4.弹性网络（ Elastic Net）

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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 ()

1.  
   print(__doc__)
2.  
    
3.  
   import numpy as np
4.  
   import matplotlib.pyplot as plt
5.  
    
6.  
   from sklearn.linear_model import lasso_path, enet_path
7.  
   from sklearn import datasets
8.  
    
9.  
   diabetes = datasets.load_diabetes()
10.  
    X = diabetes.data
11.  
    y = diabetes.target
12.  
     
13.  
    X /= X.std(axis=0) # Standardize data (easier to set the l1_ratio parameter)
14.  
     
15.  
    # Compute paths
16.  
     
17.  
    eps = 5e-3 # the smaller it is the longer is the path
18.  
     
19.  
    print("Computing regularization path using the lasso...")
20.  
    alphas_lasso, coefs_lasso, _ = lasso_path(X, y, eps, fit_intercept=False)
21.  
     
22.  
    print("Computing regularization path using the positive lasso...")
23.  
    alphas_positive_lasso, coefs_positive_lasso, _ = lasso_path(
24.  
    X, y, eps, positive=True, fit_intercept=False)
25.  
    print("Computing regularization path using the elastic net...")
26.  
    alphas_enet, coefs_enet, _ = enet_path(
27.  
    X, y, eps=eps, l1_ratio=0.8, fit_intercept=False)
28.  
     
29.  
    print("Computing regularization path using the positve elastic net...")
30.  
    alphas_positive_enet, coefs_positive_enet, _ = enet_path(
31.  
    X, y, eps=eps, l1_ratio=0.8, positive=True, fit_intercept=False)
32.  
     
33.  
    # Display results
34.  
     
35.  
    plt.figure(1)
36.  
    ax = plt.gca()
37.  
    ax.set_color_cycle(2 * ['b', 'r', 'g', 'c', 'k'])
38.  
    l1 = plt.plot(-np.log10(alphas_lasso), coefs_lasso.T)
39.  
    l2 = plt.plot(-np.log10(alphas_enet), coefs_enet.T, linestyle='--')
40.  
     
41.  
    plt.xlabel('-Log(alpha)')
42.  
    plt.ylabel('coefficients')
43.  
    plt.title('Lasso and Elastic-Net Paths')
44.  
    plt.legend((l1[-1], l2[-1]), ('Lasso', 'Elastic-Net'), loc='lower left')
45.  
    plt.axis('tight')
46.  
     
47.  
     
48.  
    plt.figure(2)
49.  
    ax = plt.gca()
50.  
    ax.set_color_cycle(2 * ['b', 'r', 'g', 'c', 'k'])
51.  
    l1 = plt.plot(-np.log10(alphas_lasso), coefs_lasso.T)
52.  
    l2 = plt.plot(-np.log10(alphas_positive_lasso), coefs_positive_lasso.T,
53.  
    linestyle='--')
54.  
     
55.  
    plt.xlabel('-Log(alpha)')
56.  
    plt.ylabel('coefficients')
57.  
    plt.title('Lasso and positive Lasso')
58.  
    plt.legend((l1[-1], l2[-1]), ('Lasso', 'positive Lasso'), loc='lower left')
59.  
    plt.axis('tight')
60.  
     
61.  
     
62.  
    plt.figure(3)
63.  
    ax = plt.gca()
64.  
    ax.set_color_cycle(2 * ['b', 'r', 'g', 'c', 'k'])
65.  
    l1 = plt.plot(-np.log10(alphas_enet), coefs_enet.T)
66.  
    l2 = plt.plot(-np.log10(alphas_positive_enet), coefs_positive_enet.T,
67.  
    linestyle='--')
68.  
     
69.  
    plt.xlabel('-Log(alpha)')
70.  
    plt.ylabel('coefficients')
71.  
    plt.title('Elastic-Net and positive Elastic-Net')
72.  
    plt.legend((l1[-1], l2[-1]), ('Elastic-Net', 'positive Elastic-Net'),
73.  
    loc='lower left')
74.  
    plt.axis('tight')
75.  
    plt.show()