initial commit

README.md

@@ -1,13 +1,15 @@
 ---
 title: Regression Models
-emoji: 🏢
+emoji: 🧪
 colorFrom: indigo
 colorTo: red
 sdk: gradio
 sdk_version: 4.20.1
 app_file: app.py
-pinned: false
+pinned: true
 license: apache-2.0
 ---
 
-Check out the configuration reference at https://huggingface.co/docs/hub/spaces-config-reference
+Play around with various regression models to see how the degree of the polynomial impacts training.
+
+You can also change the number of data points along with how noisy the data is.

app.py

@@ -0,0 +1,252 @@
+import gradio as gr
+import numpy as np
+import sympy as sp
+import seaborn as sns
+from matplotlib import pyplot as plt
+
+from sklearn.linear_model import LinearRegression
+from sklearn.preprocessing import PolynomialFeatures
+from sklearn.pipeline import make_pipeline
+
+
+sns.set_style(style="darkgrid")
+sns.set_context(context="notebook", font_scale=0.7)
+
+MAX_NOISE = 20
+DEFAULT_NOISE = 6
+SLIDE_NOISE_STEP = 2
+
+MAX_POINTS = 100
+DEFAULT_POINTS = 20
+SLIDE_POINTS_STEP = 5
+
+def generate_equation(process_params):
+    process_params = process_params.astype(float).values.tolist()
+
+    # Define symbols
+    x = sp.symbols('x')
+    coefficients = sp.symbols('a b c d e')
+
+    # Create the polynomial expression
+    polynomial_expression = None
+    for i, coef in enumerate(reversed(coefficients)):
+        polynomial_expression = polynomial_expression + coef * x**i if polynomial_expression else coef * x**i
+
+    # Parameter mapping
+    parameters = {coef: value for coef, value in zip(coefficients, process_params[0])}
+
+    # Substitute parameter values into the expression
+    polynomial_with_values = polynomial_expression.subs(parameters)
+    latex_representation = sp.latex(polynomial_with_values)
+    return fr"$${latex_representation}$$"
+
+
+def true_process(x, process_params):
+    """The true process we want to model."""
+    process_params = process_params.astype(float).values.tolist()
+    return (
+        process_params[0][0] * (x ** 4)
+        + process_params[0][1] * (x ** 3)
+        + process_params[0][2] * (x ** 2)
+        + process_params[0][3] * x
+        + process_params[0][4]
+    )
+
+
+def generate_data(num_points, noise_level, process_params):
+
+    # x is the list of input values
+    input_values = np.linspace(-5, 2, num_points)
+    input_values_dense = np.linspace(-5, 2, MAX_POINTS)
+
+    # y = f(x) is the underlying process we want to model
+    y = [true_process(x, process_params) for x in input_values]
+    y_dense = [true_process(x, process_params) for x in input_values_dense]
+
+    # however, we can only observe a noisy version of f(x)
+    noise = np.random.normal(0, noise_level, len(input_values))
+    y_noisy = y + noise
+
+    return input_values, input_values_dense, y, y_dense, y_noisy
+
+    
+def make_plot(
+        num_points, noise_level, process_params,
+        show_true_process, show_original_points,
+        show_noisy_points, show_added_noise,
+        show_learned_process, show_predicted_points,
+        show_prediction_error,
+        polynomial_degree=None
+    ):
+
+    x, x_dense, y, y_dense, y_noisy = generate_data(num_points, noise_level, process_params)
+
+    fig = plt.figure(dpi=400)
+    if show_true_process:
+        plt.plot(
+            x_dense, y_dense, "-", color="#363A4F",
+            label="True Process",
+            lw=1.5,
+        )
+    if show_added_noise:
+        plt.vlines(
+            x, y, y_noisy, color="#556D9A",
+            linestyles="dashed",
+            alpha=0.75,
+            lw=1,
+            label="Added Noise",
+        )
+    if show_original_points:
+        plt.plot(
+            x, y, "-o", color="none",
+            ms=6,
+            markerfacecolor="white",
+            markeredgecolor="#556D9A",
+            markeredgewidth=1.2,
+            label="Original Points",
+        )
+    if show_noisy_points and not polynomial_degree:
+        plt.plot(
+            x, y_noisy, "-o", color="none",
+            ms=6.5,
+            markerfacecolor="#556D9A",
+            markeredgecolor="none",
+            markeredgewidth=1.5,
+            alpha=1,
+            label="Noisy Points",
+        )
+
+    # Fit the selected regression model
+    if polynomial_degree:
+        
+        degree = polynomial_degree
+        model = make_pipeline(PolynomialFeatures(degree), LinearRegression())
+        model.fit(x.reshape(-1, 1), y_noisy)
+
+        # Plot the fitted regression model
+        y_pred_dense = model.predict(x_dense.reshape(-1, 1))
+        y_pred = model.predict(x.reshape(-1, 1))
+        if show_learned_process:
+            plt.plot(
+                x_dense, y_pred_dense, "-", color="#327747",
+                label="Learned Process",
+                lw=1.5,
