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| import gradio as gr | |
| import matplotlib.pyplot as plt | |
| import numpy as np | |
| from sklearn import datasets | |
| from sklearn.linear_model import LogisticRegression | |
| from sklearn.preprocessing import StandardScaler | |
| rng = np.random.default_rng(0) | |
| X, y = datasets.load_digits(return_X_y=True) | |
| X = StandardScaler().fit_transform(X) | |
| # classify small against large digits | |
| y = (y > 4).astype(int) | |
| # l1_ratio = 0.5 # L1 weight in the Elastic-Net regularization | |
| md_description = """ | |
| # L1 Penalty and Sparsity in Logistic Regression | |
| Comparison of the sparsity (percentage of zero coefficients) of solutions when L1, L2 and Elastic-Net penalty are used for different values of C. We can see that large values of C give more freedom to the model. Conversely, smaller values of C constrain the model more. In the L1 penalty case, this leads to sparser solutions. As expected, the Elastic-Net penalty sparsity is between that of L1 and L2. | |
| We classify 8x8 images of digits into two classes: 0-4 against 5-9. The visualization shows coefficients of the models for varying C. | |
| """ | |
| def make_regression(l1_ratio): | |
| fig, axes = plt.subplots(3, 3) | |
| # Set regularization parameter | |
| for i, (C, axes_row) in enumerate(zip((1, 0.1, 0.01), axes)): | |
| # Increase tolerance for short training time | |
| clf_l1_LR = LogisticRegression(C=C, penalty="l1", tol=0.01, solver="saga") | |
| clf_l2_LR = LogisticRegression(C=C, penalty="l2", tol=0.01, solver="saga") | |
| clf_en_LR = LogisticRegression( | |
| C=C, penalty="elasticnet", solver="saga", l1_ratio=l1_ratio, tol=0.01 | |
| ) | |
| clf_l1_LR.fit(X, y) | |
| clf_l2_LR.fit(X, y) | |
| clf_en_LR.fit(X, y) | |
| coef_l1_LR = clf_l1_LR.coef_.ravel() | |
| coef_l2_LR = clf_l2_LR.coef_.ravel() | |
| coef_en_LR = clf_en_LR.coef_.ravel() | |
| # coef_l1_LR contains zeros due to the | |
| # L1 sparsity inducing norm | |
| sparsity_l1_LR = np.mean(coef_l1_LR == 0) * 100 | |
| sparsity_l2_LR = np.mean(coef_l2_LR == 0) * 100 | |
| sparsity_en_LR = np.mean(coef_en_LR == 0) * 100 | |
| print(f"C={C:.2f}") | |
| print(f"{'Sparsity with L1 penalty:':<40} {sparsity_l1_LR:2f}%") | |
| print(f"{'Sparsity with Elastic-Net penalty:':<40} {sparsity_en_LR:.2f}%") | |
| print(f"{'Sparsity with L2 penalty:':<40} {sparsity_l2_LR:.2f}%") | |
| print(f"{'Score with L1 penalty:':<40} {clf_l1_LR.score(X, y):.2f}") | |
| print(f"{'Score with Elastic-Net penalty:':<40} {clf_en_LR.score(X, y):.2f}") | |
| print(f"{'Score with L2 penalty:':<40} {clf_l2_LR.score(X, y):.2f}") | |
| log_out = f""" | |
| C={C:.2f} | |
| {'Sparsity with L1 penalty:':<40} {sparsity_l1_LR:2f}% | |
| {'Sparsity with Elastic-Net penalty:':<40} {sparsity_en_LR:.2f}% | |
| {'Sparsity with L2 penalty:':<40} {sparsity_l2_LR:.2f}% | |
| {'Score with L1 penalty:':<40} {clf_l1_LR.score(X, y):.2f} | |
| {'Score with Elastic-Net penalty:':<40} {clf_en_LR.score(X, y):.2f} | |
| {'Score with L2 penalty:':<40} {clf_l2_LR.score(X, y):.2f} | |
| """ | |
| if i == 0: | |
| axes_row[0].set_title("L1 penalty") | |
| axes_row[1].set_title(f"Elastic-Net\nl1/l2_ratio = {l1_ratio}") | |
| axes_row[2].set_title("L2 penalty") | |
| for ax, coefs in zip(axes_row, [coef_l1_LR, coef_en_LR, coef_l2_LR]): | |
| ax.imshow( | |
| np.abs(coefs.reshape(8, 8)), | |
| interpolation="nearest", | |
| cmap="binary", | |
| vmax=1, | |
