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