Machine Learning Fundamentals-Ridge Regression-06

Ridge Regression

Standard Equation Method-Ridge Regression

import numpy as np
from numpy import genfromtxt
import matplotlib.pyplot as plt  

# 读入数据 
data = genfromtxt(r"longley.csv",delimiter=',')
print(data)

# 切分数据
x_data = data[1:,2:]
y_data = data[1:,1,np.newaxis]
print(x_data)
print(y_data)

print(np.mat(x_data).shape)
print(np.mat(y_data).shape)
# 给样本添加偏置项
X_data = np.concatenate((np.ones((16,1)),x_data),axis=1)
print(X_data.shape)

print(X_data[:3])

# 岭回归标准方程法求解回归参数
def weights(xArr, yArr, lam=0.2):
    xMat = np.mat(xArr)
    yMat = np.mat(yArr)
    xTx = xMat.T*xMat # 矩阵乘法
    rxTx = xTx + np.eye(xMat.shape[1])*lam
    # 计算矩阵的值,如果值为0，说明该矩阵没有逆矩阵
    if np.linalg.det(rxTx) == 0.0:
        print("This matrix cannot do inverse")
        return
    # xTx.I为xTx的逆矩阵
    ws = rxTx.I*xMat.T*yMat
    return ws

ws = weights(X_data,y_data)
print(ws)

# 计算预测值
np.mat(X_data)*np.mat(ws)

sklearn-ridge regression

import numpy as np
from numpy import genfromtxt
from sklearn import linear_model
import matplotlib.pyplot as plt

# 读入数据 
data = genfromtxt(r"longley.csv",delimiter=',')
print(data)

# 切分数据
x_data = data[1:,2:]
y_data = data[1:,1]
print(x_data)
print(y_data)

# 创建模型
# 生成50个值
alphas_to_test = np.linspace(0.001, 1)
# 创建模型，保存误差值
model = linear_model.RidgeCV(alphas=alphas_to_test, store_cv_values=True)
model.fit(x_data, y_data)

# 岭系数
print(model.alpha_)
# loss值
print(model.cv_values_.shape)

# 画图
# 岭系数跟loss值的关系
plt.plot(alphas_to_test, model.cv_values_.mean(axis=0))
# 选取的岭系数值的位置
plt.plot(model.alpha_, min(model.cv_values_.mean(axis=0)),'ro')
plt.show()

model.predict(x_data[2,np.newaxis])