metadata

title: sMAPE
emoji: 🤗
colorFrom: blue
colorTo: red
sdk: gradio
sdk_version: 3.19.1
app_file: app.py
pinned: false
tags:
  - evaluate
  - metric
description: >-
  Symmetric Mean Absolute Percentage Error (sMAPE) is the symmetric mean
  percentage error difference between the predicted and actual values defined by
  Chen and Yang (2004).

Metric Card for sMAPE

Metric Description

Symmetric Mean Absolute Error (sMAPE) is the symmetric mean of the percentage error of difference between the predicted $x_i$ and actual $y_i$ numeric values:

How to Use

At minimum, this metric requires predictions and references as inputs.

>>> smape_metric = evaluate.load("smape")
>>> predictions = [2.5, 0.0, 2, 8]
>>> references = [3, -0.5, 2, 7]
>>> results = smape_metric.compute(predictions=predictions, references=references)

Inputs

Mandatory inputs:

predictions: numeric array-like of shape (n_samples,) or (n_samples, n_outputs), representing the estimated target values.
references: numeric array-like of shape (n_samples,) or (n_samples, n_outputs), representing the ground truth (correct) target values.

Optional arguments:

sample_weight: numeric array-like of shape (n_samples,) representing sample weights. The default is None.
multioutput: raw_values, uniform_average or numeric array-like of shape (n_outputs,), which defines the aggregation of multiple output values. The default value is uniform_average.
- raw_values returns a full set of errors in case of multioutput input.
- uniform_average means that the errors of all outputs are averaged with uniform weight.
- the array-like value defines weights used to average errors.

Output Values

This metric outputs a dictionary, containing the mean absolute error score, which is of type:

float: if multioutput is uniform_average or an ndarray of weights, then the weighted average of all output errors is returned.
numeric array-like of shape (n_outputs,): if multioutput is raw_values, then the score is returned for each output separately.

Each sMAPE float value ranges from 0.0 to 2.0, with the best value being 0.0.

Output Example(s):

{'smape': 0.5}

If multioutput="raw_values":

{'smape': array([0.5, 1.5 ])}

Values from Popular Papers

Examples

Example with the uniform_average config:

>>> smape_metric = evaluate.load("smape")
>>> predictions = [2.5, 0.0, 2, 8]
>>> references = [3, -0.5, 2, 7]
>>> results = smape_metric.compute(predictions=predictions, references=references)
>>> print(results)
{'smape': 0.5787...}

Example with multi-dimensional lists, and the raw_values config:

>>> smape_metric = evaluate.load("smape", "multilist")
>>> predictions = [[0.5, 1], [-1, 1], [7, -6]]
>>> references = [[0.1, 2], [-1, 2], [8, -5]]
>>> results = smape_metric.compute(predictions=predictions, references=references)
>>> print(results)
{'smape': 0.8874...}
>>> results = smape_metric.compute(predictions=predictions, references=references, multioutput='raw_values')
>>> print(results)
{'smape': array([1.3749..., 0.4])}

Limitations and Bias

This metric is called a measure of "percentage error" even though there is no multiplier of 100. The range is between (0, 2) with it being two when the target and prediction are both zero.

Citation(s)

@article{article,
    author = {Chen, Zhuo and Yang, Yuhong},
    year = {2004},
    month = {04},
    pages = {},
    title = {Assessing forecast accuracy measures}
}

Further References

Symmetric Mean absolute percentage error - Wikipedia