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()