm() w_random = stdnorm.rvs(num_rows) if self.effect_on_t == "binary_flip": alpha = 2 * kappa_t - 1 if kappa_t >= 0.5 else 1 - 2 * kappa_t interval = stdnorm.interval(alpha) rel_interval = interval[0] if kappa_t >= 0.5 else interval[1] new_data.loc[rel_interval <= w_random, self._treatment_name] = ( 1 - new_data.loc[rel_interval <= w_random, self._treatment_name] ) for tname in self._treatment_name: if pd.api.types.is_bool_dtype(self._data[tname]): new_data = new_data.astype({tname: "bool"}, copy=False) elif self.effect_on_t == "linear": confounder_t_effect = kappa_t * w_random # By default, we add the effect of simulated confounder for treatment. # But subtract it from outcome to create a negative correlation # assuming that the original confounder's effect was positive on both. # This is to remove the effect of the original confounder. new_data[self._treatment_name] = new_data[self._treatment_name].values + np.ndarray( shape=(num_rows, 1), buffer=confounder_t_effect ) else: raise NotImplementedError( "'" + self.effect_on_t + "' method not supported for confounders' effect on treatment" ) if self.effect_on_y == "binary_flip": alpha = 2 * kappa_y - 1 if kappa_y >= 0.5 else 1 - 2 * kappa_y interval = stdnorm.interval(alpha) rel_interval = interval[0] if kappa_y >= 0.5 else interval[1] new_data.loc[rel_interval <= w_random, self._outcome_name] = ( 1 - new_data.loc[rel_interval <= w_random, self._outcome_name] ) for yname in self._outcome_name: if pd.api.types.is_bool_dtype(self._data[yname]): new_data = new_data.astype({yname: "bool"}, copy=False) elif self.effect_on_y == "linear": confounder_y_effect = (-1) * kappa_y * w_random # By default, we add the effect of simulated confounder for treatment. # But subtract it from outcome to create a negative correlation # assuming that the original confounder's effect was positive on both. # This is to remove the effect of the original confounder. new_data[self._outcome_name] = new_data[self._outcome_name].values + np.ndarray( shape=(num_rows, 1), buffer=confounder_y_effect ) else: raise NotImplementedError( "'" + self.effect_on_y + "' method not supported for confounders' effect on outcome" ) return new_data def include_simulated_confounder(self, convergence_threshold=0.1, c_star_max=1000): """ This function simulates an unobserved confounder based on the data using the following steps: 1. It calculates the "residuals" from the treatment and outcome model i.) The outcome model has outcome as the dependent variable and all the observed variables including treatment as independent variables ii.) The treatment model has treatment as the dependent variable and all the observed variables as independent variables. 2. U is an intermediate random variable drawn from the normal distribution with the weighted average of residuals as mean and a unit variance U ~ N(c1*d_y + c2*d_t, 1) where *d_y and d_t are residuals from the treatment and outcome model *c1 and c2 are coefficients to the residuals 3. The final U, which is the simulated unobserved confounder is obtained by debiasing the intermediate variable U by residualising it with X Choosing the coefficients c1 and c2: The coefficients are chosen based on these basic assumptions: 1. There is a hyperbolic relationship satisfying c1*c2 = c_star 2. c_star is chosen from a range of possible values based on the correlation of the obtained simulated variable with outcome and treatment. 3. The product of correlations with treatment and outcome should be at a minimum distance to the maximum correlations with treatment and outcome in any of the observed confounders 4. The ratio of the weights should be such that they maintain the ratio of the maximum possible observed coefficients within some confidence interval :param c_star_max: The maximum possible value for the hyperbolic curve on which the coefficients to the residuals lie. It defaults to 1000 in the code if not specified by the user. :type int :param convergence_threshold: The threshold to check the plateauing of the correlation while selecting a c_star. It defaults to 0.1 in the code if not specified by the user :type float :returns: The simulated values of the unobserved confounder based on the data :type pandas.core.series.Series """ # Obtaining the list of observed variables required_variables = True observed_variables = self.choose_variables(required_variables) observed_variables_with_treatment_and_outcome = observed_variables + self._treatment_name + self._outcome_name # Taking a subset of the dataframe that has only observed variables self._data = self._data[observed_variables_with_treatment_and_outcome] # Residuals from the outcome model obtained by fitting a linear model y = self._data[self._outcome_name[0]] observed_variables_with_treatment = observed_variables + self._treatment_name X = self._data[observed_variables_with_treatment] model = sm.OLS(y, X.astype("float")) results = model.fit() residuals_y = y - results.fittedvalues d_y = list(pd.Series(residuals_y)) # Residuals from the treatment model obtained by fitting a linear model t = self._data[self._treatment_name[0]].astype("int64") X = self._data[observed_variables] model = sm.OLS(t, X) results = model.fit() residuals_t = t - results.fittedvalues d_t = list(pd.Series(residuals_t)) # Initialising product_cor_metric_observed with a really low value as finding maximum product_cor_metric_observed = -10000000000 for i in observed_variables: current_obs_confounder = self._data[i] outcome_values = self._data[self._outcome_name[0]] correlation_y = current_obs_confounder.corr(outcome_values) treatment_values = t correlation_t = current_obs_confounder.corr(treatment_values) product_cor_metric_current = correlation_y * correlation_t if product_cor_metric_current >= product_cor_metric_observed: product_cor_metric_observed = product_cor_metric_current correlation_t_observed = correlation_t correlation_y_observed = correlation_y # The user has an option to give the the effect_strength_on_y and effect_strength_on_t which can be then used instead of maximum correlation with treatment and outcome in the observed variables as it specifies the desired effect. if self.kappa_t is not None: correlation_t_observed = self.kappa_t if self.kappa_y is not None: correlation_y_observed = self.kappa_y # Choosing a c_star based on the data. # The correlations stop increasing upon increasing c_star after a certain value, that is it plateaus and we choose the value of c_star to be the value it plateaus. correlation_y_list = [] correlation_t_list = [] product_cor_metric_simulated_list = [] x_list = [] step = int(c_star_max / 10) for i in range(0, int(c_star_max), step): c1 = math.sqrt(i) c2 = c1 final_U = self.generate_confounder_from_residuals(c1, c2, d_y, d_t, X) current_simulated_confounder = final_U outcome_values = self._data[self._outcome_name[0]] correlation_y = current_simulated_confounder.corr(outcome_values) correlation_y_list.append(correlation_y) treatment_values = t correlation_t = current_simulated_confounder.corr(treatment_values) correlation_t_list.append(correlation_t) product_cor_metric_simulated = correlation_y * correlation_t product_cor_metric_simulated_list.append(product_cor_metric_simulated) x_list.append(i) index = 1 while index < len(correlation_y_list): if (correlation_y_list[index] - correlation_y_list[index - 1]) <= convergence_threshold: c_star = x_list[index] break index = index + 1 # Choosing c1 and c2 based on the hyperbolic relationship once c_star is chosen by going over various combinations of c1 and c2 values and choosing the combination which # which maintains the minimum distance between the product of correlations of the simulated variable and the product of maximum correlations of one of the observed variables # and additionally checks if the ratio of the weights are such that they maintain the ratio of the maximum possible observed coefficients within some confidence interval # c1_final and c2_final are initialised to the values on the hyperbolic curve such that c1_final = c2_final and c1_final*c2_final = c_star c1_final = math.sqrt(c_star) c2_final = math.sqrt(c_star) # initialising min_distance_between_product_cor_metrics to be a value greater than 1 min_distance_between_product_cor_metrics = 1.5 i = 0.05 threshold = c_star / 0.05 while i <= threshold: c2 = i c1 = c_star / c2 final_U = self.generate_confounder_from_residuals(c1, c2, d_y, d_t, X) current_simulated_confounder = final_U outcome_values = self._data[self._outcome_name[0]] correlation_y = current_simulated_confounder.corr(outcome_values) treatment_values = t correlation_t = current_simulated_confounder.corr(treatment_values) product_cor_metric_simulated = correlation_y * correlation_t if min_distance_between_product_cor_metrics >= abs( product_cor_metric_simulated - product_cor_metric_observed ): min_distance_between_product_cor_metrics = abs( product_cor_metric_simulated - product_cor_metric_observed ) additional_condition = correlation_y_observed / correlation_t_observed if ((c1 / c2) <= (additional_condition + 0.3 * additional_condition)) and ( (c1 / c2) >= (additional_condition - 0.3 * additional_condition) ): # choose minimum positive value c1_final = c1 c2_final = c2 i = i * 1.5 """#closed form solution print("c_star_max before closed form", c_star_max) if max_correlation_with_t == -1000: c2 = 0 c1 = c_star_max else: additional_condition = abs(max_correlation_with_y/max_correlation_with_t) print("additional_condition", additional_condition) c2 = math.sqrt(c_star_max/additional_condition) c1 = c_star_max/c2""" final_U = self.generate_confounder_from_residuals(c1_final, c2_final, d_y, d_t, X) return final_U def generate_confounder_from_residuals(self, c1, c2, d_y, d_t, X): """ This function takes the residuals from the treatment and outcome model and their coefficients and simulates the intermediate random variable U by taking the row wise normal distribution corresponding to each residual value and then debiasing the intermediate variable to get the final variable. :param c1: coefficient to the residual from the outcome model :type float :param c2: coefficient to the residual from the treatment model :type float :param d_y: residuals from the outcome model :type list :param d_t: residuals from the treatment model :type list :returns: The simulated values of the unobserved confounder based on the data :type pandas.core.series.Series """ U = [] for j in range(len(d_t)): simulated_variable_mean = c1 * d_y[j] + c2 * d_t[j] simulated_variable_stddev = 1 U.append(np.random.normal(simulated_variable_mean, simulated_variable_stddev, 1)) U = np.array(U) model = sm.OLS(U, X) results = model.fit() U = U.reshape( -1, ) final_U = U - results.fittedvalues.values final_U = pd.Series(U) return final_U

anusha0409

81841c697bd5e80ecf9e731432305f6186666f1f

bb446c333f2256074304b0dec9cb5628d284b542

can be performed --> will be automatically chosen

amit-sharma

py-why/dowhy

Adding Non Linear Sensitivity Analysis

This PR implements the non-parametric sensitivity analysis from Chernozhukov et al. https://arxiv.org/abs/2112.13398 It implements two sensitivity analyzers: 1. For Partial Linear DGPs and estimators like LinearDML 2. For general non-parametric DGPs and estimators like KernelDML. The notebook in this PR provides an introduction on how the sensitivity bounds are calculated for the partial linear case. For the general nonparametric DGPs, we need to estimate a special function called the Reisz representer. For binary treatment, it is exactly the difference in outcome weighted by propensity score. So we provide two options to learn the Reisz representer, 1) plugin_reisz that uses the propensity score; and 2) general estimator that uses a custom loss function. These two are in the file reisz.py. Briefly, the sensitivity bounds depend on two parameters that denote the effect of the unobserved confounder on treatment and outcome. That's why we use the same API as for the `add_unobserved_common_cause` method and add this sensitivity analysis as a possible simulation method="non-parametric-partial-R2". The format of the plots is identical to those from the "linear-partial-r2" simulation method that is already implemented. We provide two modes for the user. 1) User specifies the effect strength parameters themselves, as a range of values. 2) User benchmarks the effect strength parameters as a multiple of the same parameters for the observed common causes. Signed-off-by: anusha <anushaagarwal2000.com>

2022-06-20 14:37:11+00:00

2022-09-16 03:57:26+00:00

dowhy/causal_refuters/add_unobserved_common_cause.py

import copy import logging import math import numpy as np import pandas as pd import scipy.stats import statsmodels.api as sm from sklearn.linear_model import LogisticRegression from sklearn.preprocessing import StandardScaler from tqdm.auto import tqdm from dowhy.causal_estimator import CausalEstimator from dowhy.causal_estimators.linear_regression_estimator import LinearRegressionEstimator from dowhy.causal_refuter import CausalRefutation, CausalRefuter from dowhy.causal_refuters.linear_sensitivity_analyzer import LinearSensitivityAnalyzer class AddUnobservedCommonCause(CausalRefuter): """Add an unobserved confounder for refutation. Supports additional parameters that can be specified in the refute_estimate() method. - 'confounders_effect_on_treatment': how the simulated confounder affects the value of treatment. This can be linear (for continuous treatment) or binary_flip (for binary treatment) - 'confounders_effect_on_outcome': how the simulated confounder affects the value of outcome. This can be linear (for continuous outcome) or binary_flip (for binary outcome) - 'effect_strength_on_treatment': parameter for the strength of the effect of simulated confounder on treatment. For linear effect, it is the regression coeffient. For binary_flip, it is the probability that simulated confounder's effect flips the value of treatment from 0 to 1 (or vice-versa). - 'effect_strength_on_outcome': parameter for the strength of the effect of simulated confounder on outcome. For linear effect, it is the regression coeffient. For binary_flip, it is the probability that simulated confounder's effect flips the value of outcome from 0 to 1 (or vice-versa). TODO: Needs an interpretation module """ def __init__(self, *args, **kwargs): """ Initialize the parameters required for the refuter. If effect_strength_on_treatment or effect_strength_on_outcome is not given, it is calculated automatically as a range between the minimum and maximum effect strength of observed confounders on treatment and outcome respectively. :param confounders_effect_on_treatment: str : The type of effect on the treatment due to the unobserved confounder. Possible values are ['binary_flip', 'linear'] :param confounders_effect_on_outcome: str : The type of effect on the outcome due to the unobserved confounder. Possible values are ['binary_flip', 'linear'] :param effect_strength_on_treatment: float, numpy.ndarray: This refers to the strength of the confounder on treatment. For a linear effect, it behaves like the regression coeffecient. For a binary flip it is the probability with which it can invert the value of the treatment. :param effect_strength_on_outcome: float, numpy.ndarray: This refers to the strength of the confounder on outcome. For a linear effect, it behaves like the regression coefficient. For a binary flip, it is the probability with which it can invert the value of the outcome. :param effect_fraction_on_treatment: float: If effect_strength_on_treatment is not provided, this parameter decides the effect strength of the simulated confounder as a fraction of the effect strength of observed confounders on treatment. Defaults to 1. :param effect_fraction_on_outcome: float: If effect_strength_on_outcome is not provided, this parameter decides the effect strength of the simulated confounder as a fraction of the effect strength of observed confounders on outcome. Defaults to 1. :param plotmethod: string: Type of plot to be shown. If None, no plot is generated. This parameter is used only only when more than one treatment confounder effect values or outcome confounder effect values are provided. Default is "colormesh". Supported values are "contour", "colormesh" when more than one value is provided for both confounder effect value parameters; "line" when provided for only one of them. :param simulated_method_name: method type to add unobserved common cause. "linear-partial-R2" for linear sensitivity analysis :param percent_change_estimate: It is the percentage of reduction of treatment estimate that could alter the results (default = 1) if percent_change_estimate = 1, the robustness value describes the strength of association of confounders with treatment and outcome in order to reduce the estimate by 100% i.e bring it down to 0. :param confounder_increases_estimate: True implies that confounder increases the absolute value of estimate and vice versa. (Default = False) :param benchmark_common_causes: names of variables for bounding strength of confounders :param significance_level: confidence interval for statistical inference(default = 0.05) :param null_hypothesis_effect: assumed effect under the null hypothesis :param plot_estimate: Generate contour plot for estimate while performing sensitivity analysis. (default = True). To override the setting, set plot_estimate = False. """ super().__init__(*args, **kwargs) self.effect_on_t = ( kwargs["confounders_effect_on_treatment"] if "confounders_effect_on_treatment" in kwargs else "binary_flip" ) self.effect_on_y = ( kwargs["confounders_effect_on_outcome"] if "confounders_effect_on_outcome" in kwargs else "linear" ) self.kappa_t = kwargs["effect_strength_on_treatment"] if "effect_strength_on_treatment" in kwargs else None self.kappa_y = kwargs["effect_strength_on_outcome"] if "effect_strength_on_outcome" in kwargs else None self.frac_strength_treatment = ( kwargs["effect_fraction_on_treatment"] if "effect_fraction_on_treatment" in kwargs else 1 ) self.frac_strength_outcome = ( kwargs["effect_fraction_on_outcome"] if "effect_fraction_on_outcome" in kwargs else 1 ) self.simulated_method_name = ( kwargs["simulated_method_name"] if "simulated_method_name" in kwargs else "linear_based" ) self.plotmethod = kwargs["plotmethod"] if "plotmethod" in kwargs else "colormesh" self.percent_change_estimate = kwargs["percent_change_estimate"] if "percent_change_estimate" in kwargs else 1.0 self.significance_level = kwargs["significance_level"] if "significance_level" in kwargs else 0.05 self.confounder_increases_estimate = ( kwargs["confounder_increases_estimate"] if "confounder_increases_estimate" in kwargs else False ) self.benchmark_common_causes = ( kwargs["benchmark_common_causes"] if "benchmark_common_causes" in kwargs else None ) self.null_hypothesis_effect = kwargs["null_hypothesis_effect"] if "null_hypothesis_effect" in kwargs else 0 self.plot_estimate = kwargs["plot_estimate"] if "plot_estimate" in kwargs else True self.logger = logging.getLogger(__name__) def infer_default_kappa_t(self, len_kappa_t=10): """Infer default effect strength of simulated confounder on treatment.""" observed_common_causes_names = self._target_estimand.get_backdoor_variables() if len(observed_common_causes_names) > 0: observed_common_causes = self._data[observed_common_causes_names] observed_common_causes = pd.get_dummies(observed_common_causes, drop_first=True) else: raise ValueError( "There needs to be at least one common cause to" + "automatically compute the default value of kappa_t." + " Provide a value for kappa_t" ) t = self._data[self._treatment_name] # Standardizing the data observed_common_causes = StandardScaler().fit_transform(observed_common_causes) if self.effect_on_t == "binary_flip": # Fit a model containing all confounders and compare predictions # using all features compared to all features except a given # confounder. tmodel = LogisticRegression().fit(observed_common_causes, t) tpred = tmodel.predict(observed_common_causes).astype(int) flips = [] for i in range(observed_common_causes.shape[1]): oldval = np.copy(observed_common_causes[:, i]) observed_common_causes[:, i] = 0 tcap = tmodel.predict(observed_common_causes).astype(int) observed_common_causes[:, i] = oldval flips.append(np.sum(abs(tcap - tpred)) / tpred.shape[0]) min_coeff, max_coeff = min(flips), max(flips) elif self.effect_on_t == "linear": # Estimating the regression coefficient from standardized features to t corrcoef_var_t = np.corrcoef(observed_common_causes, t, rowvar=False)[-1, :-1] std_dev_t = np.std(t)[0] max_coeff = max(corrcoef_var_t) * std_dev_t min_coeff = min(corrcoef_var_t) * std_dev_t else: raise NotImplementedError( "'" + self.effect_on_t + "' method not supported for confounders' effect on treatment" ) min_coeff, max_coeff = self._compute_min_max_coeff(min_coeff, max_coeff, self.frac_strength_treatment) # By default, return a plot with 10 points # consider 10 values of the effect of the unobserved confounder step = (max_coeff - min_coeff) / len_kappa_t self.logger.info("(Min, Max) kappa_t for observed common causes, ({0}, {1})".format(min_coeff, max_coeff)) if np.equal(max_coeff, min_coeff): return max_coeff else: return np.arange(min_coeff, max_coeff, step) def _compute_min_max_coeff(self, min_coeff, max_coeff, effect_strength_fraction): max_coeff = effect_strength_fraction * max_coeff min_coeff = effect_strength_fraction * min_coeff return min_coeff, max_coeff def infer_default_kappa_y(self, len_kappa_y=10): """Infer default effect strength of simulated confounder on treatment.""" observed_common_causes_names = self._target_estimand.get_backdoor_variables() if len(observed_common_causes_names) > 0: observed_common_causes = self._data[observed_common_causes_names] observed_common_causes = pd.get_dummies(observed_common_causes, drop_first=True) else: raise ValueError( "There needs to be at least one common cause to" + "automatically compute the default value of kappa_y." + " Provide a value for kappa_y" ) y = self._data[self._outcome_name] # Standardizing the data observed_common_causes = StandardScaler().fit_transform(observed_common_causes) if self.effect_on_y == "binary_flip": # Fit a model containing all confounders and compare predictions # using all features compared to all features except a given # confounder. ymodel = LogisticRegression().fit(observed_common_causes, y) ypred = ymodel.predict(observed_common_causes).astype(int) flips = [] for i in range(observed_common_causes.shape[1]): oldval = np.copy(observed_common_causes[:, i]) observed_common_causes[:, i] = 0 ycap = ymodel.predict(observed_common_causes).astype(int) observed_common_causes[:, i] = oldval flips.append(np.sum(abs(ycap - ypred)) / ypred.shape[0]) min_coeff, max_coeff = min(flips), max(flips) elif self.effect_on_y == "linear": corrcoef_var_y = np.corrcoef(observed_common_causes, y, rowvar=False)[-1, :-1] std_dev_y = np.std(y)[0] max_coeff = max(corrcoef_var_y) * std_dev_y min_coeff = min(corrcoef_var_y) * std_dev_y else: raise NotImplementedError( "'" + self.effect_on_y + "' method not supported for confounders' effect on outcome" ) min_coeff, max_coeff = self._compute_min_max_coeff(min_coeff, max_coeff, self.frac_strength_outcome) # By default, return a plot with 10 points # consider 10 values of the effect of the unobserved confounder step = (max_coeff - min_coeff) / len_kappa_y self.logger.info("(Min, Max) kappa_y for observed common causes, ({0}, {1})".format(min_coeff, max_coeff)) if np.equal(max_coeff, min_coeff): return max_coeff else: return np.arange(min_coeff, max_coeff, step) def refute_estimate(self, show_progress_bar=False): """ This function attempts to add an unobserved common cause to the outcome and the treatment. At present, we have implemented the behavior for one dimensional behaviors for continuous and binary variables. This function can either take single valued inputs or a range of inputs. The function then looks at the data type of the input and then decides on the course of action. :return: CausalRefuter: An object that contains the estimated effect and a new effect and the name of the refutation used. """ if self.simulated_method_name == "linear-partial-R2": if not (isinstance(self._estimate.estimator, LinearRegressionEstimator)): raise NotImplementedError( "Currently only LinearRegressionEstimator is supported for Sensitivity Analysis" ) if len(self._estimate.estimator._effect_modifier_names) > 0: raise NotImplementedError("The current implementation does not support effect modifiers") if self.frac_strength_outcome == 1: self.frac_strength_outcome = self.frac_strength_treatment analyzer = LinearSensitivityAnalyzer( estimator=self._estimate.estimator, data=self._data, treatment_name=self._treatment_name, percent_change_estimate=self.percent_change_estimate, significance_level=self.significance_level, benchmark_common_causes=self.benchmark_common_causes, null_hypothesis_effect=self.null_hypothesis_effect, frac_strength_treatment=self.frac_strength_treatment, frac_strength_outcome=self.frac_strength_outcome, common_causes_order=self._estimate.estimator._observed_common_causes.columns, ) analyzer.check_sensitivity(plot=self.plot_estimate) return analyzer if self.kappa_t is None: self.kappa_t = self.infer_default_kappa_t() if self.kappa_y is None: self.kappa_y = self.infer_default_kappa_y() if not isinstance(self.kappa_t, (list, np.ndarray)) and not isinstance( self.kappa_y, (list, np.ndarray) ): # Deal with single value inputs new_data = copy.deepcopy(self._data) new_data = self.include_confounders_effect(new_data, self.kappa_t, self.kappa_y) new_estimator = CausalEstimator.get_estimator_object(new_data, self._target_estimand, self._estimate) new_effect = new_estimator.estimate_effect() refute = CausalRefutation( self._estimate.value, new_effect.value, refutation_type="Refute: Add an Unobserved Common Cause" ) refute.new_effect_array = np.array(new_effect.value) refute.new_effect = new_effect.value refute.add_refuter(self) return refute else: # Deal with multiple value inputs if isinstance(self.kappa_t, (list, np.ndarray)) and isinstance( self.kappa_y, (list, np.ndarray) ): # Deal with range inputs # Get a 2D matrix of values # x,y = np.meshgrid(self.kappa_t, self.kappa_y) # x,y are both MxN results_matrix = np.random.rand( len(self.kappa_t), len(self.kappa_y) ) # Matrix to hold all the results of NxM orig_data = copy.deepcopy(self._data) for i in tqdm( range(len(self.kappa_t)), colour=CausalRefuter.PROGRESS_BAR_COLOR, disable=not show_progress_bar, desc="Refuting Estimates: ", ): for j in range(len(self.kappa_y)): new_data = self.include_confounders_effect(orig_data, self.kappa_t[i], self.kappa_y[j]) new_estimator = CausalEstimator.get_estimator_object( new_data, self._target_estimand, self._estimate ) new_effect = new_estimator.estimate_effect() refute = CausalRefutation( self._estimate.value, new_effect.value, refutation_type="Refute: Add an Unobserved Common Cause", ) results_matrix[i][j] = refute.new_effect # Populate the results refute.new_effect_array = results_matrix refute.new_effect = (np.min(results_matrix), np.max(results_matrix)) # Store the values into the refute object refute.add_refuter(self) if self.plotmethod is None: return refute import matplotlib import matplotlib.pyplot as plt fig = plt.figure(figsize=(6, 5)) left, bottom, width, height = 0.1, 0.1, 0.8, 0.8 ax = fig.add_axes([left, bottom, width, height]) oe = self._estimate.value contour_levels = [oe / 4.0, oe / 2.0, (3.0 / 4) * oe, oe] contour_levels.extend([0, np.min(results_matrix), np.max(results_matrix)]) if self.plotmethod == "contour": cp = plt.contourf(self.kappa_y, self.kappa_t, results_matrix, levels=sorted(contour_levels)) # Adding a label on the contour line for the original estimate fmt = {} trueeffect_index = np.where(cp.levels == oe)[0][0] fmt[cp.levels[trueeffect_index]] = "Estimated Effect" # Label every other level using strings plt.clabel(cp, [cp.levels[trueeffect_index]], inline=True, fmt=fmt) plt.colorbar(cp) elif self.plotmethod == "colormesh": cp = plt.pcolormesh(self.kappa_y, self.kappa_t, results_matrix, shading="nearest") plt.colorbar(cp, ticks=contour_levels) ax.yaxis.set_ticks(self.kappa_t) ax.xaxis.set_ticks(self.kappa_y) plt.xticks(rotation=45) ax.set_title("Effect of Unobserved Common Cause") ax.set_ylabel("Value of Linear Constant on Treatment") ax.set_xlabel("Value of Linear Constant on Outcome") plt.show() return refute elif isinstance(self.kappa_t, (list, np.ndarray)): outcomes = np.random.rand(len(self.kappa_t)) orig_data = copy.deepcopy(self._data) for i in tqdm( range(0, len(self.kappa_t)), colour=CausalRefuter.PROGRESS_BAR_COLOR, disable=not show_progress_bar, desc="Refuting Estimates: ", ): new_data = self.include_confounders_effect(orig_data, self.kappa_t[i], self.kappa_y) new_estimator = CausalEstimator.get_estimator_object( new_data, self._target_estimand, self._estimate ) new_effect = new_estimator.estimate_effect() refute = CausalRefutation( self._estimate.value, new_effect.value, refutation_type="Refute: Add an Unobserved Common Cause" ) self.logger.debug(refute) outcomes[i] = refute.new_effect # Populate the results refute.new_effect_array = outcomes refute.new_effect = (np.min(outcomes), np.max(outcomes)) refute.add_refuter(self) if self.plotmethod is None: return refute import matplotlib import matplotlib.pyplot as plt fig = plt.figure(figsize=(6, 5)) left, bottom, width, height = 0.1, 0.1, 0.8, 0.8 ax = fig.add_axes([left, bottom, width, height]) plt.plot(self.kappa_t, outcomes) plt.axhline(self._estimate.value, linestyle="--", color="gray") ax.set_title("Effect of Unobserved Common Cause") ax.set_xlabel("Value of Linear Constant on Treatment") ax.set_ylabel("Estimated Effect after adding the common cause") plt.show() return refute elif isinstance(self.kappa_y, (list, np.ndarray)): outcomes = np.random.rand(len(self.kappa_y)) orig_data = copy.deepcopy(self._data) for i in tqdm( range(0, len(self.kappa_y)), colour=CausalRefuter.PROGRESS_BAR_COLOR, disable=not show_progress_bar, desc="Refuting Estimates: ", ): new_data = self.include_confounders_effect(orig_data, self.kappa_t, self.kappa_y[i]) new_estimator = CausalEstimator.get_estimator_object( new_data, self._target_estimand, self._estimate ) new_effect = new_estimator.estimate_effect() refute = CausalRefutation( self._estimate.value, new_effect.value, refutation_type="Refute: Add an Unobserved Common Cause" ) self.logger.debug(refute) outcomes[i] = refute.new_effect # Populate the results refute.new_effect_array = outcomes refute.new_effect = (np.min(outcomes), np.max(outcomes)) refute.add_refuter(self) if self.plotmethod is None: return refute import matplotlib import matplotlib.pyplot as plt fig = plt.figure(figsize=(6, 5)) left, bottom, width, height = 0.1, 0.1, 0.8, 0.8 ax = fig.add_axes([left, bottom, width, height]) plt.plot(self.kappa_y, outcomes) plt.axhline(self._estimate.value, linestyle="--", color="gray") ax.set_title("Effect of Unobserved Common Cause") ax.set_xlabel("Value of Linear Constant on Outcome") ax.set_ylabel("Estimated Effect after adding the common cause") plt.show() return refute def include_confounders_effect(self, new_data, kappa_t, kappa_y): """ This function deals with the change in the value of the data due to the effect of the unobserved confounder. In the case of a binary flip, we flip only if the random number is greater than the threshold set. In the case of a linear effect, we use the variable as the linear regression constant. :param new_data: pandas.DataFrame: The data to be changed due to the effects of the unobserved confounder. :param kappa_t: numpy.float64: The value of the threshold for binary_flip or the value of the regression coefficient for linear effect. :param kappa_y: numpy.float64: The value of the threshold for binary_flip or the value of the regression coefficient for linear effect. :return: pandas.DataFrame: The DataFrame that includes the effects of the unobserved confounder. """ num_rows = self._data.shape[0] stdnorm = scipy.stats.norm() w_random = stdnorm.rvs(num_rows) if self.effect_on_t == "binary_flip": alpha = 2 * kappa_t - 1 if kappa_t >= 0.5 else 1 - 2 * kappa_t interval = stdnorm.interval(alpha) rel_interval = interval[0] if kappa_t >= 0.5 else interval[1] new_data.loc[rel_interval <= w_random, self._treatment_name] = ( 1 - new_data.loc[rel_interval <= w_random, self._treatment_name] ) for tname in self._treatment_name: if pd.api.types.is_bool_dtype(self._data[tname]): new_data = new_data.astype({tname: "bool"}, copy=False) elif self.effect_on_t == "linear": confounder_t_effect = kappa_t * w_random # By default, we add the effect of simulated confounder for treatment. # But subtract it from outcome to create a negative correlation # assuming that the original confounder's effect was positive on both. # This is to remove the effect of the original confounder. new_data[self._treatment_name] = new_data[self._treatment_name].values + np.ndarray( shape=(num_rows, 1), buffer=confounder_t_effect ) else: raise NotImplementedError( "'" + self.effect_on_t + "' method not supported for confounders' effect on treatment" ) if self.effect_on_y == "binary_flip": alpha = 2 * kappa_y - 1 if kappa_y >= 0.5 else 1 - 2 * kappa_y interval = stdnorm.interval(alpha) rel_interval = interval[0] if kappa_y >= 0.5 else interval[1] new_data.loc[rel_interval <= w_random, self._outcome_name] = ( 1 - new_data.loc[rel_interval <= w_random, self._outcome_name] ) for yname in self._outcome_name: if pd.api.types.is_bool_dtype(self._data[yname]): new_data = new_data.astype({yname: "bool"}, copy=False) elif self.effect_on_y == "linear": confounder_y_effect = (-1) * kappa_y * w_random # By default, we add the effect of simulated confounder for treatment. # But subtract it from outcome to create a negative correlation # assuming that the original confounder's effect was positive on both. # This is to remove the effect of the original confounder. new_data[self._outcome_name] = new_data[self._outcome_name].values + np.ndarray( shape=(num_rows, 1), buffer=confounder_y_effect ) else: raise NotImplementedError( "'" + self.effect_on_y + "' method not supported for confounders' effect on outcome" ) return new_data def include_simulated_confounder(self, convergence_threshold=0.1, c_star_max=1000): """ This function simulates an unobserved confounder based on the data using the following steps: 1. It calculates the "residuals" from the treatment and outcome model i.) The outcome model has outcome as the dependent variable and all the observed variables including treatment as independent variables ii.) The treatment model has treatment as the dependent variable and all the observed variables as independent variables. 2. U is an intermediate random variable drawn from the normal distribution with the weighted average of residuals as mean and a unit variance U ~ N(c1*d_y + c2*d_t, 1) where *d_y and d_t are residuals from the treatment and outcome model *c1 and c2 are coefficients to the residuals 3. The final U, which is the simulated unobserved confounder is obtained by debiasing the intermediate variable U by residualising it with X Choosing the coefficients c1 and c2: The coefficients are chosen based on these basic assumptions: 1. There is a hyperbolic relationship satisfying c1*c2 = c_star 2. c_star is chosen from a range of possible values based on the correlation of the obtained simulated variable with outcome and treatment. 3. The product of correlations with treatment and outcome should be at a minimum distance to the maximum correlations with treatment and outcome in any of the observed confounders 4. The ratio of the weights should be such that they maintain the ratio of the maximum possible observed coefficients within some confidence interval :param c_star_max: The maximum possible value for the hyperbolic curve on which the coefficients to the residuals lie. It defaults to 1000 in the code if not specified by the user. :type int :param convergence_threshold: The threshold to check the plateauing of the correlation while selecting a c_star. It defaults to 0.1 in the code if not specified by the user :type float :returns: The simulated values of the unobserved confounder based on the data :type pandas.core.series.Series """ # Obtaining the list of observed variables required_variables = True observed_variables = self.choose_variables(required_variables) observed_variables_with_treatment_and_outcome = observed_variables + self._treatment_name + self._outcome_name # Taking a subset of the dataframe that has only observed variables self._data = self._data[observed_variables_with_treatment_and_outcome] # Residuals from the outcome model obtained by fitting a linear model y = self._data[self._outcome_name[0]] observed_variables_with_treatment = observed_variables + self._treatment_name X = self._data[observed_variables_with_treatment] model = sm.OLS(y, X.astype("float")) results = model.fit() residuals_y = y - results.fittedvalues d_y = list(pd.Series(residuals_y)) # Residuals from the treatment model obtained by fitting a linear model t = self._data[self._treatment_name[0]].astype("int64") X = self._data[observed_variables] model = sm.OLS(t, X) results = model.fit() residuals_t = t - results.fittedvalues d_t = list(pd.Series(residuals_t)) # Initialising product_cor_metric_observed with a really low value as finding maximum product_cor_metric_observed = -10000000000 for i in observed_variables: current_obs_confounder = self._data[i] outcome_values = self._data[self._outcome_name[0]] correlation_y = current_obs_confounder.corr(outcome_values) treatment_values = t correlation_t = current_obs_confounder.corr(treatment_values) product_cor_metric_current = correlation_y * correlation_t if product_cor_metric_current >= product_cor_metric_observed: product_cor_metric_observed = product_cor_metric_current correlation_t_observed = correlation_t correlation_y_observed = correlation_y # The user has an option to give the the effect_strength_on_y and effect_strength_on_t which can be then used instead of maximum correlation with treatment and outcome in the observed variables as it specifies the desired effect. if self.kappa_t is not None: correlation_t_observed = self.kappa_t if self.kappa_y is not None: correlation_y_observed = self.kappa_y # Choosing a c_star based on the data. # The correlations stop increasing upon increasing c_star after a certain value, that is it plateaus and we choose the value of c_star to be the value it plateaus. correlation_y_list = [] correlation_t_list = [] product_cor_metric_simulated_list = [] x_list = [] step = int(c_star_max / 10) for i in range(0, int(c_star_max), step): c1 = math.sqrt(i) c2 = c1 final_U = self.generate_confounder_from_residuals(c1, c2, d_y, d_t, X) current_simulated_confounder = final_U outcome_values = self._data[self._outcome_name[0]] correlation_y = current_simulated_confounder.corr(outcome_values) correlation_y_list.append(correlation_y) treatment_values = t correlation_t = current_simulated_confounder.corr(treatment_values) correlation_t_list.append(correlation_t) product_cor_metric_simulated = correlation_y * correlation_t product_cor_metric_simulated_list.append(product_cor_metric_simulated) x_list.append(i) index = 1 while index < len(correlation_y_list): if (correlation_y_list[index] - correlation_y_list[index - 1]) <= convergence_threshold: c_star = x_list[index] break index = index + 1 # Choosing c1 and c2 based on the hyperbolic relationship once c_star is chosen by going over various combinations of c1 and c2 values and choosing the combination which # which maintains the minimum distance between the product of correlations of the simulated variable and the product of maximum correlations of one of the observed variables # and additionally checks if the ratio of the weights are such that they maintain the ratio of the maximum possible observed coefficients within some confidence interval # c1_final and c2_final are initialised to the values on the hyperbolic curve such that c1_final = c2_final and c1_final*c2_final = c_star c1_final = math.sqrt(c_star) c2_final = math.sqrt(c_star) # initialising min_distance_between_product_cor_metrics to be a value greater than 1 min_distance_between_product_cor_metrics = 1.5 i = 0.05 threshold = c_star / 0.05 while i <= threshold: c2 = i c1 = c_star / c2 final_U = self.generate_confounder_from_residuals(c1, c2, d_y, d_t, X) current_simulated_confounder = final_U outcome_values = self._data[self._outcome_name[0]] correlation_y = current_simulated_confounder.corr(outcome_values) treatment_values = t correlation_t = current_simulated_confounder.corr(treatment_values) product_cor_metric_simulated = correlation_y * correlation_t if min_distance_between_product_cor_metrics >= abs( product_cor_metric_simulated - product_cor_metric_observed ): min_distance_between_product_cor_metrics = abs( product_cor_metric_simulated - product_cor_metric_observed ) additional_condition = correlation_y_observed / correlation_t_observed if ((c1 / c2) <= (additional_condition + 0.3 * additional_condition)) and ( (c1 / c2) >= (additional_condition - 0.3 * additional_condition) ): # choose minimum positive value c1_final = c1 c2_final = c2 i = i * 1.5 """#closed form solution print("c_star_max before closed form", c_star_max) if max_correlation_with_t == -1000: c2 = 0 c1 = c_star_max else: additional_condition = abs(max_correlation_with_y/max_correlation_with_t) print("additional_condition", additional_condition) c2 = math.sqrt(c_star_max/additional_condition) c1 = c_star_max/c2""" final_U = self.generate_confounder_from_residuals(c1_final, c2_final, d_y, d_t, X) return final_U def generate_confounder_from_residuals(self, c1, c2, d_y, d_t, X): """ This function takes the residuals from the treatment and outcome model and their coefficients and simulates the intermediate random variable U by taking the row wise normal distribution corresponding to each residual value and then debiasing the intermediate variable to get the final variable. :param c1: coefficient to the residual from the outcome model :type float :param c2: coefficient to the residual from the treatment model :type float :param d_y: residuals from the outcome model :type list :param d_t: residuals from the treatment model :type list :returns: The simulated values of the unobserved confounder based on the data :type pandas.core.series.Series """ U = [] for j in range(len(d_t)): simulated_variable_mean = c1 * d_y[j] + c2 * d_t[j] simulated_variable_stddev = 1 U.append(np.random.normal(simulated_variable_mean, simulated_variable_stddev, 1)) U = np.array(U) model = sm.OLS(U, X) results = model.fit() U = U.reshape( -1, ) final_U = U - results.fittedvalues.values final_U = pd.Series(U) return final_U

