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__)
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3.  
   import numpy as np
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   import matplotlib.pyplot as plt
5.  
    
6.  
   from sklearn.linear_model import lasso_path, enet_path
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   from sklearn import datasets
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9.  
   diabetes = datasets.load_diabetes()
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    X = diabetes.data
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    y = diabetes.target
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13.  
    X /= X.std(axis=0) # Standardize data (easier to set the l1_ratio parameter)
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15.  
    # Compute paths
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17.  
    eps = 5e-3 # the smaller it is the longer is the path
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19.  
    print(“Computing regularization path using the lasso…”)
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    alphas_lasso, coefs_lasso, _ = lasso_path(X, y, eps, fit_intercept=False)
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22.  
    print(“Computing regularization path using the positive lasso…”)
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    alphas_positive_lasso, coefs_positive_lasso, _ = lasso_path(
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    X, y, eps, positive=True, fit_intercept=False)
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    print(“Computing regularization path using the elastic net…”)
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    alphas_enet, coefs_enet, _ = enet_path(
27.  
    X, y, eps=eps, l1_ratio=0.8, fit_intercept=False)
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29.  
    print(“Computing regularization path using the positve elastic net…”)
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    alphas_positive_enet, coefs_positive_enet, _ = enet_path(
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    X, y, eps=eps, l1_ratio=0.8, positive=True, fit_intercept=False)
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33.  
    # Display results
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35.  
    plt.figure(1)
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    ax = plt.gca()
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    ax.set_color_cycle(2 * [\’b\’, \’r\’, \’g\’, \’c\’, \’k\’])
38.  
    l1 = plt.plot(-np.log10(alphas_lasso), coefs_lasso.T)
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    l2 = plt.plot(-np.log10(alphas_enet), coefs_enet.T, linestyle=\’–\’)
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41.  
    plt.xlabel(\’-Log(alpha)\’)
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    plt.ylabel(\’coefficients\’)
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    plt.title(\’Lasso and Elastic-Net Paths\’)
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    plt.legend((l1[-1], l2[-1]), (\’Lasso\’, \’Elastic-Net\’), loc=\’lower left\’)
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    plt.axis(\’tight\’)
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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)
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    l2 = plt.plot(-np.log10(alphas_positive_lasso), coefs_positive_lasso.T,
53.  
    linestyle=\’–\’)
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55.  
    plt.xlabel(\’-Log(alpha)\’)
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    plt.ylabel(\’coefficients\’)
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    plt.title(\’Lasso and positive Lasso\’)
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    plt.legend((l1[-1], l2[-1]), (\’Lasso\’, \’positive Lasso\’), loc=\’lower left\’)
59.  
    plt.axis(\’tight\’)
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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)
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    l2 = plt.plot(-np.log10(alphas_positive_enet), coefs_positive_enet.T,
67.  
    linestyle=\’–\’)
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69.  
    plt.xlabel(\’-Log(alpha)\’)
70.  
    plt.ylabel(\’coefficients\’)
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    plt.title(\’Elastic-Net and positive Elastic-Net\’)
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    plt.legend((l1[-1], l2[-1]), (\’Elastic-Net\’, \’positive Elastic-Net\’),
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    loc=\’lower left\’)
74.  
    plt.axis(\’tight\’)
75.  
    plt.show()