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python评分卡6_Logit例2plot_logistic_path

%matplotlib inline

Regularization path of L1- Logistic Regression

Train l1-penalized logistic regression models on a binary classification
problem derived from the Iris dataset.

The models are ordered from strongest regularized to least regularized. The 4
coefficients of the models are collected and plotted as a “regularization
path”: on the left-hand side of the figure (strong regularizers), all the
coefficients are exactly 0. When regularization gets progressively looser,
coefficients can get non-zero values one after the other.

Here we choose the liblinear solver because it can efficiently optimize for the
Logistic Regression loss with a non-smooth, sparsity inducing l1 penalty.

Also note that we set a low value for the tolerance to make sure that the model
has converged before collecting the coefficients.

We also use warm_start=True which means that the coefficients of the models are
reused to initialize the next model fit to speed-up the computation of the
full-path.

L1-Logistic回归的正则化路径

训练基于Iris数据集的二元分类问题的l1正则logistic回归模型。

模型从正则化程度最高到正则化程度最低。收集模型的4个系数并绘制为“正则化路径”：在图的左侧（强正则化器），所有系数都正好为0。当正则化变得越来越松散时，系数可以一个接一个地获得非零值。

在这里，我们选择liblinear解算器，因为它可以有效地优化具有非光滑、稀疏诱导l1惩罚的Logistic回归损失。

还要注意，我们为容忍度设置了一个较低的值，以确保模型在收集系数之前已经收敛。

我们还使用warm_start=True，这意味着将重用模型的系数来初始化下一个模型拟合，以加快全路径的计算。

# Author: Alexandre Gramfort <alexandre.gramfort@inria.fr>
# License: BSD 3 clause

Load data

from sklearn import datasets

iris = datasets.load_iris()
X = iris.data
y = iris.target

X = X[y != 2]
y = y[y != 2]

X /= X.max()  # Normalize X to speed-up convergence

#X
y

array([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
       0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
       1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
       1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1])

Compute regularization path

import numpy as np

from sklearn import linear_model
from sklearn.svm import l1_min_c

cs = l1_min_c(X, y, loss="log") * np.logspace(0, 7, 16)

clf = linear_model.LogisticRegression(
    penalty="l1",
    solver="liblinear",
    tol=1e-6,
    max_iter=int(1e6),
    warm_start=True,
    intercept_scaling=10000.0,
)
coefs_ = []
for c in cs:
    clf.set_params(C=c)
    clf.fit(X, y)
    coefs_.append(clf.coef_.ravel().copy())

coefs_ = np.array(coefs_)

Plot regularization path

import matplotlib.pyplot as plt

plt.plot(np.log10(cs), coefs_, marker="o")
ymin, ymax = plt.ylim()
plt.xlabel("log(C)")
plt.ylabel("Coefficients")
plt.title("Logistic Regression Path")
plt.axis("tight")
plt.show()