import copy import logging import math import numpy as np import pandas as pd import scipy.stats import statsmodels.api as sm from sklearn.linear_model import LogisticRegression from sklearn.preprocessing import StandardScaler from tqdm.auto import tqdm import dowhy.causal_estimators.econml from dowhy.causal_estimator import CausalEstimator from dowhy.causal_estimators.linear_regression_estimator import LinearRegressionEstimator from dowhy.causal_refuter import CausalRefutation, CausalRefuter from dowhy.causal_refuters.linear_sensitivity_analyzer import LinearSensitivityAnalyzer from dowhy.causal_refuters.non_parametric_sensitivity_analyzer import NonParametricSensitivityAnalyzer from dowhy.causal_refuters.partial_linear_sensitivity_analyzer import PartialLinearSensitivityAnalyzer class AddUnobservedCommonCause(CausalRefuter): """Add an unobserved confounder for refutation. AddUnobservedCommonCause class supports three methods: 1) Simulation of an unobserved confounder 2) Linear partial R2 : Sensitivity Analysis for linear models. 3) Non-Parametric partial R2 based : Sensitivity Analyis for non-parametric models. Supports additional parameters that can be specified in the refute_estimate() method. """ def __init__(self, *args, **kwargs): """ Initialize the parameters required for the refuter. For direct_simulation, if effect_strength_on_treatment or effect_strength_on_outcome is not given, it is calculated automatically as a range between the minimum and maximum effect strength of observed confounders on treatment and outcome respectively. :param simulation_method: The method to use for simulating effect of unobserved confounder. Possible values are ["direct-simulation", "linear-partial-R2", "non-parametric-partial-R2"]. :param confounders_effect_on_treatment: str : The type of effect on the treatment due to the unobserved confounder. Possible values are ['binary_flip', 'linear'] :param confounders_effect_on_outcome: str : The type of effect on the outcome due to the unobserved confounder. Possible values are ['binary_flip', 'linear'] :param effect_strength_on_treatment: float, numpy.ndarray: [Used when simulation_method="direct-simulation"] Strength of the confounder's effect on treatment. When confounders_effect_on_treatment is linear, it is the regression coefficient. When the confounders_effect_on_treatment is binary flip, it is the probability with which effect of unobserved confounder can invert the value of the treatment. :param effect_strength_on_outcome: float, numpy.ndarray: Strength of the confounder's effect on outcome. Its interpretation depends on confounders_effect_on_outcome and the simulation_method. When simulation_method is direct-simulation, for a linear effect it behaves like the regression coefficient and for a binary flip, it is the probability with which it can invert the value of the outcome. :param partial_r2_confounder_treatment: float, numpy.ndarray: [Used when simulation_method is linear-partial-R2 or non-parametric-partial-R2] Partial R2 of the unobserved confounder wrt the treatment conditioned on the observed confounders. Only in the case of general non-parametric-partial-R2, it is the fraction of variance in the reisz representer that is explained by the unobserved confounder; specifically (1-r), where r is the ratio of variance of reisz representer, alpha^2, based on observed confounders and that based on all confounders. :param partial_r2_confounder_outcome: float, numpy.ndarray: [Used when simulation_method is linear-partial-R2 or non-parametric-partial-R2] Partial R2 of the unobserved confounder wrt the outcome conditioned on the treatment and observed confounders. :param frac_strength_treatment: float: This parameter decides the effect strength of the simulated confounder as a fraction of the effect strength of observed confounders on treatment. Defaults to 1. :param frac_strength_outcome: float: This parameter decides the effect strength of the simulated confounder as a fraction of the effect strength of observed confounders on outcome. Defaults to 1. :param plotmethod: string: Type of plot to be shown. If None, no plot is generated. This parameter is used only only when more than one treatment confounder effect values or outcome confounder effect values are provided. Default is "colormesh". Supported values are "contour", "colormesh" when more than one value is provided for both confounder effect value parameters; "line" when provided for only one of them. :param percent_change_estimate: It is the percentage of reduction of treatment estimate that could alter the results (default = 1). if percent_change_estimate = 1, the robustness value describes the strength of association of confounders with treatment and outcome in order to reduce the estimate by 100% i.e bring it down to 0. (relevant only for Linear Sensitivity Analysis, ignore for rest) :param confounder_increases_estimate: True implies that confounder increases the absolute value of estimate and vice versa. (Default = False). (relevant only for Linear Sensitivity Analysis, ignore for rest) :param benchmark_common_causes: names of variables for bounding strength of confounders. (relevant only for partial-r2 based simulation methods) :param significance_level: confidence interval for statistical inference(default = 0.05). (relevant only for partial-r2 based simulation methods) :param null_hypothesis_effect: assumed effect under the null hypothesis. (relevant only for linear-partial-R2, ignore for rest) :param plot_estimate: Generate contour plot for estimate while performing sensitivity analysis. (default = True). (relevant only for partial-r2 based simulation methods) :param num_splits: number of splits for cross validation. (default = 5). (relevant only for non-parametric-partial-R2 simulation method) :param shuffle_data : shuffle data or not before splitting into folds (default = False). (relevant only for non-parametric-partial-R2 simulation method) :param shuffle_random_seed: seed for randomly shuffling data. (relevant only for non-parametric-partial-R2 simulation method) :param alpha_s_estimator_param_list: list of dictionaries with parameters for finding alpha_s. (relevant only for non-parametric-partial-R2 simulation method) :param g_s_estimator_list: list of estimator objects for finding g_s. These objects should have fit() and predict() functions implemented. (relevant only for non-parametric-partial-R2 simulation method) :param g_s_estimator_param_list: list of dictionaries with parameters for tuning respective estimators in "g_s_estimator_list". The order of the dictionaries in the list should be consistent with the estimator objects order in "g_s_estimator_list". (relevant only for non-parametric-partial-R2 simulation method) """ super().__init__(*args, **kwargs) self.simulation_method = kwargs["simulation_method"] if "simulation_method" in kwargs else "direct-simulation" self.effect_on_t = ( kwargs["confounders_effect_on_treatment"] if "confounders_effect_on_treatment" in kwargs else "binary_flip" ) self.effect_on_y = ( kwargs["confounders_effect_on_outcome"] if "confounders_effect_on_outcome" in kwargs else "linear" ) if self.simulation_method == "direct-simulation": self.kappa_t = kwargs["effect_strength_on_treatment"] if "effect_strength_on_treatment" in kwargs else None self.kappa_y = kwargs["effect_strength_on_outcome"] if "effect_strength_on_outcome" in kwargs else None elif self.simulation_method in ["linear-partial-R2", "non-parametric-partial-R2"]: self.kappa_t = ( kwargs["partial_r2_confounder_treatment"] if "partial_r2_confounder_treatment" in kwargs else None ) self.kappa_y = ( kwargs["partial_r2_confounder_outcome"] if "partial_r2_confounder_outcome" in kwargs else None ) else: raise ValueError( "simulation method is not supported. Try direct-simulation, linear-partial-R2 or non-parametric-partial-R2" ) self.frac_strength_treatment = ( kwargs["effect_fraction_on_treatment"] if "effect_fraction_on_treatment" in kwargs else 1 ) self.frac_strength_outcome = ( kwargs["effect_fraction_on_outcome"] if "effect_fraction_on_outcome" in kwargs else 1 ) self.plotmethod = kwargs["plotmethod"] if "plotmethod" in kwargs else "colormesh" self.percent_change_estimate = kwargs["percent_change_estimate"] if "percent_change_estimate" in kwargs else 1.0 self.significance_level = kwargs["significance_level"] if "significance_level" in kwargs else 0.05 self.confounder_increases_estimate = ( kwargs["confounder_increases_estimate"] if "confounder_increases_estimate" in kwargs else False ) self.benchmark_common_causes = ( kwargs["benchmark_common_causes"] if "benchmark_common_causes" in kwargs else None ) self.null_hypothesis_effect = kwargs["null_hypothesis_effect"] if "null_hypothesis_effect" in kwargs else 0 self.plot_estimate = kwargs["plot_estimate"] if "plot_estimate" in kwargs else True self.num_splits = kwargs["num_splits"] if "num_splits" in kwargs else 5 self.shuffle_data = kwargs["shuffle_data"] if "shuffle_data" in kwargs else False self.shuffle_random_seed = kwargs["shuffle_random_seed"] if "shuffle_random_seed" in kwargs else None self.alpha_s_estimator_param_list = ( kwargs["alpha_s_estimator_param_list"] if "alpha_s_estimator_param_list" in kwargs else None ) self.alpha_s_estimator_list = kwargs["alpha_s_estimator_list"] if "alpha_s_estimator_list" in kwargs else None self.g_s_estimator_list = kwargs["g_s_estimator_list"] if "g_s_estimator_list" in kwargs else None self.g_s_estimator_param_list = ( kwargs["g_s_estimator_param_list"] if "g_s_estimator_param_list" in kwargs else None ) self.plugin_reisz = kwargs["plugin_reisz"] if "plugin_reisz" in kwargs else False self.logger = logging.getLogger(__name__) def infer_default_kappa_t(self, len_kappa_t=10): """Infer default effect strength of simulated confounder on treatment.""" observed_common_causes_names = self._target_estimand.get_backdoor_variables() if len(observed_common_causes_names) > 0: observed_common_causes = self._data[observed_common_causes_names] observed_common_causes = pd.get_dummies(observed_common_causes, drop_first=True) else: raise ValueError( "There needs to be at least one common cause to" + "automatically compute the default value of kappa_t." + " Provide a value for kappa_t" ) t = self._data[self._treatment_name] # Standardizing the data observed_common_causes = StandardScaler().fit_transform(observed_common_causes) if self.effect_on_t == "binary_flip": # Fit a model containing all confounders and compare predictions # using all features compared to all features except a given # confounder. tmodel = LogisticRegression().fit(observed_common_causes, t) tpred = tmodel.predict(observed_common_causes).astype(int) flips = [] for i in range(observed_common_causes.shape[1]): oldval = np.copy(observed_common_causes[:, i]) observed_common_causes[:, i] = 0 tcap = tmodel.predict(observed_common_causes).astype(int) observed_common_causes[:, i] = oldval flips.append(np.sum(abs(tcap - tpred)) / tpred.shape[0]) min_coeff, max_coeff = min(flips), max(flips) elif self.effect_on_t == "linear": # Estimating the regression coefficient from standardized features to t corrcoef_var_t = np.corrcoef(observed_common_causes, t, rowvar=False)[-1, :-1] std_dev_t = np.std(t)[0] max_coeff = max(corrcoef_var_t) * std_dev_t min_coeff = min(corrcoef_var_t) * std_dev_t else: raise NotImplementedError( "'" + self.effect_on_t + "' method not supported for confounders' effect on treatment" ) min_coeff, max_coeff = self._compute_min_max_coeff(min_coeff, max_coeff, self.frac_strength_treatment) # By default, return a plot with 10 points # consider 10 values of the effect of the unobserved confounder step = (max_coeff - min_coeff) / len_kappa_t self.logger.info("(Min, Max) kappa_t for observed common causes, ({0}, {1})".format(min_coeff, max_coeff)) if np.equal(max_coeff, min_coeff): return max_coeff else: return np.arange(min_coeff, max_coeff, step) def _compute_min_max_coeff(self, min_coeff, max_coeff, effect_strength_fraction): max_coeff = effect_strength_fraction * max_coeff min_coeff = effect_strength_fraction * min_coeff return min_coeff, max_coeff def infer_default_kappa_y(self, len_kappa_y=10): """Infer default effect strength of simulated confounder on treatment.""" observed_common_causes_names = self._target_estimand.get_backdoor_variables() if len(observed_common_causes_names) > 0: observed_common_causes = self._data[observed_common_causes_names] observed_common_causes = pd.get_dummies(observed_common_causes, drop_first=True) else: raise ValueError( "There needs to be at least one common cause to" + "automatically compute the default value of kappa_y." + " Provide a value for kappa_y" ) y = self._data[self._outcome_name] # Standardizing the data observed_common_causes = StandardScaler().fit_transform(observed_common_causes) if self.effect_on_y == "binary_flip": # Fit a model containing all confounders and compare predictions # using all features compared to all features except a given # confounder. ymodel = LogisticRegression().fit(observed_common_causes, y) ypred = ymodel.predict(observed_common_causes).astype(int) flips = [] for i in range(observed_common_causes.shape[1]): oldval = np.copy(observed_common_causes[:, i]) observed_common_causes[:, i] = 0 ycap = ymodel.predict(observed_common_causes).astype(int) observed_common_causes[:, i] = oldval flips.append(np.sum(abs(ycap - ypred)) / ypred.shape[0]) min_coeff, max_coeff = min(flips), max(flips) elif self.effect_on_y == "linear": corrcoef_var_y = np.corrcoef(observed_common_causes, y, rowvar=False)[-1, :-1] std_dev_y = np.std(y)[0] max_coeff = max(corrcoef_var_y) * std_dev_y min_coeff = min(corrcoef_var_y) * std_dev_y else: raise NotImplementedError( "'" + self.effect_on_y + "' method not supported for confounders' effect on outcome" ) min_coeff, max_coeff = self._compute_min_max_coeff(min_coeff, max_coeff, self.frac_strength_outcome) # By default, return a plot with 10 points # consider 10 values of the effect of the unobserved confounder step = (max_coeff - min_coeff) / len_kappa_y self.logger.info("(Min, Max) kappa_y for observed common causes, ({0}, {1})".format(min_coeff, max_coeff)) if np.equal(max_coeff, min_coeff): return max_coeff else: return np.arange(min_coeff, max_coeff, step) def refute_estimate(self, show_progress_bar=False): """ This function attempts to add an unobserved common cause to the outcome and the treatment. At present, we have implemented the behavior for one dimensional behaviors for continuous and binary variables. This function can either take single valued inputs or a range of inputs. The function then looks at the data type of the input and then decides on the course of action. :return: CausalRefuter: An object that contains the estimated effect and a new effect and the name of the refutation used. """ if self.simulation_method == "linear-partial-R2": if not (isinstance(self._estimate.estimator, LinearRegressionEstimator)): raise NotImplementedError( "Currently only LinearRegressionEstimator is supported for Sensitivity Analysis" ) if len(self._estimate.estimator._effect_modifier_names) > 0: raise NotImplementedError("The current implementation does not support effect modifiers") if self.frac_strength_outcome == 1: self.frac_strength_outcome = self.frac_strength_treatment analyzer = LinearSensitivityAnalyzer( estimator=self._estimate.estimator, data=self._data, treatment_name=self._treatment_name, percent_change_estimate=self.percent_change_estimate, significance_level=self.significance_level, benchmark_common_causes=self.benchmark_common_causes, null_hypothesis_effect=self.null_hypothesis_effect, frac_strength_treatment=self.frac_strength_treatment, frac_strength_outcome=self.frac_strength_outcome, common_causes_order=self._estimate.estimator._observed_common_causes.columns, ) analyzer.check_sensitivity(plot=self.plot_estimate) return analyzer if self.simulation_method == "non-parametric-partial-R2": # If the estimator used is LinearDML, partially linear sensitivity analysis will be automatically chosen if isinstance(self._estimate.estimator, dowhy.causal_estimators.econml.Econml): if self._estimate.estimator._econml_methodname == "econml.dml.LinearDML": analyzer = PartialLinearSensitivityAnalyzer( estimator=self._estimate._estimator_object, observed_common_causes=self._estimate.estimator._observed_common_causes, treatment=self._estimate.estimator._treatment, outcome=self._estimate.estimator._outcome, alpha_s_estimator_param_list=self.alpha_s_estimator_param_list, g_s_estimator_list=self.g_s_estimator_list, g_s_estimator_param_list=self.g_s_estimator_param_list, effect_strength_treatment=self.kappa_t, effect_strength_outcome=self.kappa_y, benchmark_common_causes=self.benchmark_common_causes, frac_strength_treatment=self.frac_strength_treatment, frac_strength_outcome=self.frac_strength_outcome, ) analyzer.check_sensitivity(plot=self.plot_estimate) return analyzer analyzer = NonParametricSensitivityAnalyzer( estimator=self._estimate.estimator, observed_common_causes=self._estimate.estimator._observed_common_causes, treatment=self._estimate.estimator._treatment, outcome=self._estimate.estimator._outcome, alpha_s_estimator_list=self.alpha_s_estimator_list, alpha_s_estimator_param_list=self.alpha_s_estimator_param_list, g_s_estimator_list=self.g_s_estimator_list, g_s_estimator_param_list=self.g_s_estimator_param_list, effect_strength_treatment=self.kappa_t, effect_strength_outcome=self.kappa_y, benchmark_common_causes=self.benchmark_common_causes, frac_strength_treatment=self.frac_strength_treatment, frac_strength_outcome=self.frac_strength_outcome, theta_s=self._estimate.value, plugin_reisz=self.plugin_reisz, ) analyzer.check_sensitivity(plot=self.plot_estimate) return analyzer if self.kappa_t is None: self.kappa_t = self.infer_default_kappa_t() if self.kappa_y is None: self.kappa_y = self.infer_default_kappa_y() if not isinstance(self.kappa_t, (list, np.ndarray)) and not isinstance( self.kappa_y, (list, np.ndarray) ): # Deal with single value inputs new_data = copy.deepcopy(self._data) new_data = self.include_confounders_effect(new_data, self.kappa_t, self.kappa_y) new_estimator = CausalEstimator.get_estimator_object(new_data, self._target_estimand, self._estimate) new_effect = new_estimator.estimate_effect() refute = CausalRefutation( self._estimate.value, new_effect.value, refutation_type="Refute: Add an Unobserved Common Cause" ) refute.new_effect_array = np.array(new_effect.value) refute.new_effect = new_effect.value refute.add_refuter(self) return refute else: # Deal with multiple value inputs if isinstance(self.kappa_t, (list, np.ndarray)) and isinstance( self.kappa_y, (list, np.ndarray) ): # Deal with range inputs # Get a 2D matrix of values # x,y = np.meshgrid(self.kappa_t, self.kappa_y) # x,y are both MxN results_matrix = np.random.rand( len(self.kappa_t), len(self.kappa_y) ) # Matrix to hold all the results of NxM orig_data = copy.deepcopy(self._data) for i in tqdm( range(len(self.kappa_t)), colour=CausalRefuter.PROGRESS_BAR_COLOR, disable=not show_progress_bar, desc="Refuting Estimates: ", ): for j in range(len(self.kappa_y)): new_data = self.include_confounders_effect(orig_data, self.kappa_t[i], self.kappa_y[j]) new_estimator = CausalEstimator.get_estimator_object( new_data, self._target_estimand, self._estimate ) new_effect = new_estimator.estimate_effect() refute = CausalRefutation( self._estimate.value, new_effect.value, refutation_type="Refute: Add an Unobserved Common Cause", ) results_matrix[i][j] = refute.new_effect # Populate the results refute.new_effect_array = results_matrix refute.new_effect = (np.min(results_matrix), np.max(results_matrix)) # Store the values into the refute object refute.add_refuter(self) if self.plotmethod is None: return refute import matplotlib import matplotlib.pyplot as plt fig = plt.figure(figsize=(6, 5)) left, bottom, width, height = 0.1, 0.1, 0.8, 0.8 ax = fig.add_axes([left, bottom, width, height]) oe = self._estimate.value contour_levels = [oe / 4.0, oe / 2.0, (3.0 / 4) * oe, oe] contour_levels.extend([0, np.min(results_matrix), np.max(results_matrix)]) if self.plotmethod == "contour": cp = plt.contourf(self.kappa_y, self.kappa_t, results_matrix, levels=sorted(contour_levels)) # Adding a label on the contour line for the original estimate fmt = {} trueeffect_index = np.where(cp.levels == oe)[0][0] fmt[cp.levels[trueeffect_index]] = "Estimated Effect" # Label every other level using strings plt.clabel(cp, [cp.levels[trueeffect_index]], inline=True, fmt=fmt) plt.colorbar(cp) elif self.plotmethod == "colormesh": cp = plt.pcolormesh(self.kappa_y, self.kappa_t, results_matrix, shading="nearest") plt.colorbar(cp, ticks=contour_levels) ax.yaxis.set_ticks(self.kappa_t) ax.xaxis.set_ticks(self.kappa_y) plt.xticks(rotation=45) ax.set_title("Effect of Unobserved Common Cause") ax.set_ylabel("Value of Linear Constant on Treatment") ax.set_xlabel("Value of Linear Constant on Outcome") plt.show() return refute elif isinstance(self.kappa_t, (list, np.ndarray)): outcomes = np.random.rand(len(self.kappa_t)) orig_data = copy.deepcopy(self._data) for i in tqdm( range(0, len(self.kappa_t)), colour=CausalRefuter.PROGRESS_BAR_COLOR, disable=not show_progress_bar, desc="Refuting Estimates: ", ): new_data = self.include_confounders_effect(orig_data, self.kappa_t[i], self.kappa_y) new_estimator = CausalEstimator.get_estimator_object( new_data, self._target_estimand, self._estimate ) new_effect = new_estimator.estimate_effect() refute = CausalRefutation( self._estimate.value, new_effect.value, refutation_type="Refute: Add an Unobserved Common Cause" ) self.logger.debug(refute) outcomes[i] = refute.new_effect # Populate the results refute.new_effect_array = outcomes refute.new_effect = (np.min(outcomes), np.max(outcomes)) refute.add_refuter(self) if self.plotmethod is None: return refute import matplotlib import matplotlib.pyplot as plt fig = plt.figure(figsize=(6, 5)) left, bottom, width, height = 0.1, 0.1, 0.8, 0.8 ax = fig.add_axes([left, bottom, width, height]) plt.plot(self.kappa_t, outcomes) plt.axhline(self._estimate.value, linestyle="--", color="gray") ax.set_title("Effect of Unobserved Common Cause") ax.set_xlabel("Value of Linear Constant on Treatment") ax.set_ylabel("Estimated Effect after adding the common cause") plt.show() return refute elif isinstance(self.kappa_y, (list, np.ndarray)): outcomes = np.random.rand(len(self.kappa_y)) orig_data = copy.deepcopy(self._data) for i in tqdm( range(0, len(self.kappa_y)), colour=CausalRefuter.PROGRESS_BAR_COLOR, disable=not show_progress_bar, desc="Refuting Estimates: ", ): new_data = self.include_confounders_effect(orig_data, self.kappa_t, self.kappa_y[i]) new_estimator = CausalEstimator.get_estimator_object( new_data, self._target_estimand, self._estimate ) new_effect = new_estimator.estimate_effect() refute = CausalRefutation( self._estimate.value, new_effect.value, refutation_type="Refute: Add an Unobserved Common Cause" ) self.logger.debug(refute) outcomes[i] = refute.new_effect # Populate the results refute.new_effect_array = outcomes refute.new_effect = (np.min(outcomes), np.max(outcomes)) refute.add_refuter(self) if self.plotmethod is None: return refute import matplotlib import matplotlib.pyplot as plt fig = plt.figure(figsize=(6, 5)) left, bottom, width, height = 0.1, 0.1, 0.8, 0.8 ax = fig.add_axes([left, bottom, width, height]) plt.plot(self.kappa_y, outcomes) plt.axhline(self._estimate.value, linestyle="--", color="gray") ax.set_title("Effect of Unobserved Common Cause") ax.set_xlabel("Value of Linear Constant on Outcome") ax.set_ylabel("Estimated Effect after adding the common cause") plt.show() return refute def include_confounders_effect(self, new_data, kappa_t, kappa_y): """ This function deals with the change in the value of the data due to the effect of the unobserved confounder. In the case of a binary flip, we flip only if the random number is greater than the threshold set. In the case of a linear effect, we use the variable as the linear regression constant. :param new_data: pandas.DataFrame: The data to be changed due to the effects of the unobserved confounder. :param kappa_t: numpy.float64: The value of the threshold for binary_flip or the value of the regression coefficient for linear effect. :param kappa_y: numpy.float64: The value of the threshold for binary_flip or the value of the regression coefficient for linear effect. :return: pandas.DataFrame: The DataFrame that includes the effects of the unobserved confounder. """ num_rows = self._data.shape[0] stdnorm = scipy.stats.norm() w_random = stdnorm.rvs(num_rows) if self.effect_on_t == "binary_flip": alpha = 2 * kappa_t - 1 if kappa_t >= 0.5 else 1 - 2 * kappa_t interval = stdnorm.interval(alpha) rel_interval = interval[0] if kappa_t >= 0.5 else interval[1] new_data.loc[rel_interval <= w_random, self._treatment_name] = ( 1 - new_data.loc[rel_interval <= w_random, self._treatment_name] ) for tname in self._treatment_name: if pd.api.types.is_bool_dtype(self._data[tname]): new_data = new_data.astype({tname: "bool"}, copy=False) elif self.effect_on_t == "linear": confounder_t_effect = kappa_t * w_random # By default, we add the effect of simulated confounder for treatment. # But subtract it from outcome to create a negative correlation # assuming that the original confounder's effect was positive on both. # This is to remove the effect of the original confounder. new_data[self._treatment_name] = new_data[self._treatment_name].values + np.ndarray( shape=(num_rows, 1), buffer=confounder_t_effect ) else: raise NotImplementedError( "'" + self.effect_on_t + "' method not supported for confounders' effect on treatment" ) if self.effect_on_y == "binary_flip": alpha = 2 * kappa_y - 1 if kappa_y >= 0.5 else 1 - 2 * kappa_y interval = stdnorm.interval(alpha) rel_interval = interval[0] if kappa_y >= 0.5 else interval[1] new_data.loc[rel_interval <= w_random, self._outcome_name] = ( 1 - new_data.loc[rel_interval <= w_random, self._outcome_name] ) for yname in self._outcome_name: if pd.api.types.is_bool_dtype(self._data[yname]): new_data = new_data.astype({yname: "bool"}, copy=False) elif self.effect_on_y == "linear": confounder_y_effect = (-1) * kappa_y * w_random # By default, we add the effect of simulated confounder for treatment. # But subtract it from outcome to create a negative correlation # assuming that the original confounder's effect was positive on both. # This is to remove the effect of the original confounder. new_data[self._outcome_name] = new_data[self._outcome_name].values + np.ndarray( shape=(num_rows, 1), buffer=confounder_y_effect ) else: raise NotImplementedError( "'" + self.effect_on_y + "' method not supported for confounders' effect on outcome" ) return new_data def include_simulated_confounder(self, convergence_threshold=0.1, c_star_max=1000): """ This function simulates an unobserved confounder based on the data using the following steps: 1. It calculates the "residuals" from the treatment and outcome model i.) The outcome model has outcome as the dependent variable and all the observed variables including treatment as independent variables ii.) The treatment model has treatment as the dependent variable and all the observed variables as independent variables. 2. U is an intermediate random variable drawn from the normal distribution with the weighted average of residuals as mean and a unit variance U ~ N(c1*d_y + c2*d_t, 1) where *d_y and d_t are residuals from the treatment and outcome model *c1 and c2 are coefficients to the residuals 3. The final U, which is the simulated unobserved confounder is obtained by debiasing the intermediate variable U by residualising it with X Choosing the coefficients c1 and c2: The coefficients are chosen based on these basic assumptions: 1. There is a hyperbolic relationship satisfying c1*c2 = c_star 2. c_star is chosen from a range of possible values based on the correlation of the obtained simulated variable with outcome and treatment. 3. The product of correlations with treatment and outcome should be at a minimum distance to the maximum correlations with treatment and outcome in any of the observed confounders 4. The ratio of the weights should be such that they maintain the ratio of the maximum possible observed coefficients within some confidence interval :param c_star_max: The maximum possible value for the hyperbolic curve on which the coefficients to the residuals lie. It defaults to 1000 in the code if not specified by the user. :type int :param convergence_threshold: The threshold to check the plateauing of the correlation while selecting a c_star. It defaults to 0.1 in the code if not specified by the user :type float :returns: The simulated values of the unobserved confounder based on the data :type pandas.core.series.Series """ # Obtaining the list of observed variables required_variables = True observed_variables = self.choose_variables(required_variables) observed_variables_with_treatment_and_outcome = observed_variables + self._treatment_name + self._outcome_name # Taking a subset of the dataframe that has only observed variables self._data = self._data[observed_variables_with_treatment_and_outcome] # Residuals from the outcome model obtained by fitting a linear model y = self._data[self._outcome_name[0]] observed_variables_with_treatment = observed_variables + self._treatment_name X = self._data[observed_variables_with_treatment] model = sm.OLS(y, X.astype("float")) results = model.fit() residuals_y = y - results.fittedvalues d_y = list(pd.Series(residuals_y)) # Residuals from the treatment model obtained by fitting a linear model t = self._data[self._treatment_name[0]].astype("int64") X = self._data[observed_variables] model = sm.OLS(t, X) results = model.fit() residuals_t = t - results.fittedvalues d_t = list(pd.Series(residuals_t)) # Initialising product_cor_metric_observed with a really low value as finding maximum product_cor_metric_observed = -10000000000 for i in observed_variables: current_obs_confounder = self._data[i] outcome_values = self._data[self._outcome_name[0]] correlation_y = current_obs_confounder.corr(outcome_values) treatment_values = t correlation_t = current_obs_confounder.corr(treatment_values) product_cor_metric_current = correlation_y * correlation_t if product_cor_metric_current >= product_cor_metric_observed: product_cor_metric_observed = product_cor_metric_current correlation_t_observed = correlation_t correlation_y_observed = correlation_y # The user has an option to give the the effect_strength_on_y and effect_strength_on_t which can be then used instead of maximum correlation with treatment and outcome in the observed variables as it specifies the desired effect. if self.kappa_t is not None: correlation_t_observed = self.kappa_t if self.kappa_y is not None: correlation_y_observed = self.kappa_y # Choosing a c_star based on the data. # The correlations stop increasing upon increasing c_star after a certain value, that is it plateaus and we choose the value of c_star to be the value it plateaus. correlation_y_list = [] correlation_t_list = [] product_cor_metric_simulated_list = [] x_list = [] step = int(c_star_max / 10) for i in range(0, int(c_star_max), step): c1 = math.sqrt(i) c2 = c1 final_U = self.generate_confounder_from_residuals(c1, c2, d_y, d_t, X) current_simulated_confounder = final_U outcome_values = self._data[self._outcome_name[0]] correlation_y = current_simulated_confounder.corr(outcome_values) correlation_y_list.append(correlation_y) treatment_values = t correlation_t = current_simulated_confounder.corr(treatment_values) correlation_t_list.append(correlation_t) product_cor_metric_simulated = correlation_y * correlation_t product_cor_metric_simulated_list.append(product_cor_metric_simulated) x_list.append(i) index = 1 while index < len(correlation_y_list): if (correlation_y_list[index] - correlation_y_list[index - 1]) <= convergence_threshold: c_star = x_list[index] break index = index + 1 # Choosing c1 and c2 based on the hyperbolic relationship once c_star is chosen by going over various combinations of c1 and c2 values and choosing the combination which # which maintains the minimum distance between the product of correlations of the simulated variable and the product of maximum correlations of one of the observed variables # and additionally checks if the ratio of the weights are such that they maintain the ratio of the maximum possible observed coefficients within some confidence interval # c1_final and c2_final are initialised to the values on the hyperbolic curve such that c1_final = c2_final and c1_final*c2_final = c_star c1_final = math.sqrt(c_star) c2_final = math.sqrt(c_star) # initialising min_distance_between_product_cor_metrics to be a value greater than 1 min_distance_between_product_cor_metrics = 1.5 i = 0.05 threshold = c_star / 0.05 while i <= threshold: c2 = i c1 = c_star / c2 final_U = self.generate_confounder_from_residuals(c1, c2, d_y, d_t, X) current_simulated_confounder = final_U outcome_values = self._data[self._outcome_name[0]] correlation_y = current_simulated_confounder.corr(outcome_values) treatment_values = t correlation_t = current_simulated_confounder.corr(treatment_values) product_cor_metric_simulated = correlation_y * correlation_t if min_distance_between_product_cor_metrics >= abs( product_cor_metric_simulated - product_cor_metric_observed ): min_distance_between_product_cor_metrics = abs( product_cor_metric_simulated - product_cor_metric_observed ) additional_condition = correlation_y_observed / correlation_t_observed if ((c1 / c2) <= (additional_condition + 0.3 * additional_condition)) and ( (c1 / c2) >= (additional_condition - 0.3 * additional_condition) ): # choose minimum positive value c1_final = c1 c2_final = c2 i = i * 1.5 """#closed form solution print("c_star_max before closed form", c_star_max) if max_correlation_with_t == -1000: c2 = 0 c1 = c_star_max else: additional_condition = abs(max_correlation_with_y/max_correlation_with_t) print("additional_condition", additional_condition) c2 = math.sqrt(c_star_max/additional_condition) c1 = c_star_max/c2""" final_U = self.generate_confounder_from_residuals(c1_final, c2_final, d_y, d_t, X) return final_U def generate_confounder_from_residuals(self, c1, c2, d_y, d_t, X): """ This function takes the residuals from the treatment and outcome model and their coefficients and simulates the intermediate random variable U by taking the row wise normal distribution corresponding to each residual value and then debiasing the intermediate variable to get the final variable. :param c1: coefficient to the residual from the outcome model :type float :param c2: coefficient to the residual from the treatment model :type float :param d_y: residuals from the outcome model :type list :param d_t: residuals from the treatment model :type list :returns: The simulated values of the unobserved confounder based on the data :type pandas.core.series.Series """ U = [] for j in range(len(d_t)): simulated_variable_mean = c1 * d_y[j] + c2 * d_t[j] simulated_variable_stddev = 1 U.append(np.random.normal(simulated_variable_mean, simulated_variable_stddev, 1)) U = np.array(U) model = sm.OLS(U, X) results = model.fit() U = U.reshape( -1, ) final_U = U - results.fittedvalues.values final_U = pd.Series(U) return final_U

anusha0409

81841c697bd5e80ecf9e731432305f6186666f1f

bb446c333f2256074304b0dec9cb5628d284b542

Q: given that the array effect_strength_on_treatment (and other parameters) have different interpretations by methods, does that mean that the user would have to pass in different array values based on what simulation_method they chose? Or is the same set of values valid and roughly similar enough that the user can change the simulation_method without also changing these other parameters? Where I'm going is that, if the parameters have different interpretations and different values for different values of simulation_method, maybe there should be different user-facing methods for the different simulation_methods? If there's a benefit to reusing structural code, then this code could be an internal helper function...

emrekiciman

py-why/dowhy

Adding Non Linear Sensitivity Analysis

This PR implements the non-parametric sensitivity analysis from Chernozhukov et al. https://arxiv.org/abs/2112.13398 It implements two sensitivity analyzers: 1. For Partial Linear DGPs and estimators like LinearDML 2. For general non-parametric DGPs and estimators like KernelDML. The notebook in this PR provides an introduction on how the sensitivity bounds are calculated for the partial linear case. For the general nonparametric DGPs, we need to estimate a special function called the Reisz representer. For binary treatment, it is exactly the difference in outcome weighted by propensity score. So we provide two options to learn the Reisz representer, 1) plugin_reisz that uses the propensity score; and 2) general estimator that uses a custom loss function. These two are in the file reisz.py. Briefly, the sensitivity bounds depend on two parameters that denote the effect of the unobserved confounder on treatment and outcome. That's why we use the same API as for the `add_unobserved_common_cause` method and add this sensitivity analysis as a possible simulation method="non-parametric-partial-R2". The format of the plots is identical to those from the "linear-partial-r2" simulation method that is already implemented. We provide two modes for the user. 1) User specifies the effect strength parameters themselves, as a range of values. 2) User benchmarks the effect strength parameters as a multiple of the same parameters for the observed common causes. Signed-off-by: anusha <anushaagarwal2000.com>

2022-06-20 14:37:11+00:00

2022-09-16 03:57:26+00:00

dowhy/causal_refuters/add_unobserved_common_cause.py

import copy import logging import math import numpy as np import pandas as pd import scipy.stats import statsmodels.api as sm from sklearn.linear_model import LogisticRegression from sklearn.preprocessing import StandardScaler from tqdm.auto import tqdm from dowhy.causal_estimator import CausalEstimator from dowhy.causal_estimators.linear_regression_estimator import LinearRegressionEstimator from dowhy.causal_refuter import CausalRefutation, CausalRefuter from dowhy.causal_refuters.linear_sensitivity_analyzer import LinearSensitivityAnalyzer class AddUnobservedCommonCause(CausalRefuter): """Add an unobserved confounder for refutation. Supports additional parameters that can be specified in the refute_estimate() method. - 'confounders_effect_on_treatment': how the simulated confounder affects the value of treatment. This can be linear (for continuous treatment) or binary_flip (for binary treatment) - 'confounders_effect_on_outcome': how the simulated confounder affects the value of outcome. This can be linear (for continuous outcome) or binary_flip (for binary outcome) - 'effect_strength_on_treatment': parameter for the strength of the effect of simulated confounder on treatment. For linear effect, it is the regression coeffient. For binary_flip, it is the probability that simulated confounder's effect flips the value of treatment from 0 to 1 (or vice-versa). - 'effect_strength_on_outcome': parameter for the strength of the effect of simulated confounder on outcome. For linear effect, it is the regression coeffient. For binary_flip, it is the probability that simulated confounder's effect flips the value of outcome from 0 to 1 (or vice-versa). TODO: Needs an interpretation module """ def __init__(self, *args, **kwargs): """ Initialize the parameters required for the refuter. If effect_strength_on_treatment or effect_strength_on_outcome is not given, it is calculated automatically as a range between the minimum and maximum effect strength of observed confounders on treatment and outcome respectively. :param confounders_effect_on_treatment: str : The type of effect on the treatment due to the unobserved confounder. Possible values are ['binary_flip', 'linear'] :param confounders_effect_on_outcome: str : The type of effect on the outcome due to the unobserved confounder. Possible values are ['binary_flip', 'linear'] :param effect_strength_on_treatment: float, numpy.ndarray: This refers to the strength of the confounder on treatment. For a linear effect, it behaves like the regression coeffecient. For a binary flip it is the probability with which it can invert the value of the treatment. :param effect_strength_on_outcome: float, numpy.ndarray: This refers to the strength of the confounder on outcome. For a linear effect, it behaves like the regression coefficient. For a binary flip, it is the probability with which it can invert the value of the outcome. :param effect_fraction_on_treatment: float: If effect_strength_on_treatment is not provided, this parameter decides the effect strength of the simulated confounder as a fraction of the effect strength of observed confounders on treatment. Defaults to 1. :param effect_fraction_on_outcome: float: If effect_strength_on_outcome is not provided, this parameter decides the effect strength of the simulated confounder as a fraction of the effect strength of observed confounders on outcome. Defaults to 1. :param plotmethod: string: Type of plot to be shown. If None, no plot is generated. This parameter is used only only when more than one treatment confounder effect values or outcome confounder effect values are provided. Default is "colormesh". Supported values are "contour", "colormesh" when more than one value is provided for both confounder effect value parameters; "line" when provided for only one of them. :param simulated_method_name: method type to add unobserved common cause. "linear-partial-R2" for linear sensitivity analysis :param percent_change_estimate: It is the percentage of reduction of treatment estimate that could alter the results (default = 1) if percent_change_estimate = 1, the robustness value describes the strength of association of confounders with treatment and outcome in order to reduce the estimate by 100% i.e bring it down to 0. :param confounder_increases_estimate: True implies that confounder increases the absolute value of estimate and vice versa. (Default = False) :param benchmark_common_causes: names of variables for bounding strength of confounders :param significance_level: confidence interval for statistical inference(default = 0.05) :param null_hypothesis_effect: assumed effect under the null hypothesis :param plot_estimate: Generate contour plot for estimate while performing sensitivity analysis. (default = True). To override the setting, set plot_estimate = False. """ super().__init__(*args, **kwargs) self.effect_on_t = ( kwargs["confounders_effect_on_treatment"] if "confounders_effect_on_treatment" in kwargs else "binary_flip" ) self.effect_on_y = ( kwargs["confounders_effect_on_outcome"] if "confounders_effect_on_outcome" in kwargs else "linear" ) self.kappa_t = kwargs["effect_strength_on_treatment"] if "effect_strength_on_treatment" in kwargs else None self.kappa_y = kwargs["effect_strength_on_outcome"] if "effect_strength_on_outcome" in kwargs else None self.frac_strength_treatment = ( kwargs["effect_fraction_on_treatment"] if "effect_fraction_on_treatment" in kwargs else 1 ) self.frac_strength_outcome = ( kwargs["effect_fraction_on_outcome"] if "effect_fraction_on_outcome" in kwargs else 1 ) self.simulated_method_name = ( kwargs["simulated_method_name"] if "simulated_method_name" in kwargs else "linear_based" ) self.plotmethod = kwargs["plotmethod"] if "plotmethod" in kwargs else "colormesh" self.percent_change_estimate = kwargs["percent_change_estimate"] if "percent_change_estimate" in kwargs else 1.0 self.significance_level = kwargs["significance_level"] if "significance_level" in kwargs else 0.05 self.confounder_increases_estimate = ( kwargs["confounder_increases_estimate"] if "confounder_increases_estimate" in kwargs else False ) self.benchmark_common_causes = ( kwargs["benchmark_common_causes"] if "benchmark_common_causes" in kwargs else None ) self.null_hypothesis_effect = kwargs["null_hypothesis_effect"] if "null_hypothesis_effect" in kwargs else 0 self.plot_estimate = kwargs["plot_estimate"] if "plot_estimate" in kwargs else True self.logger = logging.getLogger(__name__) def infer_default_kappa_t(self, len_kappa_t=10): """Infer default effect strength of simulated confounder on treatment.""" observed_common_causes_names = self._target_estimand.get_backdoor_variables() if len(observed_common_causes_names) > 0: observed_common_causes = self._data[observed_common_causes_names] observed_common_causes = pd.get_dummies(observed_common_causes, drop_first=True) else: raise ValueError( "There needs to be at least one common cause to" + "automatically compute the default value of kappa_t." + " Provide a value for kappa_t" ) t = self._data[self._treatment_name] # Standardizing the data observed_common_causes = StandardScaler().fit_transform(observed_common_causes) if self.effect_on_t == "binary_flip": # Fit a model containing all confounders and compare predictions # using all features compared to all features except a given # confounder. tmodel = LogisticRegression().fit(observed_common_causes, t) tpred = tmodel.predict(observed_common_causes).astype(int) flips = [] for i in range(observed_common_causes.shape[1]): oldval = np.copy(observed_common_causes[:, i]) observed_common_causes[:, i] = 0 tcap = tmodel.predict(observed_common_causes).astype(int) observed_common_causes[:, i] = oldval flips.append(np.sum(abs(tcap - tpred)) / tpred.shape[0]) min_coeff, max_coeff = min(flips), max(flips) elif self.effect_on_t == "linear": # Estimating the regression coefficient from standardized features to t corrcoef_var_t = np.corrcoef(observed_common_causes, t, rowvar=False)[-1, :-1] std_dev_t = np.std(t)[0] max_coeff = max(corrcoef_var_t) * std_dev_t min_coeff = min(corrcoef_var_t) * std_dev_t else: raise NotImplementedError( "'" + self.effect_on_t + "' method not supported for confounders' effect on treatment" ) min_coeff, max_coeff = self._compute_min_max_coeff(min_coeff, max_coeff, self.frac_strength_treatment) # By default, return a plot with 10 points # consider 10 values of the effect of the unobserved confounder step = (max_coeff - min_coeff) / len_kappa_t self.logger.info("(Min, Max) kappa_t for observed common causes, ({0}, {1})".format(min_coeff, max_coeff)) if np.equal(max_coeff, min_coeff): return max_coeff else: return np.arange(min_coeff, max_coeff, step) def _compute_min_max_coeff(self, min_coeff, max_coeff, effect_strength_fraction): max_coeff = effect_strength_fraction * max_coeff min_coeff = effect_strength_fraction * min_coeff return min_coeff, max_coeff def infer_default_kappa_y(self, len_kappa_y=10): """Infer default effect strength of simulated confounder on treatment.""" observed_common_causes_names = self._target_estimand.get_backdoor_variables() if len(observed_common_causes_names) > 0: observed_common_causes = self._data[observed_common_causes_names] observed_common_causes = pd.get_dummies(observed_common_causes, drop_first=True) else: raise ValueError( "There needs to be at least one common cause to" + "automatically compute the default value of kappa_y." + " Provide a value for kappa_y" ) y = self._data[self._outcome_name] # Standardizing the data observed_common_causes = StandardScaler().fit_transform(observed_common_causes) if self.effect_on_y == "binary_flip": # Fit a model containing all confounders and compare predictions # using all features compared to all features except a given # confounder. ymodel = LogisticRegression().fit(observed_common_causes, y) ypred = ymodel.predict(observed_common_causes).astype(int) flips = [] for i in range(observed_common_causes.shape[1]): oldval = np.copy(observed_common_causes[:, i]) observed_common_causes[:, i] = 0 ycap = ymodel.predict(observed_common_causes).astype(int) observed_common_causes[:, i] = oldval flips.append(np.sum(abs(ycap - ypred)) / ypred.shape[0]) min_coeff, max_coeff = min(flips), max(flips) elif self.effect_on_y == "linear": corrcoef_var_y = np.corrcoef(observed_common_causes, y, rowvar=False)[-1, :-1] std_dev_y = np.std(y)[0] max_coeff = max(corrcoef_var_y) * std_dev_y min_coeff = min(corrcoef_var_y) * std_dev_y else: raise NotImplementedError( "'" + self.effect_on_y + "' method not supported for confounders' effect on outcome" ) min_coeff, max_coeff = self._compute_min_max_coeff(min_coeff, max_coeff, self.frac_strength_outcome) # By default, return a plot with 10 points # consider 10 values of the effect of the unobserved confounder step = (max_coeff - min_coeff) / len_kappa_y self.logger.info("(Min, Max) kappa_y for observed common causes, ({0}, {1})".format(min_coeff, max_coeff)) if np.equal(max_coeff, min_coeff): return max_coeff else: return np.arange(min_coeff, max_coeff, step) def refute_estimate(self, show_progress_bar=False): """ This function attempts to add an unobserved common cause to the outcome and the treatment. At present, we have implemented the behavior for one dimensional behaviors for continuous and binary variables. This function can either take single valued inputs or a range of inputs. The function then looks at the data type of the input and then decides on the course of action. :return: CausalRefuter: An object that contains the estimated effect and a new effect and the name of the refutation used. """ if self.simulated_method_name == "linear-partial-R2": if not (isinstance(self._estimate.estimator, LinearRegressionEstimator)): raise NotImplementedError( "Currently only LinearRegressionEstimator is supported for Sensitivity Analysis" ) if len(self._estimate.estimator._effect_modifier_names) > 0: raise NotImplementedError("The current implementation does not support effect modifiers") if self.frac_strength_outcome == 1: self.frac_strength_outcome = self.frac_strength_treatment analyzer = LinearSensitivityAnalyzer( estimator=self._estimate.estimator, data=self._data, treatment_name=self._treatment_name, percent_change_estimate=self.percent_change_estimate, significance_level=self.significance_level, benchmark_common_causes=self.benchmark_common_causes, null_hypothesis_effect=self.null_hypothesis_effect, frac_strength_treatment=self.frac_strength_treatment, frac_strength_outcome=self.frac_strength_outcome, common_causes_order=self._estimate.estimator._observed_common_causes.columns, ) analyzer.check_sensitivity(plot=self.plot_estimate) return analyzer if self.kappa_t is None: self.kappa_t = self.infer_default_kappa_t() if self.kappa_y is None: self.kappa_y = self.infer_default_kappa_y() if not isinstance(self.kappa_t, (list, np.ndarray)) and not isinstance( self.kappa_y, (list, np.ndarray) ): # Deal with single value inputs new_data = copy.deepcopy(self._data) new_data = self.include_confounders_effect(new_data, self.kappa_t, self.kappa_y) new_estimator = CausalEstimator.get_estimator_object(new_data, self._target_estimand, self._estimate) new_effect = new_estimator.estimate_effect() refute = CausalRefutation( self._estimate.value, new_effect.value, refutation_type="Refute: Add an Unobserved Common Cause" ) refute.new_effect_array = np.array(new_effect.value) refute.new_effect = new_effect.value refute.add_refuter(self) return refute else: # Deal with multiple value inputs if isinstance(self.kappa_t, (list, np.ndarray)) and isinstance( self.kappa_y, (list, np.ndarray) ): # Deal with range inputs # Get a 2D matrix of values # x,y = np.meshgrid(self.kappa_t, self.kappa_y) # x,y are both MxN results_matrix = np.random.rand( len(self.kappa_t), len(self.kappa_y) ) # Matrix to hold all the results of NxM orig_data = copy.deepcopy(self._data) for i in tqdm( range(len(self.kappa_t)), colour=CausalRefuter.PROGRESS_BAR_COLOR, disable=not show_progress_bar, desc="Refuting Estimates: ", ): for j in range(len(self.kappa_y)): new_data = self.include_confounders_effect(orig_data, self.kappa_t[i], self.kappa_y[j]) new_estimator = CausalEstimator.get_estimator_object( new_data, self._target_estimand, self._estimate ) new_effect = new_estimator.estimate_effect() refute = CausalRefutation( self._estimate.value, new_effect.value, refutation_type="Refute: Add an Unobserved Common Cause", ) results_matrix[i][j] = refute.new_effect # Populate the results refute.new_effect_array = results_matrix refute.new_effect = (np.min(results_matrix), np.max(results_matrix)) # Store the values into the refute object refute.add_refuter(self) if self.plotmethod is None: return refute import matplotlib import matplotlib.pyplot as plt fig = plt.figure(figsize=(6, 5)) left, bottom, width, height = 0.1, 0.1, 0.8, 0.8 ax = fig.add_axes([left, bottom, width, height]) oe = self._estimate.value contour_levels = [oe / 4.0, oe / 2.0, (3.0 / 4) * oe, oe] contour_levels.extend([0, np.min(results_matrix), np.max(results_matrix)]) if self.plotmethod == "contour": cp = plt.contourf(self.kappa_y, self.kappa_t, results_matrix, levels=sorted(contour_levels)) # Adding a label on the contour line for the original estimate fmt = {} trueeffect_index = np.where(cp.levels == oe)[0][0] fmt[cp.levels[trueeffect_index]] = "Estimated Effect" # Label every other level using strings plt.clabel(cp, [cp.levels[trueeffect_index]], inline=True, fmt=fmt) plt.colorbar(cp) elif self.plotmethod == "colormesh": cp = plt.pcolormesh(self.kappa_y, self.kappa_t, results_matrix, shading="nearest") plt.colorbar(cp, ticks=contour_levels) ax.yaxis.set_ticks(self.kappa_t) ax.xaxis.set_ticks(self.kappa_y) plt.xticks(rotation=45) ax.set_title("Effect of Unobserved Common Cause") ax.set_ylabel("Value of Linear Constant on Treatment") ax.set_xlabel("Value of Linear Constant on Outcome") plt.show() return refute elif isinstance(self.kappa_t, (list, np.ndarray)): outcomes = np.random.rand(len(self.kappa_t)) orig_data = copy.deepcopy(self._data) for i in tqdm( range(0, len(self.kappa_t)), colour=CausalRefuter.PROGRESS_BAR_COLOR, disable=not show_progress_bar, desc="Refuting Estimates: ", ): new_data = self.include_confounders_effect(orig_data, self.kappa_t[i], self.kappa_y) new_estimator = CausalEstimator.get_estimator_object( new_data, self._target_estimand, self._estimate ) new_effect = new_estimator.estimate_effect() refute = CausalRefutation( self._estimate.value, new_effect.value, refutation_type="Refute: Add an Unobserved Common Cause" ) self.logger.debug(refute) outcomes[i] = refute.new_effect # Populate the results refute.new_effect_array = outcomes refute.new_effect = (np.min(outcomes), np.max(outcomes)) refute.add_refuter(self) if self.plotmethod is None: return refute import matplotlib import matplotlib.pyplot as plt fig = plt.figure(figsize=(6, 5)) left, bottom, width, height = 0.1, 0.1, 0.8, 0.8 ax = fig.add_axes([left, bottom, width, height]) plt.plot(self.kappa_t, outcomes) plt.axhline(self._estimate.value, linestyle="--", color="gray") ax.set_title("Effect of Unobserved Common Cause") ax.set_xlabel("Value of Linear Constant on Treatment") ax.set_ylabel("Estimated Effect after adding the common cause") plt.show() return refute elif isinstance(self.kappa_y, (list, np.ndarray)): outcomes = np.random.rand(len(self.kappa_y)) orig_data = copy.deepcopy(self._data) for i in tqdm( range(0, len(self.kappa_y)), colour=CausalRefuter.PROGRESS_BAR_COLOR, disable=not show_progress_bar, desc="Refuting Estimates: ", ): new_data = self.include_confounders_effect(orig_data, self.kappa_t, self.kappa_y[i]) new_estimator = CausalEstimator.get_estimator_object( new_data, self._target_estimand, self._estimate ) new_effect = new_estimator.estimate_effect() refute = CausalRefutation( self._estimate.value, new_effect.value, refutation_type="Refute: Add an Unobserved Common Cause" ) self.logger.debug(refute) outcomes[i] = refute.new_effect # Populate the results refute.new_effect_array = outcomes refute.new_effect = (np.min(outcomes), np.max(outcomes)) refute.add_refuter(self) if self.plotmethod is None: return refute import matplotlib import matplotlib.pyplot as plt fig = plt.figure(figsize=(6, 5)) left, bottom, width, height = 0.1, 0.1, 0.8, 0.8 ax = fig.add_axes([left, bottom, width, height]) plt.plot(self.kappa_y, outcomes) plt.axhline(self._estimate.value, linestyle="--", color="gray") ax.set_title("Effect of Unobserved Common Cause") ax.set_xlabel("Value of Linear Constant on Outcome") ax.set_ylabel("Estimated Effect after adding the common cause") plt.show() return refute def include_confounders_effect(self, new_data, kappa_t, kappa_y): """ This function deals with the change in the value of the data due to the effect of the unobserved confounder. In the case of a binary flip, we flip only if the random number is greater than the threshold set. In the case of a linear effect, we use the variable as the linear regression constant. :param new_data: pandas.DataFrame: The data to be changed due to the effects of the unobserved confounder. :param kappa_t: numpy.float64: The value of the threshold for binary_flip or the value of the regression coefficient for linear effect. :param kappa_y: numpy.float64: The value of the threshold for binary_flip or the value of the regression coefficient for linear effect. :return: pandas.DataFrame: The DataFrame that includes the effects of the unobserved confounder. """ num_rows = self._data.shape[0] stdnorm = scipy.stats.norm() w_random = stdnorm.rvs(num_rows) if self.effect_on_t == "binary_flip": alpha = 2 * kappa_t - 1 if kappa_t >= 0.5 else 1 - 2 * kappa_t interval = stdnorm.interval(alpha) rel_interval = interval[0] if kappa_t >= 0.5 else interval[1] new_data.loc[rel_interval <= w_random, self._treatment_name] = ( 1 - new_data.loc[rel_interval <= w_random, self._treatment_name] ) for tname in self._treatment_name: if pd.api.types.is_bool_dtype(self._data[tname]): new_data = new_data.astype({tname: "bool"}, copy=False) elif self.effect_on_t == "linear": confounder_t_effect = kappa_t * w_random # By default, we add the effect of simulated confounder for treatment. # But subtract it from outcome to create a negative correlation # assuming that the original confounder's effect was positive on both. # This is to remove the effect of the original confounder. new_data[self._treatment_name] = new_data[self._treatment_name].values + np.ndarray( shape=(num_rows, 1), buffer=confounder_t_effect ) else: raise NotImplementedError( "'" + self.effect_on_t + "' method not supported for confounders' effect on treatment" ) if self.effect_on_y == "binary_flip": alpha = 2 * kappa_y - 1 if kappa_y >= 0.5 else 1 - 2 * kappa_y interval = stdnorm.interval(alpha) rel_interval = interval[0] if kappa_y >= 0.5 else interval[1] new_data.loc[rel_interval <= w_random, self._outcome_name] = ( 1 - new_data.loc[rel_interval <= w_random, self._outcome_name] ) for yname in self._outcome_name: if pd.api.types.is_bool_dtype(self._data[yname]): new_data = new_data.astype({yname: "bool"}, copy=False) elif self.effect_on_y == "linear": confounder_y_effect = (-1) * kappa_y * w_random # By default, we add the effect of simulated confounder for treatment. # But subtract it from outcome to create a negative correlation # assuming that the original confounder's effect was positive on both. # This is to remove the effect of the original confounder. new_data[self._outcome_name] = new_data[self._outcome_name].values + np.ndarray( shape=(num_rows, 1), buffer=confounder_y_effect ) else: raise NotImplementedError( "'" + self.effect_on_y + "' method not supported for confounders' effect on outcome" ) return new_data def include_simulated_confounder(self, convergence_threshold=0.1, c_star_max=1000): """ This function simulates an unobserved confounder based on the data using the following steps: 1. It calculates the "residuals" from the treatment and outcome model i.) The outcome model has outcome as the dependent variable and all the observed variables including treatment as independent variables ii.) The treatment model has treatment as the dependent variable and all the observed variables as independent variables. 2. U is an intermediate random variable drawn from the normal distribution with the weighted average of residuals as mean and a unit variance U ~ N(c1*d_y + c2*d_t, 1) where *d_y and d_t are residuals from the treatment and outcome model *c1 and c2 are coefficients to the residuals 3. The final U, which is the simulated unobserved confounder is obtained by debiasing the intermediate variable U by residualising it with X Choosing the coefficients c1 and c2: The coefficients are chosen based on these basic assumptions: 1. There is a hyperbolic relationship satisfying c1*c2 = c_star 2. c_star is chosen from a range of possible values based on the correlation of the obtained simulated variable with outcome and treatment. 3. The product of correlations with treatment and outcome should be at a minimum distance to the maximum correlations with treatment and outcome in any of the observed confounders 4. The ratio of the weights should be such that they maintain the ratio of the maximum possible observed coefficients within some confidence interval :param c_star_max: The maximum possible value for the hyperbolic curve on which the coefficients to the residuals lie. It defaults to 1000 in the code if not specified by the user. :type int :param convergence_threshold: The threshold to check the plateauing of the correlation while selecting a c_star. It defaults to 0.1 in the code if not specified by the user :type float :returns: The simulated values of the unobserved confounder based on the data :type pandas.core.series.Series """ # Obtaining the list of observed variables required_variables = True observed_variables = self.choose_variables(required_variables) observed_variables_with_treatment_and_outcome = observed_variables + self._treatment_name + self._outcome_name # Taking a subset of the dataframe that has only observed variables self._data = self._data[observed_variables_with_treatment_and_outcome] # Residuals from the outcome model obtained by fitting a linear model y = self._data[self._outcome_name[0]] observed_variables_with_treatment = observed_variables + self._treatment_name X = self._data[observed_variables_with_treatment] model = sm.OLS(y, X.astype("float")) results = model.fit() residuals_y = y - results.fittedvalues d_y = list(pd.Series(residuals_y)) # Residuals from the treatment model obtained by fitting a linear model t = self._data[self._treatment_name[0]].astype("int64") X = self._data[observed_variables] model = sm.OLS(t, X) results = model.fit() residuals_t = t - results.fittedvalues d_t = list(pd.Series(residuals_t)) # Initialising product_cor_metric_observed with a really low value as finding maximum product_cor_metric_observed = -10000000000 for i in observed_variables: current_obs_confounder = self._data[i] outcome_values = self._data[self._outcome_name[0]] correlation_y = current_obs_confounder.corr(outcome_values) treatment_values = t correlation_t = current_obs_confounder.corr(treatment_values) product_cor_metric_current = correlation_y * correlation_t if product_cor_metric_current >= product_cor_metric_observed: product_cor_metric_observed = product_cor_metric_current correlation_t_observed = correlation_t correlation_y_observed = correlation_y # The user has an option to give the the effect_strength_on_y and effect_strength_on_t which can be then used instead of maximum correlation with treatment and outcome in the observed variables as it specifies the desired effect. if self.kappa_t is not None: correlation_t_observed = self.kappa_t if self.kappa_y is not None: correlation_y_observed = self.kappa_y # Choosing a c_star based on the data. # The correlations stop increasing upon increasing c_star after a certain value, that is it plateaus and we choose the value of c_star to be the value it plateaus. correlation_y_list = [] correlation_t_list = [] product_cor_metric_simulated_list = [] x_list = [] step = int(c_star_max / 10) for i in range(0, int(c_star_max), step): c1 = math.sqrt(i) c2 = c1 final_U = self.generate_confounder_from_residuals(c1, c2, d_y, d_t, X) current_simulated_confounder = final_U outcome_values = self._data[self._outcome_name[0]] correlation_y = current_simulated_confounder.corr(outcome_values) correlation_y_list.append(correlation_y) treatment_values = t correlation_t = current_simulated_confounder.corr(treatment_values) correlation_t_list.append(correlation_t) product_cor_metric_simulated = correlation_y * correlation_t product_cor_metric_simulated_list.append(product_cor_metric_simulated) x_list.append(i) index = 1 while index < len(correlation_y_list): if (correlation_y_list[index] - correlation_y_list[index - 1]) <= convergence_threshold: c_star = x_list[index] break index = index + 1 # Choosing c1 and c2 based on the hyperbolic relationship once c_star is chosen by going over various combinations of c1 and c2 values and choosing the combination which # which maintains the minimum distance between the product of correlations of the simulated variable and the product of maximum correlations of one of the observed variables # and additionally checks if the ratio of the weights are such that they maintain the ratio of the maximum possible observed coefficients within some confidence interval # c1_final and c2_final are initialised to the values on the hyperbolic curve such that c1_final = c2_final and c1_final*c2_final = c_star c1_final = math.sqrt(c_star) c2_final = math.sqrt(c_star) # initialising min_distance_between_product_cor_metrics to be a value greater than 1 min_distance_between_product_cor_metrics = 1.5 i = 0.05 threshold = c_star / 0.05 while i <= threshold: c2 = i c1 = c_star / c2 final_U = self.generate_confounder_from_residuals(c1, c2, d_y, d_t, X) current_simulated_confounder = final_U outcome_values = self._data[self._outcome_name[0]] correlation_y = current_simulated_confounder.corr(outcome_values) treatment_values = t correlation_t = current_simulated_confounder.corr(treatment_values) product_cor_metric_simulated = correlation_y * correlation_t if min_distance_between_product_cor_metrics >= abs( product_cor_metric_simulated - product_cor_metric_observed ): min_distance_between_product_cor_metrics = abs( product_cor_metric_simulated - product_cor_metric_observed ) additional_condition = correlation_y_observed / correlation_t_observed if ((c1 / c2) <= (additional_condition + 0.3 * additional_condition)) and ( (c1 / c2) >= (additional_condition - 0.3 * additional_condition) ): # choose minimum positive value c1_final = c1 c2_final = c2 i = i * 1.5 """#closed form solution print("c_star_max before closed form", c_star_max) if max_correlation_with_t == -1000: c2 = 0 c1 = c_star_max else: additional_condition = abs(max_correlation_with_y/max_correlation_with_t) print("additional_condition", additional_condition) c2 = math.sqrt(c_star_max/additional_condition) c1 = c_star_max/c2""" final_U = self.generate_confounder_from_residuals(c1_final, c2_final, d_y, d_t, X) return final_U def generate_confounder_from_residuals(self, c1, c2, d_y, d_t, X): """ This function takes the residuals from the treatment and outcome model and their coefficients and simulates the intermediate random variable U by taking the row wise normal distribution corresponding to each residual value and then debiasing the intermediate variable to get the final variable. :param c1: coefficient to the residual from the outcome model :type float :param c2: coefficient to the residual from the treatment model :type float :param d_y: residuals from the outcome model :type list :param d_t: residuals from the treatment model :type list :returns: The simulated values of the unobserved confounder based on the data :type pandas.core.series.Series """ U = [] for j in range(len(d_t)): simulated_variable_mean = c1 * d_y[j] + c2 * d_t[j] simulated_variable_stddev = 1 U.append(np.random.normal(simulated_variable_mean, simulated_variable_stddev, 1)) U = np.array(U) model = sm.OLS(U, X) results = model.fit() U = U.reshape( -1, ) final_U = U - results.fittedvalues.values final_U = pd.Series(U) return final_U

