ElasticNet 是一种使用L1和L2先验作为正则化矩阵的线性回归模型.这种组合用于只有很少的权重非零的稀疏模型，比如:class:Lasso, 但是又能保持:class:Ridge 的正则化属性.我们可以使用 l1_ratio 参数来调节L1和L2的凸组合(一类特殊的线性组合)。
当多个特征和另一个特征相关的时候弹性网络非常有用。Lasso 倾向于随机选择其中一个，而弹性网络更倾向于选择两个.
在实践中，Lasso 和 Ridge 之间权衡的一个优势是它允许在循环过程（Under rotate）中继承 Ridge 的稳定性.
弹性网络的目标函数是最小化:
ElasticNetCV 可以通过交叉验证来用来设置参数 alpha () 和 l1_ratio ()
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print(__doc__) -
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import numpy as np -
import matplotlib.pyplot as plt -
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from sklearn.linear_model import lasso_path, enet_path -
from sklearn import datasets -
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diabetes = datasets.load_diabetes() -
X = diabetes.data -
y = diabetes.target -
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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...") -
alphas_lasso, coefs_lasso, _ = lasso_path(X, y, eps, fit_intercept=False) -
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print("Computing regularization path using the positive lasso...") -
alphas_positive_lasso, coefs_positive_lasso, _ = lasso_path( -
X, y, eps, positive=True, fit_intercept=False) -
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) -
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print("Computing regularization path using the positve elastic net...") -
alphas_positive_enet, coefs_positive_enet, _ = enet_path( -
X, y, eps=eps, l1_ratio=0.8, positive=True, fit_intercept=False) -
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# Display results -
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plt.figure(1) -
ax = plt.gca() -
ax.set_color_cycle(2 * ['b', 'r', 'g', 'c', 'k']) -
l1 = plt.plot(-np.log10(alphas_lasso), coefs_lasso.T) -
l2 = plt.plot(-np.log10(alphas_enet), coefs_enet.T, linestyle='--') -
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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') -
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plt.figure(2) -
ax = plt.gca() -
ax.set_color_cycle(2 * ['b', 'r', 'g', 'c', 'k']) -
l1 = plt.plot(-np.log10(alphas_lasso), coefs_lasso.T) -
l2 = plt.plot(-np.log10(alphas_positive_lasso), coefs_positive_lasso.T, -
linestyle='--') -
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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') -
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plt.figure(3) -
ax = plt.gca() -
ax.set_color_cycle(2 * ['b', 'r', 'g', 'c', 'k']) -
l1 = plt.plot(-np.log10(alphas_enet), coefs_enet.T) -
l2 = plt.plot(-np.log10(alphas_positive_enet), coefs_positive_enet.T, -
linestyle='--') -
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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()
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