+                alpha=0.75,
+            )
+        if show_prediction_error:
+            plt.vlines(
+                x, y_pred, y_noisy, color="#43A461",
+                linestyles="dashed",
+                alpha=0.75,
+                lw=1,
+                label="Prediction Error",
+            )
+        if show_noisy_points:
+            plt.plot(
+                x, y_noisy, "-o", color="none",
+                ms=6.5,
+                markerfacecolor="#556D9A",
+                markeredgecolor="none",
+                markeredgewidth=1.5,
+                alpha=1,
+                label="Training Points",
+            )
+        if show_predicted_points:
+            plt.plot(
+                x, y_pred, "-o", color="none",
+                ms=6.5,
+                markerfacecolor="#43A461",
+                markeredgecolor="none",
+                markeredgewidth=1.5,
+                label="Predicted Points",
+                alpha=1,
+            )
+
+    plt.xlabel("x")
+    plt.ylabel("y") 
+    plt.legend(fontsize=7.5)
+    plt.tight_layout()
+    return fig
+
+# Custom CSS
+css = """
+.train-button {
+    font-size: 1.2em;
+    width: 20%!important;
+    margin: 0;
+}
+.model-section {
+    font-size: 1em;
+    width: 100%!important;
+    margin: 0 0 1em 0;
+}
+.gradio-container {
+    width: 40%!important;
+    min-width: 800px;
+}
+"""
+with gr.Blocks(css=css) as demo:
+    with gr.Row():
+        with gr.Column():
+            gr.Markdown("## Underlying Process")
+            with gr.Row():
+                process_params = gr.DataFrame(
+                    value=[[0.5, 2, -0.5, -2, 1]],
+                    label="Polynomial Coefficients",
+                    type="pandas",
+                    column_widths=("2", "1", "1", "1", "1w"),
+                    headers=["x ** 4", "x ** 3", "x ** 2", "x", "1"],
+                    interactive=True
+                )
+            equation = gr.Markdown()
+
+            gr.Markdown("## Data Generation")
+            with gr.Row():
+                num_points = gr.Slider(
+                    minimum=5,
+                    maximum=MAX_POINTS,
+                    value=DEFAULT_POINTS,
+                    step=SLIDE_POINTS_STEP,
+                    label="Number of Points"
+                )
+
+                noise_level = gr.Slider(
+                    minimum=0,
+                    maximum=MAX_NOISE,
+                    value=DEFAULT_NOISE,
+                    step=SLIDE_NOISE_STEP,
+                    label="Noise Level"
+                    )
+
+            show_params = []
+            with gr.Row():
+                with gr.Column():
+                    show_params.append(gr.Checkbox(label="Underlying Process", value=True))
+                    show_params.append(gr.Checkbox(label="Original Points", value=True))
+                    show_params.append(gr.Checkbox(label="Noisy Points", value=True))
+                    show_params.append(gr.Checkbox(label="Added Noise", value=True))
+                with gr.Column():
+                    show_params.append(gr.Checkbox(label="Learned Process", value=True))
+                    show_params.append(gr.Checkbox(label="Predicted Points", value=True))
+                    show_params.append(gr.Checkbox(label="Prediction Error", value=True))
+
+            # Add model choice dropdown and training trigger button
+            gr.Markdown("## Modelisation")
+            with gr.Row(elem_classes=["model-section"]):
+                polynomial_degree = gr.Number(label="Choose the degree of your regression model", value=1, minimum=1, maximum=15, step=1, scale=2)
+                train_button = gr.Button(value="Train Model", elem_classes=["train-button"], scale=1)
+
+            scatter_plot = gr.Plot(elem_classes=["main-plot"])
+
+    num_points.change(fn=make_plot, inputs=[num_points, noise_level, process_params, *show_params], outputs=scatter_plot)
+    noise_level.change(fn=make_plot, inputs=[num_points, noise_level, process_params, *show_params], outputs=scatter_plot)
+    process_params.change(fn=make_plot, inputs=[num_points, noise_level, process_params, *show_params], outputs=scatter_plot)
+    process_params.change(fn=generate_equation, inputs=[process_params], outputs=equation)
+    train_button.click(make_plot, inputs=[num_points, noise_level, process_params, *show_params, polynomial_degree], outputs=scatter_plot)
+    for component in show_params:
+        component.change(fn=make_plot, inputs=[num_points, noise_level, process_params, *show_params], outputs=scatter_plot)
+    demo.load(fn=make_plot, inputs=[num_points, noise_level, process_params, *show_params], outputs=scatter_plot)
+    demo.load(fn=generate_equation, inputs=[process_params], outputs=equation)
+
+if __name__ == "__main__":
+    demo.launch()

