机器学习之弹性网络（Elastic Net)

弹性网络

代码原文
下面代码参考scikit-learn中文社区，链接在上面。
但是由于scikit-learn中文社区上的代码有些地方跑不通，故对此代码做了修改，输出结果与社区中显示的结果相同。

对弹性网络进行简单的介绍：
ElasticNet是一个训练时同时用ℓ1和ℓ2范数进行正则化的线性回归模型，lasso是使用ℓ1范数进行正则化的线性回归模型。
弹性网络简弹性网络简介弹性网络简

from itertools import cycle
import numpy as np
import matplotlib.pyplot as plt
from sklearn.linear_model import lasso_path, enet_path
from sklearn import datasets

X, y = datasets.load_diabetes(return_X_y=True)


X /= X.std(axis=0)  # Standardize data (easier to set the l1_ratio parameter)
print("------------------------------------")
print(X)
print("------------------------------------")
print(y)
# 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, fit_intercept=False)
alphas_lasso, coefs_lasso, _ = lasso_path(X, y)

print("Computing regularization path using the positive lasso...")
# alphas_positive_lasso, coefs_positive_lasso, _ = lasso_path(
#     X, y, eps=eps, positive=True, fit_intercept=False)
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, fit_intercept=False)
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, fit_intercept=False)
alphas_positive_enet, coefs_positive_enet, _ = enet_path(
    X, y, eps=eps, l1_ratio=0.8, positive=True)
print("------------------------------------")
print(alphas_positive_enet)
print("------------------------------------")
print(coefs_positive_enet)
# Display results

plt.figure(1)
colors = cycle(['b', 'r', 'g', 'c', 'k'])
neg_log_alphas_lasso = -np.log10(alphas_lasso)
neg_log_alphas_enet = -np.log10(alphas_enet)
for coef_l, coef_e, c in zip(coefs_lasso, coefs_enet, colors):
    l1 = plt.plot(neg_log_alphas_lasso, coef_l, c=c)
    l2 = plt.plot(neg_log_alphas_enet, coef_e, linestyle='--', c=c)

plt.xlabel('-Log(alpha)')
plt.ylabel('coefficients')
plt.title('Lasso and Elastic-Net Paths')
plt.legend((l1[-1], l2[-1]), ('Lasso', 'Elastic-Net'), loc='lower left')
plt.axis('tight')


plt.figure(2)
neg_log_alphas_positive_lasso = -np.log10(alphas_positive_lasso)
for coef_l, coef_pl, c in zip(coefs_lasso, coefs_positive_lasso, colors):
    l1 = plt.plot(neg_log_alphas_lasso, coef_l, c=c)
    l2 = plt.plot(neg_log_alphas_positive_lasso, coef_pl, linestyle='--', c=c)

plt.xlabel('-Log(alpha)')
plt.ylabel('coefficients')
plt.title('Lasso and positive Lasso')
plt.legend((l1[-1], l2[-1]), ('Lasso', 'positive Lasso'), loc='lower left')
plt.axis('tight')


plt.figure(3)
neg_log_alphas_positive_enet = -np.log10(alphas_positive_enet)
for (coef_e, coef_pe, c) in zip(coefs_enet, coefs_positive_enet, colors):
    l1 = plt.plot(neg_log_alphas_enet, coef_e, c=c)
    l2 = plt.plot(neg_log_alphas_positive_enet, coef_pe, linestyle='--', c=c)

plt.xlabel('-Log(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 left')
plt.axis('tight')
plt.show()