Lasso、Lasso-LARS和弹性网路径#

此示例演示如何计算Lasso、Lasso-LARS和Elastic Net正则化路径中系数的“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惩罚项上添加了L2惩罚项。这允许一些系数非零，同时仍然鼓励稀疏性。

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

路径使用lasso_path、lars_path和enet_path计算。

结果显示不同的比较图。

比较Lasso和Lasso-LARS
比较Lasso和Elastic Net
比较Lasso和正Lasso
比较LARS和正LARS
比较Elastic Net和正Elastic Net

每个图都显示了模型系数随着正则化强度变化而变化的方式，从而深入了解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0.968秒）