85 lines
2.4 KiB
Python
85 lines
2.4 KiB
Python
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"""
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=====================
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Lasso and Elastic Net
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=====================
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Lasso and elastic net (L1 and L2 penalisation) implemented using a
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coordinate descent.
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The coefficients can be forced to be positive.
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"""
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# Author: Alexandre Gramfort <alexandre.gramfort@inria.fr>
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# License: BSD 3 clause
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from itertools import cycle
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import matplotlib.pyplot as plt
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from sklearn import datasets
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from sklearn.linear_model import enet_path, lasso_path
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X, y = datasets.load_diabetes(return_X_y=True)
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X /= X.std(axis=0) # Standardize data (easier to set the l1_ratio parameter)
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# Compute paths
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eps = 5e-3 # the smaller it is the longer is the path
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print("Computing regularization path using the lasso...")
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alphas_lasso, coefs_lasso, _ = lasso_path(X, y, eps=eps)
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print("Computing regularization path using the positive lasso...")
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alphas_positive_lasso, coefs_positive_lasso, _ = lasso_path(
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X, y, eps=eps, positive=True
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)
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print("Computing regularization path using the elastic net...")
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alphas_enet, coefs_enet, _ = enet_path(X, y, eps=eps, l1_ratio=0.8)
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print("Computing regularization path using the positive elastic net...")
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alphas_positive_enet, coefs_positive_enet, _ = enet_path(
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X, y, eps=eps, l1_ratio=0.8, positive=True
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)
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# Display results
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plt.figure(1)
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colors = cycle(["b", "r", "g", "c", "k"])
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for coef_l, coef_e, c in zip(coefs_lasso, coefs_enet, colors):
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l1 = plt.semilogx(alphas_lasso, coef_l, c=c)
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l2 = plt.semilogx(alphas_enet, coef_e, linestyle="--", c=c)
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plt.xlabel("alpha")
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plt.ylabel("coefficients")
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plt.title("Lasso and Elastic-Net Paths")
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plt.legend((l1[-1], l2[-1]), ("Lasso", "Elastic-Net"), loc="lower right")
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plt.axis("tight")
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plt.figure(2)
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for coef_l, coef_pl, c in zip(coefs_lasso, coefs_positive_lasso, colors):
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l1 = plt.semilogy(alphas_lasso, coef_l, c=c)
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l2 = plt.semilogy(alphas_positive_lasso, coef_pl, linestyle="--", c=c)
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plt.xlabel("alpha")
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plt.ylabel("coefficients")
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plt.title("Lasso and positive Lasso")
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plt.legend((l1[-1], l2[-1]), ("Lasso", "positive Lasso"), loc="lower right")
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plt.axis("tight")
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plt.figure(3)
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for coef_e, coef_pe, c in zip(coefs_enet, coefs_positive_enet, colors):
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l1 = plt.semilogx(alphas_enet, coef_e, c=c)
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l2 = plt.semilogx(alphas_positive_enet, coef_pe, linestyle="--", c=c)
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plt.xlabel("alpha")
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plt.ylabel("coefficients")
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plt.title("Elastic-Net and positive Elastic-Net")
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plt.legend((l1[-1], l2[-1]), ("Elastic-Net", "positive Elastic-Net"), loc="lower right")
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plt.axis("tight")
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plt.show()
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