import copy import logging import math import numpy as np import pandas as pd import scipy.stats import statsmodels.api as sm from sklearn.linear_model import LogisticRegression from sklearn.preprocessing import StandardScaler from tqdm.auto import tqdm import dowhy.causal_estimators.econml from dowhy.causal_estimator import CausalEstimator from dowhy.causal_estimators.linear_regression_estimator import LinearRegressionEstimator from dowhy.causal_refuter import CausalRefutation, CausalRefuter from dowhy.causal_refuters.linear_sensitivity_analyzer import LinearSensitivityAnalyzer from dowhy.causal_refuters.non_parametric_sensitivity_analyzer import NonParametricSensitivityAnalyzer from dowhy.causal_refuters.partial_linear_sensitivity_analyzer import PartialLinearSensitivityAnalyzer class AddUnobservedCommonCause(CausalRefuter): """Add an unobserved confounder for refutation. AddUnobservedCommonCause class supports three methods: 1) Simulation of an unobserved confounder 2) Linear partial R2 : Sensitivity Analysis for linear models. 3) Non-Parametric partial R2 based : Sensitivity Analyis for non-parametric models. Supports additional parameters that can be specified in the refute_estimate() method. """ def __init__(self, *args, **kwargs): """ Initialize the parameters required for the refuter. For direct_simulation, if effect_strength_on_treatment or effect_strength_on_outcome is not given, it is calculated automatically as a range between the minimum and maximum effect strength of observed confounders on treatment and outcome respectively. :param simulation_method: The method to use for simulating effect of unobserved confounder. Possible values are ["direct-simulation", "linear-partial-R2", "non-parametric-partial-R2"]. :param confounders_effect_on_treatment: str : The type of effect on the treatment due to the unobserved confounder. Possible values are ['binary_flip', 'linear'] :param confounders_effect_on_outcome: str : The type of effect on the outcome due to the unobserved confounder. Possible values are ['binary_flip', 'linear'] :param effect_strength_on_treatment: float, numpy.ndarray: [Used when simulation_method="direct-simulation"] Strength of the confounder's effect on treatment. When confounders_effect_on_treatment is linear, it is the regression coefficient. When the confounders_effect_on_treatment is binary flip, it is the probability with which effect of unobserved confounder can invert the value of the treatment. :param effect_strength_on_outcome: float, numpy.ndarray: Strength of the confounder's effect on outcome. Its interpretation depends on confounders_effect_on_outcome and the simulation_method. When simulation_method is direct-simulation, for a linear effect it behaves like the regression coefficient and for a binary flip, it is the probability with which it can invert the value of the outcome. :param partial_r2_confounder_treatment: float, numpy.ndarray: [Used when simulation_method is linear-partial-R2 or non-parametric-partial-R2] Partial R2 of the unobserved confounder wrt the treatment conditioned on the observed confounders. Only in the case of general non-parametric-partial-R2, it is the fraction of variance in the reisz representer that is explained by the unobserved confounder; specifically (1-r), where r is the ratio of variance of reisz representer, alpha^2, based on observed confounders and that based on all confounders. :param partial_r2_confounder_outcome: float, numpy.ndarray: [Used when simulation_method is linear-partial-R2 or non-parametric-partial-R2] Partial R2 of the unobserved confounder wrt the outcome conditioned on the treatment and observed confounders. :param frac_strength_treatment: float: This parameter decides the effect strength of the simulated confounder as a fraction of the effect strength of observed confounders on treatment. Defaults to 1. :param frac_strength_outcome: float: This parameter decides the effect strength of the simulated confounder as a fraction of the effect strength of observed confounders on outcome. Defaults to 1. :param plotmethod: string: Type of plot to be shown. If None, no plot is generated. This parameter is used only only when more than one treatment confounder effect values or outcome confounder effect values are provided. Default is "colormesh". Supported values are "contour", "colormesh" when more than one value is provided for both confounder effect value parameters; "line" when provided for only one of them. :param percent_change_estimate: It is the percentage of reduction of treatment estimate that could alter the results (default = 1). if percent_change_estimate = 1, the robustness value describes the strength of association of confounders with treatment and outcome in order to reduce the estimate by 100% i.e bring it down to 0. (relevant only for Linear Sensitivity Analysis, ignore for rest) :param confounder_increases_estimate: True implies that confounder increases the absolute value of estimate and vice versa. (Default = False). (relevant only for Linear Sensitivity Analysis, ignore for rest) :param benchmark_common_causes: names of variables for bounding strength of confounders. (relevant only for partial-r2 based simulation methods) :param significance_level: confidence interval for statistical inference(default = 0.05). (relevant only for partial-r2 based simulation methods) :param null_hypothesis_effect: assumed effect under the null hypothesis. (relevant only for linear-partial-R2, ignore for rest) :param plot_estimate: Generate contour plot for estimate while performing sensitivity analysis. (default = True). (relevant only for partial-r2 based simulation methods) :param num_splits: number of splits for cross validation. (default = 5). (relevant only for non-parametric-partial-R2 simulation method) :param shuffle_data : shuffle data or not before splitting into folds (default = False). (relevant only for non-parametric-partial-R2 simulation method) :param shuffle_random_seed: seed for randomly shuffling data. (relevant only for non-parametric-partial-R2 simulation method) :param alpha_s_estimator_param_list: list of dictionaries with parameters for finding alpha_s. (relevant only for non-parametric-partial-R2 simulation method) :param g_s_estimator_list: list of estimator objects for finding g_s. These objects should have fit() and predict() functions implemented. (relevant only for non-parametric-partial-R2 simulation method) :param g_s_estimator_param_list: list of dictionaries with parameters for tuning respective estimators in "g_s_estimator_list". The order of the dictionaries in the list should be consistent with the estimator objects order in "g_s_estimator_list". (relevant only for non-parametric-partial-R2 simulation method) """ super().__init__(*args, **kwargs) self.simulation_method = kwargs["simulation_method"] if "simulation_method" in kwargs else "direct-simulation" self.effect_on_t = ( kwargs["confounders_effect_on_treatment"] if "confounders_effect_on_treatment" in kwargs else "binary_flip" ) self.effect_on_y = ( kwargs["confounders_effect_on_outcome"] if "confounders_effect_on_outcome" in kwargs else "linear" ) if self.simulation_method == "direct-simulation": self.kappa_t = kwargs["effect_strength_on_treatment"] if "effect_strength_on_treatment" in kwargs else None self.kappa_y = kwargs["effect_strength_on_outcome"] if "effect_strength_on_outcome" in kwargs else None elif self.simulation_method in ["linear-partial-R2", "non-parametric-partial-R2"]: self.kappa_t = ( kwargs["partial_r2_confounder_treatment"] if "partial_r2_confounder_treatment" in kwargs else None ) self.kappa_y = ( kwargs["partial_r2_confounder_outcome"] if "partial_r2_confounder_outcome" in kwargs else None ) else: raise ValueError( "simulation method is not supported. Try direct-simulation, linear-partial-R2 or non-parametric-partial-R2" ) self.frac_strength_treatment = ( kwargs["effect_fraction_on_treatment"] if "effect_fraction_on_treatment" in kwargs else 1 ) self.frac_strength_outcome = ( kwargs["effect_fraction_on_outcome"] if "effect_fraction_on_outcome" in kwargs else 1 ) self.plotmethod = kwargs["plotmethod"] if "plotmethod" in kwargs else "colormesh" self.percent_change_estimate = kwargs["percent_change_estimate"] if "percent_change_estimate" in kwargs else 1.0 self.significance_level = kwargs["significance_level"] if "significance_level" in kwargs else 0.05 self.confounder_increases_estimate = ( kwargs["confounder_increases_estimate"] if "confounder_increases_estimate" in kwargs else False ) self.benchmark_common_causes = ( kwargs["benchmark_common_causes"] if "benchmark_common_causes" in kwargs else None ) self.null_hypothesis_effect = kwargs["null_hypothesis_effect"] if "null_hypothesis_effect" in kwargs else 0 self.plot_estimate = kwargs["plot_estimate"] if "plot_estimate" in kwargs else True self.num_splits = kwargs["num_splits"] if "num_splits" in kwargs else 5 self.shuffle_data = kwargs["shuffle_data"] if "shuffle_data" in kwargs else False self.shuffle_random_seed = kwargs["shuffle_random_seed"] if "shuffle_random_seed" in kwargs else None self.alpha_s_estimator_param_list = ( kwargs["alpha_s_estimator_param_list"] if "alpha_s_estimator_param_list" in kwargs else None ) self.alpha_s_estimator_list = kwargs["alpha_s_estimator_list"] if "alpha_s_estimator_list" in kwargs else None self.g_s_estimator_list = kwargs["g_s_estimator_list"] if "g_s_estimator_list" in kwargs else None self.g_s_estimator_param_list = ( kwargs["g_s_estimator_param_list"] if "g_s_estimator_param_list" in kwargs else None ) self.plugin_reisz = kwargs["plugin_reisz"] if "plugin_reisz" in kwargs else False self.logger = logging.getLogger(__name__) def infer_default_kappa_t(self, len_kappa_t=10): """Infer default effect strength of simulated confounder on treatment.""" observed_common_causes_names = self._target_estimand.get_backdoor_variables() if len(observed_common_causes_names) > 0: observed_common_causes = self._data[observed_common_causes_names] observed_common_causes = pd.get_dummies(observed_common_causes, drop_first=True) else: raise ValueError( "There needs to be at least one common cause to" + "automatically compute the default value of kappa_t." + " Provide a value for kappa_t" ) t = self._data[self._treatment_name] # Standardizing the data observed_common_causes = StandardScaler().fit_transform(observed_common_causes) if self.effect_on_t == "binary_flip": # Fit a model containing all confounders and compare predictions # using all features compared to all features except a given # confounder. tmodel = LogisticRegression().fit(observed_common_causes, t) tpred = tmodel.predict(observed_common_causes).astype(int) flips = [] for i in range(observed_common_causes.shape[1]): oldval = np.copy(observed_common_causes[:, i]) observed_common_causes[:, i] = 0 tcap = tmodel.predict(observed_common_causes).astype(int) observed_common_causes[:, i] = oldval flips.append(np.sum(abs(tcap - tpred)) / tpred.shape[0]) min_coeff, max_coeff = min(flips), max(flips) elif self.effect_on_t == "linear": # Estimating the regression coefficient from standardized features to t corrcoef_var_t = np.corrcoef(observed_common_causes, t, rowvar=False)[-1, :-1] std_dev_t = np.std(t)[0] max_coeff = max(corrcoef_var_t) * std_dev_t min_coeff = min(corrcoef_var_t) * std_dev_t else: raise NotImplementedError( "'" + self.effect_on_t + "' method not supported for confounders' effect on treatment" ) min_coeff, max_coeff = self._compute_min_max_coeff(min_coeff, max_coeff, self.frac_strength_treatment) # By default, return a plot with 10 points # consider 10 values of the effect of the unobserved confounder step = (max_coeff - min_coeff) / len_kappa_t self.logger.info("(Min, Max) kappa_t for observed common causes, ({0}, {1})".format(min_coeff, max_coeff)) if np.equal(max_coeff, min_coeff): return max_coeff else: return np.arange(min_coeff, max_coeff, step) def _compute_min_max_coeff(self, min_coeff, max_coeff, effect_strength_fraction): max_coeff = effect_strength_fraction * max_coeff min_coeff = effect_strength_fraction * min_coeff return min_coeff, max_coeff def infer_default_kappa_y(self, len_kappa_y=10): """Infer default effect strength of simulated confounder on treatment.""" observed_common_causes_names = self._target_estimand.get_backdoor_variables() if len(observed_common_causes_names) > 0: observed_common_causes = self._data[observed_common_causes_names] observed_common_causes = pd.get_dummies(observed_common_causes, drop_first=True) else: raise ValueError( "There needs to be at least one common cause to" + "automatically compute the default value of kappa_y." + " Provide a value for kappa_y" ) y = self._data[self._outcome_name] # Standardizing the data observed_common_causes = StandardScaler().fit_transform(observed_common_causes) if self.effect_on_y == "binary_flip": # Fit a model containing all confounders and compare predictions # using all features compared to all features except a given # confounder. ymodel = LogisticRegression().fit(observed_common_causes, y) ypred = ymodel.predict(observed_common_causes).astype(int) flips = [] for i in range(observed_common_causes.shape[1]): oldval = np.copy(observed_common_causes[:, i]) observed_common_causes[:, i] = 0 ycap = ymodel.predict(observed_common_causes).astype(int) observed_common_causes[:, i] = oldval flips.append(np.sum(abs(ycap - ypred)) / ypred.shape[0]) min_coeff, max_coeff = min(flips), max(flips) elif self.effect_on_y == "linear": corrcoef_var_y = np.corrcoef(observed_common_causes, y, rowvar=False)[-1, :-1] std_dev_y = np.std(y)[0] max_coeff = max(corrcoef_var_y) * std_dev_y min_coeff = min(corrcoef_var_y) * std_dev_y else: raise NotImplementedError( "'" + self.effect_on_y + "' method not supported for confounders' effect on outcome" ) min_coeff, max_coeff = self._compute_min_max_coeff(min_coeff, max_coeff, self.frac_strength_outcome) # By default, return a plot with 10 points # consider 10 values of the effect of the unobserved confounder step = (max_coeff - min_coeff) / len_kappa_y self.logger.info("(Min, Max) kappa_y for observed common causes, ({0}, {1})".format(min_coeff, max_coeff)) if np.equal(max_coeff, min_coeff): return max_coeff else: return np.arange(min_coeff, max_coeff, step) def refute_estimate(self, show_progress_bar=False): """ This function attempts to add an unobserved common cause to the outcome and the treatment. At present, we have implemented the behavior for one dimensional behaviors for continuous and binary variables. This function can either take single valued inputs or a range of inputs. The function then looks at the data type of the input and then decides on the course of action. :return: CausalRefuter: An object that contains the estimated effect and a new effect and the name of the refutation used. """ if self.simulation_method == "linear-partial-R2": if not (isinstance(self._estimate.estimator, LinearRegressionEstimator)): raise NotImplementedError( "Currently only LinearRegressionEstimator is supported for Sensitivity Analysis" ) if len(self._estimate.estimator._effect_modifier_names) > 0: raise NotImplementedError("The current implementation does not support effect modifiers") if self.frac_strength_outcome == 1: self.frac_strength_outcome = self.frac_strength_treatment analyzer = LinearSensitivityAnalyzer( estimator=self._estimate.estimator, data=self._data, treatment_name=self._treatment_name, percent_change_estimate=self.percent_change_estimate, significance_level=self.significance_level, benchmark_common_causes=self.benchmark_common_causes, null_hypothesis_effect=self.null_hypothesis_effect, frac_strength_treatment=self.frac_strength_treatment, frac_strength_outcome=self.frac_strength_outcome, common_causes_order=self._estimate.estimator._observed_common_causes.columns, ) analyzer.check_sensitivity(plot=self.plot_estimate) return analyzer if self.simulation_method == "non-parametric-partial-R2": # If the estimator used is LinearDML, partially linear sensitivity analysis will be automatically chosen if isinstance(self._estimate.estimator, dowhy.causal_estimators.econml.Econml): if self._estimate.estimator._econml_methodname == "econml.dml.LinearDML": analyzer = PartialLinearSensitivityAnalyzer( estimator=self._estimate._estimator_object, observed_common_causes=self._estimate.estimator._observed_common_causes, treatment=self._estimate.estimator._treatment, outcome=self._estimate.estimator._outcome, alpha_s_estimator_param_list=self.alpha_s_estimator_param_list, g_s_estimator_list=self.g_s_estimator_list, g_s_estimator_param_list=self.g_s_estimator_param_list, effect_strength_treatment=self.kappa_t, effect_strength_outcome=self.kappa_y, benchmark_common_causes=self.benchmark_common_causes, frac_strength_treatment=self.frac_strength_treatment, frac_strength_outcome=self.frac_strength_outcome, ) analyzer.check_sensitivity(plot=self.plot_estimate) return analyzer analyzer = NonParametricSensitivityAnalyzer( estimator=self._estimate.estimator, observed_common_causes=self._estimate.estimator._observed_common_causes, treatment=self._estimate.estimator._treatment, outcome=self._estimate.estimator._outcome, alpha_s_estimator_list=self.alpha_s_estimator_list, alpha_s_estimator_param_list=self.alpha_s_estimator_param_list, g_s_estimator_list=self.g_s_estimator_list, g_s_estimator_param_list=self.g_s_estimator_param_list, effect_strength_treatment=self.kappa_t, effect_strength_outcome=self.kappa_y, benchmark_common_causes=self.benchmark_common_causes, frac_strength_treatment=self.frac_strength_treatment, frac_strength_outcome=self.frac_strength_outcome, theta_s=self._estimate.value, plugin_reisz=self.plugin_reisz, ) analyzer.check_sensitivity(plot=self.plot_estimate) return analyzer if self.kappa_t is None: self.kappa_t = self.infer_default_kappa_t() if self.kappa_y is None: self.kappa_y = self.infer_default_kappa_y() if not isinstance(self.kappa_t, (list, np.ndarray)) and not isinstance( self.kappa_y, (list, np.ndarray) ): # Deal with single value inputs new_data = copy.deepcopy(self._data) new_data = self.include_confounders_effect(new_data, self.kappa_t, self.kappa_y) new_estimator = CausalEstimator.get_estimator_object(new_data, self._target_estimand, self._estimate) new_effect = new_estimator.estimate_effect() refute = CausalRefutation( self._estimate.value, new_effect.value, refutation_type="Refute: Add an Unobserved Common Cause" ) refute.new_effect_array = np.array(new_effect.value) refute.new_effect = new_effect.value refute.add_refuter(self) return refute else: # Deal with multiple value inputs if isinstance(self.kappa_t, (list, np.ndarray)) and isinstance( self.kappa_y, (list, np.ndarray) ): # Deal with range inputs # Get a 2D matrix of values # x,y = np.meshgrid(self.kappa_t, self.kappa_y) # x,y are both MxN results_matrix = np.random.rand( len(self.kappa_t), len(self.kappa_y) ) # Matrix to hold all the results of NxM orig_data = copy.deepcopy(self._data) for i in tqdm( range(len(self.kappa_t)), colour=CausalRefuter.PROGRESS_BAR_COLOR, disable=not show_progress_bar, desc="Refuting Estimates: ", ): for j in range(len(self.kappa_y)): new_data = self.include_confounders_effect(orig_data, self.kappa_t[i], self.kappa_y[j]) new_estimator = CausalEstimator.get_estimator_object( new_data, self._target_estimand, self._estimate ) new_effect = new_estimator.estimate_effect() refute = CausalRefutation( self._estimate.value, new_effect.value, refutation_type="Refute: Add an Unobserved Common Cause", ) results_matrix[i][j] = refute.new_effect # Populate the results refute.new_effect_array = results_matrix refute.new_effect = (np.min(results_matrix), np.max(results_matrix)) # Store the values into the refute object refute.add_refuter(self) if self.plotmethod is None: return refute import matplotlib import matplotlib.pyplot as plt fig = plt.figure(figsize=(6, 5)) left, bottom, width, height = 0.1, 0.1, 0.8, 0.8 ax = fig.add_axes([left, bottom, width, height]) oe = self._estimate.value contour_levels = [oe / 4.0, oe / 2.0, (3.0 / 4) * oe, oe] contour_levels.extend([0, np.min(results_matrix), np.max(results_matrix)]) if self.plotmethod == "contour": cp = plt.contourf(self.kappa_y, self.kappa_t, results_matrix, levels=sorted(contour_levels)) # Adding a label on the contour line for the original estimate fmt = {} trueeffect_index = np.where(cp.levels == oe)[0][0] fmt[cp.levels[trueeffect_index]] = "Estimated Effect" # Label every other level using strings plt.clabel(cp, [cp.levels[trueeffect_index]], inline=True, fmt=fmt) plt.colorbar(cp) elif self.plotmethod == "colormesh": cp = plt.pcolormesh(self.kappa_y, self.kappa_t, results_matrix, shading="nearest") plt.colorbar(cp, ticks=contour_levels) ax.yaxis.set_ticks(self.kappa_t) ax.xaxis.set_ticks(self.kappa_y) plt.xticks(rotation=45) ax.set_title("Effect of Unobserved Common Cause") ax.set_ylabel("Value of Linear Constant on Treatment") ax.set_xlabel("Value of Linear Constant on Outcome") plt.show() return refute elif isinstance(self.kappa_t, (list, np.ndarray)): outcomes = np.random.rand(len(self.kappa_t)) orig_data = copy.deepcopy(self._data) for i in tqdm( range(0, len(self.kappa_t)), colour=CausalRefuter.PROGRESS_BAR_COLOR, disable=not show_progress_bar, desc="Refuting Estimates: ", ): new_data = self.include_confounders_effect(orig_data, self.kappa_t[i], self.kappa_y) new_estimator = CausalEstimator.get_estimator_object( new_data, self._target_estimand, self._estimate ) new_effect = new_estimator.estimate_effect() refute = CausalRefutation( self._estimate.value, new_effect.value, refutation_type="Refute: Add an Unobserved Common Cause" ) self.logger.debug(refute) outcomes[i] = refute.new_effect # Populate the results refute.new_effect_array = outcomes refute.new_effect = (np.min(outcomes), np.max(outcomes)) refute.add_refuter(self) if self.plotmethod is None: return refute import matplotlib import matplotlib.pyplot as plt fig = plt.figure(figsize=(6, 5)) left, bottom, width, height = 0.1, 0.1, 0.8, 0.8 ax = fig.add_axes([left, bottom, width, height]) plt.plot(self.kappa_t, outcomes) plt.axhline(self._estimate.value, linestyle="--", color="gray") ax.set_title("Effect of Unobserved Common Cause") ax.set_xlabel("Value of Linear Constant on Treatment") ax.set_ylabel("Estimated Effect after adding the common cause") plt.show() return refute elif isinstance(self.kappa_y, (list, np.ndarray)): outcomes = np.random.rand(len(self.kappa_y)) orig_data = copy.deepcopy(self._data) for i in tqdm( range(0, len(self.kappa_y)), colour=CausalRefuter.PROGRESS_BAR_COLOR, disable=not show_progress_bar, desc="Refuting Estimates: ", ): new_data = self.include_confounders_effect(orig_data, self.kappa_t, self.kappa_y[i]) new_estimator = CausalEstimator.get_estimator_object( new_data, self._target_estimand, self._estimate ) new_effect = new_estimator.estimate_effect() refute = CausalRefutation( self._estimate.value, new_effect.value, refutation_type="Refute: Add an Unobserved Common Cause" ) self.logger.debug(refute) outcomes[i] = refute.new_effect # Populate the results refute.new_effect_array = outcomes refute.new_effect = (np.min(outcomes), np.max(outcomes)) refute.add_refuter(self) if self.plotmethod is None: return refute import matplotlib import matplotlib.pyplot as plt fig = plt.figure(figsize=(6, 5)) left, bottom, width, height = 0.1, 0.1, 0.8, 0.8 ax = fig.add_axes([left, bottom, width, height]) plt.plot(self.kappa_y, outcomes) plt.axhline(self._estimate.value, linestyle="--", color="gray") ax.set_title("Effect of Unobserved Common Cause") ax.set_xlabel("Value of Linear Constant on Outcome") ax.set_ylabel("Estimated Effect after adding the common cause") plt.show() return refute def include_confounders_effect(self, new_data, kappa_t, kappa_y): """ This function deals with the change in the value of the data due to the effect of the unobserved confounder. In the case of a binary flip, we flip only if the random number is greater than the threshold set. In the case of a linear effect, we use the variable as the linear regression constant. :param new_data: pandas.DataFrame: The data to be changed due to the effects of the unobserved confounder. :param kappa_t: numpy.float64: The value of the threshold for binary_flip or the value of the regression coefficient for linear effect. :param kappa_y: numpy.float64: The value of the threshold for binary_flip or the value of the regression coefficient for linear effect. :return: pandas.DataFrame: The DataFrame that includes the effects of the unobserved confounder. """ num_rows = self._data.shape[0] stdnorm = scipy.stats.norm() w_random = stdnorm.rvs(num_rows) if self.effect_on_t == "binary_flip": alpha = 2 * kappa_t - 1 if kappa_t >= 0.5 else 1 - 2 * kappa_t interval = stdnorm.interval(alpha) rel_interval = interval[0] if kappa_t >= 0.5 else interval[1] new_data.loc[rel_interval <= w_random, self._treatment_name] = ( 1 - new_data.loc[rel_interval <= w_random, self._treatment_name] ) for tname in self._treatment_name: if pd.api.types.is_bool_dtype(self._data[tname]): new_data = new_data.astype({tname: "bool"}, copy=False) elif self.effect_on_t == "linear": confounder_t_effect = kappa_t * w_random # By default, we add the effect of simulated confounder for treatment. # But subtract it from outcome to create a negative correlation # assuming that the original confounder's effect was positive on both. # This is to remove the effect of the original confounder. new_data[self._treatment_name] = new_data[self._treatment_name].values + np.ndarray( shape=(num_rows, 1), buffer=confounder_t_effect ) else: raise NotImplementedError( "'" + self.effect_on_t + "' method not supported for confounders' effect on treatment" ) if self.effect_on_y == "binary_flip": alpha = 2 * kappa_y - 1 if kappa_y >= 0.5 else 1 - 2 * kappa_y interval = stdnorm.interval(alpha) rel_interval = interval[0] if kappa_y >= 0.5 else interval[1] new_data.loc[rel_interval <= w_random, self._outcome_name] = ( 1 - new_data.loc[rel_interval <= w_random, self._outcome_name] ) for yname in self._outcome_name: if pd.api.types.is_bool_dtype(self._data[yname]): new_data = new_data.astype({yname: "bool"}, copy=False) elif self.effect_on_y == "linear": confounder_y_effect = (-1) * kappa_y * w_random # By default, we add the effect of simulated confounder for treatment. # But subtract it from outcome to create a negative correlation # assuming that the original confounder's effect was positive on both. # This is to remove the effect of the original confounder. new_data[self._outcome_name] = new_data[self._outcome_name].values + np.ndarray( shape=(num_rows, 1), buffer=confounder_y_effect ) else: raise NotImplementedError( "'" + self.effect_on_y + "' method not supported for confounders' effect on outcome" ) return new_data def include_simulated_confounder(self, convergence_threshold=0.1, c_star_max=1000): """ This function simulates an unobserved confounder based on the data using the following steps: 1. It calculates the "residuals" from the treatment and outcome model i.) The outcome model has outcome as the dependent variable and all the observed variables including treatment as independent variables ii.) The treatment model has treatment as the dependent variable and all the observed variables as independent variables. 2. U is an intermediate random variable drawn from the normal distribution with the weighted average of residuals as mean and a unit variance U ~ N(c1*d_y + c2*d_t, 1) where *d_y and d_t are residuals from the treatment and outcome model *c1 and c2 are coefficients to the residuals 3. The final U, which is the simulated unobserved confounder is obtained by debiasing the intermediate variable U by residualising it with X Choosing the coefficients c1 and c2: The coefficients are chosen based on these basic assumptions: 1. There is a hyperbolic relationship satisfying c1*c2 = c_star 2. c_star is chosen from a range of possible values based on the correlation of the obtained simulated variable with outcome and treatment. 3. The product of correlations with treatment and outcome should be at a minimum distance to the maximum correlations with treatment and outcome in any of the observed confounders 4. The ratio of the weights should be such that they maintain the ratio of the maximum possible observed coefficients within some confidence interval :param c_star_max: The maximum possible value for the hyperbolic curve on which the coefficients to the residuals lie. It defaults to 1000 in the code if not specified by the user. :type int :param convergence_threshold: The threshold to check the plateauing of the correlation while selecting a c_star. It defaults to 0.1 in the code if not specified by the user :type float :returns: The simulated values of the unobserved confounder based on the data :type pandas.core.series.Series """ # Obtaining the list of observed variables required_variables = True observed_variables = self.choose_variables(required_variables) observed_variables_with_treatment_and_outcome = observed_variables + self._treatment_name + self._outcome_name # Taking a subset of the dataframe that has only observed variables self._data = self._data[observed_variables_with_treatment_and_outcome] # Residuals from the outcome model obtained by fitting a linear model y = self._data[self._outcome_name[0]] observed_variables_with_treatment = observed_variables + self._treatment_name X = self._data[observed_variables_with_treatment] model = sm.OLS(y, X.astype("float")) results = model.fit() residuals_y = y - results.fittedvalues d_y = list(pd.Series(residuals_y)) # Residuals from the treatment model obtained by fitting a linear model t = self._data[self._treatment_name[0]].astype("int64") X = self._data[observed_variables] model = sm.OLS(t, X) results = model.fit() residuals_t = t - results.fittedvalues d_t = list(pd.Series(residuals_t)) # Initialising product_cor_metric_observed with a really low value as finding maximum product_cor_metric_observed = -10000000000 for i in observed_variables: current_obs_confounder = self._data[i] outcome_values = self._data[self._outcome_name[0]] correlation_y = current_obs_confounder.corr(outcome_values) treatment_values = t correlation_t = current_obs_confounder.corr(treatment_values) product_cor_metric_current = correlation_y * correlation_t if product_cor_metric_current >= product_cor_metric_observed: product_cor_metric_observed = product_cor_metric_current correlation_t_observed = correlation_t correlation_y_observed = correlation_y # The user has an option to give the the effect_strength_on_y and effect_strength_on_t which can be then used instead of maximum correlation with treatment and outcome in the observed variables as it specifies the desired effect. if self.kappa_t is not None: correlation_t_observed = self.kappa_t if self.kappa_y is not None: correlation_y_observed = self.kappa_y # Choosing a c_star based on the data. # The correlations stop increasing upon increasing c_star after a certain value, that is it plateaus and we choose the value of c_star to be the value it plateaus. correlation_y_list = [] correlation_t_list = [] product_cor_metric_simulated_list = [] x_list = [] step = int(c_star_max / 10) for i in range(0, int(c_star_max), step): c1 = math.sqrt(i) c2 = c1 final_U = self.generate_confounder_from_residuals(c1, c2, d_y, d_t, X) current_simulated_confounder = final_U outcome_values = self._data[self._outcome_name[0]] correlation_y = current_simulated_confounder.corr(outcome_values) correlation_y_list.append(correlation_y) treatment_values = t correlation_t = current_simulated_confounder.corr(treatment_values) correlation_t_list.append(correlation_t) product_cor_metric_simulated = correlation_y * correlation_t product_cor_metric_simulated_list.append(product_cor_metric_simulated) x_list.append(i) index = 1 while index < len(correlation_y_list): if (correlation_y_list[index] - correlation_y_list[index - 1]) <= convergence_threshold: c_star = x_list[index] break index = index + 1 # Choosing c1 and c2 based on the hyperbolic relationship once c_star is chosen by going over various combinations of c1 and c2 values and choosing the combination which # which maintains the minimum distance between the product of correlations of the simulated variable and the product of maximum correlations of one of the observed variables # and additionally checks if the ratio of the weights are such that they maintain the ratio of the maximum possible observed coefficients within some confidence interval # c1_final and c2_final are initialised to the values on the hyperbolic curve such that c1_final = c2_final and c1_final*c2_final = c_star c1_final = math.sqrt(c_star) c2_final = math.sqrt(c_star) # initialising min_distance_between_product_cor_metrics to be a value greater than 1 min_distance_between_product_cor_metrics = 1.5 i = 0.05 threshold = c_star / 0.05 while i <= threshold: c2 = i c1 = c_star / c2 final_U = self.generate_confounder_from_residuals(c1, c2, d_y, d_t, X) current_simulated_confounder = final_U outcome_values = self._data[self._outcome_name[0]] correlation_y = current_simulated_confounder.corr(outcome_values) treatment_values = t correlation_t = current_simulated_confounder.corr(treatment_values) product_cor_metric_simulated = correlation_y * correlation_t if min_distance_between_product_cor_metrics >= abs( product_cor_metric_simulated - product_cor_metric_observed ): min_distance_between_product_cor_metrics = abs( product_cor_metric_simulated - product_cor_metric_observed ) additional_condition = correlation_y_observed / correlation_t_observed if ((c1 / c2) <= (additional_condition + 0.3 * additional_condition)) and ( (c1 / c2) >= (additional_condition - 0.3 * additional_condition) ): # choose minimum positive value c1_final = c1 c2_final = c2 i = i * 1.5 """#closed form solution print("c_star_max before closed form", c_star_max) if max_correlation_with_t == -1000: c2 = 0 c1 = c_star_max else: additional_condition = abs(max_correlation_with_y/max_correlation_with_t) print("additional_condition", additional_condition) c2 = math.sqrt(c_star_max/additional_condition) c1 = c_star_max/c2""" final_U = self.generate_confounder_from_residuals(c1_final, c2_final, d_y, d_t, X) return final_U def generate_confounder_from_residuals(self, c1, c2, d_y, d_t, X): """ This function takes the residuals from the treatment and outcome model and their coefficients and simulates the intermediate random variable U by taking the row wise normal distribution corresponding to each residual value and then debiasing the intermediate variable to get the final variable. :param c1: coefficient to the residual from the outcome model :type float :param c2: coefficient to the residual from the treatment model :type float :param d_y: residuals from the outcome model :type list :param d_t: residuals from the treatment model :type list :returns: The simulated values of the unobserved confounder based on the data :type pandas.core.series.Series """ U = [] for j in range(len(d_t)): simulated_variable_mean = c1 * d_y[j] + c2 * d_t[j] simulated_variable_stddev = 1 U.append(np.random.normal(simulated_variable_mean, simulated_variable_stddev, 1)) U = np.array(U) model = sm.OLS(U, X) results = model.fit() U = U.reshape( -1, ) final_U = U - results.fittedvalues.values final_U = pd.Series(U) return final_U

anusha0409

81841c697bd5e80ecf9e731432305f6186666f1f

bb446c333f2256074304b0dec9cb5628d284b542

We don't have the architecture for it yet --- but an if condition such as this one --- that is checking to see what estimator was used --- makes me think that we should be prescribing the sensitivity analysis method at the same place in the code where we set the estimator method. Perhaps the estimator object registers what sensitivity analysis method should be used, or perhaps both are registered together. Spreading this logic across different parts of the code is going to cause trouble at some point. This is just me thinking out loud. I don't expect a change in this PR.

emrekiciman

py-why/dowhy

Adding Non Linear Sensitivity Analysis

This PR implements the non-parametric sensitivity analysis from Chernozhukov et al. https://arxiv.org/abs/2112.13398 It implements two sensitivity analyzers: 1. For Partial Linear DGPs and estimators like LinearDML 2. For general non-parametric DGPs and estimators like KernelDML. The notebook in this PR provides an introduction on how the sensitivity bounds are calculated for the partial linear case. For the general nonparametric DGPs, we need to estimate a special function called the Reisz representer. For binary treatment, it is exactly the difference in outcome weighted by propensity score. So we provide two options to learn the Reisz representer, 1) plugin_reisz that uses the propensity score; and 2) general estimator that uses a custom loss function. These two are in the file reisz.py. Briefly, the sensitivity bounds depend on two parameters that denote the effect of the unobserved confounder on treatment and outcome. That's why we use the same API as for the `add_unobserved_common_cause` method and add this sensitivity analysis as a possible simulation method="non-parametric-partial-R2". The format of the plots is identical to those from the "linear-partial-r2" simulation method that is already implemented. We provide two modes for the user. 1) User specifies the effect strength parameters themselves, as a range of values. 2) User benchmarks the effect strength parameters as a multiple of the same parameters for the observed common causes. Signed-off-by: anusha <anushaagarwal2000.com>

2022-06-20 14:37:11+00:00

2022-09-16 03:57:26+00:00

dowhy/causal_refuters/add_unobserved_common_cause.py

import copy import logging import math import numpy as np import pandas as pd import scipy.stats import statsmodels.api as sm from sklearn.linear_model import LogisticRegression from sklearn.preprocessing import StandardScaler from tqdm.auto import tqdm from dowhy.causal_estimator import CausalEstimator from dowhy.causal_estimators.linear_regression_estimator import LinearRegressionEstimator from dowhy.causal_refuter import CausalRefutation, CausalRefuter from dowhy.causal_refuters.linear_sensitivity_analyzer import LinearSensitivityAnalyzer class AddUnobservedCommonCause(CausalRefuter): """Add an unobserved confounder for refutation. Supports additional parameters that can be specified in the refute_estimate() method. - 'confounders_effect_on_treatment': how the simulated confounder affects the value of treatment. This can be linear (for continuous treatment) or binary_flip (for binary treatment) - 'confounders_effect_on_outcome': how the simulated confounder affects the value of outcome. This can be linear (for continuous outcome) or binary_flip (for binary outcome) - 'effect_strength_on_treatment': parameter for the strength of the effect of simulated confounder on treatment. For linear effect, it is the regression coeffient. For binary_flip, it is the probability that simulated confounder's effect flips the value of treatment from 0 to 1 (or vice-versa). - 'effect_strength_on_outcome': parameter for the strength of the effect of simulated confounder on outcome. For linear effect, it is the regression coeffient. For binary_flip, it is the probability that simulated confounder's effect flips the value of outcome from 0 to 1 (or vice-versa). TODO: Needs an interpretation module """ def __init__(self, *args, **kwargs): """ Initialize the parameters required for the refuter. If effect_strength_on_treatment or effect_strength_on_outcome is not given, it is calculated automatically as a range between the minimum and maximum effect strength of observed confounders on treatment and outcome respectively. :param confounders_effect_on_treatment: str : The type of effect on the treatment due to the unobserved confounder. Possible values are ['binary_flip', 'linear'] :param confounders_effect_on_outcome: str : The type of effect on the outcome due to the unobserved confounder. Possible values are ['binary_flip', 'linear'] :param effect_strength_on_treatment: float, numpy.ndarray: This refers to the strength of the confounder on treatment. For a linear effect, it behaves like the regression coeffecient. For a binary flip it is the probability with which it can invert the value of the treatment. :param effect_strength_on_outcome: float, numpy.ndarray: This refers to the strength of the confounder on outcome. For a linear effect, it behaves like the regression coefficient. For a binary flip, it is the probability with which it can invert the value of the outcome. :param effect_fraction_on_treatment: float: If effect_strength_on_treatment is not provided, this parameter decides the effect strength of the simulated confounder as a fraction of the effect strength of observed confounders on treatment. Defaults to 1. :param effect_fraction_on_outcome: float: If effect_strength_on_outcome is not provided, this parameter decides the effect strength of the simulated confounder as a fraction of the effect strength of observed confounders on outcome. Defaults to 1. :param plotmethod: string: Type of plot to be shown. If None, no plot is generated. This parameter is used only only when more than one treatment confounder effect values or outcome confounder effect values are provided. Default is "colormesh". Supported values are "contour", "colormesh" when more than one value is provided for both confounder effect value parameters; "line" when provided for only one of them. :param simulated_method_name: method type to add unobserved common cause. "linear-partial-R2" for linear sensitivity analysis :param percent_change_estimate: It is the percentage of reduction of treatment estimate that could alter the results (default = 1) if percent_change_estimate = 1, the robustness value describes the strength of association of confounders with treatment and outcome in order to reduce the estimate by 100% i.e bring it down to 0. :param confounder_increases_estimate: True implies that confounder increases the absolute value of estimate and vice versa. (Default = False) :param benchmark_common_causes: names of variables for bounding strength of confounders :param significance_level: confidence interval for statistical inference(default = 0.05) :param null_hypothesis_effect: assumed effect under the null hypothesis :param plot_estimate: Generate contour plot for estimate while performing sensitivity analysis. (default = True). To override the setting, set plot_estimate = False. """ super().__init__(*args, **kwargs) self.effect_on_t = ( kwargs["confounders_effect_on_treatment"] if "confounders_effect_on_treatment" in kwargs else "binary_flip" ) self.effect_on_y = ( kwargs["confounders_effect_on_outcome"] if "confounders_effect_on_outcome" in kwargs else "linear" ) self.kappa_t = kwargs["effect_strength_on_treatment"] if "effect_strength_on_treatment" in kwargs else None self.kappa_y = kwargs["effect_strength_on_outcome"] if "effect_strength_on_outcome" in kwargs else None self.frac_strength_treatment = ( kwargs["effect_fraction_on_treatment"] if "effect_fraction_on_treatment" in kwargs else 1 ) self.frac_strength_outcome = ( kwargs["effect_fraction_on_outcome"] if "effect_fraction_on_outcome" in kwargs else 1 ) self.simulated_method_name = ( kwargs["simulated_method_name"] if "simulated_method_name" in kwargs else "linear_based" ) self.plotmethod = kwargs["plotmethod"] if "plotmethod" in kwargs else "colormesh" self.percent_change_estimate = kwargs["percent_change_estimate"] if "percent_change_estimate" in kwargs else 1.0 self.significance_level = kwargs["significance_level"] if "significance_level" in kwargs else 0.05 self.confounder_increases_estimate = ( kwargs["confounder_increases_estimate"] if "confounder_increases_estimate" in kwargs else False ) self.benchmark_common_causes = ( kwargs["benchmark_common_causes"] if "benchmark_common_causes" in kwargs else None ) self.null_hypothesis_effect = kwargs["null_hypothesis_effect"] if "null_hypothesis_effect" in kwargs else 0 self.plot_estimate = kwargs["plot_estimate"] if "plot_estimate" in kwargs else True self.logger = logging.getLogger(__name__) def infer_default_kappa_t(self, len_kappa_t=10): """Infer default effect strength of simulated confounder on treatment.""" observed_common_causes_names = self._target_estimand.get_backdoor_variables() if len(observed_common_causes_names) > 0: observed_common_causes = self._data[observed_common_causes_names] observed_common_causes = pd.get_dummies(observed_common_causes, drop_first=True) else: raise ValueError( "There needs to be at least one common cause to" + "automatically compute the default value of kappa_t." + " Provide a value for kappa_t" ) t = self._data[self._treatment_name] # Standardizing the data observed_common_causes = StandardScaler().fit_transform(observed_common_causes) if self.effect_on_t == "binary_flip": # Fit a model containing all confounders and compare predictions # using all features compared to all features except a given # confounder. tmodel = LogisticRegression().fit(observed_common_causes, t) tpred = tmodel.predict(observed_common_causes).astype(int) flips = [] for i in range(observed_common_causes.shape[1]): oldval = np.copy(observed_common_causes[:, i]) observed_common_causes[:, i] = 0 tcap = tmodel.predict(observed_common_causes).astype(int) observed_common_causes[:, i] = oldval flips.append(np.sum(abs(tcap - tpred)) / tpred.shape[0]) min_coeff, max_coeff = min(flips), max(flips) elif self.effect_on_t == "linear": # Estimating the regression coefficient from standardized features to t corrcoef_var_t = np.corrcoef(observed_common_causes, t, rowvar=False)[-1, :-1] std_dev_t = np.std(t)[0] max_coeff = max(corrcoef_var_t) * std_dev_t min_coeff = min(corrcoef_var_t) * std_dev_t else: raise NotImplementedError( "'" + self.effect_on_t + "' method not supported for confounders' effect on treatment" ) min_coeff, max_coeff = self._compute_min_max_coeff(min_coeff, max_coeff, self.frac_strength_treatment) # By default, return a plot with 10 points # consider 10 values of the effect of the unobserved confounder step = (max_coeff - min_coeff) / len_kappa_t self.logger.info("(Min, Max) kappa_t for observed common causes, ({0}, {1})".format(min_coeff, max_coeff)) if np.equal(max_coeff, min_coeff): return max_coeff else: return np.arange(min_coeff, max_coeff, step) def _compute_min_max_coeff(self, min_coeff, max_coeff, effect_strength_fraction): max_coeff = effect_strength_fraction * max_coeff min_coeff = effect_strength_fraction * min_coeff return min_coeff, max_coeff def infer_default_kappa_y(self, len_kappa_y=10): """Infer default effect strength of simulated confounder on treatment.""" observed_common_causes_names = self._target_estimand.get_backdoor_variables() if len(observed_common_causes_names) > 0: observed_common_causes = self._data[observed_common_causes_names] observed_common_causes = pd.get_dummies(observed_common_causes, drop_first=True) else: raise ValueError( "There needs to be at least one common cause to" + "automatically compute the default value of kappa_y." + " Provide a value for kappa_y" ) y = self._data[self._outcome_name] # Standardizing the data observed_common_causes = StandardScaler().fit_transform(observed_common_causes) if self.effect_on_y == "binary_flip": # Fit a model containing all confounders and compare predictions # using all features compared to all features except a given # confounder. ymodel = LogisticRegression().fit(observed_common_causes, y) ypred = ymodel.predict(observed_common_causes).astype(int) flips = [] for i in range(observed_common_causes.shape[1]): oldval = np.copy(observed_common_causes[:, i]) observed_common_causes[:, i] = 0 ycap = ymodel.predict(observed_common_causes).astype(int) observed_common_causes[:, i] = oldval flips.append(np.sum(abs(ycap - ypred)) / ypred.shape[0]) min_coeff, max_coeff = min(flips), max(flips) elif self.effect_on_y == "linear": corrcoef_var_y = np.corrcoef(observed_common_causes, y, rowvar=False)[-1, :-1] std_dev_y = np.std(y)[0] max_coeff = max(corrcoef_var_y) * std_dev_y min_coeff = min(corrcoef_var_y) * std_dev_y else: raise NotImplementedError( "'" + self.effect_on_y + "' method not supported for confounders' effect on outcome" ) min_coeff, max_coeff = self._compute_min_max_coeff(min_coeff, max_coeff, self.frac_strength_outcome) # By default, return a plot with 10 points # consider 10 values of the effect of the unobserved confounder step = (max_coeff - min_coeff) / len_kappa_y self.logger.info("(Min, Max) kappa_y for observed common causes, ({0}, {1})".format(min_coeff, max_coeff)) if np.equal(max_coeff, min_coeff): return max_coeff else: return np.arange(min_coeff, max_coeff, step) def refute_estimate(self, show_progress_bar=False): """ This function attempts to add an unobserved common cause to the outcome and the treatment. At present, we have implemented the behavior for one dimensional behaviors for continuous and binary variables. This function can either take single valued inputs or a range of inputs. The function then looks at the data type of the input and then decides on the course of action. :return: CausalRefuter: An object that contains the estimated effect and a new effect and the name of the refutation used. """ if self.simulated_method_name == "linear-partial-R2": if not (isinstance(self._estimate.estimator, LinearRegressionEstimator)): raise NotImplementedError( "Currently only LinearRegressionEstimator is supported for Sensitivity Analysis" ) if len(self._estimate.estimator._effect_modifier_names) > 0: raise NotImplementedError("The current implementation does not support effect modifiers") if self.frac_strength_outcome == 1: self.frac_strength_outcome = self.frac_strength_treatment analyzer = LinearSensitivityAnalyzer( estimator=self._estimate.estimator, data=self._data, treatment_name=self._treatment_name, percent_change_estimate=self.percent_change_estimate, significance_level=self.significance_level, benchmark_common_causes=self.benchmark_common_causes, null_hypothesis_effect=self.null_hypothesis_effect, frac_strength_treatment=self.frac_strength_treatment, frac_strength_outcome=self.frac_strength_outcome, common_causes_order=self._estimate.estimator._observed_common_causes.columns, ) analyzer.check_sensitivity(plot=self.plot_estimate) return analyzer if self.kappa_t is None: self.kappa_t = self.infer_default_kappa_t() if self.kappa_y is None: self.kappa_y = self.infer_default_kappa_y() if not isinstance(self.kappa_t, (list, np.ndarray)) and not isinstance( self.kappa_y, (list, np.ndarray) ): # Deal with single value inputs new_data = copy.deepcopy(self._data) new_data = self.include_confounders_effect(new_data, self.kappa_t, self.kappa_y) new_estimator = CausalEstimator.get_estimator_object(new_data, self._target_estimand, self._estimate) new_effect = new_estimator.estimate_effect() refute = CausalRefutation( self._estimate.value, new_effect.value, refutation_type="Refute: Add an Unobserved Common Cause" ) refute.new_effect_array = np.array(new_effect.value) refute.new_effect = new_effect.value refute.add_refuter(self) return refute else: # Deal with multiple value inputs if isinstance(self.kappa_t, (list, np.ndarray)) and isinstance( self.kappa_y, (list, np.ndarray) ): # Deal with range inputs # Get a 2D matrix of values # x,y = np.meshgrid(self.kappa_t, self.kappa_y) # x,y are both MxN results_matrix = np.random.rand( len(self.kappa_t), len(self.kappa_y) ) # Matrix to hold all the results of NxM orig_data = copy.deepcopy(self._data) for i in tqdm( range(len(self.kappa_t)), colour=CausalRefuter.PROGRESS_BAR_COLOR, disable=not show_progress_bar, desc="Refuting Estimates: ", ): for j in range(len(self.kappa_y)): new_data = self.include_confounders_effect(orig_data, self.kappa_t[i], self.kappa_y[j]) new_estimator = CausalEstimator.get_estimator_object( new_data, self._target_estimand, self._estimate ) new_effect = new_estimator.estimate_effect() refute = CausalRefutation( self._estimate.value, new_effect.value, refutation_type="Refute: Add an Unobserved Common Cause", ) results_matrix[i][j] = refute.new_effect # Populate the results refute.new_effect_array = results_matrix refute.new_effect = (np.min(results_matrix), np.max(results_matrix)) # Store the values into the refute object refute.add_refuter(self) if self.plotmethod is None: return refute import matplotlib import matplotlib.pyplot as plt fig = plt.figure(figsize=(6, 5)) left, bottom, width, height = 0.1, 0.1, 0.8, 0.8 ax = fig.add_axes([left, bottom, width, height]) oe = self._estimate.value contour_levels = [oe / 4.0, oe / 2.0, (3.0 / 4) * oe, oe] contour_levels.extend([0, np.min(results_matrix), np.max(results_matrix)]) if self.plotmethod == "contour": cp = plt.contourf(self.kappa_y, self.kappa_t, results_matrix, levels=sorted(contour_levels)) # Adding a label on the contour line for the original estimate fmt = {} trueeffect_index = np.where(cp.levels == oe)[0][0] fmt[cp.levels[trueeffect_index]] = "Estimated Effect" # Label every other level using strings plt.clabel(cp, [cp.levels[trueeffect_index]], inline=True, fmt=fmt) plt.colorbar(cp) elif self.plotmethod == "colormesh": cp = plt.pcolormesh(self.kappa_y, self.kappa_t, results_matrix, shading="nearest") plt.colorbar(cp, ticks=contour_levels) ax.yaxis.set_ticks(self.kappa_t) ax.xaxis.set_ticks(self.kappa_y) plt.xticks(rotation=45) ax.set_title("Effect of Unobserved Common Cause") ax.set_ylabel("Value of Linear Constant on Treatment") ax.set_xlabel("Value of Linear Constant on Outcome") plt.show() return refute elif isinstance(self.kappa_t, (list, np.ndarray)): outcomes = np.random.rand(len(self.kappa_t)) orig_data = copy.deepcopy(self._data) for i in tqdm( range(0, len(self.kappa_t)), colour=CausalRefuter.PROGRESS_BAR_COLOR, disable=not show_progress_bar, desc="Refuting Estimates: ", ): new_data = self.include_confounders_effect(orig_data, self.kappa_t[i], self.kappa_y) new_estimator = CausalEstimator.get_estimator_object( new_data, self._target_estimand, self._estimate ) new_effect = new_estimator.estimate_effect() refute = CausalRefutation( self._estimate.value, new_effect.value, refutation_type="Refute: Add an Unobserved Common Cause" ) self.logger.debug(refute) outcomes[i] = refute.new_effect # Populate the results refute.new_effect_array = outcomes refute.new_effect = (np.min(outcomes), np.max(outcomes)) refute.add_refuter(self) if self.plotmethod is None: return refute import matplotlib import matplotlib.pyplot as plt fig = plt.figure(figsize=(6, 5)) left, bottom, width, height = 0.1, 0.1, 0.8, 0.8 ax = fig.add_axes([left, bottom, width, height]) plt.plot(self.kappa_t, outcomes) plt.axhline(self._estimate.value, linestyle="--", color="gray") ax.set_title("Effect of Unobserved Common Cause") ax.set_xlabel("Value of Linear Constant on Treatment") ax.set_ylabel("Estimated Effect after adding the common cause") plt.show() return refute elif isinstance(self.kappa_y, (list, np.ndarray)): outcomes = np.random.rand(len(self.kappa_y)) orig_data = copy.deepcopy(self._data) for i in tqdm( range(0, len(self.kappa_y)), colour=CausalRefuter.PROGRESS_BAR_COLOR, disable=not show_progress_bar, desc="Refuting Estimates: ", ): new_data = self.include_confounders_effect(orig_data, self.kappa_t, self.kappa_y[i]) new_estimator = CausalEstimator.get_estimator_object( new_data, self._target_estimand, self._estimate ) new_effect = new_estimator.estimate_effect() refute = CausalRefutation( self._estimate.value, new_effect.value, refutation_type="Refute: Add an Unobserved Common Cause" ) self.logger.debug(refute) outcomes[i] = refute.new_effect # Populate the results refute.new_effect_array = outcomes refute.new_effect = (np.min(outcomes), np.max(outcomes)) refute.add_refuter(self) if self.plotmethod is None: return refute import matplotlib import matplotlib.pyplot as plt fig = plt.figure(figsize=(6, 5)) left, bottom, width, height = 0.1, 0.1, 0.8, 0.8 ax = fig.add_axes([left, bottom, width, height]) plt.plot(self.kappa_y, outcomes) plt.axhline(self._estimate.value, linestyle="--", color="gray") ax.set_title("Effect of Unobserved Common Cause") ax.set_xlabel("Value of Linear Constant on Outcome") ax.set_ylabel("Estimated Effect after adding the common cause") plt.show() return refute def include_confounders_effect(self, new_data, kappa_t, kappa_y): """ This function deals with the change in the value of the data due to the effect of the unobserved confounder. In the case of a binary flip, we flip only if the random number is greater than the threshold set. In the case of a linear effect, we use the variable as the linear regression constant. :param new_data: pandas.DataFrame: The data to be changed due to the effects of the unobserved confounder. :param kappa_t: numpy.float64: The value of the threshold for binary_flip or the value of the regression coefficient for linear effect. :param kappa_y: numpy.float64: The value of the threshold for binary_flip or the value of the regression coefficient for linear effect. :return: pandas.DataFrame: The DataFrame that includes the effects of the unobserved confounder. """ num_rows = self._data.shape[0] stdnorm = scipy.stats.norm() w_random = stdnorm.rvs(num_rows) if self.effect_on_t == "binary_flip": alpha = 2 * kappa_t - 1 if kappa_t >= 0.5 else 1 - 2 * kappa_t interval = stdnorm.interval(alpha) rel_interval = interval[0] if kappa_t >= 0.5 else interval[1] new_data.loc[rel_interval <= w_random, self._treatment_name] = ( 1 - new_data.loc[rel_interval <= w_random, self._treatment_name] ) for tname in self._treatment_name: if pd.api.types.is_bool_dtype(self._data[tname]): new_data = new_data.astype({tname: "bool"}, copy=False) elif self.effect_on_t == "linear": confounder_t_effect = kappa_t * w_random # By default, we add the effect of simulated confounder for treatment. # But subtract it from outcome to create a negative correlation # assuming that the original confounder's effect was positive on both. # This is to remove the effect of the original confounder. new_data[self._treatment_name] = new_data[self._treatment_name].values + np.ndarray( shape=(num_rows, 1), buffer=confounder_t_effect ) else: raise NotImplementedError( "'" + self.effect_on_t + "' method not supported for confounders' effect on treatment" ) if self.effect_on_y == "binary_flip": alpha = 2 * kappa_y - 1 if kappa_y >= 0.5 else 1 - 2 * kappa_y interval = stdnorm.interval(alpha) rel_interval = interval[0] if kappa_y >= 0.5 else interval[1] new_data.loc[rel_interval <= w_random, self._outcome_name] = ( 1 - new_data.loc[rel_interval <= w_random, self._outcome_name] ) for yname in self._outcome_name: if pd.api.types.is_bool_dtype(self._data[yname]): new_data = new_data.astype({yname: "bool"}, copy=False) elif self.effect_on_y == "linear": confounder_y_effect = (-1) * kappa_y * w_random # By default, we add the effect of simulated confounder for treatment. # But subtract it from outcome to create a negative correlation # assuming that the original confounder's effect was positive on both. # This is to remove the effect of the original confounder. new_data[self._outcome_name] = new_data[self._outcome_name].values + np.ndarray( shape=(num_rows, 1), buffer=confounder_y_effect ) else: raise NotImplementedError( "'" + self.effect_on_y + "' method not supported for confounders' effect on outcome" ) return new_data def include_simulated_confounder(self, convergence_threshold=0.1, c_star_max=1000): """ This function simulates an unobserved confounder based on the data using the following steps: 1. It calculates the "residuals" from the treatment and outcome model i.) The outcome model has outcome as the dependent variable and all the observed variables including treatment as independent variables ii.) The treatment model has treatment as the dependent variable and all the observed variables as independent variables. 2. U is an intermediate random variable drawn from the normal distribution with the weighted average of residuals as mean and a unit variance U ~ N(c1*d_y + c2*d_t, 1) where *d_y and d_t are residuals from the treatment and outcome model *c1 and c2 are coefficients to the residuals 3. The final U, which is the simulated unobserved confounder is obtained by debiasing the intermediate variable U by residualising it with X Choosing the coefficients c1 and c2: The coefficients are chosen based on these basic assumptions: 1. There is a hyperbolic relationship satisfying c1*c2 = c_star 2. c_star is chosen from a range of possible values based on the correlation of the obtained simulated variable with outcome and treatment. 3. The product of correlations with treatment and outcome should be at a minimum distance to the maximum correlations with treatment and outcome in any of the observed confounders 4. The ratio of the weights should be such that they maintain the ratio of the maximum possible observed coefficients within some confidence interval :param c_star_max: The maximum possible value for the hyperbolic curve on which the coefficients to the residuals lie. It defaults to 1000 in the code if not specified by the user. :type int :param convergence_threshold: The threshold to check the plateauing of the correlation while selecting a c_star. It defaults to 0.1 in the code if not specified by the user :type float :returns: The simulated values of the unobserved confounder based on the data :type pandas.core.series.Series """ # Obtaining the list of observed variables required_variables = True observed_variables = self.choose_variables(required_variables) observed_variables_with_treatment_and_outcome = observed_variables + self._treatment_name + self._outcome_name # Taking a subset of the dataframe that has only observed variables self._data = self._data[observed_variables_with_treatment_and_outcome] # Residuals from the outcome model obtained by fitting a linear model y = self._data[self._outcome_name[0]] observed_variables_with_treatment = observed_variables + self._treatment_name X = self._data[observed_variables_with_treatment] model = sm.OLS(y, X.astype("float")) results = model.fit() residuals_y = y - results.fittedvalues d_y = list(pd.Series(residuals_y)) # Residuals from the treatment model obtained by fitting a linear model t = self._data[self._treatment_name[0]].astype("int64") X = self._data[observed_variables] model = sm.OLS(t, X) results = model.fit() residuals_t = t - results.fittedvalues d_t = list(pd.Series(residuals_t)) # Initialising product_cor_metric_observed with a really low value as finding maximum product_cor_metric_observed = -10000000000 for i in observed_variables: current_obs_confounder = self._data[i] outcome_values = self._data[self._outcome_name[0]] correlation_y = current_obs_confounder.corr(outcome_values) treatment_values = t correlation_t = current_obs_confounder.corr(treatment_values) product_cor_metric_current = correlation_y * correlation_t if product_cor_metric_current >= product_cor_metric_observed: product_cor_metric_observed = product_cor_metric_current correlation_t_observed = correlation_t correlation_y_observed = correlation_y # The user has an option to give the the effect_strength_on_y and effect_strength_on_t which can be then used instead of maximum correlation with treatment and outcome in the observed variables as it specifies the desired effect. if self.kappa_t is not None: correlation_t_observed = self.kappa_t if self.kappa_y is not None: correlation_y_observed = self.kappa_y # Choosing a c_star based on the data. # The correlations stop increasing upon increasing c_star after a certain value, that is it plateaus and we choose the value of c_star to be the value it plateaus. correlation_y_list = [] correlation_t_list = [] product_cor_metric_simulated_list = [] x_list = [] step = int(c_star_max / 10) for i in range(0, int(c_star_max), step): c1 = math.sqrt(i) c2 = c1 final_U = self.generate_confounder_from_residuals(c1, c2, d_y, d_t, X) current_simulated_confounder = final_U outcome_values = self._data[self._outcome_name[0]] correlation_y = current_simulated_confounder.corr(outcome_values) correlation_y_list.append(correlation_y) treatment_values = t correlation_t = current_simulated_confounder.corr(treatment_values) correlation_t_list.append(correlation_t) product_cor_metric_simulated = correlation_y * correlation_t product_cor_metric_simulated_list.append(product_cor_metric_simulated) x_list.append(i) index = 1 while index < len(correlation_y_list): if (correlation_y_list[index] - correlation_y_list[index - 1]) <= convergence_threshold: c_star = x_list[index] break index = index + 1 # Choosing c1 and c2 based on the hyperbolic relationship once c_star is chosen by going over various combinations of c1 and c2 values and choosing the combination which # which maintains the minimum distance between the product of correlations of the simulated variable and the product of maximum correlations of one of the observed variables # and additionally checks if the ratio of the weights are such that they maintain the ratio of the maximum possible observed coefficients within some confidence interval # c1_final and c2_final are initialised to the values on the hyperbolic curve such that c1_final = c2_final and c1_final*c2_final = c_star c1_final = math.sqrt(c_star) c2_final = math.sqrt(c_star) # initialising min_distance_between_product_cor_metrics to be a value greater than 1 min_distance_between_product_cor_metrics = 1.5 i = 0.05 threshold = c_star / 0.05 while i <= threshold: c2 = i c1 = c_star / c2 final_U = self.generate_confounder_from_residuals(c1, c2, d_y, d_t, X) current_simulated_confounder = final_U outcome_values = self._data[self._outcome_name[0]] correlation_y = current_simulated_confounder.corr(outcome_values) treatment_values = t correlation_t = current_simulated_confounder.corr(treatment_values) product_cor_metric_simulated = correlation_y * correlation_t if min_distance_between_product_cor_metrics >= abs( product_cor_metric_simulated - product_cor_metric_observed ): min_distance_between_product_cor_metrics = abs( product_cor_metric_simulated - product_cor_metric_observed ) additional_condition = correlation_y_observed / correlation_t_observed if ((c1 / c2) <= (additional_condition + 0.3 * additional_condition)) and ( (c1 / c2) >= (additional_condition - 0.3 * additional_condition) ): # choose minimum positive value c1_final = c1 c2_final = c2 i = i * 1.5 """#closed form solution print("c_star_max before closed form", c_star_max) if max_correlation_with_t == -1000: c2 = 0 c1 = c_star_max else: additional_condition = abs(max_correlation_with_y/max_correlation_with_t) print("additional_condition", additional_condition) c2 = math.sqrt(c_star_max/additional_condition) c1 = c_star_max/c2""" final_U = self.generate_confounder_from_residuals(c1_final, c2_final, d_y, d_t, X) return final_U def generate_confounder_from_residuals(self, c1, c2, d_y, d_t, X): """ This function takes the residuals from the treatment and outcome model and their coefficients and simulates the intermediate random variable U by taking the row wise normal distribution corresponding to each residual value and then debiasing the intermediate variable to get the final variable. :param c1: coefficient to the residual from the outcome model :type float :param c2: coefficient to the residual from the treatment model :type float :param d_y: residuals from the outcome model :type list :param d_t: residuals from the treatment model :type list :returns: The simulated values of the unobserved confounder based on the data :type pandas.core.series.Series """ U = [] for j in range(len(d_t)): simulated_variable_mean = c1 * d_y[j] + c2 * d_t[j] simulated_variable_stddev = 1 U.append(np.random.normal(simulated_variable_mean, simulated_variable_stddev, 1)) U = np.array(U) model = sm.OLS(U, X) results = model.fit() U = U.reshape( -1, ) final_U = U - results.fittedvalues.values final_U = pd.Series(U) return final_U

