岭回归

数据

#数据
import numpy as np
import matplotlib.pyplot as plt
np.random.seed(42)
x = np.random.uniform(-3,3,size=100)
#在最新版本的sklearn中，所有的数据都应该是二维矩阵，哪怕它只是单独一行或一列。
X = x.reshape(-1,1)
y = 0.5 * x + 3 +np.random.normal(0,1,size=100)
plt.scatter(x,y)#非线性关系

#使用多项式回归
from sklearn.pipeline import Pipeline
from sklearn.preprocessing import StandardScaler
from sklearn.preprocessing import PolynomialFeatures
from  sklearn.linear_model import LinearRegression
def PolynomialRegression(degree):
    return Pipeline([('poly',PolynomialFeatures(degree=degree)),
                     ('std_scaler',StandardScaler()),
                     ('lin_reg',LinearRegression())
                     ])

from sklearn.model_selection import train_test_split
X_train,X_test,y_train,y_test = train_test_split(X,y,random_state=666)

from sklearn.metrics import mean_squared_error
poly_reg = PolynomialRegression(degree=20)
poly_reg.fit(X_train,y_train)

y_poly_predict = poly_reg.predict(X_test)
print(mean_squared_error(y_test,y_poly_predict))

167.9401085999025

根据算法画拟合图

def plot_model(model):
    X_plot = np.linspace(-3,3,100).reshape(100,1)#不加reshpe则大小为(100,)
    y_plot = model.predict(X_plot)
    plt.scatter(x,y)
    plt.axis([-3,3,0,6])
    plt.plot(X_plot[:,0],y_plot,color = 'r')
plot_model(poly_reg)

使用岭回归，a=0.0001

#使用岭回归
from sklearn.linear_model import Ridge
def RidgeRegression(degree,alpha):
    return Pipeline([('poly',PolynomialFeatures(degree=degree)),
                     ('std_scaler',StandardScaler()),
                     ('lin_reg',Ridge(alpha = alpha))
                     ])
ridge1_reg = RidgeRegression(20,0.0001)
ridge1_reg.fit(X_train,y_train)

y1_predict = ridge1_reg.predict(X_test)
print(mean_squared_error(y_test,y1_predict))

1.3233492754136291

plot_model(ridge1_reg)

a=1

ridge2_reg = RidgeRegression(20,1)
ridge2_reg.fit(X_train,y_train)

y2_predict = ridge2_reg.predict(X_test)
print(mean_squared_error(y_test,y2_predict))

1.1888759304218461

plot_model(ridge2_reg)

a = 100

ridge2_reg = RidgeRegression(20,100)
ridge2_reg.fit(X_train,y_train)

y2_predict = ridge2_reg.predict(X_test)
print(mean_squared_error(y_test,y2_predict))
plot_model(ridge2_reg)

1.3196456113086197

a非常大所有参数都正则为0了。。。

ridge2_reg = RidgeRegression(20,1000000)#所有的参数都是0
ridge2_reg.fit(X_train,y_train)

y2_predict = ridge2_reg.predict(X_test)
print(mean_squared_error(y_test,y2_predict))
plot_model(ridge2_reg)

1.8404103153255003