第八章 变量选择与正则化 - 岭回归分析
岭回归分析0 载入库1 数据预处理2 普通线性回归和岭回归2.1 最小二乘法，参数估计2.2 岭回归，参数估计，固定岭参数2.3 岭回归，按 CV 标准自动选择岭参数2.4 列举岭参数的值，计算回归参数，画出岭迹图，计算 VIF
0 载入库
作者：喝醉酒的小白
载入 sklearn 模块中的线性回归与岭回归的函数
import numpy as np
import matplotlib.pyplot as plt
import pandas as pd
np.set_printoptions(suppress=True) #不用科学计数法输出
from sklearn.linear_model import LinearRegression
from sklearn.linear_model import Ridge
from sklearn.linear_model import RidgeCV
1 数据预处理
将自变量和因变量中心化和标准化
mydata=pd.read_csv('Regression/Regression8/longley.csv')
mydata_normd = (mydata - mydata.mean()) / mydata.std()
A = np.asmatrix(mydata_normd) #将输入解释为矩阵
X = A[:,1:]
y = A[:,0]
2 普通线性回归和岭回归
2.1 最小二乘法，参数估计
reg01 = LinearRegression()
reg01.fit(X,y)
print('OLS score:', reg01.score(X,y).round(4))
print('OLS coefficients:', reg01.coef_.round(3))
reg02 = Ridge(alpha=0.016)
reg02.fit(X,y)
print('Ridge(alpha=0.016) score:', reg01.score(X,y).round(4))
print('Ridge(alpha=0.016) coefficients:', reg02.coef_.round(3))
岭回归，给定一些岭参数，画出岭迹图
alphas = np.linspace(0,0.3,51)
betas = np.zeros((51,6))
for i in range(51):
reg03 = Ridge(alpha=alphas[i])
reg03.fit(X,y)
betas[i] = reg03.coef_
ax = plt.gca()
ax.plot(alphas, betas)
plt.xlabel('k')
plt.ylabel('beta(k)')
plt.title('Ridge coefficients as a function of k')
plt.grid(True)
alphas = np.linspace(0.0001,0.1,1000)
reg04 = RidgeCV(alphas)
reg04.fit(X,y)
print('RidgeCV score:', reg04.score(X,y).round(4))
print('RidgeCV alpha:', reg04.alpha_)
print('RidgeCV coefficients:', reg04.coef_.round(3))
B = np.dot(X.T,X)
E6 = np.diag(np.ones(6))
Nk = 101
k = np.linspace(0,0.2,Nk)
beta = np.zeros((Nk,6))
for i in range(Nk):
Binv = np.linalg.inv(B + k[i] * E6)
beta[i] = np.dot(np.dot(Binv, X.T), y).T
画图模型整段运行
for i in range(6):
plt.plot(k, beta[:,i] ,'-', label='beta_{}'.format(i+1))
plt.legend(loc='upper right')
plt.grid(True)
plt.xlabel('k')
plt.ylabel('beta hat (k)')
计算VIF
VIF=np.zeros((Nk,6))
for i in range(Nk):
Binv=np.linalg.inv(B+k[i]*E6)
C=np.dot(np.dot(Binv,B),Binv)
VIF[i]=np.diag(C)
VIF
评价回归方程的准则
作者：喝醉酒的小白