requirements.txt

@@ -0,0 +1,220 @@
+#
+# This file is autogenerated by pip-compile with Python 3.10
+# by the following command:
+#
+#    pip-compile requirements.in
+#
+aiofiles==23.2.1
+    # via gradio
+altair==5.2.0
+    # via gradio
+annotated-types==0.6.0
+    # via pydantic
+anyio==4.3.0
+    # via
+    #   httpx
+    #   starlette
+attrs==23.2.0
+    # via
+    #   jsonschema
+    #   referencing
+certifi==2024.2.2
+    # via
+    #   httpcore
+    #   httpx
+    #   requests
+charset-normalizer==3.3.2
+    # via requests
+click==8.1.7
+    # via
+    #   typer
+    #   uvicorn
+colorama==0.4.6
+    # via typer
+contourpy==1.2.0
+    # via matplotlib
+cycler==0.12.1
+    # via matplotlib
+exceptiongroup==1.2.0
+    # via anyio
+fastapi==0.110.0
+    # via gradio
+ffmpy==0.3.2
+    # via gradio
+filelock==3.13.1
+    # via huggingface-hub
+fonttools==4.49.0
+    # via matplotlib
+fsspec==2024.2.0
+    # via
+    #   gradio-client
+    #   huggingface-hub
+gradio==4.19.2
+    # via -r requirements.in
+gradio-client==0.10.1
+    # via gradio
+h11==0.14.0
+    # via
+    #   httpcore
+    #   uvicorn
+httpcore==1.0.4
+    # via httpx
+httpx==0.27.0
+    # via
+    #   gradio
+    #   gradio-client
+huggingface-hub==0.21.4
+    # via
+    #   gradio
+    #   gradio-client
+idna==3.6
+    # via
+    #   anyio
+    #   httpx
+    #   requests
+importlib-resources==6.1.3
+    # via gradio
+jinja2==3.1.3
+    # via
+    #   altair
+    #   gradio
+joblib==1.3.2
+    # via scikit-learn
+jsonschema==4.21.1
+    # via altair
+jsonschema-specifications==2023.12.1
+    # via jsonschema
+kiwisolver==1.4.5
+    # via matplotlib
+markdown-it-py==3.0.0
+    # via rich
+markupsafe==2.1.5
+    # via
+    #   gradio
+    #   jinja2
+matplotlib==3.8.3
+    # via
+    #   gradio
+    #   seaborn
+mdurl==0.1.2
+    # via markdown-it-py
+mpmath==1.3.0
+    # via sympy
+numpy==1.26.4
+    # via
+    #   -r requirements.in
+    #   altair
+    #   contourpy
+    #   gradio
+    #   matplotlib
+    #   pandas
+    #   scikit-learn
+    #   scipy
+    #   seaborn
+orjson==3.9.15
+    # via gradio
+packaging==23.2
+    # via
+    #   altair
+    #   gradio
+    #   gradio-client
+    #   huggingface-hub
+    #   matplotlib
+pandas==2.2.1
+    # via
+    #   -r requirements.in
+    #   altair
+    #   gradio
+    #   seaborn
+pillow==10.2.0
+    # via
+    #   gradio
+    #   matplotlib
+pydantic==2.6.3
+    # via
+    #   fastapi
+    #   gradio
+pydantic-core==2.16.3
+    # via pydantic
+pydub==0.25.1
+    # via gradio
+pygments==2.17.2
+    # via rich
+pyparsing==3.1.2
+    # via matplotlib
+python-dateutil==2.9.0.post0
+    # via
+    #   matplotlib
+    #   pandas
+python-multipart==0.0.9
+    # via gradio
+pytz==2024.1
+    # via pandas
+pyyaml==6.0.1
+    # via
+    #   gradio
+    #   huggingface-hub
+referencing==0.33.0
+    # via
+    #   jsonschema
+    #   jsonschema-specifications
+requests==2.31.0
+    # via huggingface-hub
+rich==13.7.1
+    # via typer
+rpds-py==0.18.0
+    # via
+    #   jsonschema
+    #   referencing
+ruff==0.3.1
+    # via gradio
+scikit-learn==1.4.1.post1
+    # via -r requirements.in
+scipy==1.12.0
+    # via scikit-learn
+seaborn==0.13.2
+    # via -r requirements.in
+semantic-version==2.10.0
+    # via gradio
+shellingham==1.5.4
+    # via typer
+six==1.16.0
+    # via python-dateutil
+sniffio==1.3.1
+    # via
+    #   anyio
+    #   httpx
+starlette==0.36.3
+    # via fastapi
+sympy==1.12
+    # via -r requirements.in
+threadpoolctl==3.3.0
+    # via scikit-learn
+tomlkit==0.12.0
+    # via gradio
+toolz==0.12.1
+    # via altair
+tqdm==4.66.2
+    # via huggingface-hub
+typer[all]==0.9.0
+    # via gradio
+typing-extensions==4.10.0
+    # via
+    #   altair
+    #   anyio
+    #   fastapi
+    #   gradio
+    #   gradio-client
+    #   huggingface-hub
+    #   pydantic
+    #   pydantic-core
+    #   typer
+    #   uvicorn
+tzdata==2024.1
+    # via pandas
+urllib3==2.2.1
+    # via requests
+uvicorn==0.27.1
+    # via gradio
+websockets==11.0.3
+    # via gradio-client