python评分卡5

python评分卡1_woe与IV值
python评分卡2_woe与IV分箱方法
python评分卡3_woe与IV分箱实现
python评分卡4_logistics原理与解法_sklearn英译汉
python评分卡5_Logit例1_plot_logistic_l1_l2_sparsity
python评分卡6_Logit例2plot_logistic_path

%matplotlib inline

Comparison of the sparsity (percentage of zero coefficients) of solutions when L1, L2 and Elastic-Net penalty are used for different values of C. We can see that large values of C give more freedom to the model. Conversely, smaller values of C constrain the model more. In the L1 penalty case, this leads to sparser solutions. As expected, the Elastic-Net penalty sparsity is between that of L1 and L2.

We classify 8x8 images of digits into two classes: 0-4 against 5-9. The visualization shows coefficients of the models for varying C.

当L1、L2和弹性网正则用于不同的C值时，比较解的稀疏性（零系数百分比）。我们可以看到，C值越大，模型就越自由。相反，较小C值对模型的约束更大。在L1正则情况下，这将导致更稀疏的解决方案。 正如所料，弹性网正则稀疏度介于L1和L2之间。
我们将8x8数字图像分为两类：0-4和5-9。可视化显示了不同C的模型系数

# Authors: Alexandre Gramfort 
#          Mathieu Blondel 
#          Andreas Mueller 
# License: BSD 3 clause

import numpy as np
import matplotlib.pyplot as plt

from sklearn.linear_model import LogisticRegression
from sklearn import datasets
from sklearn.preprocessing import StandardScaler

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

X = StandardScaler().fit_transform(X)

# classify small against large digits
y = (y > 4).astype(int)

l1_ratio = 0.5  # L1 weight in the Elastic-Net regularization

X

array([[ 0.        , -0.33501649, -0.04308102, ..., -1.14664746,
        -0.5056698 , -0.19600752],
       [ 0.        , -0.33501649, -1.09493684, ...,  0.54856067,
        -0.5056698 , -0.19600752],
       [ 0.        , -0.33501649, -1.09493684, ...,  1.56568555,
         1.6951369 , -0.19600752],
       ...,
       [ 0.        , -0.33501649, -0.88456568, ..., -0.12952258,
        -0.5056698 , -0.19600752],
       [ 0.        , -0.33501649, -0.67419451, ...,  0.8876023 ,
        -0.5056698 , -0.19600752],
       [ 0.        , -0.33501649,  1.00877481, ...,  0.8876023 ,
        -0.26113572, -0.19600752]])

fig, axes = plt.subplots(3, 3)


# Set regularization parameter
for i, (C, axes_row) in enumerate(zip((1, 0.1, 0.01), axes)):
    # turn down tolerance for short training time
    clf_l1_LR = LogisticRegression(C=C, penalty="l1", tol=0.01, solver="saga")
    clf_l2_LR = LogisticRegression(C=C, penalty="l2", tol=0.01, solver="saga")
    clf_en_LR = LogisticRegression(
        C=C, penalty="elasticnet", solver="saga", l1_ratio=l1_ratio, tol=0.01
    )
    clf_l1_LR.fit(X, y)
    clf_l2_LR.fit(X, y)
    clf_en_LR.fit(X, y)

    coef_l1_LR = clf_l1_LR.coef_.ravel()
    coef_l2_LR = clf_l2_LR.coef_.ravel()
    coef_en_LR = clf_en_LR.coef_.ravel()

    # coef_l1_LR contains zeros due to the
    # L1 sparsity inducing norm

    sparsity_l1_LR = np.mean(coef_l1_LR == 0) * 100
    sparsity_l2_LR = np.mean(coef_l2_LR == 0) * 100
    sparsity_en_LR = np.mean(coef_en_LR == 0) * 100

    print("C=%.2f" % C)
    print("{:<40} {:.2f}%".format("Sparsity with L1 penalty:", sparsity_l1_LR))
    print("{:<40} {:.2f}%".format("Sparsity with Elastic-Net penalty:", sparsity_en_LR))
    print("{:<40} {:.2f}%".format("Sparsity with L2 penalty:", sparsity_l2_LR))
    print("{:<40} {:.2f}".format("Score with L1 penalty:", clf_l1_LR.score(X, y)))
    print(
        "{:<40} {:.2f}".format("Score with Elastic-Net penalty:", clf_en_LR.score(X, y))
    )
    print("{:<40} {:.2f}".format("Score with L2 penalty:", clf_l2_LR.score(X, y)))

    if i == 0:
        axes_row[0].set_title("L1 penalty")
        axes_row[1].set_title("Elastic-Netnl1_ratio = %s" % l1_ratio)
        axes_row[2].set_title("L2 penalty")

    for ax, coefs in zip(axes_row, [coef_l1_LR, coef_en_LR, coef_l2_LR]):
        ax.imshow(
            np.abs(coefs.reshape(8, 8)),
            interpolation="nearest",
            cmap="binary",
            vmax=1,
            vmin=0,
        )
        ax.set_xticks(())
        ax.set_yticks(())

    axes_row[0].set_ylabel("C = %s" % C)

plt.show()

C=1.00
Sparsity with L1 penalty:                6.25%
Sparsity with Elastic-Net penalty:       4.69%
Sparsity with L2 penalty:                4.69%
Score with L1 penalty:                   0.90
Score with Elastic-Net penalty:          0.90
Score with L2 penalty:                   0.90
C=0.10
Sparsity with L1 penalty:                29.69%
Sparsity with Elastic-Net penalty:       15.62%
Sparsity with L2 penalty:                4.69%
Score with L1 penalty:                   0.90
Score with Elastic-Net penalty:          0.90
Score with L2 penalty:                   0.90
C=0.01
Sparsity with L1 penalty:                84.38%
Sparsity with Elastic-Net penalty:       68.75%
Sparsity with L2 penalty:                4.69%
Score with L1 penalty:                   0.86
Score with Elastic-Net penalty:          0.88
Score with L2 penalty:                   0.89