import copy import logging import math import numpy as np import pandas as pd import scipy.stats import statsmodels.api as sm from sklearn.linear_model import LogisticRegression from sklearn.preprocessing import StandardScaler from tqdm.auto import tqdm import dowhy.causal_estimators.econml from dowhy.causal_estimator import CausalEstimator from dowhy.causal_estimators.linear_regression_estimator import LinearRegressionEstimator from dowhy.causal_refuter import CausalRefutation, CausalRefuter from dowhy.causal_refuters.linear_sensitivity_analyzer import LinearSensitivityAnalyzer from dowhy.causal_refuters.non_parametric_sensitivity_analyzer import NonParametricSensitivityAnalyzer from dowhy.causal_refuters.partial_linear_sensitivity_analyzer import PartialLinearSensitivityAnalyzer class AddUnobservedCommonCause(CausalRefuter): """Add an unobserved confounder for refutation. AddUnobservedCommonCause class supports three methods: 1) Simulation of an unobserved confounder 2) Linear partial R2 : Sensitivity Analysis for linear models. 3) Non-Parametric partial R2 based : Sensitivity Analyis for non-parametric models. Supports additional parameters that can be specified in the refute_estimate() method. """ def __init__(self, *args, **kwargs): """ Initialize the parameters required for the refuter. For direct_simulation, if effect_strength_on_treatment or effect_strength_on_outcome is not given, it is calculated automatically as a range between the minimum and maximum effect strength of observed confounders on treatment and outcome respectively. :param simulation_method: The method to use for simulating effect of unobserved confounder. Possible values are ["direct-simulation", "linear-partial-R2", "non-parametric-partial-R2"]. :param confounders_effect_on_treatment: str : The type of effect on the treatment due to the unobserved confounder. Possible values are ['binary_flip', 'linear'] :param confounders_effect_on_outcome: str : The type of effect on the outcome due to the unobserved confounder. Possible values are ['binary_flip', 'linear'] :param effect_strength_on_treatment: float, numpy.ndarray: [Used when simulation_method="direct-simulation"] Strength of the confounder's effect on treatment. When confounders_effect_on_treatment is linear, it is the regression coefficient. When the confounders_effect_on_treatment is binary flip, it is the probability with which effect of unobserved confounder can invert the value of the treatment. :param effect_strength_on_outcome: float, numpy.ndarray: Strength of the confounder's effect on outcome. Its interpretation depends on confounders_effect_on_outcome and the simulation_method. When simulation_method is direct-simulation, for a linear effect it behaves like the regression coefficient and for a binary flip, it is the probability with which it can invert the value of the outcome. :param partial_r2_confounder_treatment: float, numpy.ndarray: [Used when simulation_method is linear-partial-R2 or non-parametric-partial-R2] Partial R2 of the unobserved confounder wrt the treatment conditioned on the observed confounders. Only in the case of general non-parametric-partial-R2, it is the fraction of variance in the reisz representer that is explained by the unobserved confounder; specifically (1-r), where r is the ratio of variance of reisz representer, alpha^2, based on observed confounders and that based on all confounders. :param partial_r2_confounder_outcome: float, numpy.ndarray: [Used when simulation_method is linear-partial-R2 or non-parametric-partial-R2] Partial R2 of the unobserved confounder wrt the outcome conditioned on the treatment and observed confounders. :param frac_strength_treatment: float: This parameter decides the effect strength of the simulated confounder as a fraction of the effect strength of observed confounders on treatment. Defaults to 1. :param frac_strength_outcome: float: This parameter decides the effect strength of the simulated confounder as a fraction of the effect strength of observed confounders on outcome. Defaults to 1. :param plotmethod: string: Type of plot to be shown. If None, no plot is generated. This parameter is used only only when more than one treatment confounder effect values or outcome confounder effect values are provided. Default is "colormesh". Supported values are "contour", "colormesh" when more than one value is provided for both confounder effect value parameters; "line" when provided for only one of them. :param percent_change_estimate: It is the percentage of reduction of treatment estimate that could alter the results (default = 1). if percent_change_estimate = 1, the robustness value describes the strength of association of confounders with treatment and outcome in order to reduce the estimate by 100% i.e bring it down to 0. (relevant only for Linear Sensitivity Analysis, ignore for rest) :param confounder_increases_estimate: True implies that confounder increases the absolute value of estimate and vice versa. (Default = False). (relevant only for Linear Sensitivity Analysis, ignore for rest) :param benchmark_common_causes: names of variables for bounding strength of confounders. (relevant only for partial-r2 based simulation methods) :param significance_level: confidence interval for statistical inference(default = 0.05). (relevant only for partial-r2 based simulation methods) :param null_hypothesis_effect: assumed effect under the null hypothesis. (relevant only for linear-partial-R2, ignore for rest) :param plot_estimate: Generate contour plot for estimate while performing sensitivity analysis. (default = True). (relevant only for partial-r2 based simulation methods) :param num_splits: number of splits for cross validation. (default = 5). (relevant only for non-parametric-partial-R2 simulation method) :param shuffle_data : shuffle data or not before splitting into folds (default = False). (relevant only for non-parametric-partial-R2 simulation method) :param shuffle_random_seed: seed for randomly shuffling data. (relevant only for non-parametric-partial-R2 simulation method) :param alpha_s_estimator_param_list: list of dictionaries with parameters for finding alpha_s. (relevant only for non-parametric-partial-R2 simulation method) :param g_s_estimator_list: list of estimator objects for finding g_s. These objects should have fit() and predict() functions implemented. (relevant only for non-parametric-partial-R2 simulation method) :param g_s_estimator_param_list: list of dictionaries with parameters for tuning respective estimators in "g_s_estimator_list". The order of the dictionaries in the list should be consistent with the estimator objects order in "g_s_estimator_list". (relevant only for non-parametric-partial-R2 simulation method) """ super().__init__(*args, **kwargs) self.simulation_method = kwargs["simulation_method"] if "simulation_method" in kwargs else "direct-simulation" self.effect_on_t = ( kwargs["confounders_effect_on_treatment"] if "confounders_effect_on_treatment" in kwargs else "binary_flip" ) self.effect_on_y = ( kwargs["confounders_effect_on_outcome"] if "confounders_effect_on_outcome" in kwargs else "linear" ) if self.simulation_method == "direct-simulation": self.kappa_t = kwargs["effect_strength_on_treatment"] if "effect_strength_on_treatment" in kwargs else None self.kappa_y = kwargs["effect_strength_on_outcome"] if "effect_strength_on_outcome" in kwargs else None elif self.simulation_method in ["linear-partial-R2", "non-parametric-partial-R2"]: self.kappa_t = ( kwargs["partial_r2_confounder_treatment"] if "partial_r2_confounder_treatment" in kwargs else None ) self.kappa_y = ( kwargs["partial_r2_confounder_outcome"] if "partial_r2_confounder_outcome" in kwargs else None ) else: raise ValueError( "simulation method is not supported. Try direct-simulation, linear-partial-R2 or non-parametric-partial-R2" ) self.frac_strength_treatment = ( kwargs["effect_fraction_on_treatment"] if "effect_fraction_on_treatment" in kwargs else 1 ) self.frac_strength_outcome = ( kwargs["effect_fraction_on_outcome"] if "effect_fraction_on_outcome" in kwargs else 1 ) self.plotmethod = kwargs["plotmethod"] if "plotmethod" in kwargs else "colormesh" self.percent_change_estimate = kwargs["percent_change_estimate"] if "percent_change_estimate" in kwargs else 1.0 self.significance_level = kwargs["significance_level"] if "significance_level" in kwargs else 0.05 self.confounder_increases_estimate = ( kwargs["confounder_increases_estimate"] if "confounder_increases_estimate" in kwargs else False ) self.benchmark_common_causes = ( kwargs["benchmark_common_causes"] if "benchmark_common_causes" in kwargs else None ) self.null_hypothesis_effect = kwargs["null_hypothesis_effect"] if "null_hypothesis_effect" in kwargs else 0 self.plot_estimate = kwargs["plot_estimate"] if "plot_estimate" in kwargs else True self.num_splits = kwargs["num_splits"] if "num_splits" in kwargs else 5 self.shuffle_data = kwargs["shuffle_data"] if "shuffle_data" in kwargs else False self.shuffle_random_seed = kwargs["shuffle_random_seed"] if "shuffle_random_seed" in kwargs else None self.alpha_s_estimator_param_list = ( kwargs["alpha_s_estimator_param_list"] if "alpha_s_estimator_param_list" in kwargs else None ) self.alpha_s_estimator_list = kwargs["alpha_s_estimator_list"] if "alpha_s_estimator_list" in kwargs else None self.g_s_estimator_list = kwargs["g_s_estimator_list"] if "g_s_estimator_list" in kwargs else None self.g_s_estimator_param_list = ( kwargs["g_s_estimator_param_list"] if "g_s_estimator_param_list" in kwargs else None ) self.plugin_reisz = kwargs["plugin_reisz"] if "plugin_reisz" in kwargs else False self.logger = logging.getLogger(__name__) def infer_default_kappa_t(self, len_kappa_t=10): """Infer default effect strength of simulated confounder on treatment.""" observed_common_causes_names = self._target_estimand.get_backdoor_variables() if len(observed_common_causes_names) > 0: observed_common_causes = self._data[observed_common_causes_names] observed_common_causes = pd.get_dummies(observed_common_causes, drop_first=True) else: raise ValueError( "There needs to be at least one common cause to" + "automatically compute the default value of kappa_t." + " Provide a value for kappa_t" ) t = self._data[self._treatment_name] # Standardizing the data observed_common_causes = StandardScaler().fit_transform(observed_common_causes) if self.effect_on_t == "binary_flip": # Fit a model containing all confounders and compare predictions # using all features compared to all features except a given # confounder. tmodel = LogisticRegression().fit(observed_common_causes, t) tpred = tmodel.predict(observed_common_causes).astype(int) flips = [] for i in range(observed_common_causes.shape[1]): oldval = np.copy(observed_common_causes[:, i]) observed_common_causes[:, i] = 0 tcap = tmodel.predict(observed_common_causes).astype(int) observed_common_causes[:, i] = oldval flips.append(np.sum(abs(tcap - tpred)) / tpred.shape[0]) min_coeff, max_coeff = min(flips), max(flips) elif self.effect_on_t == "linear": # Estimating the regression coefficient from standardized features to t corrcoef_var_t = np.corrcoef(observed_common_causes, t, rowvar=False)[-1, :-1] std_dev_t = np.std(t)[0] max_coeff = max(corrcoef_var_t) * std_dev_t min_coeff = min(corrcoef_var_t) * std_dev_t else: raise NotImplementedError( "'" + self.effect_on_t + "' method not supported for confounders' effect on treatment" ) min_coeff, max_coeff = self._compute_min_max_coeff(min_coeff, max_coeff, self.frac_strength_treatment) # By default, return a plot with 10 points # consider 10 values of the effect of the unobserved confounder step = (max_coeff - min_coeff) / len_kappa_t self.logger.info("(Min, Max) kappa_t for observed common causes, ({0}, {1})".format(min_coeff, max_coeff)) if np.equal(max_coeff, min_coeff): return max_coeff else: return np.arange(min_coeff, max_coeff, step) def _compute_min_max_coeff(self, min_coeff, max_coeff, effect_strength_fraction): max_coeff = effect_strength_fraction * max_coeff min_coeff = effect_strength_fraction * min_coeff return min_coeff, max_coeff def infer_default_kappa_y(self, len_kappa_y=10): """Infer default effect strength of simulated confounder on treatment.""" observed_common_causes_names = self._target_estimand.get_backdoor_variables() if len(observed_common_causes_names) > 0: observed_common_causes = self._data[observed_common_causes_names] observed_common_causes = pd.get_dummies(observed_common_causes, drop_first=True) else: raise ValueError( "There needs to be at least one common cause to" + "automatically compute the default value of kappa_y." + " Provide a value for kappa_y" ) y = self._data[self._outcome_name] # Standardizing the data observed_common_causes = StandardScaler().fit_transform(observed_common_causes) if self.effect_on_y == "binary_flip": # Fit a model containing all confounders and compare predictions # using all features compared to all features except a given # confounder. ymodel = LogisticRegression().fit(observed_common_causes, y) ypred = ymodel.predict(observed_common_causes).astype(int) flips = [] for i in range(observed_common_causes.shape[1]): oldval = np.copy(observed_common_causes[:, i]) observed_common_causes[:, i] = 0 ycap = ymodel.predict(observed_common_causes).astype(int) observed_common_causes[:, i] = oldval flips.append(np.sum(abs(ycap - ypred)) / ypred.shape[0]) min_coeff, max_coeff = min(flips), max(flips) elif self.effect_on_y == "linear": corrcoef_var_y = np.corrcoef(observed_common_causes, y, rowvar=False)[-1, :-1] std_dev_y = np.std(y)[0] max_coeff = max(corrcoef_var_y) * std_dev_y min_coeff = min(corrcoef_var_y) * std_dev_y else: raise NotImplementedError( "'" + self.effect_on_y + "' method not supported for confounders' effect on outcome" ) min_coeff, max_coeff = self._compute_min_max_coeff(min_coeff, max_coeff, self.frac_strength_outcome) # By default, return a plot with 10 points # consider 10 values of the effect of the unobserved confounder step = (max_coeff - min_coeff) / len_kappa_y self.logger.info("(Min, Max) kappa_y for observed common causes, ({0}, {1})".format(min_coeff, max_coeff)) if np.equal(max_coeff, min_coeff): return max_coeff else: return np.arange(min_coeff, max_coeff, step) def refute_estimate(self, show_progress_bar=False): """ This function attempts to add an unobserved common cause to the outcome and the treatment. At present, we have implemented the behavior for one dimensional behaviors for continuous and binary variables. This function can either take single valued inputs or a range of inputs. The function then looks at the data type of the input and then decides on the course of action. :return: CausalRefuter: An object that contains the estimated effect and a new effect and the name of the refutation used. """ if self.simulation_method == "linear-partial-R2": if not (isinstance(self._estimate.estimator, LinearRegressionEstimator)): raise NotImplementedError( "Currently only LinearRegressionEstimator is supported for Sensitivity Analysis" ) if len(self._estimate.estimator._effect_modifier_names) > 0: raise NotImplementedError("The current implementation does not support effect modifiers") if self.frac_strength_outcome == 1: self.frac_strength_outcome = self.frac_strength_treatment analyzer = LinearSensitivityAnalyzer( estimator=self._estimate.estimator, data=self._data, treatment_name=self._treatment_name, percent_change_estimate=self.percent_change_estimate, significance_level=self.significance_level, benchmark_common_causes=self.benchmark_common_causes, null_hypothesis_effect=self.null_hypothesis_effect, frac_strength_treatment=self.frac_strength_treatment, frac_strength_outcome=self.frac_strength_outcome, common_causes_order=self._estimate.estimator._observed_common_causes.columns, ) analyzer.check_sensitivity(plot=self.plot_estimate) return analyzer if self.simulation_method == "non-parametric-partial-R2": # If the estimator used is LinearDML, partially linear sensitivity analysis will be automatically chosen if isinstance(self._estimate.estimator, dowhy.causal_estimators.econml.Econml): if self._estimate.estimator._econml_methodname == "econml.dml.LinearDML": analyzer = PartialLinearSensitivityAnalyzer( estimator=self._estimate._estimator_object, observed_common_causes=self._estimate.estimator._observed_common_causes, treatment=self._estimate.estimator._treatment, outcome=self._estimate.estimator._outcome, alpha_s_estimator_param_list=self.alpha_s_estimator_param_list, g_s_estimator_list=self.g_s_estimator_list, g_s_estimator_param_list=self.g_s_estimator_param_list, effect_strength_treatment=self.kappa_t, effect_strength_outcome=self.kappa_y, benchmark_common_causes=self.benchmark_common_causes, frac_strength_treatment=self.frac_strength_treatment, frac_strength_outcome=self.frac_strength_outcome, ) analyzer.check_sensitivity(plot=self.plot_estimate) return analyzer analyzer = NonParametricSensitivityAnalyzer( estimator=self._estimate.estimator, observed_common_causes=self._estimate.estimator._observed_common_causes, treatment=self._estimate.estimator._treatment, outcome=self._estimate.estimator._outcome, alpha_s_estimator_list=self.alpha_s_estimator_list, alpha_s_estimator_param_list=self.alpha_s_estimator_param_list, g_s_estimator_list=self.g_s_estimator_list, g_s_estimator_param_list=self.g_s_estimator_param_list, effect_strength_treatment=self.kappa_t, effect_strength_outcome=self.kappa_y, benchmark_common_causes=self.benchmark_common_causes, frac_strength_treatment=self.frac_strength_treatment, frac_strength_outcome=self.frac_strength_outcome, theta_s=self._estimate.value, plugin_reisz=self.plugin_reisz, ) analyzer.check_sensitivity(plot=self.plot_estimate) return analyzer if self.kappa_t is None: self.kappa_t = self.infer_default_kappa_t() if self.kappa_y is None: self.kappa_y = self.infer_default_kappa_y() if not isinstance(self.kappa_t, (list, np.ndarray)) and not isinstance( self.kappa_y, (list, np.ndarray) ): # Deal with single value inputs new_data = copy.deepcopy(self._data) new_data = self.include_confounders_effect(new_data, self.kappa_t, self.kappa_y) new_estimator = CausalEstimator.get_estimator_object(new_data, self._target_estimand, self._estimate) new_effect = new_estimator.estimate_effect() refute = CausalRefutation( self._estimate.value, new_effect.value, refutation_type="Refute: Add an Unobserved Common Cause" ) refute.new_effect_array = np.array(new_effect.value) refute.new_effect = new_effect.value refute.add_refuter(self) return refute else: # Deal with multiple value inputs if isinstance(self.kappa_t, (list, np.ndarray)) and isinstance( self.kappa_y, (list, np.ndarray) ): # Deal with range inputs # Get a 2D matrix of values # x,y = np.meshgrid(self.kappa_t, self.kappa_y) # x,y are both MxN results_matrix = np.random.rand( len(self.kappa_t), len(self.kappa_y) ) # Matrix to hold all the results of NxM orig_data = copy.deepcopy(self._data) for i in tqdm( range(len(self.kappa_t)), colour=CausalRefuter.PROGRESS_BAR_COLOR, disable=not show_progress_bar, desc="Refuting Estimates: ", ): for j in range(len(self.kappa_y)): new_data = self.include_confounders_effect(orig_data, self.kappa_t[i], self.kappa_y[j]) new_estimator = CausalEstimator.get_estimator_object( new_data, self._target_estimand, self._estimate ) new_effect = new_estimator.estimate_effect() refute = CausalRefutation( self._estimate.value, new_effect.value, refutation_type="Refute: Add an Unobserved Common Cause", ) results_matrix[i][j] = refute.new_effect # Populate the results refute.new_effect_array = results_matrix refute.new_effect = (np.min(results_matrix), np.max(results_matrix)) # Store the values into the refute object refute.add_refuter(self) if self.plotmethod is None: return refute import matplotlib import matplotlib.pyplot as plt fig = plt.figure(figsize=(6, 5)) left, bottom, width, height = 0.1, 0.1, 0.8, 0.8 ax = fig.add_axes([left, bottom, width, height]) oe = self._estimate.value contour_levels = [oe / 4.0, oe / 2.0, (3.0 / 4) * oe, oe] contour_levels.extend([0, np.min(results_matrix), np.max(results_matrix)]) if self.plotmethod == "contour": cp = plt.contourf(self.kappa_y, self.kappa_t, results_matrix, levels=sorted(contour_levels)) # Adding a label on the contour line for the original estimate fmt = {} trueeffect_index = np.where(cp.levels == oe)[0][0] fmt[cp.levels[trueeffect_index]] = "Estimated Effect" # Label every other level using strings plt.clabel(cp, [cp.levels[trueeffect_index]], inline=True, fmt=fmt) plt.colorbar(cp) elif self.plotmethod == "colormesh": cp = plt.pcolormesh(self.kappa_y, self.kappa_t, results_matrix, shading="nearest") plt.colorbar(cp, ticks=contour_levels) ax.yaxis.set_ticks(self.kappa_t) ax.xaxis.set_ticks(self.kappa_y) plt.xticks(rotation=45) ax.set_title("Effect of Unobserved Common Cause") ax.set_ylabel("Value of Linear Constant on Treatment") ax.set_xlabel("Value of Linear Constant on Outcome") plt.show() return refute elif isinstance(self.kappa_t, (list, np.ndarray)): outcomes = np.random.rand(len(self.kappa_t)) orig_data = copy.deepcopy(self._data) for i in tqdm( range(0, len(self.kappa_t)), colour=CausalRefuter.PROGRESS_BAR_COLOR, disable=not show_progress_bar, desc="Refuting Estimates: ", ): new_data = self.include_confounders_effect(orig_data, self.kappa_t[i], self.kappa_y) new_estimator = CausalEstimator.get_estimator_object( new_data, self._target_estimand, self._estimate ) new_effect = new_estimator.estimate_effect() refute = CausalRefutation( self._estimate.value, new_effect.value, refutation_type="Refute: Add an Unobserved Common Cause" ) self.logger.debug(refute) outcomes[i] = refute.new_effect # Populate the results refute.new_effect_array = outcomes refute.new_effect = (np.min(outcomes), np.max(outcomes)) refute.add_refuter(self) if self.plotmethod is None: return refute import matplotlib import matplotlib.pyplot as plt fig = plt.figure(figsize=(6, 5)) left, bottom, width, height = 0.1, 0.1, 0.8, 0.8 ax = fig.add_axes([left, bottom, width, height]) plt.plot(self.kappa_t, outcomes) plt.axhline(self._estimate.value, linestyle="--", color="gray") ax.set_title("Effect of Unobserved Common Cause") ax.set_xlabel("Value of Linear Constant on Treatment") ax.set_ylabel("Estimated Effect after adding the common cause") plt.show() return refute elif isinstance(self.kappa_y, (list, np.ndarray)): outcomes = np.random.rand(len(self.kappa_y)) orig_data = copy.deepcopy(self._data) for i in tqdm( range(0, len(self.kappa_y)), colour=CausalRefuter.PROGRESS_BAR_COLOR, disable=not show_progress_bar, desc="Refuting Estimates: ", ): new_data = self.include_confounders_effect(orig_data, self.kappa_t, self.kappa_y[i]) new_estimator = CausalEstimator.get_estimator_object( new_data, self._target_estimand, self._estimate ) new_effect = new_estimator.estimate_effect() refute = CausalRefutation( self._estimate.value, new_effect.value, refutation_type="Refute: Add an Unobserved Common Cause" ) self.logger.debug(refute) outcomes[i] = refute.new_effect # Populate the results refute.new_effect_array = outcomes refute.new_effect = (np.min(outcomes), np.max(outcomes)) refute.add_refuter(self) if self.plotmethod is None: return refute import matplotlib import matplotlib.pyplot as plt fig = plt.figure(figsize=(6, 5)) left, bottom, width, height = 0.1, 0.1, 0.8, 0.8 ax = fig.add_axes([left, bottom, width, height]) plt.plot(self.kappa_y, outcomes) plt.axhline(self._estimate.value, linestyle="--", color="gray") ax.set_title("Effect of Unobserved Common Cause") ax.set_xlabel("Value of Linear Constant on Outcome") ax.set_ylabel("Estimated Effect after adding the common cause") plt.show() return refute def include_confounders_effect(self, new_data, kappa_t, kappa_y): """ This function deals with the change in the value of the data due to the effect of the unobserved confounder. In the case of a binary flip, we flip only if the random number is greater than the threshold set. In the case of a linear effect, we use the variable as the linear regression constant. :param new_data: pandas.DataFrame: The data to be changed due to the effects of the unobserved confounder. :param kappa_t: numpy.float64: The value of the threshold for binary_flip or the value of the regression coefficient for linear effect. :param kappa_y: numpy.float64: The value of the threshold for binary_flip or the value of the regression coefficient for linear effect. :return: pandas.DataFrame: The DataFrame that includes the effects of the unobserved confounder. """ num_rows = self._data.shape[0] stdnorm = scipy.stats.norm() w_random = stdnorm.rvs(num_rows) if self.effect_on_t == "binary_flip": alpha = 2 * kappa_t - 1 if kappa_t >= 0.5 else 1 - 2 * kappa_t interval = stdnorm.interval(alpha) rel_interval = interval[0] if kappa_t >= 0.5 else interval[1] new_data.loc[rel_interval <= w_random, self._treatment_name] = ( 1 - new_data.loc[rel_interval <= w_random, self._treatment_name] ) for tname in self._treatment_name: if pd.api.types.is_bool_dtype(self._data[tname]): new_data = new_data.astype({tname: "bool"}, copy=False) elif self.effect_on_t == "linear": confounder_t_effect = kappa_t * w_random # By default, we add the effect of simulated confounder for treatment. # But subtract it from outcome to create a negative correlation # assuming that the original confounder's effect was positive on both. # This is to remove the effect of the original confounder. new_data[self._treatment_name] = new_data[self._treatment_name].values + np.ndarray( shape=(num_rows, 1), buffer=confounder_t_effect ) else: raise NotImplementedError( "'" + self.effect_on_t + "' method not supported for confounders' effect on treatment" ) if self.effect_on_y == "binary_flip": alpha = 2 * kappa_y - 1 if kappa_y >= 0.5 else 1 - 2 * kappa_y interval = stdnorm.interval(alpha) rel_interval = interval[0] if kappa_y >= 0.5 else interval[1] new_data.loc[rel_interval <= w_random, self._outcome_name] = ( 1 - new_data.loc[rel_interval <= w_random, self._outcome_name] ) for yname in self._outcome_name: if pd.api.types.is_bool_dtype(self._data[yname]): new_data = new_data.astype({yname: "bool"}, copy=False) elif self.effect_on_y == "linear": confounder_y_effect = (-1) * kappa_y * w_random # By default, we add the effect of simulated confounder for treatment. # But subtract it from outcome to create a negative correlation # assuming that the original confounder's effect was positive on both. # This is to remove the effect of the original confounder. new_data[self._outcome_name] = new_data[self._outcome_name].values + np.ndarray( shape=(num_rows, 1), buffer=confounder_y_effect ) else: raise NotImplementedError( "'" + self.effect_on_y + "' method not supported for confounders' effect on outcome" ) return new_data def include_simulated_confounder(self, convergence_threshold=0.1, c_star_max=1000): """ This function simulates an unobserved confounder based on the data using the following steps: 1. It calculates the "residuals" from the treatment and outcome model i.) The outcome model has outcome as the dependent variable and all the observed variables including treatment as independent variables ii.) The treatment model has treatment as the dependent variable and all the observed variables as independent variables. 2. U is an intermediate random variable drawn from the normal distribution with the weighted average of residuals as mean and a unit variance U ~ N(c1*d_y + c2*d_t, 1) where *d_y and d_t are residuals from the treatment and outcome model *c1 and c2 are coefficients to the residuals 3. The final U, which is the simulated unobserved confounder is obtained by debiasing the intermediate variable U by residualising it with X Choosing the coefficients c1 and c2: The coefficients are chosen based on these basic assumptions: 1. There is a hyperbolic relationship satisfying c1*c2 = c_star 2. c_star is chosen from a range of possible values based on the correlation of the obtained simulated variable with outcome and treatment. 3. The product of correlations with treatment and outcome should be at a minimum distance to the maximum correlations with treatment and outcome in any of the observed confounders 4. The ratio of the weights should be such that they maintain the ratio of the maximum possible observed coefficients within some confidence interval :param c_star_max: The maximum possible value for the hyperbolic curve on which the coefficients to the residuals lie. It defaults to 1000 in the code if not specified by the user. :type int :param convergence_threshold: The threshold to check the plateauing of the correlation while selecting a c_star. It defaults to 0.1 in the code if not specified by the user :type float :returns: The simulated values of the unobserved confounder based on the data :type pandas.core.series.Series """ # Obtaining the list of observed variables required_variables = True observed_variables = self.choose_variables(required_variables) observed_variables_with_treatment_and_outcome = observed_variables + self._treatment_name + self._outcome_name # Taking a subset of the dataframe that has only observed variables self._data = self._data[observed_variables_with_treatment_and_outcome] # Residuals from the outcome model obtained by fitting a linear model y = self._data[self._outcome_name[0]] observed_variables_with_treatment = observed_variables + self._treatment_name X = self._data[observed_variables_with_treatment] model = sm.OLS(y, X.astype("float")) results = model.fit() residuals_y = y - results.fittedvalues d_y = list(pd.Series(residuals_y)) # Residuals from the treatment model obtained by fitting a linear model t = self._data[self._treatment_name[0]].astype("int64") X = self._data[observed_variables] model = sm.OLS(t, X) results = model.fit() residuals_t = t - results.fittedvalues d_t = list(pd.Series(residuals_t)) # Initialising product_cor_metric_observed with a really low value as finding maximum product_cor_metric_observed = -10000000000 for i in observed_variables: current_obs_confounder = self._data[i] outcome_values = self._data[self._outcome_name[0]] correlation_y = current_obs_confounder.corr(outcome_values) treatment_values = t correlation_t = current_obs_confounder.corr(treatment_values) product_cor_metric_current = correlation_y * correlation_t if product_cor_metric_current >= product_cor_metric_observed: product_cor_metric_observed = product_cor_metric_current correlation_t_observed = correlation_t correlation_y_observed = correlation_y # The user has an option to give the the effect_strength_on_y and effect_strength_on_t which can be then used instead of maximum correlation with treatment and outcome in the observed variables as it specifies the desired effect. if self.kappa_t is not None: correlation_t_observed = self.kappa_t if self.kappa_y is not None: correlation_y_observed = self.kappa_y # Choosing a c_star based on the data. # The correlations stop increasing upon increasing c_star after a certain value, that is it plateaus and we choose the value of c_star to be the value it plateaus. correlation_y_list = [] correlation_t_list = [] product_cor_metric_simulated_list = [] x_list = [] step = int(c_star_max / 10) for i in range(0, int(c_star_max), step): c1 = math.sqrt(i) c2 = c1 final_U = self.generate_confounder_from_residuals(c1, c2, d_y, d_t, X) current_simulated_confounder = final_U outcome_values = self._data[self._outcome_name[0]] correlation_y = current_simulated_confounder.corr(outcome_values) correlation_y_list.append(correlation_y) treatment_values = t correlation_t = current_simulated_confounder.corr(treatment_values) correlation_t_list.append(correlation_t) product_cor_metric_simulated = correlation_y * correlation_t product_cor_metric_simulated_list.append(product_cor_metric_simulated) x_list.append(i) index = 1 while index < len(correlation_y_list): if (correlation_y_list[index] - correlation_y_list[index - 1]) <= convergence_threshold: c_star = x_list[index] break index = index + 1 # Choosing c1 and c2 based on the hyperbolic relationship once c_star is chosen by going over various combinations of c1 and c2 values and choosing the combination which # which maintains the minimum distance between the product of correlations of the simulated variable and the product of maximum correlations of one of the observed variables # and additionally checks if the ratio of the weights are such that they maintain the ratio of the maximum possible observed coefficients within some confidence interval # c1_final and c2_final are initialised to the values on the hyperbolic curve such that c1_final = c2_final and c1_final*c2_final = c_star c1_final = math.sqrt(c_star) c2_final = math.sqrt(c_star) # initialising min_distance_between_product_cor_metrics to be a value greater than 1 min_distance_between_product_cor_metrics = 1.5 i = 0.05 threshold = c_star / 0.05 while i <= threshold: c2 = i c1 = c_star / c2 final_U = self.generate_confounder_from_residuals(c1, c2, d_y, d_t, X) current_simulated_confounder = final_U outcome_values = self._data[self._outcome_name[0]] correlation_y = current_simulated_confounder.corr(outcome_values) treatment_values = t correlation_t = current_simulated_confounder.corr(treatment_values) product_cor_metric_simulated = correlation_y * correlation_t if min_distance_between_product_cor_metrics >= abs( product_cor_metric_simulated - product_cor_metric_observed ): min_distance_between_product_cor_metrics = abs( product_cor_metric_simulated - product_cor_metric_observed ) additional_condition = correlation_y_observed / correlation_t_observed if ((c1 / c2) <= (additional_condition + 0.3 * additional_condition)) and ( (c1 / c2) >= (additional_condition - 0.3 * additional_condition) ): # choose minimum positive value c1_final = c1 c2_final = c2 i = i * 1.5 """#closed form solution print("c_star_max before closed form", c_star_max) if max_correlation_with_t == -1000: c2 = 0 c1 = c_star_max else: additional_condition = abs(max_correlation_with_y/max_correlation_with_t) print("additional_condition", additional_condition) c2 = math.sqrt(c_star_max/additional_condition) c1 = c_star_max/c2""" final_U = self.generate_confounder_from_residuals(c1_final, c2_final, d_y, d_t, X) return final_U def generate_confounder_from_residuals(self, c1, c2, d_y, d_t, X): """ This function takes the residuals from the treatment and outcome model and their coefficients and simulates the intermediate random variable U by taking the row wise normal distribution corresponding to each residual value and then debiasing the intermediate variable to get the final variable. :param c1: coefficient to the residual from the outcome model :type float :param c2: coefficient to the residual from the treatment model :type float :param d_y: residuals from the outcome model :type list :param d_t: residuals from the treatment model :type list :returns: The simulated values of the unobserved confounder based on the data :type pandas.core.series.Series """ U = [] for j in range(len(d_t)): simulated_variable_mean = c1 * d_y[j] + c2 * d_t[j] simulated_variable_stddev = 1 U.append(np.random.normal(simulated_variable_mean, simulated_variable_stddev, 1)) U = np.array(U) model = sm.OLS(U, X) results = model.fit() U = U.reshape( -1, ) final_U = U - results.fittedvalues.values final_U = pd.Series(U) return final_U

anusha0409

81841c697bd5e80ecf9e731432305f6186666f1f

bb446c333f2256074304b0dec9cb5628d284b542

great point, Emre. Yes, let's take it up when we discuss how to refactor refutations to work across the estimation pipeline.

amit-sharma

py-why/dowhy

Adding Non Linear Sensitivity Analysis

This PR implements the non-parametric sensitivity analysis from Chernozhukov et al. https://arxiv.org/abs/2112.13398 It implements two sensitivity analyzers: 1. For Partial Linear DGPs and estimators like LinearDML 2. For general non-parametric DGPs and estimators like KernelDML. The notebook in this PR provides an introduction on how the sensitivity bounds are calculated for the partial linear case. For the general nonparametric DGPs, we need to estimate a special function called the Reisz representer. For binary treatment, it is exactly the difference in outcome weighted by propensity score. So we provide two options to learn the Reisz representer, 1) plugin_reisz that uses the propensity score; and 2) general estimator that uses a custom loss function. These two are in the file reisz.py. Briefly, the sensitivity bounds depend on two parameters that denote the effect of the unobserved confounder on treatment and outcome. That's why we use the same API as for the `add_unobserved_common_cause` method and add this sensitivity analysis as a possible simulation method="non-parametric-partial-R2". The format of the plots is identical to those from the "linear-partial-r2" simulation method that is already implemented. We provide two modes for the user. 1) User specifies the effect strength parameters themselves, as a range of values. 2) User benchmarks the effect strength parameters as a multiple of the same parameters for the observed common causes. Signed-off-by: anusha <anushaagarwal2000.com>