| vmin=0, | |
| ) | |
| ax.set_xticks(()) | |
| ax.set_yticks(()) | |
| axes_row[0].set_ylabel(f"{C=}") | |
| return fig, log_out, make_example(l1_ratio) | |
| def make_example(l1_ratio): | |
| return f""" | |
| With the following code you can reproduce this example with the current values of the sliders and the same data in a notebook: | |
| ```python | |
| import numpy as np | |
| import matplotlib.pyplot as plt | |
| from sklearn.linear_model import LogisticRegression | |
| from sklearn import datasets | |
| from sklearn.preprocessing import StandardScaler | |
| rng = np.random.default_rng(0) | |
| X, y = datasets.load_digits(return_X_y=True) | |
| X = StandardScaler().fit_transform(X) | |
| # classify small against large digits | |
| y = (y > 4).astype(int) | |
| l1_ratio = 0.5 # L1 weight in the Elastic-Net regularization | |
| fig, axes = plt.subplots(3, 3) | |
| # Set regularization parameter | |
| for i, (C, axes_row) in enumerate(zip((1, 0.1, 0.01), axes)): | |
| # Increase tolerance for short training time | |
| clf_l1_LR = LogisticRegression(C=C, penalty="l1", tol=0.01, solver="saga") | |
| clf_l2_LR = LogisticRegression(C=C, penalty="l2", tol=0.01, solver="saga") | |
| clf_en_LR = LogisticRegression( | |
| C=C, penalty="elasticnet", solver="saga", l1_ratio=l1_ratio, tol=0.01 | |
| ) | |
| clf_l1_LR.fit(X, y) | |
| clf_l2_LR.fit(X, y) | |
| clf_en_LR.fit(X, y) | |
| coef_l1_LR = clf_l1_LR.coef_.ravel() | |
| coef_l2_LR = clf_l2_LR.coef_.ravel() | |
| coef_en_LR = clf_en_LR.coef_.ravel() | |
| # coef_l1_LR contains zeros due to the | |
| # L1 sparsity inducing norm | |
| sparsity_l1_LR = np.mean(coef_l1_LR == 0) * 100 | |
| sparsity_l2_LR = np.mean(coef_l2_LR == 0) * 100 | |
| sparsity_en_LR = np.mean(coef_en_LR == 0) * 100 | |
| print(f"C={{C:.2f}}") | |
| print(f"{{'Sparsity with L1 penalty:':<40}} {{sparsity_l1_LR:2f}}%\") | |
| print(f"{{'Sparsity with Elastic-Net penalty:':<40}} {{sparsity_en_LR:.2f}}%") | |
| print(f"{{'Sparsity with L2 penalty:':<40}} {{sparsity_l2_LR:.2f}}%") | |
| print(f"{{'Score with L1 penalty:':<40}} {{clf_l1_LR.score(X, y):.2f}}") | |
| print(f"{{'Score with Elastic-Net penalty:':<40}} {{clf_en_LR.score(X, y):.2f}}") | |
| print(f"{{'Score with L2 penalty:':<40}} {{clf_l2_LR.score(X, y):.2f}}") | |
| if i == 0: | |
| axes_row[0].set_title("L1 penalty") | |
| axes_row[1].set_title(f"Elastic-Net\\nl1/l2_ratio = {l1_ratio}") | |
| axes_row[2].set_title("L2 penalty") | |
| for ax, coefs in zip(axes_row, [coef_l1_LR, coef_en_LR, coef_l2_LR]): | |
| ax.imshow( | |
| np.abs(coefs.reshape(8, 8)), | |
| interpolation="nearest", | |
| cmap="binary", | |
| vmax=1, | |
| vmin=0, | |
| ) | |
| ax.set_xticks(()) | |
| ax.set_yticks(()) | |
| axes_row[0].set_ylabel(f"{{C=}}") | |
| plt.show() | |
| ``` | |
| """ | |
| with gr.Blocks() as demo: | |
| with gr.Row(): | |
| gr.Markdown(md_description) | |
| with gr.Row(): | |
| with gr.Column(): | |
| ratio_slider = gr.Slider(minimum=0, maximum=1, label="L1/L2 ratio", step=0.1, value=0.5) | |
| button = gr.Button(value="Generate") | |
| with gr.Column(): | |
| plot = gr.Plot(label="Output") | |
| log = gr.Markdown("", label="Log") | |
| with gr.Row(): | |
| example = gr.Markdown(make_example(ratio_slider.value)) | |
| button.click(make_regression, inputs=[ratio_slider], outputs=[plot, log, example]) | |
| ratio_slider.change(fn=make_regression, inputs=[ratio_slider], outputs=[plot, log, example]) | |
| demo.launch() | |