python-岭回归模型

 https://zhuanlan.zhihu.com/p/30535220

岭回归模型的应用

①可视化方法确定值

当回归系数随着值的增加而趋近于稳定的点时就是所要寻找的值

import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
import matplotlib
from sklearn import model_selection
from sklearn.linear_model import Ridge, RidgeCV
font = {
    'family': 'FangSong',
    'weight': 'bold',
    'size': 12
}
matplotlib.rc("font", **font)
# 读取糖尿病数据集
diabetes = pd.read_excel('./data/diabetes.xlsx')
# 构造自变量(剔除患者性别、年龄和因变量)
predictors = diabetes.iloc[:, 2: -1]
# 将数据集拆分成训练集和测试集
x_train, x_test, y_train, y_test = model_selection.train_test_split(predictors, diabetes['Y'], test_size=0.2, random_state=1234)
'''
可视化方法确定λ的值
'''
# 构造不同的Lambda值
Lambdas = np.logspace(-5, 2, 200)
# 构造空列表，用于存储模型的偏回归系数
ridge_cofficients = []
# 循环迭代不同的Lambda值
for Lambda in Lambdas:
    ridge = Ridge(alpha=Lambda, normalize=True)
    ridge.fit(x_train, y_train)
    ridge_cofficients.append(ridge.coef_)

# 设置绘图风格
plt.style.use('ggplot')
plt.plot(Lambdas, ridge_cofficients)
# 对x轴做对数处理
plt.xscale('log')
# 设置折线图x轴和y轴标签
plt.xlabel('Log(Lambda)')
plt.ylabel('Cofficients')
# 显示图形
plt.show()

②交叉验证法确定值

# 设置交叉验证的参数，对于每一个Lambda值都执行10重交叉验证
ridge_cv = RidgeCV(alphas=Lambdas, normalize=True, scoring='neg_mean_squared_error', cv=10)
# 模型拟合
ridge_cv.fit(x_train, y_train)
# 返回最佳的lambda
ridge_best_Lambda = ridge_cv.alpha_  # 0.013509935211980266

③模型的预测

# 基于最佳的Lambda值建模
ridge = Ridge(alpha=ridge_best_Lambda, normalize=True)
ridge.fit(x_train, y_train)
# 返回岭回归系数
res = pd.Series(index=['Intercept'] + x_train.columns.tolist(), data=[ridge.intercept_]+ridge.coef_.tolist())
print(res)
# 导入第三方包中的函数
from sklearn.metrics import mean_squared_error
# 测试值与正确值做对比
ridge_predict = ridge.predict(x_test)
res = pd.DataFrame({
    'real': y_test,
    'pred': ridge_predict
})

④预测效果验证

RMSE = np.sqrt(mean_squared_error(y_test, ridge_predict))  # 53.1236169466197 RMSE越小越好