2022-06-20 14:37:11+00:00

2022-09-16 03:57:26+00:00

dowhy/causal_refuters/add_unobserved_common_cause.py

import copy import logging import math import numpy as np import pandas as pd import scipy.stats import statsmodels.api as sm from sklearn.linear_model import LogisticRegression from sklearn.preprocessing import StandardScaler from tqdm.auto import tqdm from dowhy.causal_estimator import CausalEstimator from dowhy.causal_estimators.linear_regression_estimator import LinearRegressionEstimator from dowhy.causal_refuter import CausalRefutation, CausalRefuter from dowhy.causal_refuters.linear_sensitivity_analyzer import LinearSensitivityAnalyzer class AddUnobservedCommonCause(CausalRefuter): """Add an unobserved confounder for refutation. Supports additional parameters that can be specified in the refute_estimate() method. - 'confounders_effect_on_treatment': how the simulated confounder affects the value of treatment. This can be linear (for continuous treatment) or binary_flip (for binary treatment) - 'confounders_effect_on_outcome': how the simulated confounder affects the value of outcome. This can be linear (for continuous outcome) or binary_flip (for binary outcome) - 'effect_strength_on_treatment': parameter for the strength of the effect of simulated confounder on treatment. For linear effect, it is the regression coeffient. For binary_flip, it is the probability that simulated confounder's effect flips the value of treatment from 0 to 1 (or vice-versa). - 'effect_strength_on_outcome': parameter for the strength of the effect of simulated confounder on outcome. For linear effect, it is the regression coeffient. For binary_flip, it is the probability that simulated confounder's effect flips the value of outcome from 0 to 1 (or vice-versa). TODO: Needs an interpretation module """ def __init__(self, *args, **kwargs): """ Initialize the parameters required for the refuter. If effect_strength_on_treatment or effect_strength_on_outcome is not given, it is calculated automatically as a range between the minimum and maximum effect strength of observed confounders on treatment and outcome respectively. :param confounders_effect_on_treatment: str : The type of effect on the treatment due to the unobserved confounder. Possible values are ['binary_flip', 'linear'] :param confounders_effect_on_outcome: str : The type of effect on the outcome due to the unobserved confounder. Possible values are ['binary_flip', 'linear'] :param effect_strength_on_treatment: float, numpy.ndarray: This refers to the strength of the confounder on treatment. For a linear effect, it behaves like the regression coeffecient. For a binary flip it is the probability with which it can invert the value of the treatment. :param effect_strength_on_outcome: float, numpy.ndarray: This refers to the strength of the confounder on outcome. For a linear effect, it behaves like the regression coefficient. For a binary flip, it is the probability with which it can invert the value of the outcome. :param effect_fraction_on_treatment: float: If effect_strength_on_treatment is not provided, this parameter decides the effect strength of the simulated confounder as a fraction of the effect strength of observed confounders on treatment. Defaults to 1. :param effect_fraction_on_outcome: float: If effect_strength_on_outcome is not provided, this parameter decides the effect strength of the simulated confounder as a fraction of the effect strength of observed confounders on outcome. Defaults to 1. :param plotmethod: string: Type of plot to be shown. If None, no plot is generated. This parameter is used only only when more than one treatment confounder effect values or outcome confounder effect values are provided. Default is "colormesh". Supported values are "contour", "colormesh" when more than one value is provided for both confounder effect value parameters; "line" when provided for only one of them. :param simulated_method_name: method type to add unobserved common cause. "linear-partial-R2" for linear sensitivity analysis :param percent_change_estimate: It is the percentage of reduction of treatment estimate that could alter the results (default = 1) if percent_change_estimate = 1, the robustness value describes the strength of association of confounders with treatment and outcome in order to reduce the estimate by 100% i.e bring it down to 0. :param confounder_increases_estimate: True implies that confounder increases the absolute value of estimate and vice versa. (Default = False) :param benchmark_common_causes: names of variables for bounding strength of confounders :param significance_level: confidence interval for statistical inference(default = 0.05) :param null_hypothesis_effect: assumed effect under the null hypothesis :param plot_estimate: Generate contour plot for estimate while performing sensitivity analysis. (default = True). To override the setting, set plot_estimate = False. """ super().__init__(*args, **kwargs) self.effect_on_t = ( kwargs["confounders_effect_on_treatment"] if "confounders_effect_on_treatment" in kwargs else "binary_flip" ) self.effect_on_y = ( kwargs["confounders_effect_on_outcome"] if "confounders_effect_on_outcome" in kwargs else "linear" ) self.kappa_t = kwargs["effect_strength_on_treatment"] if "effect_strength_on_treatment" in kwargs else None self.kappa_y = kwargs["effect_strength_on_outcome"] if "effect_strength_on_outcome" in kwargs else None self.frac_strength_treatment = ( kwargs["effect_fraction_on_treatment"] if "effect_fraction_on_treatment" in kwargs else 1 ) self.frac_strength_outcome = ( kwargs["effect_fraction_on_outcome"] if "effect_fraction_on_outcome" in kwargs else 1 ) self.simulated_method_name = ( kwargs["simulated_method_name"] if "simulated_method_name" in kwargs else "linear_based" ) self.plotmethod = kwargs["plotmethod"] if "plotmethod" in kwargs else "colormesh" self.percent_change_estimate = kwargs["percent_change_estimate"] if "percent_change_estimate" in kwargs else 1.0 self.significance_level = kwargs["significance_level"] if "significance_level" in kwargs else 0.05 self.confounder_increases_estimate = ( kwargs["confounder_increases_estimate"] if "confounder_increases_estimate" in kwargs else False ) self.benchmark_common_causes = ( kwargs["benchmark_common_causes"] if "benchmark_common_causes" in kwargs else None ) self.null_hypothesis_effect = kwargs["null_hypothesis_effect"] if "null_hypothesis_effect" in kwargs else 0 self.plot_estimate = kwargs["plot_estimate"] if "plot_estimate" in kwargs else True self.logger = logging.getLogger(__name__) def infer_default_kappa_t(self, len_kappa_t=10): """Infer default effect strength of simulated confounder on treatment.""" observed_common_causes_names = self._target_estimand.get_backdoor_variables() if len(observed_common_causes_names) > 0: observed_common_causes = self._data[observed_common_causes_names] observed_common_causes = pd.get_dummies(observed_common_causes, drop_first=True) else: raise ValueError( "There needs to be at least one common cause to" + "automatically compute the default value of kappa_t." + " Provide a value for kappa_t" ) t = self._data[self._treatment_name] # Standardizing the data observed_common_causes = StandardScaler().fit_transform(observed_common_causes) if self.effect_on_t == "binary_flip": # Fit a model containing all confounders and compare predictions # using all features compared to all features except a given # confounder. tmodel = LogisticRegression().fit(observed_common_causes, t) tpred = tmodel.predict(observed_common_causes).astype(int) flips = [] for i in range(observed_common_causes.shape[1]): oldval = np.copy(observed_common_causes[:, i]) observed_common_causes[:, i] = 0 tcap = tmodel.predict(observed_common_causes).astype(int) observed_common_causes[:, i] = oldval flips.append(np.sum(abs(tcap - tpred)) / tpred.shape[0]) min_coeff, max_coeff = min(flips), max(flips) elif self.effect_on_t == "linear": # Estimating the regression coefficient from standardized features to t corrcoef_var_t = np.corrcoef(observed_common_causes, t, rowvar=False)[-1, :-1] std_dev_t = np.std(t)[0] max_coeff = max(corrcoef_var_t) * std_dev_t min_coeff = min(corrcoef_var_t) * std_dev_t else: raise NotImplementedError( "'" + self.effect_on_t + "' method not supported for confounders' effect on treatment" ) min_coeff, max_coeff = self._compute_min_max_coeff(min_coeff, max_coeff, self.frac_strength_treatment) # By default, return a plot with 10 points # consider 10 values of the effect of the unobserved confounder step = (max_coeff - min_coeff) / len_kappa_t self.logger.info("(Min, Max) kappa_t for observed common causes, ({0}, {1})".format(min_coeff, max_coeff)) if np.equal(max_coeff, min_coeff): return max_coeff else: return np.arange(min_coeff, max_coeff, step) def _compute_min_max_coeff(self, min_coeff, max_coeff, effect_strength_fraction): max_coeff = effect_strength_fraction * max_coeff min_coeff = effect_strength_fraction * min_coeff return min_coeff, max_coeff def infer_default_kappa_y(self, len_kappa_y=10): """Infer default effect strength of simulated confounder on treatment.""" observed_common_causes_names = self._target_estimand.get_backdoor_variables() if len(observed_common_causes_names) > 0: observed_common_causes = self._data[observed_common_causes_names] observed_common_causes = pd.get_dummies(observed_common_causes, drop_first=True) else: raise ValueError( "There needs to be at least one common cause to" + "automatically compute the default value of kappa_y." + " Provide a value for kappa_y" ) y = self._data[self._outcome_name] # Standardizing the data observed_common_causes = StandardScaler().fit_transform(observed_common_causes) if self.effect_on_y == "binary_flip": # Fit a model containing all confounders and compare predictions # using all features compared to all features except a given # confounder. ymodel = LogisticRegression().fit(observed_common_causes, y) ypred = ymodel.predict(observed_common_causes).astype(int) flips = [] for i in range(observed_common_causes.shape[1]): oldval = np.copy(observed_common_causes[:, i]) observed_common_causes[:, i] = 0 ycap = ymodel.predict(observed_common_causes).astype(int) observed_common_causes[:, i] = oldval flips.append(np.sum(abs(ycap - ypred)) / ypred.shape[0]) min_coeff, max_coeff = min(flips), max(flips) elif self.effect_on_y == "linear": corrcoef_var_y = np.corrcoef(observed_common_causes, y, rowvar=False)[-1, :-1] std_dev_y = np.std(y)[0] max_coeff = max(corrcoef_var_y) * std_dev_y min_coeff = min(corrcoef_var_y) * std_dev_y else: raise NotImplementedError( "'" + self.effect_on_y + "' method not supported for confounders' effect on outcome" ) min_coeff, max_coeff = self._compute_min_max_coeff(min_coeff, max_coeff, self.frac_strength_outcome) # By default, return a plot with 10 points # consider 10 values of the effect of the unobserved confounder step = (max_coeff - min_coeff) / len_kappa_y self.logger.info("(Min, Max) kappa_y for observed common causes, ({0}, {1})".format(min_coeff, max_coeff)) if np.equal(max_coeff, min_coeff): return max_coeff else: return np.arange(min_coeff, max_coeff, step) def refute_estimate(self, show_progress_bar=False): """ This function attempts to add an unobserved common cause to the outcome and the treatment. At present, we have implemented the behavior for one dimensional behaviors for continuous and binary variables. This function can either take single valued inputs or a range of inputs. The function then looks at the data type of the input and then decides on the course of action. :return: CausalRefuter: An object that contains the estimated effect and a new effect and the name of the refutation used. """ if self.simulated_method_name == "linear-partial-R2": if not (isinstance(self._estimate.estimator, LinearRegressionEstimator)): raise NotImplementedError( "Currently only LinearRegressionEstimator is supported for Sensitivity Analysis" ) if len(self._estimate.estimator._effect_modifier_names) > 0: raise NotImplementedError("The current implementation does not support effect modifiers") if self.frac_strength_outcome == 1: self.frac_strength_outcome = self.frac_strength_treatment analyzer = LinearSensitivityAnalyzer( estimator=self._estimate.estimator, data=self._data, treatment_name=self._treatment_name, percent_change_estimate=self.percent_change_estimate, significance_level=self.significance_level, benchmark_common_causes=self.benchmark_common_causes, null_hypothesis_effect=self.null_hypothesis_effect, frac_strength_treatment=self.frac_strength_treatment, frac_strength_outcome=self.frac_strength_outcome, common_causes_order=self._estimate.estimator._observed_common_causes.columns, ) analyzer.check_sensitivity(plot=self.plot_estimate) return analyzer if self.kappa_t is None: self.kappa_t = self.infer_default_kappa_t() if self.kappa_y is None: self.kappa_y = self.infer_default_kappa_y() if not isinstance(self.kappa_t, (list, np.ndarray)) and not isinstance( self.kappa_y, (list, np.ndarray) ): # Deal with single value inputs new_data = copy.deepcopy(self._data) new_data = self.include_confounders_effect(new_data, self.kappa_t, self.kappa_y) new_estimator = CausalEstimator.get_estimator_object(new_data, self._target_estimand, self._estimate) new_effect = new_estimator.estimate_effect() refute = CausalRefutation( self._estimate.value, new_effect.value, refutation_type="Refute: Add an Unobserved Common Cause" ) refute.new_effect_array = np.array(new_effect.value) refute.new_effect = new_effect.value refute.add_refuter(self) return refute else: # Deal with multiple value inputs if isinstance(self.kappa_t, (list, np.ndarray)) and isinstance( self.kappa_y, (list, np.ndarray) ): # Deal with range inputs # Get a 2D matrix of values # x,y = np.meshgrid(self.kappa_t, self.kappa_y) # x,y are both MxN results_matrix = np.random.rand( len(self.kappa_t), len(self.kappa_y) ) # Matrix to hold all the results of NxM orig_data = copy.deepcopy(self._data) for i in tqdm( range(len(self.kappa_t)), colour=CausalRefuter.PROGRESS_BAR_COLOR, disable=not show_progress_bar, desc="Refuting Estimates: ", ): for j in range(len(self.kappa_y)): new_data = self.include_confounders_effect(orig_data, self.kappa_t[i], self.kappa_y[j]) new_estimator = CausalEstimator.get_estimator_object( new_data, self._target_estimand, self._estimate ) new_effect = new_estimator.estimate_effect() refute = CausalRefutation( self._estimate.value, new_effect.value, refutation_type="Refute: Add an Unobserved Common Cause", ) results_matrix[i][j] = refute.new_effect # Populate the results refute.new_effect_array = results_matrix refute.new_effect = (np.min(results_matrix), np.max(results_matrix)) # Store the values into the refute object refute.add_refuter(self) if self.plotmethod is None: return refute import matplotlib import matplotlib.pyplot as plt fig = plt.figure(figsize=(6, 5)) left, bottom, width, height = 0.1, 0.1, 0.8, 0.8 ax = fig.add_axes([left, bottom, width, height]) oe = self._estimate.value contour_levels = [oe / 4.0, oe / 2.0, (3.0 / 4) * oe, oe] contour_levels.extend([0, np.min(results_matrix), np.max(results_matrix)]) if self.plotmethod == "contour": cp = plt.contourf(self.kappa_y, self.kappa_t, results_matrix, levels=sorted(contour_levels)) # Adding a label on the contour line for the original estimate fmt = {} trueeffect_index = np.where(cp.levels == oe)[0][0] fmt[cp.levels[trueeffect_index]] = "Estimated Effect" # Label every other level using strings plt.clabel(cp, [cp.levels[trueeffect_index]], inline=True, fmt=fmt) plt.colorbar(cp) elif self.plotmethod == "colormesh": cp = plt.pcolormesh(self.kappa_y, self.kappa_t, results_matrix, shading="nearest") plt.colorbar(cp, ticks=contour_levels) ax.yaxis.set_ticks(self.kappa_t) ax.xaxis.set_ticks(self.kappa_y) plt.xticks(rotation=45) ax.set_title("Effect of Unobserved Common Cause") ax.set_ylabel("Value of Linear Constant on Treatment") ax.set_xlabel("Value of Linear Constant on Outcome") plt.show() return refute elif isinstance(self.kappa_t, (list, np.ndarray)): outcomes = np.random.rand(len(self.kappa_t)) orig_data = copy.deepcopy(self._data) for i in tqdm( range(0, len(self.kappa_t)), colour=CausalRefuter.PROGRESS_BAR_COLOR, disable=not show_progress_bar, desc="Refuting Estimates: ", ): new_data = self.include_confounders_effect(orig_data, self.kappa_t[i], self.kappa_y) new_estimator = CausalEstimator.get_estimator_object( new_data, self._target_estimand, self._estimate ) new_effect = new_estimator.estimate_effect() refute = CausalRefutation( self._estimate.value, new_effect.value, refutation_type="Refute: Add an Unobserved Common Cause" ) self.logger.debug(refute) outcomes[i] = refute.new_effect # Populate the results refute.new_effect_array = outcomes refute.new_effect = (np.min(outcomes), np.max(outcomes)) refute.add_refuter(self) if self.plotmethod is None: return refute import matplotlib import matplotlib.pyplot as plt fig = plt.figure(figsize=(6, 5)) left, bottom, width, height = 0.1, 0.1, 0.8, 0.8 ax = fig.add_axes([left, bottom, width, height]) plt.plot(self.kappa_t, outcomes) plt.axhline(self._estimate.value, linestyle="--", color="gray") ax.set_title("Effect of Unobserved Common Cause") ax.set_xlabel("Value of Linear Constant on Treatment") ax.set_ylabel("Estimated Effect after adding the common cause") plt.show() return refute elif isinstance(self.kappa_y, (list, np.ndarray)): outcomes = np.random.rand(len(self.kappa_y)) orig_data = copy.deepcopy(self._data) for i in tqdm( range(0, len(self.kappa_y)), colour=CausalRefuter.PROGRESS_BAR_COLOR, disable=not show_progress_bar, desc="Refuting Estimates: ", ): new_data = self.include_confounders_effect(orig_data, self.kappa_t, self.kappa_y[i]) new_estimator = CausalEstimator.get_estimator_object( new_data, self._target_estimand, self._estimate ) new_effect = new_estimator.estimate_effect() refute = CausalRefutation( self._estimate.value, new_effect.value, refutation_type="Refute: Add an Unobserved Common Cause" ) self.logger.debug(refute) outcomes[i] = refute.new_effect # Populate the results refute.new_effect_array = outcomes refute.new_effect = (np.min(outcomes), np.max(outcomes)) refute.add_refuter(self) if self.plotmethod is None: return refute import matplotlib import matplotlib.pyplot as plt fig = plt.figure(figsize=(6, 5)) left, bottom, width, height = 0.1, 0.1, 0.8, 0.8 ax = fig.add_axes([left, bottom, width, height]) plt.plot(self.kappa_y, outcomes) plt.axhline(self._estimate.value, linestyle="--", color="gray") ax.set_title("Effect of Unobserved Common Cause") ax.set_xlabel("Value of Linear Constant on Outcome") ax.set_ylabel("Estimated Effect after adding the common cause") plt.show() return refute def include_confounders_effect(self, new_data, kappa_t, kappa_y): """ This function deals with the change in the value of the data due to the effect of the unobserved confounder. In the case of a binary flip, we flip only if the random number is greater than the threshold set. In the case of a linear effect, we use the variable as the linear regression constant. :param new_data: pandas.DataFrame: The data to be changed due to the effects of the unobserved confounder. :param kappa_t: numpy.float64: The value of the threshold for binary_flip or the value of the regression coefficient for linear effect. :param kappa_y: numpy.float64: The value of the threshold for binary_flip or the value of the regression coefficient for linear effect. :return: pandas.DataFrame: The DataFrame that includes the effects of the unobserved confounder. """ num_rows = self._data.shape[0] stdnorm = scipy.stats.norm() w_random = stdnorm.rvs(num_rows) if self.effect_on_t == "binary_flip": alpha = 2 * kappa_t - 1 if kappa_t >= 0.5 else 1 - 2 * kappa_t interval = stdnorm.interval(alpha) rel_interval = interval[0] if kappa_t >= 0.5 else interval[1] new_data.loc[rel_interval <= w_random, self._treatment_name] = ( 1 - new_data.loc[rel_interval <= w_random, self._treatment_name] ) for tname in self._treatment_name: if pd.api.types.is_bool_dtype(self._data[tname]): new_data = new_data.astype({tname: "bool"}, copy=False) elif self.effect_on_t == "linear": confounder_t_effect = kappa_t * w_random # By default, we add the effect of simulated confounder for treatment. # But subtract it from outcome to create a negative correlation # assuming that the original confounder's effect was positive on both. # This is to remove the effect of the original confounder. new_data[self._treatment_name] = new_data[self._treatment_name].values + np.ndarray( shape=(num_rows, 1), buffer=confounder_t_effect ) else: raise NotImplementedError( "'" + self.effect_on_t + "' method not supported for confounders' effect on treatment" ) if self.effect_on_y == "binary_flip": alpha = 2 * kappa_y - 1 if kappa_y >= 0.5 else 1 - 2 * kappa_y interval = stdnorm.interval(alpha) rel_interval = interval[0] if kappa_y >= 0.5 else interval[1] new_data.loc[rel_interval <= w_random, self._outcome_name] = ( 1 - new_data.loc[rel_interval <= w_random, self._outcome_name] ) for yname in self._outcome_name: if pd.api.types.is_bool_dtype(self._data[yname]): new_data = new_data.astype({yname: "bool"}, copy=False) elif self.effect_on_y == "linear": confounder_y_effect = (-1) * kappa_y * w_random # By default, we add the effect of simulated confounder for treatment. # But subtract it from outcome to create a negative correlation # assuming that the original confounder's effect was positive on both. # This is to remove the effect of the original confounder. new_data[self._outcome_name] = new_data[self._outcome_name].values + np.ndarray( shape=(num_rows, 1), buffer=confounder_y_effect ) else: raise NotImplementedError( "'" + self.effect_on_y + "' method not supported for confounders' effect on outcome" ) return new_data def include_simulated_confounder(self, convergence_threshold=0.1, c_star_max=1000): """ This function simulates an unobserved confounder based on the data using the following steps: 1. It calculates the "residuals" from the treatment and outcome model i.) The outcome model has outcome as the dependent variable and all the observed variables including treatment as independent variables ii.) The treatment model has treatment as the dependent variable and all the observed variables as independent variables. 2. U is an intermediate random variable drawn from the normal distribution with the weighted average of residuals as mean and a unit variance U ~ N(c1*d_y + c2*d_t, 1) where *d_y and d_t are residuals from the treatment and outcome model *c1 and c2 are coefficients to the residuals 3. The final U, which is the simulated unobserved confounder is obtained by debiasing the intermediate variable U by residualising it with X Choosing the coefficients c1 and c2: The coefficients are chosen based on these basic assumptions: 1. There is a hyperbolic relationship satisfying c1*c2 = c_star 2. c_star is chosen from a range of possible values based on the correlation of the obtained simulated variable with outcome and treatment. 3. The product of correlations with treatment and outcome should be at a minimum distance to the maximum correlations with treatment and outcome in any of the observed confounders 4. The ratio of the weights should be such that they maintain the ratio of the maximum possible observed coefficients within some confidence interval :param c_star_max: The maximum possible value for the hyperbolic curve on which the coefficients to the residuals lie. It defaults to 1000 in the code if not specified by the user. :type int :param convergence_threshold: The threshold to check the plateauing of the correlation while selecting a c_star. It defaults to 0.1 in the code if not specified by the user :type float :returns: The simulated values of the unobserved confounder based on the data :type pandas.core.series.Series """ # Obtaining the list of observed variables required_variables = True observed_variables = self.choose_variables(required_variables) observed_variables_with_treatment_and_outcome = observed_variables + self._treatment_name + self._outcome_name # Taking a subset of the dataframe that has only observed variables self._data = self._data[observed_variables_with_treatment_and_outcome] # Residuals from the outcome model obtained by fitting a linear model y = self._data[self._outcome_name[0]] observed_variables_with_treatment = observed_variables + self._treatment_name X = self._data[observed_variables_with_treatment] model = sm.OLS(y, X.astype("float")) results = model.fit() residuals_y = y - results.fittedvalues d_y = list(pd.Series(residuals_y)) # Residuals from the treatment model obtained by fitting a linear model t = self._data[self._treatment_name[0]].astype("int64") X = self._data[observed_variables] model = sm.OLS(t, X) results = model.fit() residuals_t = t - results.fittedvalues d_t = list(pd.Series(residuals_t)) # Initialising product_cor_metric_observed with a really low value as finding maximum product_cor_metric_observed = -10000000000 for i in observed_variables: current_obs_confounder = self._data[i] outcome_values = self._data[self._outcome_name[0]] correlation_y = current_obs_confounder.corr(outcome_values) treatment_values = t correlation_t = current_obs_confounder.corr(treatment_values) product_cor_metric_current = correlation_y * correlation_t if product_cor_metric_current >= product_cor_metric_observed: product_cor_metric_observed = product_cor_metric_current correlation_t_observed = correlation_t correlation_y_observed = correlation_y # The user has an option to give the the effect_strength_on_y and effect_strength_on_t which can be then used instead of maximum correlation with treatment and outcome in the observed variables as it specifies the desired effect. if self.kappa_t is not None: correlation_t_observed = self.kappa_t if self.kappa_y is not None: correlation_y_observed = self.kappa_y # Choosing a c_star based on the data. # The correlations stop increasing upon increasing c_star after a certain value, that is it plateaus and we choose the value of c_star to be the value it plateaus. correlation_y_list = [] correlation_t_list = [] product_cor_metric_simulated_list = [] x_list = [] step = int(c_star_max / 10) for i in range(0, int(c_star_max), step): c1 = math.sqrt(i) c2 = c1 final_U = self.generate_confounder_from_residuals(c1, c2, d_y, d_t, X) current_simulated_confounder = final_U outcome_values = self._data[self._outcome_name[0]] correlation_y = current_simulated_confounder.corr(outcome_values) correlation_y_list.append(correlation_y) treatment_values = t correlation_t = current_simulated_confounder.corr(treatment_values) correlation_t_list.append(correlation_t) product_cor_metric_simulated = correlation_y * correlation_t product_cor_metric_simulated_list.append(product_cor_metric_simulated) x_list.append(i) index = 1 while index < len(correlation_y_list): if (correlation_y_list[index] - correlation_y_list[index - 1]) <= convergence_threshold: c_star = x_list[index] break index = index + 1 # Choosing c1 and c2 based on the hyperbolic relationship once c_star is chosen by going over various combinations of c1 and c2 values and choosing the combination which # which maintains the minimum distance between the product of correlations of the simulated variable and the product of maximum correlations of one of the observed variables # and additionally checks if the ratio of the weights are such that they maintain the ratio of the maximum possible observed coefficients within some confidence interval # c1_final and c2_final are initialised to the values on the hyperbolic curve such that c1_final = c2_final and c1_final*c2_final = c_star c1_final = math.sqrt(c_star) c2_final = math.sqrt(c_star) # initialising min_distance_between_product_cor_metrics to be a value greater than 1 min_distance_between_product_cor_metrics = 1.5 i = 0.05 threshold = c_star / 0.05 while i <= threshold: c2 = i c1 = c_star / c2 final_U = self.generate_confounder_from_residuals(c1, c2, d_y, d_t, X) current_simulated_confounder = final_U outcome_values = self._data[self._outcome_name[0]] correlation_y = current_simulated_confounder.corr(outcome_values) treatment_values = t correlation_t = current_simulated_confounder.corr(treatment_values) product_cor_metric_simulated = correlation_y * correlation_t if min_distance_between_product_cor_metrics >= abs( product_cor_metric_simulated - product_cor_metric_observed ): min_distance_between_product_cor_metrics = abs( product_cor_metric_simulated - product_cor_metric_observed ) additional_condition = correlation_y_observed / correlation_t_observed if ((c1 / c2) <= (additional_condition + 0.3 * additional_condition)) and ( (c1 / c2) >= (additional_condition - 0.3 * additional_condition) ): # choose minimum positive value c1_final = c1 c2_final = c2 i = i * 1.5 """#closed form solution print("c_star_max before closed form", c_star_max) if max_correlation_with_t == -1000: c2 = 0 c1 = c_star_max else: additional_condition = abs(max_correlation_with_y/max_correlation_with_t) print("additional_condition", additional_condition) c2 = math.sqrt(c_star_max/additional_condition) c1 = c_star_max/c2""" final_U = self.generate_confounder_from_residuals(c1_final, c2_final, d_y, d_t, X) return final_U def generate_confounder_from_residuals(self, c1, c2, d_y, d_t, X): """ This function takes the residuals from the treatment and outcome model and their coefficients and simulates the intermediate random variable U by taking the row wise normal distribution corresponding to each residual value and then debiasing the intermediate variable to get the final variable. :param c1: coefficient to the residual from the outcome model :type float :param c2: coefficient to the residual from the treatment model :type float :param d_y: residuals from the outcome model :type list :param d_t: residuals from the treatment model :type list :returns: The simulated values of the unobserved confounder based on the data :type pandas.core.series.Series """ U = [] for j in range(len(d_t)): simulated_variable_mean = c1 * d_y[j] + c2 * d_t[j] simulated_variable_stddev = 1 U.append(np.random.normal(simulated_variable_mean, simulated_variable_stddev, 1)) U = np.array(U) model = sm.OLS(U, X) results = model.fit() U = U.reshape( -1, ) final_U = U - results.fittedvalues.values final_U = pd.Series(U) return final_U

import copy import logging import math import numpy as np import pandas as pd import scipy.stats import statsmodels.api as sm from sklearn.linear_model import LogisticRegression from sklearn.preprocessing import StandardScaler from tqdm.auto import tqdm import dowhy.causal_estimators.econml from dowhy.causal_estimator import CausalEstimator from dowhy.causal_estimators.linear_regression_estimator import LinearRegressionEstimator from dowhy.causal_refuter import CausalRefutation, CausalRefuter from dowhy.causal_refuters.linear_sensitivity_analyzer import LinearSensitivityAnalyzer from dowhy.causal_refuters.non_parametric_sensitivity_analyzer import NonParametricSensitivityAnalyzer from dowhy.causal_refuters.partial_linear_sensitivity_analyzer import PartialLinearSensitivityAnalyzer class AddUnobservedCommonCause(CausalRefuter): """Add an unobserved confounder for refutation. AddUnobservedCommonCause class supports three methods: 1) Simulation of an unobserved confounder 2) Linear partial R2 : Sensitivity Analysis for linear models. 3) Non-Parametric partial R2 based : Sensitivity Analyis for non-parametric models. Supports additional parameters that can be specified in the refute_estimate() method. """ def __init__(self, *args, **kwargs): """ Initialize the parameters required for the refuter. For direct_simulation, if effect_strength_on_treatment or effect_strength_on_outcome is not given, it is calculated automatically as a range between the minimum and maximum effect strength of observed confounders on treatment and outcome respectively. :param simulation_method: The method to use for simulating effect of unobserved confounder. Possible values are ["direct-simulation", "linear-partial-R2", "non-parametric-partial-R2"]. :param confounders_effect_on_treatment: str : The type of effect on the treatment due to the unobserved confounder. Possible values are ['binary_flip', 'linear'] :param confounders_effect_on_outcome: str : The type of effect on the outcome due to the unobserved confounder. Possible values are ['binary_flip', 'linear'] :param effect_strength_on_treatment: float, numpy.ndarray: [Used when simulation_method="direct-simulation"] Strength of the confounder's effect on treatment. When confounders_effect_on_treatment is linear, it is the regression coefficient. When the confounders_effect_on_treatment is binary flip, it is the probability with which effect of unobserved confounder can invert the value of the treatment. :param effect_strength_on_outcome: float, numpy.ndarray: Strength of the confounder's effect on outcome. Its interpretation depends on confounders_effect_on_outcome and the simulation_method. When simulation_method is direct-simulation, for a linear effect it behaves like the regression coefficient and for a binary flip, it is the probability with which it can invert the value of the outcome. :param partial_r2_confounder_treatment: float, numpy.ndarray: [Used when simulation_method is linear-partial-R2 or non-parametric-partial-R2] Partial R2 of the unobserved confounder wrt the treatment conditioned on the observed confounders. Only in the case of general non-parametric-partial-R2, it is the fraction of variance in the reisz representer that is explained by the unobserved confounder; specifically (1-r), where r is the ratio of variance of reisz representer, alpha^2, based on observed confounders and that based on all confounders. :param partial_r2_confounder_outcome: float, numpy.ndarray: [Used when simulation_method is linear-partial-R2 or non-parametric-partial-R2] Partial R2 of the unobserved confounder wrt the outcome conditioned on the treatment and observed confounders. :param frac_strength_treatment: float: This parameter decides the effect strength of the simulated confounder as a fraction of the effect strength of observed confounders on treatment. Defaults to 1. :param frac_strength_outcome: float: This parameter decides the effect strength of the simulated confounder as a fraction of the effect strength of observed confounders on outcome. Defaults to 1. :param plotmethod: string: Type of plot to be shown. If None, no plot is generated. This parameter is used only only when more than one treatment confounder effect values or outcome confounder effect values are provided. Default is "colormesh". Supported values are "contour", "colormesh" when more than one value is provided for both confounder effect value parameters; "line" when provided for only one of them. :param percent_change_estimate: It is the percentage of reduction of treatment estimate that could alter the results (default = 1). if percent_change_estimate = 1, the robustness value describes the strength of association of confounders with treatment and outcome in order to reduce the estimate by 100% i.e bring it down to 0. (relevant only for Linear Sensitivity Analysis, ignore for rest) :param confounder_increases_estimate: True implies that confounder increases the absolute value of estimate and vice versa. (Default = False). (relevant only for Linear Sensitivity Analysis, ignore for rest) :param benchmark_common_causes: names of variables for bounding strength of confounders. (relevant only for partial-r2 based simulation methods) :param significance_level: confidence interval for statistical inference(default = 0.05). (relevant only for partial-r2 based simulation methods) :param null_hypothesis_effect: assumed effect under the null hypothesis. (relevant only for linear-partial-R2, ignore for rest) :param plot_estimate: Generate contour plot for estimate while performing sensitivity analysis. (default = True). (relevant only for partial-r2 based simulation methods) :param num_splits: number of splits for cross validation. (default = 5). (relevant only for non-parametric-partial-R2 simulation method) :param shuffle_data : shuffle data or not before splitting into folds (default = False). (relevant only for non-parametric-partial-R2 simulation method) :param shuffle_random_seed: seed for randomly shuffling data. (relevant only for non-parametric-partial-R2 simulation method) :param alpha_s_estimator_param_list: list of dictionaries with parameters for finding alpha_s. (relevant only for non-parametric-partial-R2 simulation method) :param g_s_estimator_list: list of estimator objects for finding g_s. These objects should have fit() and predict() functions implemented. (relevant only for non-parametric-partial-R2 simulation method) :param g_s_estimator_param_list: list of dictionaries with parameters for tuning respective estimators in "g_s_estimator_list". The order of the dictionaries in the list should be consistent with the estimator objects order in "g_s_estimator_list". (relevant only for non-parametric-partial-R2 simulation method) """ super().__init__(*args, **kwargs) self.simulation_method = kwargs["simulation_method"] if "simulation_method" in kwargs else "direct-simulation" self.effect_on_t = ( kwargs["confounders_effect_on_treatment"] if "confounders_effect_on_treatment" in kwargs else "binary_flip" ) self.effect_on_y = ( kwargs["confounders_effect_on_outcome"] if "confounders_effect_on_outcome" in kwargs else "linear" ) if self.simulation_method == "direct-simulation": self.kappa_t = kwargs["effect_strength_on_treatment"] if "effect_strength_on_treatment" in kwargs else None self.kappa_y = kwargs["effect_strength_on_outcome"] if "effect_strength_on_outcome" in kwargs else None elif self.simulation_method in ["linear-partial-R2", "non-parametric-partial-R2"]: self.kappa_t = ( kwargs["partial_r2_confounder_treatment"] if "partial_r2_confounder_treatment" in kwargs else None ) self.kappa_y = ( kwargs["partial_r2_confounder_outcome"] if "partial_r2_confounder_outcome" in kwargs else None ) else: raise ValueError( "simulation method is not supported. Try direct-simulation, linear-partial-R2 or non-parametric-partial-R2" ) self.frac_strength_treatment = ( kwargs["effect_fraction_on_treatment"] if "effect_fraction_on_treatment" in kwargs else 1 ) self.frac_strength_outcome = ( kwargs["effect_fraction_on_outcome"] if "effect_fraction_on_outcome" in kwargs else 1 ) self.plotmethod = kwargs["plotmethod"] if "plotmethod" in kwargs else "colormesh" self.percent_change_estimate = kwargs["percent_change_estimate"] if "percent_change_estimate" in kwargs else 1.0 self.significance_level = kwargs["significance_level"] if "significance_level" in kwargs else 0.05 self.confounder_increases_estimate = ( kwargs["confounder_increases_estimate"] if "confounder_increases_estimate" in kwargs else False ) self.benchmark_common_causes = ( kwargs["benchmark_common_causes"] if "benchmark_common_causes" in kwargs else None ) self.null_hypothesis_effect = kwargs["null_hypothesis_effect"] if "null_hypothesis_effect" in kwargs else 0 self.plot_estimate = kwargs["plot_estimate"] if "plot_estimate" in kwargs else True self.num_splits = kwargs["num_splits"] if "num_splits" in kwargs else 5 self.shuffle_data = kwargs["shuffle_data"] if "shuffle_data" in kwargs else False self.shuffle_random_seed = kwargs["shuffle_random_seed"] if "shuffle_random_seed" in kwargs else None self.alpha_s_estimator_param_list = ( kwargs["alpha_s_estimator_param_list"] if "alpha_s_estimator_param_list" in kwargs else None ) self.alpha_s_estimator_list = kwargs["alpha_s_estimator_list"] if "alpha_s_estimator_list" in kwargs else None self.g_s_estimator_list = kwargs["g_s_estimator_list"] if "g_s_estimator_list" in kwargs else None self.g_s_estimator_param_list = ( kwargs["g_s_estimator_param_list"] if "g_s_estimator_param_list" in kwargs else None ) self.plugin_reisz = kwargs["plugin_reisz"] if "plugin_reisz" in kwargs else False self.logger = logging.getLogger(__name__) def infer_default_kappa_t(self, len_kappa_t=10): """Infer default effect strength of simulated confounder on treatment.""" observed_common_causes_names = self._target_estimand.get_backdoor_variables() if len(observed_common_causes_names) > 0: observed_common_causes = self._data[observed_common_causes_names] observed_common_causes = pd.get_dummies(observed_common_causes, drop_first=True) else: raise ValueError( "There needs to be at least one common cause to" + "automatically compute the default value of kappa_t." + " Provide a value for kappa_t" ) t = self._data[self._treatment_name] # Standardizing the data observed_common_causes = StandardScaler().fit_transform(observed_common_causes) if self.effect_on_t == "binary_flip": # Fit a model containing all confounders and compare predictions # using all features compared to all features except a given # confounder. tmodel = LogisticRegression().fit(observed_common_causes, t) tpred = tmodel.predict(observed_common_causes).astype(int) flips = [] for i in range(observed_common_causes.shape[1]): oldval = np.copy(observed_common_causes[:, i]) observed_common_causes[:, i] = 0 tcap = tmodel.predict(observed_common_causes).astype(int) observed_common_causes[:, i] = oldval flips.append(np.sum(abs(tcap - tpred)) / tpred.shape[0]) min_coeff, max_coeff = min(flips), max(flips) elif self.effect_on_t == "linear": # Estimating the regression coefficient from standardized features to t corrcoef_var_t = np.corrcoef(observed_common_causes, t, rowvar=False)[-1, :-1] std_dev_t = np.std(t)[0] max_coeff = max(corrcoef_var_t) * std_dev_t min_coeff = min(corrcoef_var_t) * std_dev_t else: raise NotImplementedError( "'" + self.effect_on_t + "' method not supported for confounders' effect on treatment" ) min_coeff, max_coeff = self._compute_min_max_coeff(min_coeff, max_coeff, self.frac_strength_treatment) # By default, return a plot with 10 points # consider 10 values of the effect of the unobserved confounder step = (max_coeff - min_coeff) / len_kappa_t self.logger.info("(Min, Max) kappa_t for observed common causes, ({0}, {1})".format(min_coeff, max_coeff)) if np.equal(max_coeff, min_coeff): return max_coeff else: return np.arange(min_coeff, max_coeff, step) def _compute_min_max_coeff(self, min_coeff, max_coeff, effect_strength_fraction): max_coeff = effect_strength_fraction * max_coeff min_coeff = effect_strength_fraction * min_coeff return min_coeff, max_coeff def infer_default_kappa_y(self, len_kappa_y=10): """Infer default effect strength of simulated confounder on treatment.""" observed_common_causes_names = self._target_estimand.get_backdoor_variables() if len(observed_common_causes_names) > 0: observed_common_causes = self._data[observed_common_causes_names] observed_common_causes = pd.get_dummies(observed_common_causes, drop_first=True) else: raise ValueError( "There needs to be at least one common cause to" + "automatically compute the default value of kappa_y." + " Provide a value for kappa_y" ) y = self._data[self._outcome_name] # Standardizing the data observed_common_causes = StandardScaler().fit_transform(observed_common_causes) if self.effect_on_y == "binary_flip": # Fit a model containing all confounders and compare predictions # using all features compared to all features except a given # confounder. ymodel = LogisticRegression().fit(observed_common_causes, y) ypred = ymodel.predict(observed_common_causes).astype(int) flips = [] for i in range(observed_common_causes.shape[1]): oldval = np.copy(observed_common_causes[:, i]) observed_common_causes[:, i] = 0 ycap = ymodel.predict(observed_common_causes).astype(int) observed_common_causes[:, i] = oldval flips.append(np.sum(abs(ycap - ypred)) / ypred.shape[0]) min_coeff, max_coeff = min(flips), max(flips) elif self.effect_on_y == "linear": corrcoef_var_y = np.corrcoef(observed_common_causes, y, rowvar=False)[-1, :-1] std_dev_y = np.std(y)[0] max_coeff = max(corrcoef_var_y) * std_dev_y min_coeff = min(corrcoef_var_y) * std_dev_y else: raise NotImplementedError( "'" + self.effect_on_y + "' method not supported for confounders' effect on outcome" ) min_coeff, max_coeff = self._compute_min_max_coeff(min_coeff, max_coeff, self.frac_strength_outcome) # By default, return a plot with 10 points # consider 10 values of the effect of the unobserved confounder step = (max_coeff - min_coeff) / len_kappa_y self.logger.info("(Min, Max) kappa_y for observed common causes, ({0}, {1})".format(min_coeff, max_coeff)) if np.equal(max_coeff, min_coeff): return max_coeff else: return np.arange(min_coeff, max_coeff, step) def refute_estimate(self, show_progress_bar=False): """ This function attempts to add an unobserved common cause to the outcome and the treatment. At present, we have implemented the behavior for one dimensional behaviors for continuous and binary variables. This function can either take single valued inputs or a range of inputs. The function then looks at the data type of the input and then decides on the course of action. :return: CausalRefuter: An object that contains the estimated effect and a new effect and the name of the refutation used. """ if self.simulation_method == "linear-partial-R2": if not (isinstance(self._estimate.estimator, LinearRegressionEstimator)): raise NotImplementedError( "Currently only LinearRegressionEstimator is supported for Sensitivity Analysis" ) if len(self._estimate.estimator._effect_modifier_names) > 0: raise NotImplementedError("The current implementation does not support effect modifiers") if self.frac_strength_outcome == 1: self.frac_strength_outcome = self.frac_strength_treatment analyzer = LinearSensitivityAnalyzer( estimator=self._estimate.estimator, data=self._data, treatment_name=self._treatment_name, percent_change_estimate=self.percent_change_estimate, significance_level=self.significance_level, benchmark_common_causes=self.benchmark_common_causes, null_hypothesis_effect=self.null_hypothesis_effect, frac_strength_treatment=self.frac_strength_treatment, frac_strength_outcome=self.frac_strength_outcome, common_causes_order=self._estimate.estimator._observed_common_causes.columns, ) analyzer.check_sensitivity(plot=self.plot_estimate) return analyzer if self.simulation_method == "non-parametric-partial-R2": # If the estimator used is LinearDML, partially linear sensitivity analysis will be automatically chosen if isinstance(self._estimate.estimator, dowhy.causal_estimators.econml.Econml): if self._estimate.estimator._econml_methodname == "econml.dml.LinearDML": analyzer = PartialLinearSensitivityAnalyzer( estimator=self._estimate._estimator_object, observed_common_causes=self._estimate.estimator._observed_common_causes, treatment=self._estimate.estimator._treatment, outcome=self._estimate.estimator._outcome, alpha_s_estimator_param_list=self.alpha_s_estimator_param_list, g_s_estimator_list=self.g_s_estimator_list, g_s_estimator_param_list=self.g_s_estimator_param_list, effect_strength_treatment=self.kappa_t, effect_strength_outcome=self.kappa_y, benchmark_common_causes=self.benchmark_common_causes, frac_strength_treatment=self.frac_strength_treatment, frac_strength_outcome=self.frac_strength_outcome, ) analyzer.check_sensitivity(plot=self.plot_estimate) return analyzer analyzer = NonParametricSensitivityAnalyzer( estimator=self._estimate.estimator, observed_common_causes=self._estimate.estimator._observed_common_causes, treatment=self._estimate.estimator._treatment, outcome=self._estimate.estimator._outcome, alpha_s_estimator_list=self.alpha_s_estimator_list, alpha_s_estimator_param_list=self.alpha_s_estimator_param_list, g_s_estimator_list=self.g_s_estimator_list, g_s_estimator_param_list=self.g_s_estimator_param_list, effect_strength_treatment=self.kappa_t, effect_strength_outcome=self.kappa_y, benchmark_common_causes=self.benchmark_common_causes, frac_strength_treatment=self.frac_strength_treatment, frac_strength_outcome=self.frac_strength_outcome, theta_s=self._estimate.value, plugin_reisz=self.plugin_reisz, ) analyzer.check_sensitivity(plot=self.plot_estimate) return analyzer if self.kappa_t is None: self.kappa_t = self.infer_default_kappa_t() if self.kappa_y is None: self.kappa_y = self.infer_default_kappa_y() if not isinstance(self.kappa_t, (list, np.ndarray)) and not isinstance( self.kappa_y, (list, np.ndarray) ): # Deal with single value inputs new_data = copy.deepcopy(self._data) new_data = self.include_confounders_effect(new_data, self.kappa_t, self.kappa_y) new_estimator = CausalEstimator.get_estimator_object(new_data, self._target_estimand, self._estimate) new_effect = new_estimator.estimate_effect() refute = CausalRefutation( self._estimate.value, new_effect.value, refutation_type="Refute: Add an Unobserved Common Cause" ) refute.new_effect_array = np.array(new_effect.value) refute.new_effect = new_effect.value refute.add_refuter(self) return refute else: # Deal with multiple value inputs if isinstance(self.kappa_t, (list, np.ndarray)) and isinstance( self.kappa_y, (list, np.ndarray) ): # Deal with range inputs # Get a 2D matrix of values # x,y = np.meshgrid(self.kappa_t, self.kappa_y) # x,y are both MxN results_matrix = np.random.rand( len(self.kappa_t), len(self.kappa_y) ) # Matrix to hold all the results of NxM orig_data = copy.deepcopy(self._data) for i in tqdm( range(len(self.kappa_t)), colour=CausalRefuter.PROGRESS_BAR_COLOR, disable=not show_progress_bar, desc="Refuting Estimates: ", ): for j in range(len(self.kappa_y)): new_data = self.include_confounders_effect(orig_data, self.kappa_t[i], self.kappa_y[j]) new_estimator = CausalEstimator.get_estimator_object( new_data, self._target_estimand, self._estimate ) new_effect = new_estimator.estimate_effect() refute = CausalRefutation( self._estimate.value, new_effect.value, refutation_type="Refute: Add an Unobserved Common Cause", ) results_matrix[i][j] = refute.new_effect # Populate the results refute.new_effect_array = results_matrix refute.new_effect = (np.min(results_matrix), np.max(results_matrix)) # Store the values into the refute object refute.add_refuter(self) if self.plotmethod is None: return refute import matplotlib import matplotlib.pyplot as plt fig = plt.figure(figsize=(6, 5)) left, bottom, width, height = 0.1, 0.1, 0.8, 0.8 ax = fig.add_axes([left, bottom, width, height]) oe = self._estimate.value contour_levels = [oe / 4.0, oe / 2.0, (3.0 / 4) * oe, oe] contour_levels.extend([0, np.min(results_matrix), np.max(results_matrix)]) if self.plotmethod == "contour": cp = plt.contourf(self.kappa_y, self.kappa_t, results_matrix, levels=sorted(contour_levels)) # Adding a label on the contour line for the original estimate fmt = {} trueeffect_index = np.where(cp.levels == oe)[0][0] fmt[cp.levels[trueeffect_index]] = "Estimated Effect" # Label every other level using strings plt.clabel(cp, [cp.levels[trueeffect_index]], inline=True, fmt=fmt) plt.colorbar(cp) elif self.plotmethod == "colormesh": cp = plt.pcolormesh(self.kappa_y, self.kappa_t, results_matrix, shading="nearest") plt.colorbar(cp, ticks=contour_levels) ax.yaxis.set_ticks(self.kappa_t) ax.xaxis.set_ticks(self.kappa_y) plt.xticks(rotation=45) ax.set_title("Effect of Unobserved Common Cause") ax.set_ylabel("Value of Linear Constant on Treatment") ax.set_xlabel("Value of Linear Constant on Outcome") plt.show() return refute elif isinstance(self.kappa_t, (list, np.ndarray)): outcomes = np.random.rand(len(self.kappa_t)) orig_data = copy.deepcopy(self._data) for i in tqdm( range(0, len(self.kappa_t)), colour=CausalRefuter.PROGRESS_BAR_COLOR, disable=not show_progress_bar, desc="Refuting Estimates: ", ): new_data = self.include_confounders_effect(orig_data, self.kappa_t[i], self.kappa_y) new_estimator = CausalEstimator.get_estimator_object( new_data, self._target_estimand, self._estimate ) new_effect = new_estimator.estimate_effect() refute = CausalRefutation( self._estimate.value, new_effect.value, refutation_type="Refute: Add an Unobserved Common Cause" ) self.logger.debug(refute) outcomes[i] = refute.new_effect # Populate the results refute.new_effect_array = outcomes refute.new_effect = (np.min(outcomes), np.max(outcomes)) refute.add_refuter(self) if self.plotmethod is None: return refute import matplotlib import matplotlib.pyplot as plt fig = plt.figure(figsize=(6, 5)) left, bottom, width, height = 0.1, 0.1, 0.8, 0.8 ax = fig.add_axes([left, bottom, width, height]) plt.plot(self.kappa_t, outcomes) plt.axhline(self._estimate.value, linestyle="--", color="gray") ax.set_title("Effect of Unobserved Common Cause") ax.set_xlabel("Value of Linear Constant on Treatment") ax.set_ylabel("Estimated Effect after adding the common cause") plt.show() return refute elif isinstance(self.kappa_y, (list, np.ndarray)): outcomes = np.random.rand(len(self.kappa_y)) orig_data = copy.deepcopy(self._data) for i in tqdm( range(0, len(self.kappa_y)), colour=CausalRefuter.PROGRESS_BAR_COLOR, disable=not show_progress_bar, desc="Refuting Estimates: ", ): new_data = self.include_confounders_effect(orig_data, self.kappa_t, self.kappa_y[i]) new_estimator = CausalEstimator.get_estimator_object( new_data, self._target_estimand, self._estimate ) new_effect = new_estimator.estimate_effect() refute = CausalRefutation( self._estimate.value, new_effect.value, refutation_type="Refute: Add an Unobserved Common Cause" ) self.logger.debug(refute) outcomes[i] = refute.new_effect # Populate the results refute.new_effect_array = outcomes refute.new_effect = (np.min(outcomes), np.max(outcomes)) refute.add_refuter(self) if self.plotmethod is None: return refute import matplotlib import matplotlib.pyplot as plt fig = plt.figure(figsize=(6, 5)) left, bottom, width, height = 0.1, 0.1, 0.8, 0.8 ax = fig.add_axes([left, bottom, width, height]) plt.plot(self.kappa_y, outcomes) plt.axhline(self._estimate.value, linestyle="--", color="gray") ax.set_title("Effect of Unobserved Common Cause") ax.set_xlabel("Value of Linear Constant on Outcome") ax.set_ylabel("Estimated Effect after adding the common cause") plt.show() return refute def include_confounders_effect(self, new_data, kappa_t, kappa_y): """ This function deals with the change in the value of the data due to the effect of the unobserved confounder. In the case of a binary flip, we flip only if the random number is greater than the threshold set. In the case of a linear effect, we use the variable as the linear regression constant. :param new_data: pandas.DataFrame: The data to be changed due to the effects of the unobserved confounder. :param kappa_t: numpy.float64: The value of the threshold for binary_flip or the value of the regression coefficient for linear effect. :param kappa_y: numpy.float64: The value of the threshold for binary_flip or the value of the regression coefficient for linear effect. :return: pandas.DataFrame: The DataFrame that includes the effects of the unobserved confounder. """ num_rows = self._data.shape[0] stdnorm = scipy.stats.norm() w_random = stdnorm.rvs(num_rows) if self.effect_on_t == "binary_flip": alpha = 2 * kappa_t - 1 if kappa_t >= 0.5 else 1 - 2 * kappa_t interval = stdnorm.interval(alpha) rel_interval = interval[0] if kappa_t >= 0.5 else interval[1] new_data.loc[rel_interval <= w_random, self._treatment_name] = ( 1 - new_data.loc[rel_interval <= w_random, self._treatment_name] ) for tname in self._treatment_name: if pd.api.types.is_bool_dtype(self._data[tname]): new_data = new_data.astype({tname: "bool"}, copy=False) elif self.effect_on_t == "linear": confounder_t_effect = kappa_t * w_random # By default, we add the effect of simulated confounder for treatment. # But subtract it from outcome to create a negative correlation # assuming that the original confounder's effect was positive on both. # This is to remove the effect of the original confounder. new_data[self._treatment_name] = new_data[self._treatment_name].values + np.ndarray( shape=(num_rows, 1), buffer=confounder_t_effect ) else: raise NotImplementedError( "'" + self.effect_on_t + "' method not supported for confounders' effect on treatment" ) if self.effect_on_y == "binary_flip": alpha = 2 * kappa_y - 1 if kappa_y >= 0.5 else 1 - 2 * kappa_y interval = stdnorm.interval(alpha) rel_interval = interval[0] if kappa_y >= 0.5 else interval[1] new_data.loc[rel_interval <= w_random, self._outcome_name] = ( 1 - new_data.loc[rel_interval <= w_random, self._outcome_name] ) for yname in self._outcome_name: if pd.api.types.is_bool_dtype(self._data[yname]): new_data = new_data.astype({yname: "bool"}, copy=False) elif self.effect_on_y == "linear": confounder_y_effect = (-1) * kappa_y * w_random # By default, we add the effect of simulated confounder for treatment. # But subtract it from outcome to create a negative correlation # assuming that the original confounder's effect was positive on both. # This is to remove the effect of the original confounder. new_data[self._outcome_name] = new_data[self._outcome_name].values + np.ndarray( shape=(num_rows, 1), buffer=confounder_y_effect ) else: raise NotImplementedError( "'" + self.effect_on_y + "' method not supported for confounders' effect on outcome" ) return new_data def include_simulated_confounder(self, convergence_threshold=0.1, c_star_max=1000): """ This function simulates an unobserved confounder based on the data using the following steps: 1. It calculates the "residuals" from the treatment and outcome model i.) The outcome model has outcome as the dependent variable and all the observed variables including treatment as independent variables ii.) The treatment model has treatment as the dependent variable and all the observed variables as independent variables. 2. U is an intermediate random variable drawn from the normal distribution with the weighted average of residuals as mean and a unit variance U ~ N(c1*d_y + c2*d_t, 1) where *d_y and d_t are residuals from the treatment and outcome model *c1 and c2 are coefficients to the residuals 3. The final U, which is the simulated unobserved confounder is obtained by debiasing the intermediate variable U by residualising it with X Choosing the coefficients c1 and c2: The coefficients are chosen based on these basic assumptions: 1. There is a hyperbolic relationship satisfying c1*c2 = c_star 2. c_star is chosen from a range of possible values based on the correlation of the obtained simulated variable with outcome and treatment. 3. The product of correlations with treatment and outcome should be at a minimum distance to the maximum correlations with treatment and outcome in any of the observed confounders 4. The ratio of the weights should be such that they maintain the ratio of the maximum possible observed coefficients within some confidence interval :param c_star_max: The maximum possible value for the hyperbolic curve on which the coefficients to the residuals lie. It defaults to 1000 in the code if not specified by the user. :type int :param convergence_threshold: The threshold to check the plateauing of the correlation while selecting a c_star. It defaults to 0.1 in the code if not specified by the user :type float :returns: The simulated values of the unobserved confounder based on the data :type pandas.core.series.Series """ # Obtaining the list of observed variables required_variables = True observed_variables = self.choose_variables(required_variables) observed_variables_with_treatment_and_outcome = observed_variables + self._treatment_name + self._outcome_name # Taking a subset of the dataframe that has only observed variables self._data = self._data[observed_variables_with_treatment_and_outcome] # Residuals from the outcome model obtained by fitting a linear model y = self._data[self._outcome_name[0]] observed_variables_with_treatment = observed_variables + self._treatment_name X = self._data[observed_variables_with_treatment] model = sm.OLS(y, X.astype("float")) results = model.fit() residuals_y = y - results.fittedvalues d_y = list(pd.Series(residuals_y)) # Residuals from the treatment model obtained by fitting a linear model t = self._data[self._treatment_name[0]].astype("int64") X = self._data[observed_variables] model = sm.OLS(t, X) results = model.fit() residuals_t = t - results.fittedvalues d_t = list(pd.Series(residuals_t)) # Initialising product_cor_metric_observed with a really low value as finding maximum product_cor_metric_observed = -10000000000 for i in observed_variables: current_obs_confounder = self._data[i] outcome_values = self._data[self._outcome_name[0]] correlation_y = current_obs_confounder.corr(outcome_values) treatment_values = t correlation_t = current_obs_confounder.corr(treatment_values) product_cor_metric_current = correlation_y * correlation_t if product_cor_metric_current >= product_cor_metric_observed: product_cor_metric_observed = product_cor_metric_current correlation_t_observed = correlation_t correlation_y_observed = correlation_y # The user has an option to give the the effect_strength_on_y and effect_strength_on_t which can be then used instead of maximum correlation with treatment and outcome in the observed variables as it specifies the desired effect. if self.kappa_t is not None: correlation_t_observed = self.kappa_t if self.kappa_y is not None: correlation_y_observed = self.kappa_y # Choosing a c_star based on the data. # The correlations stop increasing upon increasing c_star after a certain value, that is it plateaus and we choose the value of c_star to be the value it plateaus. correlation_y_list = [] correlation_t_list = [] product_cor_metric_simulated_list = [] x_list = [] step = int(c_star_max / 10) for i in range(0, int(c_star_max), step): c1 = math.sqrt(i) c2 = c1 final_U = self.generate_confounder_from_residuals(c1, c2, d_y, d_t, X) current_simulated_confounder = final_U outcome_values = self._data[self._outcome_name[0]] correlation_y = current_simulated_confounder.corr(outcome_values) correlation_y_list.append(correlation_y) treatment_values = t correlation_t = current_simulated_confounder.corr(treatment_values) correlation_t_list.append(correlation_t) product_cor_metric_simulated = correlation_y * correlation_t product_cor_metric_simulated_list.append(product_cor_metric_simulated) x_list.append(i) index = 1 while index < len(correlation_y_list): if (correlation_y_list[index] - correlation_y_list[index - 1]) <= convergence_threshold: c_star = x_list[index] break index = index + 1 # Choosing c1 and c2 based on the hyperbolic relationship once c_star is chosen by going over various combinations of c1 and c2 values and choosing the combination which # which maintains the minimum distance between the product of correlations of the simulated variable and the product of maximum correlations of one of the observed variables # and additionally checks if the ratio of the weights are such that they maintain the ratio of the maximum possible observed coefficients within some confidence interval # c1_final and c2_final are initialised to the values on the hyperbolic curve such that c1_final = c2_final and c1_final*c2_final = c_star c1_final = math.sqrt(c_star) c2_final = math.sqrt(c_star) # initialising min_distance_between_product_cor_metrics to be a value greater than 1 min_distance_between_product_cor_metrics = 1.5 i = 0.05 threshold = c_star / 0.05 while i <= threshold: c2 = i c1 = c_star / c2 final_U = self.generate_confounder_from_residuals(c1, c2, d_y, d_t, X) current_simulated_confounder = final_U outcome_values = self._data[self._outcome_name[0]] correlation_y = current_simulated_confounder.corr(outcome_values) treatment_values = t correlation_t = current_simulated_confounder.corr(treatment_values) product_cor_metric_simulated = correlation_y * correlation_t if min_distance_between_product_cor_metrics >= abs( product_cor_metric_simulated - product_cor_metric_observed ): min_distance_between_product_cor_metrics = abs( product_cor_metric_simulated - product_cor_metric_observed ) additional_condition = correlation_y_observed / correlation_t_observed if ((c1 / c2) <= (additional_condition + 0.3 * additional_condition)) and ( (c1 / c2) >= (additional_condition - 0.3 * additional_condition) ): # choose minimum positive value c1_final = c1 c2_final = c2 i = i * 1.5 """#closed form solution print("c_star_max before closed form", c_star_max) if max_correlation_with_t == -1000: c2 = 0 c1 = c_star_max else: additional_condition = abs(max_correlation_with_y/max_correlation_with_t) print("additional_condition", additional_condition) c2 = math.sqrt(c_star_max/additional_condition) c1 = c_star_max/c2""" final_U = self.generate_confounder_from_residuals(c1_final, c2_final, d_y, d_t, X) return final_U def generate_confounder_from_residuals(self, c1, c2, d_y, d_t, X): """ This function takes the residuals from the treatment and outcome model and their coefficients and simulates the intermediate random variable U by taking the row wise normal distribution corresponding to each residual value and then debiasing the intermediate variable to get the final variable. :param c1: coefficient to the residual from the outcome model :type float :param c2: coefficient to the residual from the treatment model :type float :param d_y: residuals from the outcome model :type list :param d_t: residuals from the treatment model :type list :returns: The simulated values of the unobserved confounder based on the data :type pandas.core.series.Series """ U = [] for j in range(len(d_t)): simulated_variable_mean = c1 * d_y[j] + c2 * d_t[j] simulated_variable_stddev = 1 U.append(np.random.normal(simulated_variable_mean, simulated_variable_stddev, 1)) U = np.array(U) model = sm.OLS(U, X) results = model.fit() U = U.reshape( -1, ) final_U = U - results.fittedvalues.values final_U = pd.Series(U) return final_U

anusha0409

81841c697bd5e80ecf9e731432305f6186666f1f

bb446c333f2256074304b0dec9cb5628d284b542

This is a good point. For all the partial-r2 based methods (linear and non-parametric), it has the same interpretation. But the interpretation is different between direct_simulation and partial-r2 based simulations. So to avoid confusion, I have created two additional parameters. The first two (effect_strength) are used for direct_simulation, while the next two (partial_r2_confounder) are used for the partial-r2 based methods. This is still a hacky solution. The ideal solution will be achieved in the new API where we can wrap the method specific parameters within the call to the method class. (and create separate method names and remove the simulation method parameter). ``` refute_estimate(..., method=AddSimulatedConfounder(effect_strength_on_treatment=a, effect_strength_on_outcome=b)) # if we want to use partial R2 methods refute_estimate(..., method=NonParametricPartialR2Sensitivity(partial_r2_confounder_treatment=a, partial_r2_confounder_outcome=b)) ```

amit-sharma

py-why/dowhy

Adding Non Linear Sensitivity Analysis

This PR implements the non-parametric sensitivity analysis from Chernozhukov et al. https://arxiv.org/abs/2112.13398 It implements two sensitivity analyzers: 1. For Partial Linear DGPs and estimators like LinearDML 2. For general non-parametric DGPs and estimators like KernelDML. The notebook in this PR provides an introduction on how the sensitivity bounds are calculated for the partial linear case. For the general nonparametric DGPs, we need to estimate a special function called the Reisz representer. For binary treatment, it is exactly the difference in outcome weighted by propensity score. So we provide two options to learn the Reisz representer, 1) plugin_reisz that uses the propensity score; and 2) general estimator that uses a custom loss function. These two are in the file reisz.py. Briefly, the sensitivity bounds depend on two parameters that denote the effect of the unobserved confounder on treatment and outcome. That's why we use the same API as for the `add_unobserved_common_cause` method and add this sensitivity analysis as a possible simulation method="non-parametric-partial-R2". The format of the plots is identical to those from the "linear-partial-r2" simulation method that is already implemented. We provide two modes for the user. 1) User specifies the effect strength parameters themselves, as a range of values. 2) User benchmarks the effect strength parameters as a multiple of the same parameters for the observed common causes. Signed-off-by: anusha <anushaagarwal2000.com>

