Lasso、Lasso-LARS 和 Elastic Net 路径#

此示例展示了如何计算沿 Lasso、Lasso-LARS 和 Elastic Net 正则化路径的系数“路径”。换句话说，它展示了正则化参数（alpha）与系数之间的关系。

Lasso 和 Lasso-LARS 对系数施加了稀疏性约束，鼓励其中一些系数为零。Elastic Net 是 Lasso 的推广，它在 L1 惩罚项中添加了 L2 惩罚项。这使得一些系数可以不为零，同时仍然鼓励稀疏性。

Lasso 和 Elastic Net 使用坐标下降法来计算路径，而 Lasso-LARS 使用 LARS 算法来计算路径。

这些路径是使用 lasso_path、lars_path 和 enet_path 计算的。

结果显示了不同的比较图

比较 Lasso 和 Lasso-LARS
比较 Lasso 和 Elastic Net
比较 Lasso 和 Positive Lasso
比较 LARS 和 Positive LARS
比较 Elastic Net 和 Positive Elastic Net

每个图都显示了模型系数如何随着正则化强度的变化而变化，从而深入了解了这些模型在不同约束下的行为。

Computing regularization path using the lasso...
Computing regularization path using the positive lasso...
Computing regularization path using the LARS...
Computing regularization path using the positive LARS...
Computing regularization path using the elastic net...
Computing regularization path using the positive elastic net...

# Authors: The scikit-learn developers
# SPDX-License-Identifier: BSD-3-Clause

from itertools import cycle

import matplotlib.pyplot as plt

from sklearn.datasets import load_diabetes
from sklearn.linear_model import enet_path, lars_path, lasso_path

X, y = 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 LARS...")
alphas_lars, _, coefs_lars = lars_path(X, y, method="lasso")

print("Computing regularization path using the positive LARS...")
alphas_positive_lars, _, coefs_positive_lars = lars_path(
    X, y, method="lasso", 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_lasso, coef_lars, c in zip(coefs_lasso, coefs_lars, colors):
    l1 = plt.semilogx(alphas_lasso, coef_lasso, c=c)
    l2 = plt.semilogx(alphas_lars, coef_lars, linestyle="--", c=c)

plt.xlabel("alpha")
plt.ylabel("coefficients")
plt.title("Lasso and LARS Paths")
plt.legend((l1[-1], l2[-1]), ("Lasso", "LARS"), loc="lower right")
plt.axis("tight")

plt.figure(2)
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(3)
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(4)
colors = cycle(["b", "r", "g", "c", "k"])
for coef_lars, coef_positive_lars, c in zip(coefs_lars, coefs_positive_lars, colors):
    l1 = plt.semilogx(alphas_lars, coef_lars, c=c)
    l2 = plt.semilogx(alphas_positive_lars, coef_positive_lars, linestyle="--", c=c)

plt.xlabel("alpha")
plt.ylabel("coefficients")
plt.title("LARS and Positive LARS")
plt.legend((l1[-1], l2[-1]), ("LARS", "Positive LARS"), loc="lower right")
plt.axis("tight")

plt.figure(5)
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()

脚本总运行时间： (0 分钟 0.844 秒)

Lasso、Lasso-LARS 和 Elastic Net 路径#

本页