2022-06-20 14:37:11+00:00

2022-09-16 03:57:26+00:00

dowhy/causal_refuters/add_unobserved_common_cause.py

import copy import logging import math import numpy as np import pandas as pd import scipy.stats import statsmodels.api as sm from sklearn.linear_model import LogisticRegression from sklearn.preprocessing import StandardScaler from tqdm.auto import tqdm from dowhy.causal_estimator import CausalEstimator from dowhy.causal_estimators.linear_regression_estimator import LinearRegressionEstimator from dowhy.causal_refuter import CausalRefutation, CausalRefuter from dowhy.causal_refuters.linear_sensitivity_analyzer import LinearSensitivityAnalyzer class AddUnobservedCommonCause(CausalRefuter): """Add an unobserved confounder for refutation. Supports additional parameters that can be specified in the refute_estimate() method. - 'confounders_effect_on_treatment': how the simulated confounder affects the value of treatment. This can be linear (for continuous treatment) or binary_flip (for binary treatment) - 'confounders_effect_on_outcome': how the simulated confounder affects the value of outcome. This can be linear (for continuous outcome) or binary_flip (for binary outcome) - 'effect_strength_on_treatment': parameter for the strength of the effect of simulated confounder on treatment. For linear effect, it is the regression coeffient. For binary_flip, it is the probability that simulated confounder's effect flips the value of treatment from 0 to 1 (or vice-versa). - 'effect_strength_on_outcome': parameter for the strength of the effect of simulated confounder on outcome. For linear effect, it is the regression coeffient. For binary_flip, it is the probability that simulated confounder's effect flips the value of outcome from 0 to 1 (or vice-versa). TODO: Needs an interpretation module """ def __init__(self, *args, **kwargs): """ Initialize the parameters required for the refuter. If effect_strength_on_treatment or effect_strength_on_outcome is not given, it is calculated automatically as a range between the minimum and maximum effect strength of observed confounders on treatment and outcome respectively. :param confounders_effect_on_treatment: str : The type of effect on the treatment due to the unobserved confounder. Possible values are ['binary_flip', 'linear'] :param confounders_effect_on_outcome: str : The type of effect on the outcome due to the unobserved confounder. Possible values are ['binary_flip', 'linear'] :param effect_strength_on_treatment: float, numpy.ndarray: This refers to the strength of the confounder on treatment. For a linear effect, it behaves like the regression coeffecient. For a binary flip it is the probability with which it can invert the value of the treatment. :param effect_strength_on_outcome: float, numpy.ndarray: This refers to the strength of the confounder on outcome. For a linear effect, it behaves like the regression coefficient. For a binary flip, it is the probability with which it can invert the value of the outcome. :param effect_fraction_on_treatment: float: If effect_strength_on_treatment is not provided, this parameter decides the effect strength of the simulated confounder as a fraction of the effect strength of observed confounders on treatment. Defaults to 1. :param effect_fraction_on_outcome: float: If effect_strength_on_outcome is not provided, this parameter decides the effect strength of the simulated confounder as a fraction of the effect strength of observed confounders on outcome. Defaults to 1. :param plotmethod: string: Type of plot to be shown. If None, no plot is generated. This parameter is used only only when more than one treatment confounder effect values or outcome confounder effect values are provided. Default is "colormesh". Supported values are "contour", "colormesh" when more than one value is provided for both confounder effect value parameters; "line" when provided for only one of them. :param simulated_method_name: method type to add unobserved common cause. "linear-partial-R2" for linear sensitivity analysis :param percent_change_estimate: It is the percentage of reduction of treatment estimate that could alter the results (default = 1) if percent_change_estimate = 1, the robustness value describes the strength of association of confounders with treatment and outcome in order to reduce the estimate by 100% i.e bring it down to 0. :param confounder_increases_estimate: True implies that confounder increases the absolute value of estimate and vice versa. (Default = False) :param benchmark_common_causes: names of variables for bounding strength of confounders :param significance_level: confidence interval for statistical inference(default = 0.05) :param null_hypothesis_effect: assumed effect under the null hypothesis :param plot_estimate: Generate contour plot for estimate while performing sensitivity analysis. (default = True). To override the setting, set plot_estimate = False. """ super().__init__(*args, **kwargs) self.effect_on_t = ( kwargs["confounders_effect_on_treatment"] if "confounders_effect_on_treatment" in kwargs else "binary_flip" ) self.effect_on_y = ( kwargs["confounders_effect_on_outcome"] if "confounders_effect_on_outcome" in kwargs else "linear" ) self.kappa_t = kwargs["effect_strength_on_treatment"] if "effect_strength_on_treatment" in kwargs else None self.kappa_y = kwargs["effect_strength_on_outcome"] if "effect_strength_on_outcome" in kwargs else None self.frac_strength_treatment = ( kwargs["effect_fraction_on_treatment"] if "effect_fraction_on_treatment" in kwargs else 1 ) self.frac_strength_outcome = ( kwargs["effect_fraction_on_outcome"] if "effect_fraction_on_outcome" in kwargs else 1 ) self.simulated_method_name = ( kwargs["simulated_method_name"] if "simulated_method_name" in kwargs else "linear_based" ) self.plotmethod = kwargs["plotmethod"] if "plotmethod" in kwargs else "colormesh" self.percent_change_estimate = kwargs["percent_change_estimate"] if "percent_change_estimate" in kwargs else 1.0 self.significance_level = kwargs["significance_level"] if "significance_level" in kwargs else 0.05 self.confounder_increases_estimate = ( kwargs["confounder_increases_estimate"] if "confounder_increases_estimate" in kwargs else False ) self.benchmark_common_causes = ( kwargs["benchmark_common_causes"] if "benchmark_common_causes" in kwargs else None ) self.null_hypothesis_effect = kwargs["null_hypothesis_effect"] if "null_hypothesis_effect" in kwargs else 0 self.plot_estimate = kwargs["plot_estimate"] if "plot_estimate" in kwargs else True self.logger = logging.getLogger(__name__) def infer_default_kappa_t(self, len_kappa_t=10): """Infer default effect strength of simulated confounder on treatment.""" observed_common_causes_names = self._target_estimand.get_backdoor_variables() if len(observed_common_causes_names) > 0: observed_common_causes = self._data[observed_common_causes_names] observed_common_causes = pd.get_dummies(observed_common_causes, drop_first=True) else: raise ValueError( "There needs to be at least one common cause to" + "automatically compute the default value of kappa_t." + " Provide a value for kappa_t" ) t = self._data[self._treatment_name] # Standardizing the data observed_common_causes = StandardScaler().fit_transform(observed_common_causes) if self.effect_on_t == "binary_flip": # Fit a model containing all confounders and compare predictions # using all features compared to all features except a given # confounder. tmodel = LogisticRegression().fit(observed_common_causes, t) tpred = tmodel.predict(observed_common_causes).astype(int) flips = [] for i in range(observed_common_causes.shape[1]): oldval = np.copy(observed_common_causes[:, i]) observed_common_causes[:, i] = 0 tcap = tmodel.predict(observed_common_causes).astype(int) observed_common_causes[:, i] = oldval flips.append(np.sum(abs(tcap - tpred)) / tpred.shape[0]) min_coeff, max_coeff = min(flips), max(flips) elif self.effect_on_t == "linear": # Estimating the regression coefficient from standardized features to t corrcoef_var_t = np.corrcoef(observed_common_causes, t, rowvar=False)[-1, :-1] std_dev_t = np.std(t)[0] max_coeff = max(corrcoef_var_t) * std_dev_t min_coeff = min(corrcoef_var_t) * std_dev_t else: raise NotImplementedError( "'" + self.effect_on_t + "' method not supported for confounders' effect on treatment" ) min_coeff, max_coeff = self._compute_min_max_coeff(min_coeff, max_coeff, self.frac_strength_treatment) # By default, return a plot with 10 points # consider 10 values of the effect of the unobserved confounder step = (max_coeff - min_coeff) / len_kappa_t self.logger.info("(Min, Max) kappa_t for observed common causes, ({0}, {1})".format(min_coeff, max_coeff)) if np.equal(max_coeff, min_coeff): return max_coeff else: return np.arange(min_coeff, max_coeff, step) def _compute_min_max_coeff(self, min_coeff, max_coeff, effect_strength_fraction): max_coeff = effect_strength_fraction * max_coeff min_coeff = effect_strength_fraction * min_coeff return min_coeff, max_coeff def infer_default_kappa_y(self, len_kappa_y=10): """Infer default effect strength of simulated confounder on treatment.""" observed_common_causes_names = self._target_estimand.get_backdoor_variables() if len(observed_common_causes_names) > 0: observed_common_causes = self._data[observed_common_causes_names] observed_common_causes = pd.get_dummies(observed_common_causes, drop_first=True) else: raise ValueError( "There needs to be at least one common cause to" + "automatically compute the default value of kappa_y." + " Provide a value for kappa_y" ) y = self._data[self._outcome_name] # Standardizing the data observed_common_causes = StandardScaler().fit_transform(observed_common_causes) if self.effect_on_y == "binary_flip": # Fit a model containing all confounders and compare predictions # using all features compared to all features except a given # confounder. ymodel = LogisticRegression().fit(observed_common_causes, y) ypred = ymodel.predict(observed_common_causes).astype(int) flips = [] for i in range(observed_common_causes.shape[1]): oldval = np.copy(observed_common_causes[:, i]) observed_common_causes[:, i] = 0 ycap = ymodel.predict(observed_common_causes).astype(int) observed_common_causes[:, i] = oldval flips.append(np.sum(abs(ycap - ypred)) / ypred.shape[0]) min_coeff, max_coeff = min(flips), max(flips) elif self.effect_on_y == "linear": corrcoef_var_y = np.corrcoef(observed_common_causes, y, rowvar=False)[-1, :-1] std_dev_y = np.std(y)[0] max_coeff = max(corrcoef_var_y) * std_dev_y min_coeff = min(corrcoef_var_y) * std_dev_y else: raise NotImplementedError( "'" + self.effect_on_y + "' method not supported for confounders' effect on outcome" ) min_coeff, max_coeff = self._compute_min_max_coeff(min_coeff, max_coeff, self.frac_strength_outcome) # By default, return a plot with 10 points # consider 10 values of the effect of the unobserved confounder step = (max_coeff - min_coeff) / len_kappa_y self.logger.info("(Min, Max) kappa_y for observed common causes, ({0}, {1})".format(min_coeff, max_coeff)) if np.equal(max_coeff, min_coeff): return max_coeff else: return np.arange(min_coeff, max_coeff, step) def refute_estimate(self, show_progress_bar=False): """ This function attempts to add an unobserved common cause to the outcome and the treatment. At present, we have implemented the behavior for one dimensional behaviors for continuous and binary variables. This function can either take single valued inputs or a range of inputs. The function then looks at the data type of the input and then decides on the course of action. :return: CausalRefuter: An object that contains the estimated effect and a new effect and the name of the refutation used. """ if self.simulated_method_name == "linear-partial-R2": if not (isinstance(self._estimate.estimator, LinearRegressionEstimator)): raise NotImplementedError( "Currently only LinearRegressionEstimator is supported for Sensitivity Analysis" ) if len(self._estimate.estimator._effect_modifier_names) > 0: raise NotImplementedError("The current implementation does not support effect modifiers") if self.frac_strength_outcome == 1: self.frac_strength_outcome = self.frac_strength_treatment analyzer = LinearSensitivityAnalyzer( estimator=self._estimate.estimator, data=self._data, treatment_name=self._treatment_name, percent_change_estimate=self.percent_change_estimate, significance_level=self.significance_level, benchmark_common_causes=self.benchmark_common_causes, null_hypothesis_effect=self.null_hypothesis_effect, frac_strength_treatment=self.frac_strength_treatment, frac_strength_outcome=self.frac_strength_outcome, common_causes_order=self._estimate.estimator._observed_common_causes.columns, ) analyzer.check_sensitivity(plot=self.plot_estimate) return analyzer if self.kappa_t is None: self.kappa_t = self.infer_default_kappa_t() if self.kappa_y is None: self.kappa_y = self.infer_default_kappa_y() if not isinstance(self.kappa_t, (list, np.ndarray)) and not isinstance( self.kappa_y, (list, np.ndarray) ): # Deal with single value inputs new_data = copy.deepcopy(self._data) new_data = self.include_confounders_effect(new_data, self.kappa_t, self.kappa_y) new_estimator = CausalEstimator.get_estimator_object(new_data, self._target_estimand, self._estimate) new_effect = new_estimator.estimate_effect() refute = CausalRefutation( self._estimate.value, new_effect.value, refutation_type="Refute: Add an Unobserved Common Cause" ) refute.new_effect_array = np.array(new_effect.value) refute.new_effect = new_effect.value refute.add_refuter(self) return refute else: # Deal with multiple value inputs if isinstance(self.kappa_t, (list, np.ndarray)) and isinstance( self.kappa_y, (list, np.ndarray) ): # Deal with range inputs # Get a 2D matrix of values # x,y = np.meshgrid(self.kappa_t, self.kappa_y) # x,y are both MxN results_matrix = np.random.rand( len(self.kappa_t), len(self.kappa_y) ) # Matrix to hold all the results of NxM orig_data = copy.deepcopy(self._data) for i in tqdm( range(len(self.kappa_t)), colour=CausalRefuter.PROGRESS_BAR_COLOR, disable=not show_progress_bar, desc="Refuting Estimates: ", ): for j in range(len(self.kappa_y)): new_data = self.include_confounders_effect(orig_data, self.kappa_t[i], self.kappa_y[j]) new_estimator = CausalEstimator.get_estimator_object( new_data, self._target_estimand, self._estimate ) new_effect = new_estimator.estimate_effect() refute = CausalRefutation( self._estimate.value, new_effect.value, refutation_type="Refute: Add an Unobserved Common Cause", ) results_matrix[i][j] = refute.new_effect # Populate the results refute.new_effect_array = results_matrix refute.new_effect = (np.min(results_matrix), np.max(results_matrix)) # Store the values into the refute object refute.add_refuter(self) if self.plotmethod is None: return refute import matplotlib import matplotlib.pyplot as plt fig = plt.figure(figsize=(6, 5)) left, bottom, width, height = 0.1, 0.1, 0.8, 0.8 ax = fig.add_axes([left, bottom, width, height]) oe = self._estimate.value contour_levels = [oe / 4.0, oe / 2.0, (3.0 / 4) * oe, oe] contour_levels.extend([0, np.min(results_matrix), np.max(results_matrix)]) if self.plotmethod == "contour": cp = plt.contourf(self.kappa_y, self.kappa_t, results_matrix, levels=sorted(contour_levels)) # Adding a label on the contour line for the original estimate fmt = {} trueeffect_index = np.where(cp.levels == oe)[0][0] fmt[cp.levels[trueeffect_index]] = "Estimated Effect" # Label every other level using strings plt.clabel(cp, [cp.levels[trueeffect_index]], inline=True, fmt=fmt) plt.colorbar(cp) elif self.plotmethod == "colormesh": cp = plt.pcolormesh(self.kappa_y, self.kappa_t, results_matrix, shading="nearest") plt.colorbar(cp, ticks=contour_levels) ax.yaxis.set_ticks(self.kappa_t) ax.xaxis.set_ticks(self.kappa_y) plt.xticks(rotation=45) ax.set_title("Effect of Unobserved Common Cause") ax.set_ylabel("Value of Linear Constant on Treatment") ax.set_xlabel("Value of Linear Constant on Outcome") plt.show() return refute elif isinstance(self.kappa_t, (list, np.ndarray)): outcomes = np.random.rand(len(self.kappa_t)) orig_data = copy.deepcopy(self._data) for i in tqdm( range(0, len(self.kappa_t)), colour=CausalRefuter.PROGRESS_BAR_COLOR, disable=not show_progress_bar, desc="Refuting Estimates: ", ): new_data = self.include_confounders_effect(orig_data, self.kappa_t[i], self.kappa_y) new_estimator = CausalEstimator.get_estimator_object( new_data, self._target_estimand, self._estimate ) new_effect = new_estimator.estimate_effect() refute = CausalRefutation( self._estimate.value, new_effect.value, refutation_type="Refute: Add an Unobserved Common Cause" ) self.logger.debug(refute) outcomes[i] = refute.new_effect # Populate the results refute.new_effect_array = outcomes refute.new_effect = (np.min(outcomes), np.max(outcomes)) refute.add_refuter(self) if self.plotmethod is None: return refute import matplotlib import matplotlib.pyplot as plt fig = plt.figure(figsize=(6, 5)) left, bottom, width, height = 0.1, 0.1, 0.8, 0.8 ax = fig.add_axes([left, bottom, width, height]) plt.plot(self.kappa_t, outcomes) plt.axhline(self._estimate.value, linestyle="--", color="gray") ax.set_title("Effect of Unobserved Common Cause") ax.set_xlabel("Value of Linear Constant on Treatment") ax.set_ylabel("Estimated Effect after adding the common cause") plt.show() return refute elif isinstance(self.kappa_y, (list, np.ndarray)): outcomes = np.random.rand(len(self.kappa_y)) orig_data = copy.deepcopy(self._data) for i in tqdm( range(0, len(self.kappa_y)), colour=CausalRefuter.PROGRESS_BAR_COLOR, disable=not show_progress_bar, desc="Refuting Estimates: ", ): new_data = self.include_confounders_effect(orig_data, self.kappa_t, self.kappa_y[i]) new_estimator = CausalEstimator.get_estimator_object( new_data, self._target_estimand, self._estimate ) new_effect = new_estimator.estimate_effect() refute = CausalRefutation( self._estimate.value, new_effect.value, refutation_type="Refute: Add an Unobserved Common Cause" ) self.logger.debug(refute) outcomes[i] = refute.new_effect # Populate the results refute.new_effect_array = outcomes refute.new_effect = (np.min(outcomes), np.max(outcomes)) refute.add_refuter(self) if self.plotmethod is None: return refute import matplotlib import matplotlib.pyplot as plt fig = plt.figure(figsize=(6, 5)) left, bottom, width, height = 0.1, 0.1, 0.8, 0.8 ax = fig.add_axes([left, bottom, width, height]) plt.plot(self.kappa_y, outcomes) plt.axhline(self._estimate.value, linestyle="--", color="gray") ax.set_title("Effect of Unobserved Common Cause") ax.set_xlabel("Value of Linear Constant on Outcome") ax.set_ylabel("Estimated Effect after adding the common cause") plt.show() return refute def include_confounders_effect(self, new_data, kappa_t, kappa_y): """ This function deals with the change in the value of the data due to the effect of the unobserved confounder. In the case of a binary flip, we flip only if the random number is greater than the threshold set. In the case of a linear effect, we use the variable as the linear regression constant. :param new_data: pandas.DataFrame: The data to be changed due to the effects of the unobserved confounder. :param kappa_t: numpy.float64: The value of the threshold for binary_flip or the value of the regression coefficient for linear effect. :param kappa_y: numpy.float64: The value of the threshold for binary_flip or the value of the regression coefficient for linear effect. :return: pandas.DataFrame: The DataFrame that includes the effects of the unobserved confounder. """ num_rows = self._data.shape[0] stdnorm = scipy.stats.norm() w_random = stdnorm.rvs(num_rows) if self.effect_on_t == "binary_flip": alpha = 2 * kappa_t - 1 if kappa_t >= 0.5 else 1 - 2 * kappa_t interval = stdnorm.interval(alpha) rel_interval = interval[0] if kappa_t >= 0.5 else interval[1] new_data.loc[rel_interval <= w_random, self._treatment_name] = ( 1 - new_data.loc[rel_interval <= w_random, self._treatment_name] ) for tname in self._treatment_name: if pd.api.types.is_bool_dtype(self._data[tname]): new_data = new_data.astype({tname: "bool"}, copy=False) elif self.effect_on_t == "linear": confounder_t_effect = kappa_t * w_random # By default, we add the effect of simulated confounder for treatment. # But subtract it from outcome to create a negative correlation # assuming that the original confounder's effect was positive on both. # This is to remove the effect of the original confounder. new_data[self._treatment_name] = new_data[self._treatment_name].values + np.ndarray( shape=(num_rows, 1), buffer=confounder_t_effect ) else: raise NotImplementedError( "'" + self.effect_on_t + "' method not supported for confounders' effect on treatment" ) if self.effect_on_y == "binary_flip": alpha = 2 * kappa_y - 1 if kappa_y >= 0.5 else 1 - 2 * kappa_y interval = stdnorm.interval(alpha) rel_interval = interval[0] if kappa_y >= 0.5 else interval[1] new_data.loc[rel_interval <= w_random, self._outcome_name] = ( 1 - new_data.loc[rel_interval <= w_random, self._outcome_name] ) for yname in self._outcome_name: if pd.api.types.is_bool_dtype(self._data[yname]): new_data = new_data.astype({yname: "bool"}, copy=False) elif self.effect_on_y == "linear": confounder_y_effect = (-1) * kappa_y * w_random # By default, we add the effect of simulated confounder for treatment. # But subtract it from outcome to create a negative correlation # assuming that the original confounder's effect was positive on both. # This is to remove the effect of the original confounder. new_data[self._outcome_name] = new_data[self._outcome_name].values + np.ndarray( shape=(num_rows, 1), buffer=confounder_y_effect ) else: raise NotImplementedError( "'" + self.effect_on_y + "' method not supported for confounders' effect on outcome" ) return new_data def include_simulated_confounder(self, convergence_threshold=0.1, c_star_max=1000): """ This function simulates an unobserved confounder based on the data using the following steps: 1. It calculates the "residuals" from the treatment and outcome model i.) The outcome model has outcome as the dependent variable and all the observed variables including treatment as independent variables ii.) The treatment model has treatment as the dependent variable and all the observed variables as independent variables. 2. U is an intermediate random variable drawn from the normal distribution with the weighted average of residuals as mean and a unit variance U ~ N(c1*d_y + c2*d_t, 1) where *d_y and d_t are residuals from the treatment and outcome model *c1 and c2 are coefficients to the residuals 3. The final U, which is the simulated unobserved confounder is obtained by debiasing the intermediate variable U by residualising it with X Choosing the coefficients c1 and c2: The coefficients are chosen based on these basic assumptions: 1. There is a hyperbolic relationship satisfying c1*c2 = c_star 2. c_star is chosen from a range of possible values based on the correlation of the obtained simulated variable with outcome and treatment. 3. The product of correlations with treatment and outcome should be at a minimum distance to the maximum correlations with treatment and outcome in any of the observed confounders 4. The ratio of the weights should be such that they maintain the ratio of the maximum possible observed coefficients within some confidence interval :param c_star_max: The maximum possible value for the hyperbolic curve on which the coefficients to the residuals lie. It defaults to 1000 in the code if not specified by the user. :type int :param convergence_threshold: The threshold to check the plateauing of the correlation while selecting a c_star. It defaults to 0.1 in the code if not specified by the user :type float :returns: The simulated values of the unobserved confounder based on the data :type pandas.core.series.Series """ # Obtaining the list of observed variables required_variables = True observed_variables = self.choose_variables(required_variables) observed_variables_with_treatment_and_outcome = observed_variables + self._treatment_name + self._outcome_name # Taking a subset of the dataframe that has only observed variables self._data = self._data[observed_variables_with_treatment_and_outcome] # Residuals from the outcome model obtained by fitting a linear model y = self._data[self._outcome_name[0]] observed_variables_with_treatment = observed_variables + self._treatment_name X = self._data[observed_variables_with_treatment] model = sm.OLS(y, X.astype("float")) results = model.fit() residuals_y = y - results.fittedvalues d_y = list(pd.Series(residuals_y)) # Residuals from the treatment model obtained by fitting a linear model t = self._data[self._treatment_name[0]].astype("int64") X = self._data[observed_variables] model = sm.OLS(t, X) results = model.fit() residuals_t = t - results.fittedvalues d_t = list(pd.Series(residuals_t)) # Initialising product_cor_metric_observed with a really low value as finding maximum product_cor_metric_observed = -10000000000 for i in observed_variables: current_obs_confounder = self._data[i] outcome_values = self._data[self._outcome_name[0]] correlation_y = current_obs_confounder.corr(outcome_values) treatment_values = t correlation_t = current_obs_confounder.corr(treatment_values) product_cor_metric_current = correlation_y * correlation_t if product_cor_metric_current >= product_cor_metric_observed: product_cor_metric_observed = product_cor_metric_current correlation_t_observed = correlation_t correlation_y_observed = correlation_y # The user has an option to give the the effect_strength_on_y and effect_strength_on_t which can be then used instead of maximum correlation with treatment and outcome in the observed variables as it specifies the desired effect. if self.kappa_t is not None: correlation_t_observed = self.kappa_t if self.kappa_y is not None: correlation_y_observed = self.kappa_y # Choosing a c_star based on the data. # The correlations stop increasing upon increasing c_star after a certain value, that is it plateaus and we choose the value of c_star to be the value it plateaus. correlation_y_list = [] correlation_t_list = [] product_cor_metric_simulated_list = [] x_list = [] step = int(c_star_max / 10) for i in range(0, int(c_star_max), step): c1 = math.sqrt(i) c2 = c1 final_U = self.generate_confounder_from_residuals(c1, c2, d_y, d_t, X) current_simulated_confounder = final_U outcome_values = self._data[self._outcome_name[0]] correlation_y = current_simulated_confounder.corr(outcome_values) correlation_y_list.append(correlation_y) treatment_values = t correlation_t = current_simulated_confounder.corr(treatment_values) correlation_t_list.append(correlation_t) product_cor_metric_simulated = correlation_y * correlation_t product_cor_metric_simulated_list.append(product_cor_metric_simulated) x_list.append(i) index = 1 while index < len(correlation_y_list): if (correlation_y_list[index] - correlation_y_list[index - 1]) <= convergence_threshold: c_star = x_list[index] break index = index + 1 # Choosing c1 and c2 based on the hyperbolic relationship once c_star is chosen by going over various combinations of c1 and c2 values and choosing the combination which # which maintains the minimum distance between the product of correlations of the simulated variable and the product of maximum correlations of one of the observed variables # and additionally checks if the ratio of the weights are such that they maintain the ratio of the maximum possible observed coefficients within some confidence interval # c1_final and c2_final are initialised to the values on the hyperbolic curve such that c1_final = c2_final and c1_final*c2_final = c_star c1_final = math.sqrt(c_star) c2_final = math.sqrt(c_star) # initialising min_distance_between_product_cor_metrics to be a value greater than 1 min_distance_between_product_cor_metrics = 1.5 i = 0.05 threshold = c_star / 0.05 while i <= threshold: c2 = i c1 = c_star / c2 final_U = self.generate_confounder_from_residuals(c1, c2, d_y, d_t, X) current_simulated_confounder = final_U outcome_values = self._data[self._outcome_name[0]] correlation_y = current_simulated_confounder.corr(outcome_values) treatment_values = t correlation_t = current_simulated_confounder.corr(treatment_values) product_cor_metric_simulated = correlation_y * correlation_t if min_distance_between_product_cor_metrics >= abs( product_cor_metric_simulated - product_cor_metric_observed ): min_distance_between_product_cor_metrics = abs( product_cor_metric_simulated - product_cor_metric_observed ) additional_condition = correlation_y_observed / correlation_t_observed if ((c1 / c2) <= (additional_condition + 0.3 * additional_condition)) and ( (c1 / c2) >= (additional_condition - 0.3 * additional_condition) ): # choose minimum positive value c1_final = c1 c2_final = c2 i = i * 1.5 """#closed form solution print("c_star_max before closed form", c_star_max) if max_correlation_with_t == -1000: c2 = 0 c1 = c_star_max else: additional_condition = abs(max_correlation_with_y/max_correlation_with_t) print("additional_condition", additional_condition) c2 = math.sqrt(c_star_max/additional_condition) c1 = c_star_max/c2""" final_U = self.generate_confounder_from_residuals(c1_final, c2_final, d_y, d_t, X) return final_U def generate_confounder_from_residuals(self, c1, c2, d_y, d_t, X): """ This function takes the residuals from the treatment and outcome model and their coefficients and simulates the intermediate random variable U by taking the row wise normal distribution corresponding to each residual value and then debiasing the intermediate variable to get the final variable. :param c1: coefficient to the residual from the outcome model :type float :param c2: coefficient to the residual from the treatment model :type float :param d_y: residuals from the outcome model :type list :param d_t: residuals from the treatment model :type list :returns: The simulated values of the unobserved confounder based on the data :type pandas.core.series.Series """ U = [] for j in range(len(d_t)): simulated_variable_mean = c1 * d_y[j] + c2 * d_t[j] simulated_variable_stddev = 1 U.append(np.random.normal(simulated_variable_mean, simulated_variable_stddev, 1)) U = np.array(U) model = sm.OLS(U, X) results = model.fit() U = U.reshape( -1, ) final_U = U - results.fittedvalues.values final_U = pd.Series(U) return final_U

import copy import logging import math import numpy as np import pandas as pd import scipy.stats import statsmodels.api as sm from sklearn.linear_model import LogisticRegression from sklearn.preprocessing import StandardScaler from tqdm.auto import tqdm import dowhy.causal_estimators.econml from dowhy.causal_estimator import CausalEstimator from dowhy.causal_estimators.linear_regression_estimator import LinearRegressionEstimator from dowhy.causal_refuter import CausalRefutation, CausalRefuter from dowhy.causal_refuters.linear_sensitivity_analyzer import LinearSensitivityAnalyzer from dowhy.causal_refuters.non_parametric_sensitivity_analyzer import NonParametricSensitivityAnalyzer from dowhy.causal_refuters.partial_linear_sensitivity_analyzer import PartialLinearSensitivityAnalyzer class AddUnobservedCommonCause(CausalRefuter): """Add an unobserved confounder for refutation. AddUnobservedCommonCause class supports three methods: 1) Simulation of an unobserved confounder 2) Linear partial R2 : Sensitivity Analysis for linear models. 3) Non-Parametric partial R2 based : Sensitivity Analyis for non-parametric models. Supports additional parameters that can be specified in the refute_estimate() method. """ def __init__(self, *args, **kwargs): """ Initialize the parameters required for the refuter. For direct_simulation, if effect_strength_on_treatment or effect_strength_on_outcome is not given, it is calculated automatically as a range between the minimum and maximum effect strength of observed confounders on treatment and outcome respectively. :param simulation_method: The method to use for simulating effect of unobserved confounder. Possible values are ["direct-simulation", "linear-partial-R2", "non-parametric-partial-R2"]. :param confounders_effect_on_treatment: str : The type of effect on the treatment due to the unobserved confounder. Possible values are ['binary_flip', 'linear'] :param confounders_effect_on_outcome: str : The type of effect on the outcome due to the unobserved confounder. Possible values are ['binary_flip', 'linear'] :param effect_strength_on_treatment: float, numpy.ndarray: [Used when simulation_method="direct-simulation"] Strength of the confounder's effect on treatment. When confounders_effect_on_treatment is linear, it is the regression coefficient. When the confounders_effect_on_treatment is binary flip, it is the probability with which effect of unobserved confounder can invert the value of the treatment. :param effect_strength_on_outcome: float, numpy.ndarray: Strength of the confounder's effect on outcome. Its interpretation depends on confounders_effect_on_outcome and the simulation_method. When simulation_method is direct-simulation, for a linear effect it behaves like the regression coefficient and for a binary flip, it is the probability with which it can invert the value of the outcome. :param partial_r2_confounder_treatment: float, numpy.ndarray: [Used when simulation_method is linear-partial-R2 or non-parametric-partial-R2] Partial R2 of the unobserved confounder wrt the treatment conditioned on the observed confounders. Only in the case of general non-parametric-partial-R2, it is the fraction of variance in the reisz representer that is explained by the unobserved confounder; specifically (1-r), where r is the ratio of variance of reisz representer, alpha^2, based on observed confounders and that based on all confounders. :param partial_r2_confounder_outcome: float, numpy.ndarray: [Used when simulation_method is linear-partial-R2 or non-parametric-partial-R2] Partial R2 of the unobserved confounder wrt the outcome conditioned on the treatment and observed confounders. :param frac_strength_treatment: float: This parameter decides the effect strength of the simulated confounder as a fraction of the effect strength of observed confounders on treatment. Defaults to 1. :param frac_strength_outcome: float: This parameter decides the effect strength of the simulated confounder as a fraction of the effect strength of observed confounders on outcome. Defaults to 1. :param plotmethod: string: Type of plot to be shown. If None, no plot is generated. This parameter is used only only when more than one treatment confounder effect values or outcome confounder effect values are provided. Default is "colormesh". Supported values are "contour", "colormesh" when more than one value is provided for both confounder effect value parameters; "line" when provided for only one of them. :param percent_change_estimate: It is the percentage of reduction of treatment estimate that could alter the results (default = 1). if percent_change_estimate = 1, the robustness value describes the strength of association of confounders with treatment and outcome in order to reduce the estimate by 100% i.e bring it down to 0. (relevant only for Linear Sensitivity Analysis, ignore for rest) :param confounder_increases_estimate: True implies that confounder increases the absolute value of estimate and vice versa. (Default = False). (relevant only for Linear Sensitivity Analysis, ignore for rest) :param benchmark_common_causes: names of variables for bounding strength of confounders. (relevant only for partial-r2 based simulation methods) :param significance_level: confidence interval for statistical inference(default = 0.05). (relevant only for partial-r2 based simulation methods) :param null_hypothesis_effect: assumed effect under the null hypothesis. (relevant only for linear-partial-R2, ignore for rest) :param plot_estimate: Generate contour plot for estimate while performing sensitivity analysis. (default = True). (relevant only for partial-r2 based simulation methods) :param num_splits: number of splits for cross validation. (default = 5). (relevant only for non-parametric-partial-R2 simulation method) :param shuffle_data : shuffle data or not before splitting into folds (default = False). (relevant only for non-parametric-partial-R2 simulation method) :param shuffle_random_seed: seed for randomly shuffling data. (relevant only for non-parametric-partial-R2 simulation method) :param alpha_s_estimator_param_list: list of dictionaries with parameters for finding alpha_s. (relevant only for non-parametric-partial-R2 simulation method) :param g_s_estimator_list: list of estimator objects for finding g_s. These objects should have fit() and predict() functions implemented. (relevant only for non-parametric-partial-R2 simulation method) :param g_s_estimator_param_list: list of dictionaries with parameters for tuning respective estimators in "g_s_estimator_list". The order of the dictionaries in the list should be consistent with the estimator objects order in "g_s_estimator_list". (relevant only for non-parametric-partial-R2 simulation method) """ super().__init__(*args, **kwargs) self.simulation_method = kwargs["simulation_method"] if "simulation_method" in kwargs else "direct-simulation" self.effect_on_t = ( kwargs["confounders_effect_on_treatment"] if "confounders_effect_on_treatment" in kwargs else "binary_flip" ) self.effect_on_y = ( kwargs["confounders_effect_on_outcome"] if "confounders_effect_on_outcome" in kwargs else "linear" ) if self.simulation_method == "direct-simulation": self.kappa_t = kwargs["effect_strength_on_treatment"] if "effect_strength_on_treatment" in kwargs else None self.kappa_y = kwargs["effect_strength_on_outcome"] if "effect_strength_on_outcome" in kwargs else None elif self.simulation_method in ["linear-partial-R2", "non-parametric-partial-R2"]: self.kappa_t = ( kwargs["partial_r2_confounder_treatment"] if "partial_r2_confounder_treatment" in kwargs else None ) self.kappa_y = ( kwargs["partial_r2_confounder_outcome"] if "partial_r2_confounder_outcome" in kwargs else None ) else: raise ValueError( "simulation method is not supported. Try direct-simulation, linear-partial-R2 or non-parametric-partial-R2" ) self.frac_strength_treatment = ( kwargs["effect_fraction_on_treatment"] if "effect_fraction_on_treatment" in kwargs else 1 ) self.frac_strength_outcome = ( kwargs["effect_fraction_on_outcome"] if "effect_fraction_on_outcome" in kwargs else 1 ) self.plotmethod = kwargs["plotmethod"] if "plotmethod" in kwargs else "colormesh" self.percent_change_estimate = kwargs["percent_change_estimate"] if "percent_change_estimate" in kwargs else 1.0 self.significance_level = kwargs["significance_level"] if "significance_level" in kwargs else 0.05 self.confounder_increases_estimate = ( kwargs["confounder_increases_estimate"] if "confounder_increases_estimate" in kwargs else False ) self.benchmark_common_causes = ( kwargs["benchmark_common_causes"] if "benchmark_common_causes" in kwargs else None ) self.null_hypothesis_effect = kwargs["null_hypothesis_effect"] if "null_hypothesis_effect" in kwargs else 0 self.plot_estimate = kwargs["plot_estimate"] if "plot_estimate" in kwargs else True self.num_splits = kwargs["num_splits"] if "num_splits" in kwargs else 5 self.shuffle_data = kwargs["shuffle_data"] if "shuffle_data" in kwargs else False self.shuffle_random_seed = kwargs["shuffle_random_seed"] if "shuffle_random_seed" in kwargs else None self.alpha_s_estimator_param_list = ( kwargs["alpha_s_estimator_param_list"] if "alpha_s_estimator_param_list" in kwargs else None ) self.alpha_s_estimator_list = kwargs["alpha_s_estimator_list"] if "alpha_s_estimator_list" in kwargs else None self.g_s_estimator_list = kwargs["g_s_estimator_list"] if "g_s_estimator_list" in kwargs else None self.g_s_estimator_param_list = ( kwargs["g_s_estimator_param_list"] if "g_s_estimator_param_list" in kwargs else None ) self.plugin_reisz = kwargs["plugin_reisz"] if "plugin_reisz" in kwargs else False self.logger = logging.getLogger(__name__) def infer_default_kappa_t(self, len_kappa_t=10): """Infer default effect strength of simulated confounder on treatment.""" observed_common_causes_names = self._target_estimand.get_backdoor_variables() if len(observed_common_causes_names) > 0: observed_common_causes = self._data[observed_common_causes_names] observed_common_causes = pd.get_dummies(observed_common_causes, drop_first=True) else: raise ValueError( "There needs to be at least one common cause to" + "automatically compute the default value of kappa_t." + " Provide a value for kappa_t" ) t = self._data[self._treatment_name] # Standardizing the data observed_common_causes = StandardScaler().fit_transform(observed_common_causes) if self.effect_on_t == "binary_flip": # Fit a model containing all confounders and compare predictions # using all features compared to all features except a given # confounder. tmodel = LogisticRegression().fit(observed_common_causes, t) tpred = tmodel.predict(observed_common_causes).astype(int) flips = [] for i in range(observed_common_causes.shape[1]): oldval = np.copy(observed_common_causes[:, i]) observed_common_causes[:, i] = 0 tcap = tmodel.predict(observed_common_causes).astype(int) observed_common_causes[:, i] = oldval flips.append(np.sum(abs(tcap - tpred)) / tpred.shape[0]) min_coeff, max_coeff = min(flips), max(flips) elif self.effect_on_t == "linear": # Estimating the regression coefficient from standardized features to t corrcoef_var_t = np.corrcoef(observed_common_causes, t, rowvar=False)[-1, :-1] std_dev_t = np.std(t)[0] max_coeff = max(corrcoef_var_t) * std_dev_t min_coeff = min(corrcoef_var_t) * std_dev_t else: raise NotImplementedError( "'" + self.effect_on_t + "' method not supported for confounders' effect on treatment" ) min_coeff, max_coeff = self._compute_min_max_coeff(min_coeff, max_coeff, self.frac_strength_treatment) # By default, return a plot with 10 points # consider 10 values of the effect of the unobserved confounder step = (max_coeff - min_coeff) / len_kappa_t self.logger.info("(Min, Max) kappa_t for observed common causes, ({0}, {1})".format(min_coeff, max_coeff)) if np.equal(max_coeff, min_coeff): return max_coeff else: return np.arange(min_coeff, max_coeff, step) def _compute_min_max_coeff(self, min_coeff, max_coeff, effect_strength_fraction): max_coeff = effect_strength_fraction * max_coeff min_coeff = effect_strength_fraction * min_coeff return min_coeff, max_coeff def infer_default_kappa_y(self, len_kappa_y=10): """Infer default effect strength of simulated confounder on treatment.""" observed_common_causes_names = self._target_estimand.get_backdoor_variables() if len(observed_common_causes_names) > 0: observed_common_causes = self._data[observed_common_causes_names] observed_common_causes = pd.get_dummies(observed_common_causes, drop_first=True) else: raise ValueError( "There needs to be at least one common cause to" + "automatically compute the default value of kappa_y." + " Provide a value for kappa_y" ) y = self._data[self._outcome_name] # Standardizing the data observed_common_causes = StandardScaler().fit_transform(observed_common_causes) if self.effect_on_y == "binary_flip": # Fit a model containing all confounders and compare predictions # using all features compared to all features except a given # confounder. ymodel = LogisticRegression().fit(observed_common_causes, y) ypred = ymodel.predict(observed_common_causes).astype(int) flips = [] for i in range(observed_common_causes.shape[1]): oldval = np.copy(observed_common_causes[:, i]) observed_common_causes[:, i] = 0 ycap = ymodel.predict(observed_common_causes).astype(int) observed_common_causes[:, i] = oldval flips.append(np.sum(abs(ycap - ypred)) / ypred.shape[0]) min_coeff, max_coeff = min(flips), max(flips) elif self.effect_on_y == "linear": corrcoef_var_y = np.corrcoef(observed_common_causes, y, rowvar=False)[-1, :-1] std_dev_y = np.std(y)[0] max_coeff = max(corrcoef_var_y) * std_dev_y min_coeff = min(corrcoef_var_y) * std_dev_y else: raise NotImplementedError( "'" + self.effect_on_y + "' method not supported for confounders' effect on outcome" ) min_coeff, max_coeff = self._compute_min_max_coeff(min_coeff, max_coeff, self.frac_strength_outcome) # By default, return a plot with 10 points # consider 10 values of the effect of the unobserved confounder step = (max_coeff - min_coeff) / len_kappa_y self.logger.info("(Min, Max) kappa_y for observed common causes, ({0}, {1})".format(min_coeff, max_coeff)) if np.equal(max_coeff, min_coeff): return max_coeff else: return np.arange(min_coeff, max_coeff, step) def refute_estimate(self, show_progress_bar=False): """ This function attempts to add an unobserved common cause to the outcome and the treatment. At present, we have implemented the behavior for one dimensional behaviors for continuous and binary variables. This function can either take single valued inputs or a range of inputs. The function then looks at the data type of the input and then decides on the course of action. :return: CausalRefuter: An object that contains the estimated effect and a new effect and the name of the refutation used. """ if self.simulation_method == "linear-partial-R2": if not (isinstance(self._estimate.estimator, LinearRegressionEstimator)): raise NotImplementedError( "Currently only LinearRegressionEstimator is supported for Sensitivity Analysis" ) if len(self._estimate.estimator._effect_modifier_names) > 0: raise NotImplementedError("The current implementation does not support effect modifiers") if self.frac_strength_outcome == 1: self.frac_strength_outcome = self.frac_strength_treatment analyzer = LinearSensitivityAnalyzer( estimator=self._estimate.estimator, data=self._data, treatment_name=self._treatment_name, percent_change_estimate=self.percent_change_estimate, significance_level=self.significance_level, benchmark_common_causes=self.benchmark_common_causes, null_hypothesis_effect=self.null_hypothesis_effect, frac_strength_treatment=self.frac_strength_treatment, frac_strength_outcome=self.frac_strength_outcome, common_causes_order=self._estimate.estimator._observed_common_causes.columns, ) analyzer.check_sensitivity(plot=self.plot_estimate) return analyzer if self.simulation_method == "non-parametric-partial-R2": # If the estimator used is LinearDML, partially linear sensitivity analysis will be automatically chosen if isinstance(self._estimate.estimator, dowhy.causal_estimators.econml.Econml): if self._estimate.estimator._econml_methodname == "econml.dml.LinearDML": analyzer = PartialLinearSensitivityAnalyzer( estimator=self._estimate._estimator_object, observed_common_causes=self._estimate.estimator._observed_common_causes, treatment=self._estimate.estimator._treatment, outcome=self._estimate.estimator._outcome, alpha_s_estimator_param_list=self.alpha_s_estimator_param_list, g_s_estimator_list=self.g_s_estimator_list, g_s_estimator_param_list=self.g_s_estimator_param_list, effect_strength_treatment=self.kappa_t, effect_strength_outcome=self.kappa_y, benchmark_common_causes=self.benchmark_common_causes, frac_strength_treatment=self.frac_strength_treatment, frac_strength_outcome=self.frac_strength_outcome, ) analyzer.check_sensitivity(plot=self.plot_estimate) return analyzer analyzer = NonParametricSensitivityAnalyzer( estimator=self._estimate.estimator, observed_common_causes=self._estimate.estimator._observed_common_causes, treatment=self._estimate.estimator._treatment, outcome=self._estimate.estimator._outcome, alpha_s_estimator_list=self.alpha_s_estimator_list, alpha_s_estimator_param_list=self.alpha_s_estimator_param_list, g_s_estimator_list=self.g_s_estimator_list, g_s_estimator_param_list=self.g_s_estimator_param_list, effect_strength_treatment=self.kappa_t, effect_strength_outcome=self.kappa_y, benchmark_common_causes=self.benchmark_common_causes, frac_strength_treatment=self.frac_strength_treatment, frac_strength_outcome=self.frac_strength_outcome, theta_s=self._estimate.value, plugin_reisz=self.plugin_reisz, ) analyzer.check_sensitivity(plot=self.plot_estimate) return analyzer if self.kappa_t is None: self.kappa_t = self.infer_default_kappa_t() if self.kappa_y is None: self.kappa_y = self.infer_default_kappa_y() if not isinstance(self.kappa_t, (list, np.ndarray)) and not isinstance( self.kappa_y, (list, np.ndarray) ): # Deal with single value inputs new_data = copy.deepcopy(self._data) new_data = self.include_confounders_effect(new_data, self.kappa_t, self.kappa_y) new_estimator = CausalEstimator.get_estimator_object(new_data, self._target_estimand, self._estimate) new_effect = new_estimator.estimate_effect() refute = CausalRefutation( self._estimate.value, new_effect.value, refutation_type="Refute: Add an Unobserved Common Cause" ) refute.new_effect_array = np.array(new_effect.value) refute.new_effect = new_effect.value refute.add_refuter(self) return refute else: # Deal with multiple value inputs if isinstance(self.kappa_t, (list, np.ndarray)) and isinstance( self.kappa_y, (list, np.ndarray) ): # Deal with range inputs # Get a 2D matrix of values # x,y = np.meshgrid(self.kappa_t, self.kappa_y) # x,y are both MxN results_matrix = np.random.rand( len(self.kappa_t), len(self.kappa_y) ) # Matrix to hold all the results of NxM orig_data = copy.deepcopy(self._data) for i in tqdm( range(len(self.kappa_t)), colour=CausalRefuter.PROGRESS_BAR_COLOR, disable=not show_progress_bar, desc="Refuting Estimates: ", ): for j in range(len(self.kappa_y)): new_data = self.include_confounders_effect(orig_data, self.kappa_t[i], self.kappa_y[j]) new_estimator = CausalEstimator.get_estimator_object( new_data, self._target_estimand, self._estimate ) new_effect = new_estimator.estimate_effect() refute = CausalRefutation( self._estimate.value, new_effect.value, refutation_type="Refute: Add an Unobserved Common Cause", ) results_matrix[i][j] = refute.new_effect # Populate the results refute.new_effect_array = results_matrix refute.new_effect = (np.min(results_matrix), np.max(results_matrix)) # Store the values into the refute object refute.add_refuter(self) if self.plotmethod is None: return refute import matplotlib import matplotlib.pyplot as plt fig = plt.figure(figsize=(6, 5)) left, bottom, width, height = 0.1, 0.1, 0.8, 0.8 ax = fig.add_axes([left, bottom, width, height]) oe = self._estimate.value contour_levels = [oe / 4.0, oe / 2.0, (3.0 / 4) * oe, oe] contour_levels.extend([0, np.min(results_matrix), np.max(results_matrix)]) if self.plotmethod == "contour": cp = plt.contourf(self.kappa_y, self.kappa_t, results_matrix, levels=sorted(contour_levels)) # Adding a label on the contour line for the original estimate fmt = {} trueeffect_index = np.where(cp.levels == oe)[0][0] fmt[cp.levels[trueeffect_index]] = "Estimated Effect" # Label every other level using strings plt.clabel(cp, [cp.levels[trueeffect_index]], inline=True, fmt=fmt) plt.colorbar(cp) elif self.plotmethod == "colormesh": cp = plt.pcolormesh(self.kappa_y, self.kappa_t, results_matrix, shading="nearest") plt.colorbar(cp, ticks=contour_levels) ax.yaxis.set_ticks(self.kappa_t) ax.xaxis.set_ticks(self.kappa_y) plt.xticks(rotation=45) ax.set_title("Effect of Unobserved Common Cause") ax.set_ylabel("Value of Linear Constant on Treatment") ax.set_xlabel("Value of Linear Constant on Outcome") plt.show() return refute elif isinstance(self.kappa_t, (list, np.ndarray)): outcomes = np.random.rand(len(self.kappa_t)) orig_data = copy.deepcopy(self._data) for i in tqdm( range(0, len(self.kappa_t)), colour=CausalRefuter.PROGRESS_BAR_COLOR, disable=not show_progress_bar, desc="Refuting Estimates: ", ): new_data = self.include_confounders_effect(orig_data, self.kappa_t[i], self.kappa_y) new_estimator = CausalEstimator.get_estimator_object( new_data, self._target_estimand, self._estimate ) new_effect = new_estimator.estimate_effect() refute = CausalRefutation( self._estimate.value, new_effect.value, refutation_type="Refute: Add an Unobserved Common Cause" ) self.logger.debug(refute) outcomes[i] = refute.new_effect # Populate the results refute.new_effect_array = outcomes refute.new_effect = (np.min(outcomes), np.max(outcomes)) refute.add_refuter(self) if self.plotmethod is None: return refute import matplotlib import matplotlib.pyplot as plt fig = plt.figure(figsize=(6, 5)) left, bottom, width, height = 0.1, 0.1, 0.8, 0.8 ax = fig.add_axes([left, bottom, width, height]) plt.plot(self.kappa_t, outcomes) plt.axhline(self._estimate.value, linestyle="--", color="gray") ax.set_title("Effect of Unobserved Common Cause") ax.set_xlabel("Value of Linear Constant on Treatment") ax.set_ylabel("Estimated Effect after adding the common cause") plt.show() return refute elif isinstance(self.kappa_y, (list, np.ndarray)): outcomes = np.random.rand(len(self.kappa_y)) orig_data = copy.deepcopy(self._data) for i in tqdm( range(0, len(self.kappa_y)), colour=CausalRefuter.PROGRESS_BAR_COLOR, disable=not show_progress_bar, desc="Refuting Estimates: ", ): new_data = self.include_confounders_effect(orig_data, self.kappa_t, self.kappa_y[i]) new_estimator = CausalEstimator.get_estimator_object( new_data, self._target_estimand, self._estimate ) new_effect = new_estimator.estimate_effect() refute = CausalRefutation( self._estimate.value, new_effect.value, refutation_type="Refute: Add an Unobserved Common Cause" ) self.logger.debug(refute) outcomes[i] = refute.new_effect # Populate the results refute.new_effect_array = outcomes refute.new_effect = (np.min(outcomes), np.max(outcomes)) refute.add_refuter(self) if self.plotmethod is None: return refute import matplotlib import matplotlib.pyplot as plt fig = plt.figure(figsize=(6, 5)) left, bottom, width, height = 0.1, 0.1, 0.8, 0.8 ax = fig.add_axes([left, bottom, width, height]) plt.plot(self.kappa_y, outcomes) plt.axhline(self._estimate.value, linestyle="--", color="gray") ax.set_title("Effect of Unobserved Common Cause") ax.set_xlabel("Value of Linear Constant on Outcome") ax.set_ylabel("Estimated Effect after adding the common cause") plt.show() return refute def include_confounders_effect(self, new_data, kappa_t, kappa_y): """ This function deals with the change in the value of the data due to the effect of the unobserved confounder. In the case of a binary flip, we flip only if the random number is greater than the threshold set. In the case of a linear effect, we use the variable as the linear regression constant. :param new_data: pandas.DataFrame: The data to be changed due to the effects of the unobserved confounder. :param kappa_t: numpy.float64: The value of the threshold for binary_flip or the value of the regression coefficient for linear effect. :param kappa_y: numpy.float64: The value of the threshold for binary_flip or the value of the regression coefficient for linear effect. :return: pandas.DataFrame: The DataFrame that includes the effects of the unobserved confounder. """ num_rows = self._data.shape[0] stdnorm = scipy.stats.norm() w_random = stdnorm.rvs(num_rows) if self.effect_on_t == "binary_flip": alpha = 2 * kappa_t - 1 if kappa_t >= 0.5 else 1 - 2 * kappa_t interval = stdnorm.interval(alpha) rel_interval = interval[0] if kappa_t >= 0.5 else interval[1] new_data.loc[rel_interval <= w_random, self._treatment_name] = ( 1 - new_data.loc[rel_interval <= w_random, self._treatment_name] ) for tname in self._treatment_name: if pd.api.types.is_bool_dtype(self._data[tname]): new_data = new_data.astype({tname: "bool"}, copy=False) elif self.effect_on_t == "linear": confounder_t_effect = kappa_t * w_random # By default, we add the effect of simulated confounder for treatment. # But subtract it from outcome to create a negative correlation # assuming that the original confounder's effect was positive on both. # This is to remove the effect of the original confounder. new_data[self._treatment_name] = new_data[self._treatment_name].values + np.ndarray( shape=(num_rows, 1), buffer=confounder_t_effect ) else: raise NotImplementedError( "'" + self.effect_on_t + "' method not supported for confounders' effect on treatment" ) if self.effect_on_y == "binary_flip": alpha = 2 * kappa_y - 1 if kappa_y >= 0.5 else 1 - 2 * kappa_y interval = stdnorm.interval(alpha) rel_interval = interval[0] if kappa_y >= 0.5 else interval[1] new_data.loc[rel_interval <= w_random, self._outcome_name] = ( 1 - new_data.loc[rel_interval <= w_random, self._outcome_name] ) for yname in self._outcome_name: if pd.api.types.is_bool_dtype(self._data[yname]): new_data = new_data.astype({yname: "bool"}, copy=False) elif self.effect_on_y == "linear": confounder_y_effect = (-1) * kappa_y * w_random # By default, we add the effect of simulated confounder for treatment. # But subtract it from outcome to create a negative correlation # assuming that the original confounder's effect was positive on both. # This is to remove the effect of the original confounder. new_data[self._outcome_name] = new_data[self._outcome_name].values + np.ndarray( shape=(num_rows, 1), buffer=confounder_y_effect ) else: raise NotImplementedError( "'" + self.effect_on_y + "' method not supported for confounders' effect on outcome" ) return new_data def include_simulated_confounder(self, convergence_threshold=0.1, c_star_max=1000): """ This function simulates an unobserved confounder based on the data using the following steps: 1. It calculates the "residuals" from the treatment and outcome model i.) The outcome model has outcome as the dependent variable and all the observed variables including treatment as independent variables ii.) The treatment model has treatment as the dependent variable and all the observed variables as independent variables. 2. U is an intermediate random variable drawn from the normal distribution with the weighted average of residuals as mean and a unit variance U ~ N(c1*d_y + c2*d_t, 1) where *d_y and d_t are residuals from the treatment and outcome model *c1 and c2 are coefficients to the residuals 3. The final U, which is the simulated unobserved confounder is obtained by debiasing the intermediate variable U by residualising it with X Choosing the coefficients c1 and c2: The coefficients are chosen based on these basic assumptions: 1. There is a hyperbolic relationship satisfying c1*c2 = c_star 2. c_star is chosen from a range of possible values based on the correlation of the obtained simulated variable with outcome and treatment. 3. The product of correlations with treatment and outcome should be at a minimum distance to the maximum correlations with treatment and outcome in any of the observed confounders 4. The ratio of the weights should be such that they maintain the ratio of the maximum possible observed coefficients within some confidence interval :param c_star_max: The maximum possible value for the hyperbolic curve on which the coefficients to the residuals lie. It defaults to 1000 in the code if not specified by the user. :type int :param convergence_threshold: The threshold to check the plateauing of the correlation while selecting a c_star. It defaults to 0.1 in the code if not specified by the user :type float :returns: The simulated values of the unobserved confounder based on the data :type pandas.core.series.Series """ # Obtaining the list of observed variables required_variables = True observed_variables = self.choose_variables(required_variables) observed_variables_with_treatment_and_outcome = observed_variables + self._treatment_name + self._outcome_name # Taking a subset of the dataframe that has only observed variables self._data = self._data[observed_variables_with_treatment_and_outcome] # Residuals from the outcome model obtained by fitting a linear model y = self._data[self._outcome_name[0]] observed_variables_with_treatment = observed_variables + self._treatment_name X = self._data[observed_variables_with_treatment] model = sm.OLS(y, X.astype("float")) results = model.fit() residuals_y = y - results.fittedvalues d_y = list(pd.Series(residuals_y)) # Residuals from the treatment model obtained by fitting a linear model t = self._data[self._treatment_name[0]].astype("int64") X = self._data[observed_variables] model = sm.OLS(t, X) results = model.fit() residuals_t = t - results.fittedvalues d_t = list(pd.Series(residuals_t)) # Initialising product_cor_metric_observed with a really low value as finding maximum product_cor_metric_observed = -10000000000 for i in observed_variables: current_obs_confounder = self._data[i] outcome_values = self._data[self._outcome_name[0]] correlation_y = current_obs_confounder.corr(outcome_values) treatment_values = t correlation_t = current_obs_confounder.corr(treatment_values) product_cor_metric_current = correlation_y * correlation_t if product_cor_metric_current >= product_cor_metric_observed: product_cor_metric_observed = product_cor_metric_current correlation_t_observed = correlation_t correlation_y_observed = correlation_y # The user has an option to give the the effect_strength_on_y and effect_strength_on_t which can be then used instead of maximum correlation with treatment and outcome in the observed variables as it specifies the desired effect. if self.kappa_t is not None: correlation_t_observed = self.kappa_t if self.kappa_y is not None: correlation_y_observed = self.kappa_y # Choosing a c_star based on the data. # The correlations stop increasing upon increasing c_star after a certain value, that is it plateaus and we choose the value of c_star to be the value it plateaus. correlation_y_list = [] correlation_t_list = [] product_cor_metric_simulated_list = [] x_list = [] step = int(c_star_max / 10) for i in range(0, int(c_star_max), step): c1 = math.sqrt(i) c2 = c1 final_U = self.generate_confounder_from_residuals(c1, c2, d_y, d_t, X) current_simulated_confounder = final_U outcome_values = self._data[self._outcome_name[0]] correlation_y = current_simulated_confounder.corr(outcome_values) correlation_y_list.append(correlation_y) treatment_values = t correlation_t = current_simulated_confounder.corr(treatment_values) correlation_t_list.append(correlation_t) product_cor_metric_simulated = correlation_y * correlation_t product_cor_metric_simulated_list.append(product_cor_metric_simulated) x_list.append(i) index = 1 while index < len(correlation_y_list): if (correlation_y_list[index] - correlation_y_list[index - 1]) <= convergence_threshold: c_star = x_list[index] break index = index + 1 # Choosing c1 and c2 based on the hyperbolic relationship once c_star is chosen by going over various combinations of c1 and c2 values and choosing the combination which # which maintains the minimum distance between the product of correlations of the simulated variable and the product of maximum correlations of one of the observed variables # and additionally checks if the ratio of the weights are such that they maintain the ratio of the maximum possible observed coefficients within some confidence interval # c1_final and c2_final are initialised to the values on the hyperbolic curve such that c1_final = c2_final and c1_final*c2_final = c_star c1_final = math.sqrt(c_star) c2_final = math.sqrt(c_star) # initialising min_distance_between_product_cor_metrics to be a value greater than 1 min_distance_between_product_cor_metrics = 1.5 i = 0.05 threshold = c_star / 0.05 while i <= threshold: c2 = i c1 = c_star / c2 final_U = self.generate_confounder_from_residuals(c1, c2, d_y, d_t, X) current_simulated_confounder = final_U outcome_values = self._data[self._outcome_name[0]] correlation_y = current_simulated_confounder.corr(outcome_values) treatment_values = t correlation_t = current_simulated_confounder.corr(treatment_values) product_cor_metric_simulated = correlation_y * correlation_t if min_distance_between_product_cor_metrics >= abs( product_cor_metric_simulated - product_cor_metric_observed ): min_distance_between_product_cor_metrics = abs( product_cor_metric_simulated - product_cor_metric_observed ) additional_condition = correlation_y_observed / correlation_t_observed if ((c1 / c2) <= (additional_condition + 0.3 * additional_condition)) and ( (c1 / c2) >= (additional_condition - 0.3 * additional_condition) ): # choose minimum positive value c1_final = c1 c2_final = c2 i = i * 1.5 """#closed form solution print("c_star_max before closed form", c_star_max) if max_correlation_with_t == -1000: c2 = 0 c1 = c_star_max else: additional_condition = abs(max_correlation_with_y/max_correlation_with_t) print("additional_condition", additional_condition) c2 = math.sqrt(c_star_max/additional_condition) c1 = c_star_max/c2""" final_U = self.generate_confounder_from_residuals(c1_final, c2_final, d_y, d_t, X) return final_U def generate_confounder_from_residuals(self, c1, c2, d_y, d_t, X): """ This function takes the residuals from the treatment and outcome model and their coefficients and simulates the intermediate random variable U by taking the row wise normal distribution corresponding to each residual value and then debiasing the intermediate variable to get the final variable. :param c1: coefficient to the residual from the outcome model :type float :param c2: coefficient to the residual from the treatment model :type float :param d_y: residuals from the outcome model :type list :param d_t: residuals from the treatment model :type list :returns: The simulated values of the unobserved confounder based on the data :type pandas.core.series.Series """ U = [] for j in range(len(d_t)): simulated_variable_mean = c1 * d_y[j] + c2 * d_t[j] simulated_variable_stddev = 1 U.append(np.random.normal(simulated_variable_mean, simulated_variable_stddev, 1)) U = np.array(U) model = sm.OLS(U, X) results = model.fit() U = U.reshape( -1, ) final_U = U - results.fittedvalues.values final_U = pd.Series(U) return final_U

anusha0409

81841c697bd5e80ecf9e731432305f6186666f1f

bb446c333f2256074304b0dec9cb5628d284b542

Thanks for making this change. It is clearer, and will hopefully also make it easier to separate further in the future.

emrekiciman

py-why/dowhy

Adding Non Linear Sensitivity Analysis

This PR implements the non-parametric sensitivity analysis from Chernozhukov et al. https://arxiv.org/abs/2112.13398 It implements two sensitivity analyzers: 1. For Partial Linear DGPs and estimators like LinearDML 2. For general non-parametric DGPs and estimators like KernelDML. The notebook in this PR provides an introduction on how the sensitivity bounds are calculated for the partial linear case. For the general nonparametric DGPs, we need to estimate a special function called the Reisz representer. For binary treatment, it is exactly the difference in outcome weighted by propensity score. So we provide two options to learn the Reisz representer, 1) plugin_reisz that uses the propensity score; and 2) general estimator that uses a custom loss function. These two are in the file reisz.py. Briefly, the sensitivity bounds depend on two parameters that denote the effect of the unobserved confounder on treatment and outcome. That's why we use the same API as for the `add_unobserved_common_cause` method and add this sensitivity analysis as a possible simulation method="non-parametric-partial-R2". The format of the plots is identical to those from the "linear-partial-r2" simulation method that is already implemented. We provide two modes for the user. 1) User specifies the effect strength parameters themselves, as a range of values. 2) User benchmarks the effect strength parameters as a multiple of the same parameters for the observed common causes. Signed-off-by: anusha <anushaagarwal2000.com>

2022-06-20 14:37:11+00:00

2022-09-16 03:57:26+00:00

dowhy/causal_refuters/linear_sensitivity_analyzer.py

import logging import sys import matplotlib.pyplot as plt import numpy as np import pandas as pd import statsmodels.api as sm from scipy.stats import t from dowhy.utils.api import parse_state class LinearSensitivityAnalyzer: """ Class to perform sensitivity analysis See: https://carloscinelli.com/files/Cinelli%20and%20Hazlett%20(2020)%20-%20Making%20Sense%20of%20Sensitivity.pdf :param estimator: linear estimator of the causal model :param data: Pandas dataframe :param treatment_name: name of treatment :param percent_change_estimate: It is the percentage of reduction of treatment estimate that could alter the results (default = 1) if percent_change_estimate = 1, the robustness value describes the strength of association of confounders with treatment and outcome in order to reduce the estimate by 100% i.e bring it down to 0. :param null_hypothesis_effect: assumed effect under the null hypothesis :param confounder_increases_estimate: True implies that confounder increases the absolute value of estimate and vice versa. (Default = True) :param benchmark_common_causes: names of variables for bounding strength of confounders :param significance_level: confidence interval for statistical inference(default = 0.05) :param frac_strength_treatment: strength of association between unobserved confounder and treatment compared to benchmark covariate :param frac_strength_outcome: strength of association between unobserved confounder and outcome compared to benchmark covariate :param common_causes_order: The order of column names in OLS regression data """ def __init__( self, estimator=None, data=None, treatment_name=None, percent_change_estimate=1.0, significance_level=0.05, confounder_increases_estimate=True, benchmark_common_causes=None, null_hypothesis_effect=0, frac_strength_treatment=None, frac_strength_outcome=None, common_causes_order=None, ): self.data = data self.treatment_name = [] # original_treatment_name: : stores original variable names for labelling self.original_treatment_name = treatment_name for t in range(len(treatment_name)): self.treatment_name.append("x" + str(t + 1)) self.percent_change_estimate = percent_change_estimate self.significance_level = significance_level self.confounder_increases_estimate = confounder_increases_estimate self.estimator = estimator self.estimator_model = estimator.model self.null_hypothesis_effect = null_hypothesis_effect # common_causes_map : maps the original variable names to variable names in OLS regression self.common_causes_map = {} for i in range(len(common_causes_order)): self.common_causes_map[common_causes_order[i]] = "x" + str(len(self.treatment_name) + i + 1) # benchmark_common_causes: stores variable names in terms of regression model variables benchmark_common_causes = parse_state(benchmark_common_causes) self.benchmark_common_causes = [] # original_benchmark_covariates: stores original variable names for labelling self.original_benchmark_covariates = benchmark_common_causes for i in range(len(benchmark_common_causes)): self.benchmark_common_causes.append(self.common_causes_map[benchmark_common_causes[i]]) if type(frac_strength_treatment) in [int, list, float]: self.frac_strength_treatment = np.array(frac_strength_treatment) if type(frac_strength_outcome) in [int, list, float]: self.frac_strength_outcome = np.array(frac_strength_outcome) # estimate: estimate of regression self.estimate = None # degree_of_freedom: degree of freedom of error in regression self.degree_of_freedom = None # standard_error: standard error in regression self.standard_error = None # t_stats: Treatment coefficient t-value - measures how many standard errors the estimate is away from zero. self.t_stats = None # partial_f2: value to determine if a regression model and a nested version of it have a statistically significant difference between them self.partial_f2 = None # r2tu_w: partial R^2 of unobserved confounder "u" with treatment "t", after conditioning on observed covariates "w" self.r2tu_w = None # r2yu_tw: partial R^2 of unobserved confounder "u" with outcome "y", after conditioning on observed covariates "w" and treatment "t" self.r2yu_tw = None # r2twj_w: partial R^2 of observed covariate wj with treatment "t", after conditioning on observed covariates "w" excluding wj self.r2twj_w = None # r2ywj_tw: partial R^2 of observed covariate wj with outcome "y", after conditioning on observed covariates "w" (excluding wj) and treatment "t" self.r2ywj_tw = None # benchmarking_results: dataframe containing information about bounds and bias adjusted terms self.benchmarking_results = None # stats: dictionary containing information like robustness value, partial R^2, estimate, standard error , degree of freedom, partial f^2, t-statistic self.stats = None self.logger = logging.getLogger(__name__) def treatment_regression(self): """ Function to perform regression with treatment as outcome :returns: new OLS regression model """ features = self.estimator._observed_common_causes.copy() treatment_df = self.estimator._treatment.copy() features = sm.tools.add_constant(features) features.rename(columns=self.common_causes_map, inplace=True) model = sm.OLS(treatment_df, features) estimator_model = model.fit() return estimator_model def partial_r2_func(self, estimator_model=None, treatment=None): """ Computes the partial R^2 of regression model :param estimator_model: Linear regression model :param treatment: treatment name :returns: partial R^2 value """ estimate = estimator_model.params[treatment] degree_of_freedom = int(estimator_model.df_resid) if np.isscalar(estimate): # for single covariate t_stats = estimator_model.tvalues[treatment] return t_stats**2 / (t_stats**2 + degree_of_freedom) else: # compute for a group of covariates covariance_matrix = estimator_model.cov_params().loc[treatment, :][treatment] n = len(estimate) # number of parameters in model f_stat = ( np.matmul(np.matmul(estimate.values.T, np.linalg.inv(covariance_matrix.values)), estimate.values) / n ) return f_stat * n / (f_stat * n + degree_of_freedom) def robustness_value_func(self, alpha=1.0): """ Function to calculate the robustness value. It is the minimum strength of association that confounders must have with treatment and outcome to change conclusions. Robustness value describes how strong the association must be in order to reduce the estimated effect by (100 * percent_change_estimate)%. Robustness value close to 1 means the treatment effect can handle strong confounders explaining almost all residual variation of the treatment and the outcome. Robustness value close to 0 means that even very weak confounders can also change the results. :param alpha: confidence interval (default = 1) :returns: robustness value """ partial_cohen_f = abs( self.t_stats / np.sqrt(self.degree_of_freedom) ) # partial f of treatment t with outcome y. f = t_val/sqrt(dof) f_q = self.percent_change_estimate * partial_cohen_f t_alpha_df_1 = t.ppf( alpha / 2, self.degree_of_freedom - 1 ) # t-value threshold with alpha significance level and dof-1 degrees of freedom f_critical = abs(t_alpha_df_1) / np.sqrt(self.degree_of_freedom - 1) f_adjusted = f_q - f_critical if f_adjusted < 0: r_value = 0 else: r_value = 0.5 * (np.sqrt(f_adjusted**4 + (4 * f_adjusted**2)) - f_adjusted**2) if f_adjusted > 0 and f_q > 1 / f_critical: r_value = (f_q**2 - f_critical**2) / (1 + f_q**2) return r_value def compute_bias_adjusted(self, r2tu_w, r2yu_tw): """ Computes the bias adjusted estimate, standard error, t-value, partial R2, confidence intervals :param r2tu_w: partial r^2 from regressing unobserved confounder u on treatment t after conditioning on observed covariates w :param r2yu_tw: partial r^2 from regressing unobserved confounder u on outcome y after conditioning on observed covariates w and treatment t :returns: Python dictionary with information about partial R^2 of confounders with treatment and outcome and bias adjusted variables """ bias_factor = np.sqrt((r2yu_tw * r2tu_w) / (1 - r2tu_w)) bias = bias_factor * (self.standard_error * np.sqrt(self.degree_of_freedom)) if self.confounder_increases_estimate: bias_adjusted_estimate = np.sign(self.estimate) * (abs(self.estimate) - bias) else: bias_adjusted_estimate = np.sign(self.estimate) * (abs(self.estimate) + bias) bias_adjusted_se = ( np.sqrt((1 - r2yu_tw) / (1 - r2tu_w)) * self.standard_error * np.sqrt(self.degree_of_freedom / (self.degree_of_freedom - 1)) ) bias_adjusted_t = (bias_adjusted_estimate - self.null_hypothesis_effect) / bias_adjusted_se bias_adjusted_partial_r2 = bias_adjusted_t**2 / ( bias_adjusted_t**2 + (self.degree_of_freedom - 1) ) # partial r2 formula used with new t value and dof - 1 num_se = t.ppf( self.significance_level / 2, self.degree_of_freedom ) # Number of standard errors within Confidence Interval bias_adjusted_upper_CI = bias_adjusted_estimate - num_se * bias_adjusted_se bias_adjusted_lower_CI = bias_adjusted_estimate + num_se * bias_adjusted_se benchmarking_results = { "r2tu_w": r2tu_w, "r2yu_tw": r2yu_tw, "bias_adjusted_estimate": bias_adjusted_estimate, "bias_adjusted_se": bias_adjusted_se, "bias_adjusted_t": bias_adjusted_t, "bias_adjusted_lower_CI": bias_adjusted_lower_CI, "bias_adjusted_upper_CI": bias_adjusted_upper_CI, } return benchmarking_results def check_sensitivity(self, plot=True): """ Function to perform sensitivity analysis. :param plot: plot = True generates a plot of point estimate and the variations with respect to unobserved confounding. plot = False overrides the setting :returns: instance of LinearSensitivityAnalyzer class """ self.standard_error = np.array(self.estimator_model.bse[1 : (len(self.treatment_name) + 1)])[0] self.degree_of_freedom = int(self.estimator_model.df_resid) self.estimate = np.array(self.estimator_model.params[1 : (len(self.treatment_name) + 1)])[0] self.t_stats = np.array(self.estimator_model.tvalues[self.treatment_name])[0] # partial R^2 (r2yt_w) is the proportion of variation in outcome uniquely explained by treatment partial_r2 = self.partial_r2_func(self.estimator_model, self.treatment_name) RVq = self.robustness_value_func() RV_qalpha = self.robustness_value_func(alpha=self.significance_level) if self.confounder_increases_estimate: self.null_hypothesis_effect = self.estimate * (1 - self.percent_change_estimate) else: self.null_hypothesis_effect = self.estimate * (1 + self.percent_change_estimate) self.t_stats = (self.estimate - self.null_hypothesis_effect) / self.standard_error self.partial_f2 = self.t_stats**2 / self.degree_of_freedom # build a new regression model by considering treatment variables as outcome treatment_linear_model = self.treatment_regression() # r2twj_w is partial R^2 of covariate wj with treatment "t", after conditioning on covariates w(excluding wj) # r2ywj_tw is partial R^2 of covariate wj with outcome "y", after conditioning on covariates w(excluding wj) and treatment "t" self.r2twj_w = [] self.r2ywj_tw = [] for covariate in self.benchmark_common_causes: self.r2ywj_tw.append(self.partial_r2_func(self.estimator_model, covariate)) self.r2twj_w.append(self.partial_r2_func(treatment_linear_model, covariate)) for i in range(len(self.benchmark_common_causes)): r2twj_w = self.r2twj_w[i] r2ywj_tw = self.r2ywj_tw[i] # r2tu_w is the partial r^2 from regressing u on t after conditioning on w self.r2tu_w = self.frac_strength_treatment * (r2twj_w / (1 - r2twj_w)) if any(val >= 1 for val in self.r2tu_w): raise ValueError("r2tu_w can not be >= 1. Try a lower frac_strength_treatment value") r2uwj_wt = ( self.frac_strength_treatment * (r2twj_w**2) / ((1 - self.frac_strength_treatment * r2twj_w) * (1 - r2twj_w)) ) if any(val >= 1 for val in r2uwj_wt): raise ValueError("r2uwj_wt can not be >= 1. Try a lower frac_strength_treatment value") self.r2yu_tw = ((np.sqrt(self.frac_strength_outcome) + np.sqrt(r2uwj_wt)) / np.sqrt(1 - r2uwj_wt)) ** 2 * ( r2ywj_tw / (1 - r2ywj_tw) ) if any(val > 1 for val in self.r2yu_tw): for i in range(len(self.r2yu_tw)): if self.r2yu_tw[i] > 1: self.r2yu_tw[i] = 1 self.logger.warning( "Warning: r2yu_tw can not be > 1. Try a lower frac_strength_treatment. Setting r2yu_tw to 1" ) # Compute bias adjusted terms self.benchmarking_results = self.compute_bias_adjusted(self.r2tu_w, self.r2yu_tw) if plot == True: self.plot() self.stats = { "estimate": self.estimate, "standard_error": self.standard_error, "degree of freedom": self.degree_of_freedom, "t_statistic": self.t_stats, "r2yt_w": partial_r2, "partial_f2": self.partial_f2, "robustness_value": RVq, "robustness_value_alpha": RV_qalpha, } self.benchmarking_results = pd.DataFrame.from_dict(self.benchmarking_results) return self def plot_estimate(self, r2tu_w, r2yu_tw): """ Computes the contours, threshold line and bounds for plotting estimates. Contour lines (z - axis) correspond to the adjusted estimate values for different values of r2tu_w (x) and r2yu_tw (y). :param r2tu_w: hypothetical partial R^2 of confounder with treatment(x - axis) :param r2yu_tw: hypothetical partial R^2 of confounder with outcome(y - axis) :returns: contour_values : values of contour lines for the plot critical_estimate : threshold point estimate_bounds : estimate values for unobserved confounders (bias adjusted estimates) """ critical_estimate = self.null_hypothesis_effect contour_values = np.zeros((len(r2yu_tw), len(r2tu_w))) for i in range(len(r2yu_tw)): y = r2tu_w[i] for j in range(len(r2tu_w)): x = r2yu_tw[j] benchmarking_results = self.compute_bias_adjusted(r2tu_w=x, r2yu_tw=y) estimate = benchmarking_results["bias_adjusted_estimate"] contour_values[i][j] = estimate estimate_bounds = self.benchmarking_results["bias_adjusted_estimate"] return contour_values, critical_estimate, estimate_bounds def plot_t(self, r2tu_w, r2yu_tw): """ Computes the contours, threshold line and bounds for plotting t. Contour lines (z - axis) correspond to the adjusted t values for different values of r2tu_w (x) and r2yu_tw (y). :param r2tu_w: hypothetical partial R^2 of confounder with treatment(x - axis) :param r2yu_tw: hypothetical partial R^2 of confounder with outcome(y - axis) :returns: contour_values : values of contour lines for the plot critical_t : threshold point t_bounds : t-value for unobserved confounders (bias adjusted t values) """ t_alpha_df_1 = t.ppf( self.significance_level / 2, self.degree_of_freedom - 1 ) # t-value threshold with alpha significance level and dof-1 degrees of freedom critical_t = abs(t_alpha_df_1) * np.sign(self.t_stats) contour_values = [] for x in r2tu_w: contour = [] for y in r2yu_tw: benchmarking_results = self.compute_bias_adjusted(r2tu_w=x, r2yu_tw=y) t_value = benchmarking_results["bias_adjusted_t"] contour.append(t_value) contour_values.append(contour) t_bounds = self.benchmarking_results["bias_adjusted_t"] return contour_values, critical_t, t_bounds def plot( self, plot_type="estimate", critical_value=None, x_limit=0.8, y_limit=0.8, num_points_per_contour=200, plot_size=(7, 7), contours_color="blue", critical_contour_color="red", label_fontsize=9, contour_linewidths=0.75, contour_linestyles="solid", contours_label_color="black", critical_label_color="red", unadjusted_estimate_marker="D", unadjusted_estimate_color="black", adjusted_estimate_marker="^", adjusted_estimate_color="red", legend_position=(1.6, 0.6), ): """ Plots and summarizes the sensitivity bounds as a contour plot, as they vary with the partial R^2 of the unobserved confounder(s) with the treatment and the outcome Two types of plots can be generated, based on adjusted estimates or adjusted t-values X-axis: Partial R^2 of treatment and unobserved confounder(s) Y-axis: Partial R^2 of outcome and unobserved confounder(s) We also plot bounds on the partial R^2 of the unobserved confounders obtained from observed covariates :param plot_type: "estimate" or "t-value" :param critical_value: special reference value of the estimate or t-value that will be highlighted in the plot :param x_limit: plot's maximum x_axis value (default = 0.8) :param y_limit: plot's minimum y_axis value (default = 0.8) :param num_points_per_contour: number of points to calculate and plot each contour line (default = 200) :param plot_size: tuple denoting the size of the plot (default = (7,7)) :param contours_color: color of contour line (default = blue) String or array. If array, lines will be plotted with the specific color in ascending order. :param critical_contour_color: color of threshold line (default = red) :param label_fontsize: fontsize for labelling contours (default = 9) :param contour_linewidths: linewidths for contours (default = 0.75) :param contour_linestyles: linestyles for contours (default = "solid") See : https://matplotlib.org/3.5.0/gallery/lines_bars_and_markers/linestyles.html for more examples :param contours_label_color: color of contour line label (default = black) :param critical_label_color: color of threshold line label (default = red) :param unadjusted_estimate_marker: marker type for unadjusted estimate in the plot (default = 'D') See: https://matplotlib.org/stable/api/markers_api.html :parm unadjusted_estimate_color: marker color for unadjusted estimate in the plot (default = "black") :param adjusted_estimate_marker: marker type for bias adjusted estimates in the plot (default = '^') :parm adjusted_estimate_color: marker color for bias adjusted estimates in the plot (default = "red") :param legend_position:tuple denoting the position of the legend (default = (1.6, 0.6)) """ # Plotting the contour plot if plot_type == "estimate": critical_value = 0 # default value of estimate else: critical_value = 2 # default t-value (usual approx for 95% CI) fig, ax = plt.subplots(1, 1, figsize=plot_size) ax.set_title("Sensitivity contour plot of %s" % plot_type) ax.set_xlabel("Partial R^2 of confounder with treatment") ax.set_ylabel("Partial R^2 of confounder with outcome") for i in range(len(self.r2tu_w)): x = self.r2tu_w[i] y = self.r2yu_tw[i] if x > 0.8 or y > 0.8: x_limit = 0.99 y_limit = 0.99 break r2tu_w = np.arange(0.0, x_limit, x_limit / num_points_per_contour) r2yu_tw = np.arange(0.0, y_limit, y_limit / num_points_per_contour) unadjusted_point_estimate = None if plot_type == "estimate": contour_values, critical_value, bound_values = self.plot_estimate(r2tu_w, r2yu_tw) unadjusted_estimate = self.estimate unadjusted_point_estimate = unadjusted_estimate elif plot_type == "t-value": contour_values, critical_value, bound_values = self.plot_t(r2tu_w, r2yu_tw) unadjusted_t = self.t_stats unadjusted_point_estimate = unadjusted_t else: raise ValueError("Current plotting method only supports 'estimate' and 't-value' ") # Adding contours contour_plot = ax.contour( r2tu_w, r2yu_tw, contour_values, colors=contours_color, linewidths=contour_linewidths, linestyles=contour_linestyles, ) ax.clabel(contour_plot, inline=1, fontsize=label_fontsize, colors=contours_label_color) # Adding threshold contour line contour_plot = ax.contour( r2tu_w, r2yu_tw, contour_values, colors=critical_contour_color, linewidths=contour_linewidths, levels=[critical_value], ) ax.clabel(contour_plot, [critical_value], inline=1, fontsize=label_fontsize, colors=critical_label_color) # Adding unadjusted point estimate ax.scatter( [0], [0], marker=unadjusted_estimate_marker, color=unadjusted_estimate_color, label="Unadjusted({:1.2f})".format(unadjusted_point_estimate), ) # Adding bounds to partial R^2 values for given strength of confounders for i in range(len(self.frac_strength_treatment)): frac_strength_treatment = self.frac_strength_treatment[i] frac_strength_outcome = self.frac_strength_outcome[i] if frac_strength_treatment == frac_strength_outcome: signs = str(round(frac_strength_treatment, 2)) else: signs = str(round(frac_strength_treatment, 2)) + "/" + str(round(frac_strength_outcome, 2)) label = ( str(i + 1) + " " + signs + " X " + str(self.original_benchmark_covariates) + " ({:1.2f}) ".format(bound_values[i]) ) ax.scatter( self.r2tu_w[i], self.r2yu_tw[i], color=adjusted_estimate_color, marker=adjusted_estimate_marker, label=label, ) ax.annotate(str(i + 1), (self.r2tu_w[i] + 0.005, self.r2yu_tw[i] + 0.005)) ax.legend(bbox_to_anchor=legend_position) plt.show() def __str__(self): s = "Sensitivity Analysis to Unobserved Confounding using R^2 paramterization\n\n" s += "Unadjusted Estimates of Treatment {0} :\n".format(self.original_treatment_name) s += "Coefficient Estimate : {0}\n".format(self.estimate) s += "Degree of Freedom : {0}\n".format(self.degree_of_freedom) s += "Standard Error : {0}\n".format(self.standard_error) s += "t-value : {0}\n".format(self.t_stats) s += "F^2 value : {0}\n\n".format(self.partial_f2) s += "Sensitivity Statistics : \n" s += "Partial R2 of treatment with outcome : {0}\n".format(self.stats["r2yt_w"]) s += "Robustness Value : {0}\n\n".format(self.stats["robustness_value"]) s += "Interpretation of results :\n" s += "Any confounder explaining less than {0}% percent of the residual variance of both the treatment and the outcome would not be strong enough to explain away the observed effect i.e bring down the estimate to 0 \n\n".format( round(self.stats["robustness_value"] * 100, 2) ) s += "For a significance level of {0}%, any confounder explaining more than {1}% percent of the residual variance of both the treatment and the outcome would be strong enough to make the estimated effect not 'statistically significant'\n\n".format( self.significance_level * 100, round(self.stats["robustness_value_alpha"] * 100, 2) ) s += "If confounders explained 100% of the residual variance of the outcome, they would need to explain at least {0}% of the residual variance of the treatment to bring down the estimated effect to 0\n".format( round(self.stats["r2yt_w"] * 100, 2) ) return s

import logging import sys import matplotlib.pyplot as plt import numpy as np import pandas as pd import statsmodels.api as sm from scipy.stats import t from dowhy.utils.api import parse_state class LinearSensitivityAnalyzer: """ Class to perform sensitivity analysis See: https://carloscinelli.com/files/Cinelli%20and%20Hazlett%20(2020)%20-%20Making%20Sense%20of%20Sensitivity.pdf :param estimator: linear estimator of the causal model :param data: Pandas dataframe :param treatment_name: name of treatment :param percent_change_estimate: It is the percentage of reduction of treatment estimate that could alter the results (default = 1) if percent_change_estimate = 1, the robustness value describes the strength of association of confounders with treatment and outcome in order to reduce the estimate by 100% i.e bring it down to 0. :param null_hypothesis_effect: assumed effect under the null hypothesis :param confounder_increases_estimate: True implies that confounder increases the absolute value of estimate and vice versa. (Default = True) :param benchmark_common_causes: names of variables for bounding strength of confounders :param significance_level: confidence interval for statistical inference(default = 0.05) :param frac_strength_treatment: strength of association between unobserved confounder and treatment compared to benchmark covariate :param frac_strength_outcome: strength of association between unobserved confounder and outcome compared to benchmark covariate :param common_causes_order: The order of column names in OLS regression data """ def __init__( self, estimator=None, data=None, treatment_name=None, percent_change_estimate=1.0, significance_level=0.05, confounder_increases_estimate=True, benchmark_common_causes=None, null_hypothesis_effect=0, frac_strength_treatment=None, frac_strength_outcome=None, common_causes_order=None, ): self.data = data self.treatment_name = [] # original_treatment_name: : stores original variable names for labelling self.original_treatment_name = treatment_name for t in range(len(treatment_name)): self.treatment_name.append("x" + str(t + 1)) self.percent_change_estimate = percent_change_estimate self.significance_level = significance_level self.confounder_increases_estimate = confounder_increases_estimate self.estimator = estimator self.estimator_model = estimator.model self.null_hypothesis_effect = null_hypothesis_effect # common_causes_map : maps the original variable names to variable names in OLS regression self.common_causes_map = {} for i in range(len(common_causes_order)): self.common_causes_map[common_causes_order[i]] = "x" + str(len(self.treatment_name) + i + 1) # benchmark_common_causes: stores variable names in terms of regression model variables benchmark_common_causes = parse_state(benchmark_common_causes) self.benchmark_common_causes = [] # original_benchmark_covariates: stores original variable names for labelling self.original_benchmark_covariates = benchmark_common_causes for i in range(len(benchmark_common_causes)): self.benchmark_common_causes.append(self.common_causes_map[benchmark_common_causes[i]]) if type(frac_strength_treatment) in [int, list, float]: self.frac_strength_treatment = np.array(frac_strength_treatment) if type(frac_strength_outcome) in [int, list, float]: self.frac_strength_outcome = np.array(frac_strength_outcome) # estimate: estimate of regression self.estimate = None # degree_of_freedom: degree of freedom of error in regression self.degree_of_freedom = None # standard_error: standard error in regression self.standard_error = None # t_stats: Treatment coefficient t-value - measures how many standard errors the estimate is away from zero. self.t_stats = None # partial_f2: value to determine if a regression model and a nested version of it have a statistically significant difference between them self.partial_f2 = None # r2tu_w: partial R^2 of unobserved confounder "u" with treatment "t", after conditioning on observed covariates "w" self.r2tu_w = None # r2yu_tw: partial R^2 of unobserved confounder "u" with outcome "y", after conditioning on observed covariates "w" and treatment "t" self.r2yu_tw = None # r2twj_w: partial R^2 of observed covariate wj with treatment "t", after conditioning on observed covariates "w" excluding wj self.r2twj_w = None # r2ywj_tw: partial R^2 of observed covariate wj with outcome "y", after conditioning on observed covariates "w" (excluding wj) and treatment "t" self.r2ywj_tw = None # benchmarking_results: dataframe containing information about bounds and bias adjusted terms self.benchmarking_results = None # stats: dictionary containing information like robustness value, partial R^2, estimate, standard error , degree of freedom, partial f^2, t-statistic self.stats = None self.logger = logging.getLogger(__name__) def treatment_regression(self): """ Function to perform regression with treatment as outcome :returns: new OLS regression model """ features = self.estimator._observed_common_causes.copy() treatment_df = self.estimator._treatment.copy() features = sm.tools.add_constant(features) features.rename(columns=self.common_causes_map, inplace=True) model = sm.OLS(treatment_df, features) estimator_model = model.fit() return estimator_model def partial_r2_func(self, estimator_model=None, treatment=None): """ Computes the partial R^2 of regression model :param estimator_model: Linear regression model :param treatment: treatment name :returns: partial R^2 value """ estimate = estimator_model.params[treatment] degree_of_freedom = int(estimator_model.df_resid) if np.isscalar(estimate): # for single covariate t_stats = estimator_model.tvalues[treatment] return t_stats**2 / (t_stats**2 + degree_of_freedom) else: # compute for a group of covariates covariance_matrix = estimator_model.cov_params().loc[treatment, :][treatment] n = len(estimate) # number of parameters in model f_stat = ( np.matmul(np.matmul(estimate.values.T, np.linalg.inv(covariance_matrix.values)), estimate.values) / n ) return f_stat * n / (f_stat * n + degree_of_freedom) def robustness_value_func(self, alpha=1.0): """ Function to calculate the robustness value. It is the minimum strength of association that confounders must have with treatment and outcome to change conclusions. Robustness value describes how strong the association must be in order to reduce the estimated effect by (100 * percent_change_estimate)%. Robustness value close to 1 means the treatment effect can handle strong confounders explaining almost all residual variation of the treatment and the outcome. Robustness value close to 0 means that even very weak confounders can also change the results. :param alpha: confidence interval (default = 1) :returns: robustness value """ partial_cohen_f = abs( self.t_stats / np.sqrt(self.degree_of_freedom) ) # partial f of treatment t with outcome y. f = t_val/sqrt(dof) f_q = self.percent_change_estimate * partial_cohen_f t_alpha_df_1 = t.ppf( alpha / 2, self.degree_of_freedom - 1 ) # t-value threshold with alpha significance level and dof-1 degrees of freedom f_critical = abs(t_alpha_df_1) / np.sqrt(self.degree_of_freedom - 1) f_adjusted = f_q - f_critical if f_adjusted < 0: r_value = 0 else: r_value = 0.5 * (np.sqrt(f_adjusted**4 + (4 * f_adjusted**2)) - f_adjusted**2) if f_adjusted > 0 and f_q > 1 / f_critical: r_value = (f_q**2 - f_critical**2) / (1 + f_q**2) return r_value def compute_bias_adjusted(self, r2tu_w, r2yu_tw): """ Computes the bias adjusted estimate, standard error, t-value, partial R2, confidence intervals :param r2tu_w: partial r^2 from regressing unobserved confounder u on treatment t after conditioning on observed covariates w :param r2yu_tw: partial r^2 from regressing unobserved confounder u on outcome y after conditioning on observed covariates w and treatment t :returns: Python dictionary with information about partial R^2 of confounders with treatment and outcome and bias adjusted variables """ bias_factor = np.sqrt((r2yu_tw * r2tu_w) / (1 - r2tu_w)) bias = bias_factor * (self.standard_error * np.sqrt(self.degree_of_freedom)) if self.confounder_increases_estimate: bias_adjusted_estimate = np.sign(self.estimate) * (abs(self.estimate) - bias) else: bias_adjusted_estimate = np.sign(self.estimate) * (abs(self.estimate) + bias) bias_adjusted_se = ( np.sqrt((1 - r2yu_tw) / (1 - r2tu_w)) * self.standard_error * np.sqrt(self.degree_of_freedom / (self.degree_of_freedom - 1)) ) bias_adjusted_t = (bias_adjusted_estimate - self.null_hypothesis_effect) / bias_adjusted_se bias_adjusted_partial_r2 = bias_adjusted_t**2 / ( bias_adjusted_t**2 + (self.degree_of_freedom - 1) ) # partial r2 formula used with new t value and dof - 1 num_se = t.ppf( self.significance_level / 2, self.degree_of_freedom ) # Number of standard errors within Confidence Interval bias_adjusted_upper_CI = bias_adjusted_estimate - num_se * bias_adjusted_se bias_adjusted_lower_CI = bias_adjusted_estimate + num_se * bias_adjusted_se benchmarking_results = { "r2tu_w": r2tu_w, "r2yu_tw": r2yu_tw, "bias_adjusted_estimate": bias_adjusted_estimate, "bias_adjusted_se": bias_adjusted_se, "bias_adjusted_t": bias_adjusted_t, "bias_adjusted_lower_CI": bias_adjusted_lower_CI, "bias_adjusted_upper_CI": bias_adjusted_upper_CI, } return benchmarking_results def check_sensitivity(self, plot=True): """ Function to perform sensitivity analysis. :param plot: plot = True generates a plot of point estimate and the variations with respect to unobserved confounding. plot = False overrides the setting :returns: instance of LinearSensitivityAnalyzer class """ self.standard_error = np.array(self.estimator_model.bse[1 : (len(self.treatment_name) + 1)])[0] self.degree_of_freedom = int(self.estimator_model.df_resid) self.estimate = np.array(self.estimator_model.params[1 : (len(self.treatment_name) + 1)])[0] self.t_stats = np.array(self.estimator_model.tvalues[self.treatment_name])[0] # partial R^2 (r2yt_w) is the proportion of variation in outcome uniquely explained by treatment partial_r2 = self.partial_r2_func(self.estimator_model, self.treatment_name) RVq = self.robustness_value_func() RV_qalpha = self.robustness_value_func(alpha=self.significance_level) if self.confounder_increases_estimate: self.null_hypothesis_effect = self.estimate * (1 - self.percent_change_estimate) else: self.null_hypothesis_effect = self.estimate * (1 + self.percent_change_estimate) self.t_stats = (self.estimate - self.null_hypothesis_effect) / self.standard_error self.partial_f2 = self.t_stats**2 / self.degree_of_freedom # build a new regression model by considering treatment variables as outcome treatment_linear_model = self.treatment_regression() # r2twj_w is partial R^2 of covariate wj with treatment "t", after conditioning on covariates w(excluding wj) # r2ywj_tw is partial R^2 of covariate wj with outcome "y", after conditioning on covariates w(excluding wj) and treatment "t" self.r2twj_w = [] self.r2ywj_tw = [] for covariate in self.benchmark_common_causes: self.r2ywj_tw.append(self.partial_r2_func(self.estimator_model, covariate)) self.r2twj_w.append(self.partial_r2_func(treatment_linear_model, covariate)) for i in range(len(self.benchmark_common_causes)): r2twj_w = self.r2twj_w[i] r2ywj_tw = self.r2ywj_tw[i] # r2tu_w is the partial r^2 from regressing u on t after conditioning on w self.r2tu_w = self.frac_strength_treatment * (r2twj_w / (1 - r2twj_w)) if any(val >= 1 for val in self.r2tu_w): raise ValueError("r2tu_w can not be >= 1. Try a lower frac_strength_treatment value") r2uwj_wt = ( self.frac_strength_treatment * (r2twj_w**2) / ((1 - self.frac_strength_treatment * r2twj_w) * (1 - r2twj_w)) ) if any(val >= 1 for val in r2uwj_wt): raise ValueError("r2uwj_wt can not be >= 1. Try a lower frac_strength_treatment value") self.r2yu_tw = ((np.sqrt(self.frac_strength_outcome) + np.sqrt(r2uwj_wt)) / np.sqrt(1 - r2uwj_wt)) ** 2 * ( r2ywj_tw / (1 - r2ywj_tw) ) if any(val > 1 for val in self.r2yu_tw): for i in range(len(self.r2yu_tw)): if self.r2yu_tw[i] > 1: self.r2yu_tw[i] = 1 self.logger.warning( "Warning: r2yu_tw can not be > 1. Try a lower frac_strength_treatment. Setting r2yu_tw to 1" ) # Compute bias adjusted terms self.benchmarking_results = self.compute_bias_adjusted(self.r2tu_w, self.r2yu_tw) if plot == True: self.plot() self.stats = { "estimate": self.estimate, "standard_error": self.standard_error, "degree of freedom": self.degree_of_freedom, "t_statistic": self.t_stats, "r2yt_w": partial_r2, "partial_f2": self.partial_f2, "robustness_value": RVq, "robustness_value_alpha": RV_qalpha, } self.benchmarking_results = pd.DataFrame.from_dict(self.benchmarking_results) return self def plot_estimate(self, r2tu_w, r2yu_tw): """ Computes the contours, threshold line and bounds for plotting estimates. Contour lines (z - axis) correspond to the adjusted estimate values for different values of r2tu_w (x) and r2yu_tw (y). :param r2tu_w: hypothetical partial R^2 of confounder with treatment(x - axis) :param r2yu_tw: hypothetical partial R^2 of confounder with outcome(y - axis) :returns: contour_values : values of contour lines for the plot critical_estimate : threshold point estimate_bounds : estimate values for unobserved confounders (bias adjusted estimates) """ critical_estimate = self.null_hypothesis_effect contour_values = np.zeros((len(r2yu_tw), len(r2tu_w))) for i in range(len(r2yu_tw)): y = r2yu_tw[i] for j in range(len(r2tu_w)): x = r2tu_w[j] benchmarking_results = self.compute_bias_adjusted(r2tu_w=x, r2yu_tw=y) estimate = benchmarking_results["bias_adjusted_estimate"] contour_values[i][j] = estimate estimate_bounds = self.benchmarking_results["bias_adjusted_estimate"] return contour_values, critical_estimate, estimate_bounds def plot_t(self, r2tu_w, r2yu_tw): """ Computes the contours, threshold line and bounds for plotting t. Contour lines (z - axis) correspond to the adjusted t values for different values of r2tu_w (x) and r2yu_tw (y). :param r2tu_w: hypothetical partial R^2 of confounder with treatment(x - axis) :param r2yu_tw: hypothetical partial R^2 of confounder with outcome(y - axis) :returns: contour_values : values of contour lines for the plot critical_t : threshold point t_bounds : t-value for unobserved confounders (bias adjusted t values) """ t_alpha_df_1 = t.ppf( self.significance_level / 2, self.degree_of_freedom - 1 ) # t-value threshold with alpha significance level and dof-1 degrees of freedom critical_t = abs(t_alpha_df_1) * np.sign(self.t_stats) contour_values = [] for x in r2tu_w: contour = [] for y in r2yu_tw: benchmarking_results = self.compute_bias_adjusted(r2tu_w=x, r2yu_tw=y) t_value = benchmarking_results["bias_adjusted_t"] contour.append(t_value) contour_values.append(contour) t_bounds = self.benchmarking_results["bias_adjusted_t"] return contour_values, critical_t, t_bounds def plot( self, plot_type="estimate", critical_value=None, x_limit=0.8, y_limit=0.8, num_points_per_contour=200, plot_size=(7, 7), contours_color="blue", critical_contour_color="red", label_fontsize=9, contour_linewidths=0.75, contour_linestyles="solid", contours_label_color="black", critical_label_color="red", unadjusted_estimate_marker="D", unadjusted_estimate_color="black", adjusted_estimate_marker="^", adjusted_estimate_color="red", legend_position=(1.6, 0.6), ): """ Plots and summarizes the sensitivity bounds as a contour plot, as they vary with the partial R^2 of the unobserved confounder(s) with the treatment and the outcome Two types of plots can be generated, based on adjusted estimates or adjusted t-values X-axis: Partial R^2 of treatment and unobserved confounder(s) Y-axis: Partial R^2 of outcome and unobserved confounder(s) We also plot bounds on the partial R^2 of the unobserved confounders obtained from observed covariates :param plot_type: "estimate" or "t-value" :param critical_value: special reference value of the estimate or t-value that will be highlighted in the plot :param x_limit: plot's maximum x_axis value (default = 0.8) :param y_limit: plot's minimum y_axis value (default = 0.8) :param num_points_per_contour: number of points to calculate and plot each contour line (default = 200) :param plot_size: tuple denoting the size of the plot (default = (7,7)) :param contours_color: color of contour line (default = blue) String or array. If array, lines will be plotted with the specific color in ascending order. :param critical_contour_color: color of threshold line (default = red) :param label_fontsize: fontsize for labelling contours (default = 9) :param contour_linewidths: linewidths for contours (default = 0.75) :param contour_linestyles: linestyles for contours (default = "solid") See : https://matplotlib.org/3.5.0/gallery/lines_bars_and_markers/linestyles.html for more examples :param contours_label_color: color of contour line label (default = black) :param critical_label_color: color of threshold line label (default = red) :param unadjusted_estimate_marker: marker type for unadjusted estimate in the plot (default = 'D') See: https://matplotlib.org/stable/api/markers_api.html :parm unadjusted_estimate_color: marker color for unadjusted estimate in the plot (default = "black") :param adjusted_estimate_marker: marker type for bias adjusted estimates in the plot (default = '^') :parm adjusted_estimate_color: marker color for bias adjusted estimates in the plot (default = "red") :param legend_position:tuple denoting the position of the legend (default = (1.6, 0.6)) """ # Plotting the contour plot if plot_type == "estimate": critical_value = 0 # default value of estimate else: critical_value = 2 # default t-value (usual approx for 95% CI) fig, ax = plt.subplots(1, 1, figsize=plot_size) ax.set_title("Sensitivity contour plot of %s" % plot_type) ax.set_xlabel("Partial R^2 of confounder with treatment") ax.set_ylabel("Partial R^2 of confounder with outcome") for i in range(len(self.r2tu_w)): x = self.r2tu_w[i] y = self.r2yu_tw[i] if x > 0.8 or y > 0.8: x_limit = 0.99 y_limit = 0.99 break r2tu_w = np.arange(0.0, x_limit, x_limit / num_points_per_contour) r2yu_tw = np.arange(0.0, y_limit, y_limit / num_points_per_contour) unadjusted_point_estimate = None if plot_type == "estimate": contour_values, critical_value, bound_values = self.plot_estimate(r2tu_w, r2yu_tw) unadjusted_estimate = self.estimate unadjusted_point_estimate = unadjusted_estimate elif plot_type == "t-value": contour_values, critical_value, bound_values = self.plot_t(r2tu_w, r2yu_tw) unadjusted_t = self.t_stats unadjusted_point_estimate = unadjusted_t else: raise ValueError("Current plotting method only supports 'estimate' and 't-value' ") # Adding contours contour_plot = ax.contour( r2tu_w, r2yu_tw, contour_values, colors=contours_color, linewidths=contour_linewidths, linestyles=contour_linestyles, ) ax.clabel(contour_plot, inline=1, fontsize=label_fontsize, colors=contours_label_color) # Adding threshold contour line contour_plot = ax.contour( r2tu_w, r2yu_tw, contour_values, colors=critical_contour_color, linewidths=contour_linewidths, levels=[critical_value], ) ax.clabel(contour_plot, [critical_value], inline=1, fontsize=label_fontsize, colors=critical_label_color) # Adding unadjusted point estimate ax.scatter( [0], [0], marker=unadjusted_estimate_marker, color=unadjusted_estimate_color, label="Unadjusted({:1.2f})".format(unadjusted_point_estimate), ) # Adding bounds to partial R^2 values for given strength of confounders for i in range(len(self.frac_strength_treatment)): frac_strength_treatment = self.frac_strength_treatment[i] frac_strength_outcome = self.frac_strength_outcome[i] if frac_strength_treatment == frac_strength_outcome: signs = str(round(frac_strength_treatment, 2)) else: signs = str(round(frac_strength_treatment, 2)) + "/" + str(round(frac_strength_outcome, 2)) label = ( str(i + 1) + " " + signs + " X " + str(self.original_benchmark_covariates) + " ({:1.2f}) ".format(bound_values[i]) ) ax.scatter( self.r2tu_w[i], self.r2yu_tw[i], color=adjusted_estimate_color, marker=adjusted_estimate_marker, label=label, ) ax.annotate(str(i + 1), (self.r2tu_w[i] + 0.005, self.r2yu_tw[i] + 0.005)) ax.legend(bbox_to_anchor=legend_position) plt.show() def __str__(self): s = "Sensitivity Analysis to Unobserved Confounding using R^2 paramterization\n\n" s += "Unadjusted Estimates of Treatment {0} :\n".format(self.original_treatment_name) s += "Coefficient Estimate : {0}\n".format(self.estimate) s += "Degree of Freedom : {0}\n".format(self.degree_of_freedom) s += "Standard Error : {0}\n".format(self.standard_error) s += "t-value : {0}\n".format(self.t_stats) s += "F^2 value : {0}\n\n".format(self.partial_f2) s += "Sensitivity Statistics : \n" s += "Partial R2 of treatment with outcome : {0}\n".format(self.stats["r2yt_w"]) s += "Robustness Value : {0}\n\n".format(self.stats["robustness_value"]) s += "Interpretation of results :\n" s += "Any confounder explaining less than {0}% percent of the residual variance of both the treatment and the outcome would not be strong enough to explain away the observed effect i.e bring down the estimate to 0 \n\n".format( round(self.stats["robustness_value"] * 100, 2) ) s += "For a significance level of {0}%, any confounder explaining more than {1}% percent of the residual variance of both the treatment and the outcome would be strong enough to make the estimated effect not 'statistically significant'\n\n".format( self.significance_level * 100, round(self.stats["robustness_value_alpha"] * 100, 2) ) s += "If confounders explained 100% of the residual variance of the outcome, they would need to explain at least {0}% of the residual variance of the treatment to bring down the estimated effect to 0\n".format( round(self.stats["r2yt_w"] * 100, 2) ) return s

anusha0409

81841c697bd5e80ecf9e731432305f6186666f1f

bb446c333f2256074304b0dec9cb5628d284b542

should this be y=r2yu_tw?

amit-sharma

py-why/dowhy

Adding Non Linear Sensitivity Analysis

This PR implements the non-parametric sensitivity analysis from Chernozhukov et al. https://arxiv.org/abs/2112.13398 It implements two sensitivity analyzers: 1. For Partial Linear DGPs and estimators like LinearDML 2. For general non-parametric DGPs and estimators like KernelDML. The notebook in this PR provides an introduction on how the sensitivity bounds are calculated for the partial linear case. For the general nonparametric DGPs, we need to estimate a special function called the Reisz representer. For binary treatment, it is exactly the difference in outcome weighted by propensity score. So we provide two options to learn the Reisz representer, 1) plugin_reisz that uses the propensity score; and 2) general estimator that uses a custom loss function. These two are in the file reisz.py. Briefly, the sensitivity bounds depend on two parameters that denote the effect of the unobserved confounder on treatment and outcome. That's why we use the same API as for the `add_unobserved_common_cause` method and add this sensitivity analysis as a possible simulation method="non-parametric-partial-R2". The format of the plots is identical to those from the "linear-partial-r2" simulation method that is already implemented. We provide two modes for the user. 1) User specifies the effect strength parameters themselves, as a range of values. 2) User benchmarks the effect strength parameters as a multiple of the same parameters for the observed common causes. Signed-off-by: anusha <anushaagarwal2000.com>

2022-06-20 14:37:11+00:00

2022-09-16 03:57:26+00:00

dowhy/causal_refuters/linear_sensitivity_analyzer.py

import logging import sys import matplotlib.pyplot as plt import numpy as np import pandas as pd import statsmodels.api as sm from scipy.stats import t from dowhy.utils.api import parse_state class LinearSensitivityAnalyzer: """ Class to perform sensitivity analysis See: https://carloscinelli.com/files/Cinelli%20and%20Hazlett%20(2020)%20-%20Making%20Sense%20of%20Sensitivity.pdf :param estimator: linear estimator of the causal model :param data: Pandas dataframe :param treatment_name: name of treatment :param percent_change_estimate: It is the percentage of reduction of treatment estimate that could alter the results (default = 1) if percent_change_estimate = 1, the robustness value describes the strength of association of confounders with treatment and outcome in order to reduce the estimate by 100% i.e bring it down to 0. :param null_hypothesis_effect: assumed effect under the null hypothesis :param confounder_increases_estimate: True implies that confounder increases the absolute value of estimate and vice versa. (Default = True) :param benchmark_common_causes: names of variables for bounding strength of confounders :param significance_level: confidence interval for statistical inference(default = 0.05) :param frac_strength_treatment: strength of association between unobserved confounder and treatment compared to benchmark covariate :param frac_strength_outcome: strength of association between unobserved confounder and outcome compared to benchmark covariate :param common_causes_order: The order of column names in OLS regression data """ def __init__( self, estimator=None, data=None, treatment_name=None, percent_change_estimate=1.0, significance_level=0.05, confounder_increases_estimate=True, benchmark_common_causes=None, null_hypothesis_effect=0, frac_strength_treatment=None, frac_strength_outcome=None, common_causes_order=None, ): self.data = data self.treatment_name = [] # original_treatment_name: : stores original variable names for labelling self.original_treatment_name = treatment_name for t in range(len(treatment_name)): self.treatment_name.append("x" + str(t + 1)) self.percent_change_estimate = percent_change_estimate self.significance_level = significance_level self.confounder_increases_estimate = confounder_increases_estimate self.estimator = estimator self.estimator_model = estimator.model self.null_hypothesis_effect = null_hypothesis_effect # common_causes_map : maps the original variable names to variable names in OLS regression self.common_causes_map = {} for i in range(len(common_causes_order)): self.common_causes_map[common_causes_order[i]] = "x" + str(len(self.treatment_name) + i + 1) # benchmark_common_causes: stores variable names in terms of regression model variables benchmark_common_causes = parse_state(benchmark_common_causes) self.benchmark_common_causes = [] # original_benchmark_covariates: stores original variable names for labelling self.original_benchmark_covariates = benchmark_common_causes for i in range(len(benchmark_common_causes)): self.benchmark_common_causes.append(self.common_causes_map[benchmark_common_causes[i]]) if type(frac_strength_treatment) in [int, list, float]: self.frac_strength_treatment = np.array(frac_strength_treatment) if type(frac_strength_outcome) in [int, list, float]: self.frac_strength_outcome = np.array(frac_strength_outcome) # estimate: estimate of regression self.estimate = None # degree_of_freedom: degree of freedom of error in regression self.degree_of_freedom = None # standard_error: standard error in regression self.standard_error = None # t_stats: Treatment coefficient t-value - measures how many standard errors the estimate is away from zero. self.t_stats = None # partial_f2: value to determine if a regression model and a nested version of it have a statistically significant difference between them self.partial_f2 = None # r2tu_w: partial R^2 of unobserved confounder "u" with treatment "t", after conditioning on observed covariates "w" self.r2tu_w = None # r2yu_tw: partial R^2 of unobserved confounder "u" with outcome "y", after conditioning on observed covariates "w" and treatment "t" self.r2yu_tw = None # r2twj_w: partial R^2 of observed covariate wj with treatment "t", after conditioning on observed covariates "w" excluding wj self.r2twj_w = None # r2ywj_tw: partial R^2 of observed covariate wj with outcome "y", after conditioning on observed covariates "w" (excluding wj) and treatment "t" self.r2ywj_tw = None # benchmarking_results: dataframe containing information about bounds and bias adjusted terms self.benchmarking_results = None # stats: dictionary containing information like robustness value, partial R^2, estimate, standard error , degree of freedom, partial f^2, t-statistic self.stats = None self.logger = logging.getLogger(__name__) def treatment_regression(self): """ Function to perform regression with treatment as outcome :returns: new OLS regression model """ features = self.estimator._observed_common_causes.copy() treatment_df = self.estimator._treatment.copy() features = sm.tools.add_constant(features) features.rename(columns=self.common_causes_map, inplace=True) model = sm.OLS(treatment_df, features) estimator_model = model.fit() return estimator_model def partial_r2_func(self, estimator_model=None, treatment=None): """ Computes the partial R^2 of regression model :param estimator_model: Linear regression model :param treatment: treatment name :returns: partial R^2 value """ estimate = estimator_model.params[treatment] degree_of_freedom = int(estimator_model.df_resid) if np.isscalar(estimate): # for single covariate t_stats = estimator_model.tvalues[treatment] return t_stats**2 / (t_stats**2 + degree_of_freedom) else: # compute for a group of covariates covariance_matrix = estimator_model.cov_params().loc[treatment, :][treatment] n = len(estimate) # number of parameters in model f_stat = ( np.matmul(np.matmul(estimate.values.T, np.linalg.inv(covariance_matrix.values)), estimate.values) / n ) return f_stat * n / (f_stat * n + degree_of_freedom) def robustness_value_func(self, alpha=1.0): """ Function to calculate the robustness value. It is the minimum strength of association that confounders must have with treatment and outcome to change conclusions. Robustness value describes how strong the association must be in order to reduce the estimated effect by (100 * percent_change_estimate)%. Robustness value close to 1 means the treatment effect can handle strong confounders explaining almost all residual variation of the treatment and the outcome. Robustness value close to 0 means that even very weak confounders can also change the results. :param alpha: confidence interval (default = 1) :returns: robustness value """ partial_cohen_f = abs( self.t_stats / np.sqrt(self.degree_of_freedom) ) # partial f of treatment t with outcome y. f = t_val/sqrt(dof) f_q = self.percent_change_estimate * partial_cohen_f t_alpha_df_1 = t.ppf( alpha / 2, self.degree_of_freedom - 1 ) # t-value threshold with alpha significance level and dof-1 degrees of freedom f_critical = abs(t_alpha_df_1) / np.sqrt(self.degree_of_freedom - 1) f_adjusted = f_q - f_critical if f_adjusted < 0: r_value = 0 else: r_value = 0.5 * (np.sqrt(f_adjusted**4 + (4 * f_adjusted**2)) - f_adjusted**2) if f_adjusted > 0 and f_q > 1 / f_critical: r_value = (f_q**2 - f_critical**2) / (1 + f_q**2) return r_value def compute_bias_adjusted(self, r2tu_w, r2yu_tw): """ Computes the bias adjusted estimate, standard error, t-value, partial R2, confidence intervals :param r2tu_w: partial r^2 from regressing unobserved confounder u on treatment t after conditioning on observed covariates w :param r2yu_tw: partial r^2 from regressing unobserved confounder u on outcome y after conditioning on observed covariates w and treatment t :returns: Python dictionary with information about partial R^2 of confounders with treatment and outcome and bias adjusted variables """ bias_factor = np.sqrt((r2yu_tw * r2tu_w) / (1 - r2tu_w)) bias = bias_factor * (self.standard_error * np.sqrt(self.degree_of_freedom)) if self.confounder_increases_estimate: bias_adjusted_estimate = np.sign(self.estimate) * (abs(self.estimate) - bias) else: bias_adjusted_estimate = np.sign(self.estimate) * (abs(self.estimate) + bias) bias_adjusted_se = ( np.sqrt((1 - r2yu_tw) / (1 - r2tu_w)) * self.standard_error * np.sqrt(self.degree_of_freedom / (self.degree_of_freedom - 1)) ) bias_adjusted_t = (bias_adjusted_estimate - self.null_hypothesis_effect) / bias_adjusted_se bias_adjusted_partial_r2 = bias_adjusted_t**2 / ( bias_adjusted_t**2 + (self.degree_of_freedom - 1) ) # partial r2 formula used with new t value and dof - 1 num_se = t.ppf( self.significance_level / 2, self.degree_of_freedom ) # Number of standard errors within Confidence Interval bias_adjusted_upper_CI = bias_adjusted_estimate - num_se * bias_adjusted_se bias_adjusted_lower_CI = bias_adjusted_estimate + num_se * bias_adjusted_se benchmarking_results = { "r2tu_w": r2tu_w, "r2yu_tw": r2yu_tw, "bias_adjusted_estimate": bias_adjusted_estimate, "bias_adjusted_se": bias_adjusted_se, "bias_adjusted_t": bias_adjusted_t, "bias_adjusted_lower_CI": bias_adjusted_lower_CI, "bias_adjusted_upper_CI": bias_adjusted_upper_CI, } return benchmarking_results def check_sensitivity(self, plot=True): """ Function to perform sensitivity analysis. :param plot: plot = True generates a plot of point estimate and the variations with respect to unobserved confounding. plot = False overrides the setting :returns: instance of LinearSensitivityAnalyzer class """ self.standard_error = np.array(self.estimator_model.bse[1 : (len(self.treatment_name) + 1)])[0] self.degree_of_freedom = int(self.estimator_model.df_resid) self.estimate = np.array(self.estimator_model.params[1 : (len(self.treatment_name) + 1)])[0] self.t_stats = np.array(self.estimator_model.tvalues[self.treatment_name])[0] # partial R^2 (r2yt_w) is the proportion of variation in outcome uniquely explained by treatment partial_r2 = self.partial_r2_func(self.estimator_model, self.treatment_name) RVq = self.robustness_value_func() RV_qalpha = self.robustness_value_func(alpha=self.significance_level) if self.confounder_increases_estimate: self.null_hypothesis_effect = self.estimate * (1 - self.percent_change_estimate) else: self.null_hypothesis_effect = self.estimate * (1 + self.percent_change_estimate) self.t_stats = (self.estimate - self.null_hypothesis_effect) / self.standard_error self.partial_f2 = self.t_stats**2 / self.degree_of_freedom # build a new regression model by considering treatment variables as outcome treatment_linear_model = self.treatment_regression() # r2twj_w is partial R^2 of covariate wj with treatment "t", after conditioning on covariates w(excluding wj) # r2ywj_tw is partial R^2 of covariate wj with outcome "y", after conditioning on covariates w(excluding wj) and treatment "t" self.r2twj_w = [] self.r2ywj_tw = [] for covariate in self.benchmark_common_causes: self.r2ywj_tw.append(self.partial_r2_func(self.estimator_model, covariate)) self.r2twj_w.append(self.partial_r2_func(treatment_linear_model, covariate)) for i in range(len(self.benchmark_common_causes)): r2twj_w = self.r2twj_w[i] r2ywj_tw = self.r2ywj_tw[i] # r2tu_w is the partial r^2 from regressing u on t after conditioning on w self.r2tu_w = self.frac_strength_treatment * (r2twj_w / (1 - r2twj_w)) if any(val >= 1 for val in self.r2tu_w): raise ValueError("r2tu_w can not be >= 1. Try a lower frac_strength_treatment value") r2uwj_wt = ( self.frac_strength_treatment * (r2twj_w**2) / ((1 - self.frac_strength_treatment * r2twj_w) * (1 - r2twj_w)) ) if any(val >= 1 for val in r2uwj_wt): raise ValueError("r2uwj_wt can not be >= 1. Try a lower frac_strength_treatment value") self.r2yu_tw = ((np.sqrt(self.frac_strength_outcome) + np.sqrt(r2uwj_wt)) / np.sqrt(1 - r2uwj_wt)) ** 2 * ( r2ywj_tw / (1 - r2ywj_tw) ) if any(val > 1 for val in self.r2yu_tw): for i in range(len(self.r2yu_tw)): if self.r2yu_tw[i] > 1: self.r2yu_tw[i] = 1 self.logger.warning( "Warning: r2yu_tw can not be > 1. Try a lower frac_strength_treatment. Setting r2yu_tw to 1" ) # Compute bias adjusted terms self.benchmarking_results = self.compute_bias_adjusted(self.r2tu_w, self.r2yu_tw) if plot == True: self.plot() self.stats = { "estimate": self.estimate, "standard_error": self.standard_error, "degree of freedom": self.degree_of_freedom, "t_statistic": self.t_stats, "r2yt_w": partial_r2, "partial_f2": self.partial_f2, "robustness_value": RVq, "robustness_value_alpha": RV_qalpha, } self.benchmarking_results = pd.DataFrame.from_dict(self.benchmarking_results) return self def plot_estimate(self, r2tu_w, r2yu_tw): """ Computes the contours, threshold line and bounds for plotting estimates. Contour lines (z - axis) correspond to the adjusted estimate values for different values of r2tu_w (x) and r2yu_tw (y). :param r2tu_w: hypothetical partial R^2 of confounder with treatment(x - axis) :param r2yu_tw: hypothetical partial R^2 of confounder with outcome(y - axis) :returns: contour_values : values of contour lines for the plot critical_estimate : threshold point estimate_bounds : estimate values for unobserved confounders (bias adjusted estimates) """ critical_estimate = self.null_hypothesis_effect contour_values = np.zeros((len(r2yu_tw), len(r2tu_w))) for i in range(len(r2yu_tw)): y = r2tu_w[i] for j in range(len(r2tu_w)): x = r2yu_tw[j] benchmarking_results = self.compute_bias_adjusted(r2tu_w=x, r2yu_tw=y) estimate = benchmarking_results["bias_adjusted_estimate"] contour_values[i][j] = estimate estimate_bounds = self.benchmarking_results["bias_adjusted_estimate"] return contour_values, critical_estimate, estimate_bounds def plot_t(self, r2tu_w, r2yu_tw): """ Computes the contours, threshold line and bounds for plotting t. Contour lines (z - axis) correspond to the adjusted t values for different values of r2tu_w (x) and r2yu_tw (y). :param r2tu_w: hypothetical partial R^2 of confounder with treatment(x - axis) :param r2yu_tw: hypothetical partial R^2 of confounder with outcome(y - axis) :returns: contour_values : values of contour lines for the plot critical_t : threshold point t_bounds : t-value for unobserved confounders (bias adjusted t values) """ t_alpha_df_1 = t.ppf( self.significance_level / 2, self.degree_of_freedom - 1 ) # t-value threshold with alpha significance level and dof-1 degrees of freedom critical_t = abs(t_alpha_df_1) * np.sign(self.t_stats) contour_values = [] for x in r2tu_w: contour = [] for y in r2yu_tw: benchmarking_results = self.compute_bias_adjusted(r2tu_w=x, r2yu_tw=y) t_value = benchmarking_results["bias_adjusted_t"] contour.append(t_value) contour_values.append(contour) t_bounds = self.benchmarking_results["bias_adjusted_t"] return contour_values, critical_t, t_bounds def plot( self, plot_type="estimate", critical_value=None, x_limit=0.8, y_limit=0.8, num_points_per_contour=200, plot_size=(7, 7), contours_color="blue", critical_contour_color="red", label_fontsize=9, contour_linewidths=0.75, contour_linestyles="solid", contours_label_color="black", critical_label_color="red", unadjusted_estimate_marker="D", unadjusted_estimate_color="black", adjusted_estimate_marker="^", adjusted_estimate_color="red", legend_position=(1.6, 0.6), ): """ Plots and summarizes the sensitivity bounds as a contour plot, as they vary with the partial R^2 of the unobserved confounder(s) with the treatment and the outcome Two types of plots can be generated, based on adjusted estimates or adjusted t-values X-axis: Partial R^2 of treatment and unobserved confounder(s) Y-axis: Partial R^2 of outcome and unobserved confounder(s) We also plot bounds on the partial R^2 of the unobserved confounders obtained from observed covariates :param plot_type: "estimate" or "t-value" :param critical_value: special reference value of the estimate or t-value that will be highlighted in the plot :param x_limit: plot's maximum x_axis value (default = 0.8) :param y_limit: plot's minimum y_axis value (default = 0.8) :param num_points_per_contour: number of points to calculate and plot each contour line (default = 200) :param plot_size: tuple denoting the size of the plot (default = (7,7)) :param contours_color: color of contour line (default = blue) String or array. If array, lines will be plotted with the specific color in ascending order. :param critical_contour_color: color of threshold line (default = red) :param label_fontsize: fontsize for labelling contours (default = 9) :param contour_linewidths: linewidths for contours (default = 0.75) :param contour_linestyles: linestyles for contours (default = "solid") See : https://matplotlib.org/3.5.0/gallery/lines_bars_and_markers/linestyles.html for more examples :param contours_label_color: color of contour line label (default = black) :param critical_label_color: color of threshold line label (default = red) :param unadjusted_estimate_marker: marker type for unadjusted estimate in the plot (default = 'D') See: https://matplotlib.org/stable/api/markers_api.html :parm unadjusted_estimate_color: marker color for unadjusted estimate in the plot (default = "black") :param adjusted_estimate_marker: marker type for bias adjusted estimates in the plot (default = '^') :parm adjusted_estimate_color: marker color for bias adjusted estimates in the plot (default = "red") :param legend_position:tuple denoting the position of the legend (default = (1.6, 0.6)) """ # Plotting the contour plot if plot_type == "estimate": critical_value = 0 # default value of estimate else: critical_value = 2 # default t-value (usual approx for 95% CI) fig, ax = plt.subplots(1, 1, figsize=plot_size) ax.set_title("Sensitivity contour plot of %s" % plot_type) ax.set_xlabel("Partial R^2 of confounder with treatment") ax.set_ylabel("Partial R^2 of confounder with outcome") for i in range(len(self.r2tu_w)): x = self.r2tu_w[i] y = self.r2yu_tw[i] if x > 0.8 or y > 0.8: x_limit = 0.99 y_limit = 0.99 break r2tu_w = np.arange(0.0, x_limit, x_limit / num_points_per_contour) r2yu_tw = np.arange(0.0, y_limit, y_limit / num_points_per_contour) unadjusted_point_estimate = None if plot_type == "estimate": contour_values, critical_value, bound_values = self.plot_estimate(r2tu_w, r2yu_tw) unadjusted_estimate = self.estimate unadjusted_point_estimate = unadjusted_estimate elif plot_type == "t-value": contour_values, critical_value, bound_values = self.plot_t(r2tu_w, r2yu_tw) unadjusted_t = self.t_stats unadjusted_point_estimate = unadjusted_t else: raise ValueError("Current plotting method only supports 'estimate' and 't-value' ") # Adding contours contour_plot = ax.contour( r2tu_w, r2yu_tw, contour_values, colors=contours_color, linewidths=contour_linewidths, linestyles=contour_linestyles, ) ax.clabel(contour_plot, inline=1, fontsize=label_fontsize, colors=contours_label_color) # Adding threshold contour line contour_plot = ax.contour( r2tu_w, r2yu_tw, contour_values, colors=critical_contour_color, linewidths=contour_linewidths, levels=[critical_value], ) ax.clabel(contour_plot, [critical_value], inline=1, fontsize=label_fontsize, colors=critical_label_color) # Adding unadjusted point estimate ax.scatter( [0], [0], marker=unadjusted_estimate_marker, color=unadjusted_estimate_color, label="Unadjusted({:1.2f})".format(unadjusted_point_estimate), ) # Adding bounds to partial R^2 values for given strength of confounders for i in range(len(self.frac_strength_treatment)): frac_strength_treatment = self.frac_strength_treatment[i] frac_strength_outcome = self.frac_strength_outcome[i] if frac_strength_treatment == frac_strength_outcome: signs = str(round(frac_strength_treatment, 2)) else: signs = str(round(frac_strength_treatment, 2)) + "/" + str(round(frac_strength_outcome, 2)) label = ( str(i + 1) + " " + signs + " X " + str(self.original_benchmark_covariates) + " ({:1.2f}) ".format(bound_values[i]) ) ax.scatter( self.r2tu_w[i], self.r2yu_tw[i], color=adjusted_estimate_color, marker=adjusted_estimate_marker, label=label, ) ax.annotate(str(i + 1), (self.r2tu_w[i] + 0.005, self.r2yu_tw[i] + 0.005)) ax.legend(bbox_to_anchor=legend_position) plt.show() def __str__(self): s = "Sensitivity Analysis to Unobserved Confounding using R^2 paramterization\n\n" s += "Unadjusted Estimates of Treatment {0} :\n".format(self.original_treatment_name) s += "Coefficient Estimate : {0}\n".format(self.estimate) s += "Degree of Freedom : {0}\n".format(self.degree_of_freedom) s += "Standard Error : {0}\n".format(self.standard_error) s += "t-value : {0}\n".format(self.t_stats) s += "F^2 value : {0}\n\n".format(self.partial_f2) s += "Sensitivity Statistics : \n" s += "Partial R2 of treatment with outcome : {0}\n".format(self.stats["r2yt_w"]) s += "Robustness Value : {0}\n\n".format(self.stats["robustness_value"]) s += "Interpretation of results :\n" s += "Any confounder explaining less than {0}% percent of the residual variance of both the treatment and the outcome would not be strong enough to explain away the observed effect i.e bring down the estimate to 0 \n\n".format( round(self.stats["robustness_value"] * 100, 2) ) s += "For a significance level of {0}%, any confounder explaining more than {1}% percent of the residual variance of both the treatment and the outcome would be strong enough to make the estimated effect not 'statistically significant'\n\n".format( self.significance_level * 100, round(self.stats["robustness_value_alpha"] * 100, 2) ) s += "If confounders explained 100% of the residual variance of the outcome, they would need to explain at least {0}% of the residual variance of the treatment to bring down the estimated effect to 0\n".format( round(self.stats["r2yt_w"] * 100, 2) ) return s

import logging import sys import matplotlib.pyplot as plt import numpy as np import pandas as pd import statsmodels.api as sm from scipy.stats import t from dowhy.utils.api import parse_state class LinearSensitivityAnalyzer: """ Class to perform sensitivity analysis See: https://carloscinelli.com/files/Cinelli%20and%20Hazlett%20(2020)%20-%20Making%20Sense%20of%20Sensitivity.pdf :param estimator: linear estimator of the causal model :param data: Pandas dataframe :param treatment_name: name of treatment :param percent_change_estimate: It is the percentage of reduction of treatment estimate that could alter the results (default = 1) if percent_change_estimate = 1, the robustness value describes the strength of association of confounders with treatment and outcome in order to reduce the estimate by 100% i.e bring it down to 0. :param null_hypothesis_effect: assumed effect under the null hypothesis :param confounder_increases_estimate: True implies that confounder increases the absolute value of estimate and vice versa. (Default = True) :param benchmark_common_causes: names of variables for bounding strength of confounders :param significance_level: confidence interval for statistical inference(default = 0.05) :param frac_strength_treatment: strength of association between unobserved confounder and treatment compared to benchmark covariate :param frac_strength_outcome: strength of association between unobserved confounder and outcome compared to benchmark covariate :param common_causes_order: The order of column names in OLS regression data """ def __init__( self, estimator=None, data=None, treatment_name=None, percent_change_estimate=1.0, significance_level=0.05, confounder_increases_estimate=True, benchmark_common_causes=None, null_hypothesis_effect=0, frac_strength_treatment=None, frac_strength_outcome=None, common_causes_order=None, ): self.data = data self.treatment_name = [] # original_treatment_name: : stores original variable names for labelling self.original_treatment_name = treatment_name for t in range(len(treatment_name)): self.treatment_name.append("x" + str(t + 1)) self.percent_change_estimate = percent_change_estimate self.significance_level = significance_level self.confounder_increases_estimate = confounder_increases_estimate self.estimator = estimator self.estimator_model = estimator.model self.null_hypothesis_effect = null_hypothesis_effect # common_causes_map : maps the original variable names to variable names in OLS regression self.common_causes_map = {} for i in range(len(common_causes_order)): self.common_causes_map[common_causes_order[i]] = "x" + str(len(self.treatment_name) + i + 1) # benchmark_common_causes: stores variable names in terms of regression model variables benchmark_common_causes = parse_state(benchmark_common_causes) self.benchmark_common_causes = [] # original_benchmark_covariates: stores original variable names for labelling self.original_benchmark_covariates = benchmark_common_causes for i in range(len(benchmark_common_causes)): self.benchmark_common_causes.append(self.common_causes_map[benchmark_common_causes[i]]) if type(frac_strength_treatment) in [int, list, float]: self.frac_strength_treatment = np.array(frac_strength_treatment) if type(frac_strength_outcome) in [int, list, float]: self.frac_strength_outcome = np.array(frac_strength_outcome) # estimate: estimate of regression self.estimate = None # degree_of_freedom: degree of freedom of error in regression self.degree_of_freedom = None # standard_error: standard error in regression self.standard_error = None # t_stats: Treatment coefficient t-value - measures how many standard errors the estimate is away from zero. self.t_stats = None # partial_f2: value to determine if a regression model and a nested version of it have a statistically significant difference between them self.partial_f2 = None # r2tu_w: partial R^2 of unobserved confounder "u" with treatment "t", after conditioning on observed covariates "w" self.r2tu_w = None # r2yu_tw: partial R^2 of unobserved confounder "u" with outcome "y", after conditioning on observed covariates "w" and treatment "t" self.r2yu_tw = None # r2twj_w: partial R^2 of observed covariate wj with treatment "t", after conditioning on observed covariates "w" excluding wj self.r2twj_w = None # r2ywj_tw: partial R^2 of observed covariate wj with outcome "y", after conditioning on observed covariates "w" (excluding wj) and treatment "t" self.r2ywj_tw = None # benchmarking_results: dataframe containing information about bounds and bias adjusted terms self.benchmarking_results = None # stats: dictionary containing information like robustness value, partial R^2, estimate, standard error , degree of freedom, partial f^2, t-statistic self.stats = None self.logger = logging.getLogger(__name__) def treatment_regression(self): """ Function to perform regression with treatment as outcome :returns: new OLS regression model """ features = self.estimator._observed_common_causes.copy() treatment_df = self.estimator._treatment.copy() features = sm.tools.add_constant(features) features.rename(columns=self.common_causes_map, inplace=True) model = sm.OLS(treatment_df, features) estimator_model = model.fit() return estimator_model def partial_r2_func(self, estimator_model=None, treatment=None): """ Computes the partial R^2 of regression model :param estimator_model: Linear regression model :param treatment: treatment name :returns: partial R^2 value """ estimate = estimator_model.params[treatment] degree_of_freedom = int(estimator_model.df_resid) if np.isscalar(estimate): # for single covariate t_stats = estimator_model.tvalues[treatment] return t_stats**2 / (t_stats**2 + degree_of_freedom) else: # compute for a group of covariates covariance_matrix = estimator_model.cov_params().loc[treatment, :][treatment] n = len(estimate) # number of parameters in model f_stat = ( np.matmul(np.matmul(estimate.values.T, np.linalg.inv(covariance_matrix.values)), estimate.values) / n ) return f_stat * n / (f_stat * n + degree_of_freedom) def robustness_value_func(self, alpha=1.0): """ Function to calculate the robustness value. It is the minimum strength of association that confounders must have with treatment and outcome to change conclusions. Robustness value describes how strong the association must be in order to reduce the estimated effect by (100 * percent_change_estimate)%. Robustness value close to 1 means the treatment effect can handle strong confounders explaining almost all residual variation of the treatment and the outcome. Robustness value close to 0 means that even very weak confounders can also change the results. :param alpha: confidence interval (default = 1) :returns: robustness value """ partial_cohen_f = abs( self.t_stats / np.sqrt(self.degree_of_freedom) ) # partial f of treatment t with outcome y. f = t_val/sqrt(dof) f_q = self.percent_change_estimate * partial_cohen_f t_alpha_df_1 = t.ppf( alpha / 2, self.degree_of_freedom - 1 ) # t-value threshold with alpha significance level and dof-1 degrees of freedom f_critical = abs(t_alpha_df_1) / np.sqrt(self.degree_of_freedom - 1) f_adjusted = f_q - f_critical if f_adjusted < 0: r_value = 0 else: r_value = 0.5 * (np.sqrt(f_adjusted**4 + (4 * f_adjusted**2)) - f_adjusted**2) if f_adjusted > 0 and f_q > 1 / f_critical: r_value = (f_q**2 - f_critical**2) / (1 + f_q**2) return r_value def compute_bias_adjusted(self, r2tu_w, r2yu_tw): """ Computes the bias adjusted estimate, standard error, t-value, partial R2, confidence intervals :param r2tu_w: partial r^2 from regressing unobserved confounder u on treatment t after conditioning on observed covariates w :param r2yu_tw: partial r^2 from regressing unobserved confounder u on outcome y after conditioning on observed covariates w and treatment t :returns: Python dictionary with information about partial R^2 of confounders with treatment and outcome and bias adjusted variables """ bias_factor = np.sqrt((r2yu_tw * r2tu_w) / (1 - r2tu_w)) bias = bias_factor * (self.standard_error * np.sqrt(self.degree_of_freedom)) if self.confounder_increases_estimate: bias_adjusted_estimate = np.sign(self.estimate) * (abs(self.estimate) - bias) else: bias_adjusted_estimate = np.sign(self.estimate) * (abs(self.estimate) + bias) bias_adjusted_se = ( np.sqrt((1 - r2yu_tw) / (1 - r2tu_w)) * self.standard_error * np.sqrt(self.degree_of_freedom / (self.degree_of_freedom - 1)) ) bias_adjusted_t = (bias_adjusted_estimate - self.null_hypothesis_effect) / bias_adjusted_se bias_adjusted_partial_r2 = bias_adjusted_t**2 / ( bias_adjusted_t**2 + (self.degree_of_freedom - 1) ) # partial r2 formula used with new t value and dof - 1 num_se = t.ppf( self.significance_level / 2, self.degree_of_freedom ) # Number of standard errors within Confidence Interval bias_adjusted_upper_CI = bias_adjusted_estimate - num_se * bias_adjusted_se bias_adjusted_lower_CI = bias_adjusted_estimate + num_se * bias_adjusted_se benchmarking_results = { "r2tu_w": r2tu_w, "r2yu_tw": r2yu_tw, "bias_adjusted_estimate": bias_adjusted_estimate, "bias_adjusted_se": bias_adjusted_se, "bias_adjusted_t": bias_adjusted_t, "bias_adjusted_lower_CI": bias_adjusted_lower_CI, "bias_adjusted_upper_CI": bias_adjusted_upper_CI, } return benchmarking_results def check_sensitivity(self, plot=True): """ Function to perform sensitivity analysis. :param plot: plot = True generates a plot of point estimate and the variations with respect to unobserved confounding. plot = False overrides the setting :returns: instance of LinearSensitivityAnalyzer class """ self.standard_error = np.array(self.estimator_model.bse[1 : (len(self.treatment_name) + 1)])[0] self.degree_of_freedom = int(self.estimator_model.df_resid) self.estimate = np.array(self.estimator_model.params[1 : (len(self.treatment_name) + 1)])[0] self.t_stats = np.array(self.estimator_model.tvalues[self.treatment_name])[0] # partial R^2 (r2yt_w) is the proportion of variation in outcome uniquely explained by treatment partial_r2 = self.partial_r2_func(self.estimator_model, self.treatment_name) RVq = self.robustness_value_func() RV_qalpha = self.robustness_value_func(alpha=self.significance_level) if self.confounder_increases_estimate: self.null_hypothesis_effect = self.estimate * (1 - self.percent_change_estimate) else: self.null_hypothesis_effect = self.estimate * (1 + self.percent_change_estimate) self.t_stats = (self.estimate - self.null_hypothesis_effect) / self.standard_error self.partial_f2 = self.t_stats**2 / self.degree_of_freedom # build a new regression model by considering treatment variables as outcome treatment_linear_model = self.treatment_regression() # r2twj_w is partial R^2 of covariate wj with treatment "t", after conditioning on covariates w(excluding wj) # r2ywj_tw is partial R^2 of covariate wj with outcome "y", after conditioning on covariates w(excluding wj) and treatment "t" self.r2twj_w = [] self.r2ywj_tw = [] for covariate in self.benchmark_common_causes: self.r2ywj_tw.append(self.partial_r2_func(self.estimator_model, covariate)) self.r2twj_w.append(self.partial_r2_func(treatment_linear_model, covariate)) for i in range(len(self.benchmark_common_causes)): r2twj_w = self.r2twj_w[i] r2ywj_tw = self.r2ywj_tw[i] # r2tu_w is the partial r^2 from regressing u on t after conditioning on w self.r2tu_w = self.frac_strength_treatment * (r2twj_w / (1 - r2twj_w)) if any(val >= 1 for val in self.r2tu_w): raise ValueError("r2tu_w can not be >= 1. Try a lower frac_strength_treatment value") r2uwj_wt = ( self.frac_strength_treatment * (r2twj_w**2) / ((1 - self.frac_strength_treatment * r2twj_w) * (1 - r2twj_w)) ) if any(val >= 1 for val in r2uwj_wt): raise ValueError("r2uwj_wt can not be >= 1. Try a lower frac_strength_treatment value") self.r2yu_tw = ((np.sqrt(self.frac_strength_outcome) + np.sqrt(r2uwj_wt)) / np.sqrt(1 - r2uwj_wt)) ** 2 * ( r2ywj_tw / (1 - r2ywj_tw) ) if any(val > 1 for val in self.r2yu_tw): for i in range(len(self.r2yu_tw)): if self.r2yu_tw[i] > 1: self.r2yu_tw[i] = 1 self.logger.warning( "Warning: r2yu_tw can not be > 1. Try a lower frac_strength_treatment. Setting r2yu_tw to 1" ) # Compute bias adjusted terms self.benchmarking_results = self.compute_bias_adjusted(self.r2tu_w, self.r2yu_tw) if plot == True: self.plot() self.stats = { "estimate": self.estimate, "standard_error": self.standard_error, "degree of freedom": self.degree_of_freedom, "t_statistic": self.t_stats, "r2yt_w": partial_r2, "partial_f2": self.partial_f2, "robustness_value": RVq, "robustness_value_alpha": RV_qalpha, } self.benchmarking_results = pd.DataFrame.from_dict(self.benchmarking_results) return self def plot_estimate(self, r2tu_w, r2yu_tw): """ Computes the contours, threshold line and bounds for plotting estimates. Contour lines (z - axis) correspond to the adjusted estimate values for different values of r2tu_w (x) and r2yu_tw (y). :param r2tu_w: hypothetical partial R^2 of confounder with treatment(x - axis) :param r2yu_tw: hypothetical partial R^2 of confounder with outcome(y - axis) :returns: contour_values : values of contour lines for the plot critical_estimate : threshold point estimate_bounds : estimate values for unobserved confounders (bias adjusted estimates) """ critical_estimate = self.null_hypothesis_effect contour_values = np.zeros((len(r2yu_tw), len(r2tu_w))) for i in range(len(r2yu_tw)): y = r2yu_tw[i] for j in range(len(r2tu_w)): x = r2tu_w[j] benchmarking_results = self.compute_bias_adjusted(r2tu_w=x, r2yu_tw=y) estimate = benchmarking_results["bias_adjusted_estimate"] contour_values[i][j] = estimate estimate_bounds = self.benchmarking_results["bias_adjusted_estimate"] return contour_values, critical_estimate, estimate_bounds def plot_t(self, r2tu_w, r2yu_tw): """ Computes the contours, threshold line and bounds for plotting t. Contour lines (z - axis) correspond to the adjusted t values for different values of r2tu_w (x) and r2yu_tw (y). :param r2tu_w: hypothetical partial R^2 of confounder with treatment(x - axis) :param r2yu_tw: hypothetical partial R^2 of confounder with outcome(y - axis) :returns: contour_values : values of contour lines for the plot critical_t : threshold point t_bounds : t-value for unobserved confounders (bias adjusted t values) """ t_alpha_df_1 = t.ppf( self.significance_level / 2, self.degree_of_freedom - 1 ) # t-value threshold with alpha significance level and dof-1 degrees of freedom critical_t = abs(t_alpha_df_1) * np.sign(self.t_stats) contour_values = [] for x in r2tu_w: contour = [] for y in r2yu_tw: benchmarking_results = self.compute_bias_adjusted(r2tu_w=x, r2yu_tw=y) t_value = benchmarking_results["bias_adjusted_t"] contour.append(t_value) contour_values.append(contour) t_bounds = self.benchmarking_results["bias_adjusted_t"] return contour_values, critical_t, t_bounds def plot( self, plot_type="estimate", critical_value=None, x_limit=0.8, y_limit=0.8, num_points_per_contour=200, plot_size=(7, 7), contours_color="blue", critical_contour_color="red", label_fontsize=9, contour_linewidths=0.75, contour_linestyles="solid", contours_label_color="black", critical_label_color="red", unadjusted_estimate_marker="D", unadjusted_estimate_color="black", adjusted_estimate_marker="^", adjusted_estimate_color="red", legend_position=(1.6, 0.6), ): """ Plots and summarizes the sensitivity bounds as a contour plot, as they vary with the partial R^2 of the unobserved confounder(s) with the treatment and the outcome Two types of plots can be generated, based on adjusted estimates or adjusted t-values X-axis: Partial R^2 of treatment and unobserved confounder(s) Y-axis: Partial R^2 of outcome and unobserved confounder(s) We also plot bounds on the partial R^2 of the unobserved confounders obtained from observed covariates :param plot_type: "estimate" or "t-value" :param critical_value: special reference value of the estimate or t-value that will be highlighted in the plot :param x_limit: plot's maximum x_axis value (default = 0.8) :param y_limit: plot's minimum y_axis value (default = 0.8) :param num_points_per_contour: number of points to calculate and plot each contour line (default = 200) :param plot_size: tuple denoting the size of the plot (default = (7,7)) :param contours_color: color of contour line (default = blue) String or array. If array, lines will be plotted with the specific color in ascending order. :param critical_contour_color: color of threshold line (default = red) :param label_fontsize: fontsize for labelling contours (default = 9) :param contour_linewidths: linewidths for contours (default = 0.75) :param contour_linestyles: linestyles for contours (default = "solid") See : https://matplotlib.org/3.5.0/gallery/lines_bars_and_markers/linestyles.html for more examples :param contours_label_color: color of contour line label (default = black) :param critical_label_color: color of threshold line label (default = red) :param unadjusted_estimate_marker: marker type for unadjusted estimate in the plot (default = 'D') See: https://matplotlib.org/stable/api/markers_api.html :parm unadjusted_estimate_color: marker color for unadjusted estimate in the plot (default = "black") :param adjusted_estimate_marker: marker type for bias adjusted estimates in the plot (default = '^') :parm adjusted_estimate_color: marker color for bias adjusted estimates in the plot (default = "red") :param legend_position:tuple denoting the position of the legend (default = (1.6, 0.6)) """ # Plotting the contour plot if plot_type == "estimate": critical_value = 0 # default value of estimate else: critical_value = 2 # default t-value (usual approx for 95% CI) fig, ax = plt.subplots(1, 1, figsize=plot_size) ax.set_title("Sensitivity contour plot of %s" % plot_type) ax.set_xlabel("Partial R^2 of confounder with treatment") ax.set_ylabel("Partial R^2 of confounder with outcome") for i in range(len(self.r2tu_w)): x = self.r2tu_w[i] y = self.r2yu_tw[i] if x > 0.8 or y > 0.8: x_limit = 0.99 y_limit = 0.99 break r2tu_w = np.arange(0.0, x_limit, x_limit / num_points_per_contour) r2yu_tw = np.arange(0.0, y_limit, y_limit / num_points_per_contour) unadjusted_point_estimate = None if plot_type == "estimate": contour_values, critical_value, bound_values = self.plot_estimate(r2tu_w, r2yu_tw) unadjusted_estimate = self.estimate unadjusted_point_estimate = unadjusted_estimate elif plot_type == "t-value": contour_values, critical_value, bound_values = self.plot_t(r2tu_w, r2yu_tw) unadjusted_t = self.t_stats unadjusted_point_estimate = unadjusted_t else: raise ValueError("Current plotting method only supports 'estimate' and 't-value' ") # Adding contours contour_plot = ax.contour( r2tu_w, r2yu_tw, contour_values, colors=contours_color, linewidths=contour_linewidths, linestyles=contour_linestyles, ) ax.clabel(contour_plot, inline=1, fontsize=label_fontsize, colors=contours_label_color) # Adding threshold contour line contour_plot = ax.contour( r2tu_w, r2yu_tw, contour_values, colors=critical_contour_color, linewidths=contour_linewidths, levels=[critical_value], ) ax.clabel(contour_plot, [critical_value], inline=1, fontsize=label_fontsize, colors=critical_label_color) # Adding unadjusted point estimate ax.scatter( [0], [0], marker=unadjusted_estimate_marker, color=unadjusted_estimate_color, label="Unadjusted({:1.2f})".format(unadjusted_point_estimate), ) # Adding bounds to partial R^2 values for given strength of confounders for i in range(len(self.frac_strength_treatment)): frac_strength_treatment = self.frac_strength_treatment[i] frac_strength_outcome = self.frac_strength_outcome[i] if frac_strength_treatment == frac_strength_outcome: signs = str(round(frac_strength_treatment, 2)) else: signs = str(round(frac_strength_treatment, 2)) + "/" + str(round(frac_strength_outcome, 2)) label = ( str(i + 1) + " " + signs + " X " + str(self.original_benchmark_covariates) + " ({:1.2f}) ".format(bound_values[i]) ) ax.scatter( self.r2tu_w[i], self.r2yu_tw[i], color=adjusted_estimate_color, marker=adjusted_estimate_marker, label=label, ) ax.annotate(str(i + 1), (self.r2tu_w[i] + 0.005, self.r2yu_tw[i] + 0.005)) ax.legend(bbox_to_anchor=legend_position) plt.show() def __str__(self): s = "Sensitivity Analysis to Unobserved Confounding using R^2 paramterization\n\n" s += "Unadjusted Estimates of Treatment {0} :\n".format(self.original_treatment_name) s += "Coefficient Estimate : {0}\n".format(self.estimate) s += "Degree of Freedom : {0}\n".format(self.degree_of_freedom) s += "Standard Error : {0}\n".format(self.standard_error) s += "t-value : {0}\n".format(self.t_stats) s += "F^2 value : {0}\n\n".format(self.partial_f2) s += "Sensitivity Statistics : \n" s += "Partial R2 of treatment with outcome : {0}\n".format(self.stats["r2yt_w"]) s += "Robustness Value : {0}\n\n".format(self.stats["robustness_value"]) s += "Interpretation of results :\n" s += "Any confounder explaining less than {0}% percent of the residual variance of both the treatment and the outcome would not be strong enough to explain away the observed effect i.e bring down the estimate to 0 \n\n".format( round(self.stats["robustness_value"] * 100, 2) ) s += "For a significance level of {0}%, any confounder explaining more than {1}% percent of the residual variance of both the treatment and the outcome would be strong enough to make the estimated effect not 'statistically significant'\n\n".format( self.significance_level * 100, round(self.stats["robustness_value_alpha"] * 100, 2) ) s += "If confounders explained 100% of the residual variance of the outcome, they would need to explain at least {0}% of the residual variance of the treatment to bring down the estimated effect to 0\n".format( round(self.stats["r2yt_w"] * 100, 2) ) return s

anusha0409

81841c697bd5e80ecf9e731432305f6186666f1f

bb446c333f2256074304b0dec9cb5628d284b542

Why were r2tu_w and r2yu_tw swapped in the inner/outer loops here? It looks like this was a bug in the prior code?

emrekiciman