L1_L2_Regulation

#!/usr/bin/env python3
# -*- coding: utf-8 -*-

"""
正则化消除过拟合示例
"""


"""过拟合示例"""
    """S1.准备数据"""
import numpy as np
import matplotlib.pyplot as plt

np.random.seed(888)
x = np.random.uniform(-3, 3, size=100)
X = x.reshape(-1, 1)
y = 0.5 + x**2 + x + 2 + np.random.normal(0, 1, size=100)
plt.scatter(x, y)
plt.show()


    """S2.多项式回归（30）"""
from sklearn.linear_model import LinearRegression
from sklearn.pipeline import Pipeline
from sklearn.preprocessing import StandardScaler
from sklearn.preprocessing import PolynomialFeatures
from sklearn.metrics import mean_squared_error
from sklearn.model_selection import train_test_split

lin_reg = LinearRegression()

def PolynomialRegression(degree):
    return Pipeline([
            ('Poly', PolynomialFeatures(degree)),
            ('std_scaler', StandardScaler()),
            ('lin_reg', lin_reg)
            ])
    
X_train, X_test, y_train, y_test = train_test_split(X, y, random_state=666)

poly30_reg = PolynomialRegression(degree = 30)
poly30_reg.fit(X_train, y_train)
y30_predict = poly30_reg.predict(X_test)
mean_squared_error(y_test, y30_predict)   # 9.040049628217018

    """S3.绘制拟合结果"""
X_plot = np.linspace(-3,3,100).reshape(100,1)
y_plot = poly30_reg.predict(X_plot)
plt.scatter(X,y)
plt.plot(X_plot[:,0],y_plot,color='r')
plt.axis([-3,3,0,10])
plt.show()


"""L1正则化：LASSO回归"""
from sklearn.linear_model import Lasso

def LassoRegression(degree, alpha):    # 封装lasso回归的pipeline
    return Pipeline([
            ('Poly', PolynomialFeatures(degree=degree)),
            ('std_scaler', StandardScaler()),
            ('lasso_reg', Lasso(alpha=alpha))            
            ])

def plot_model(plot_reg):    # 定义模型结果的绘制函数
    X_plot = np.linspace(-3,3,100).reshape(100,1)
    y_plot = plot_reg.predict(X_plot)
    plt.scatter(X,y)
    plt.plot(X_plot[:,0],y_plot,color='r')
    plt.axis([-3,3,0,10])
    plt.show()
    

lasso_reg1 = LassoRegression(30, 0.0001)
lasso_reg1.fit(X_train, y_train)
y1_predict = lasso_reg1.predict(X_test)
mean_squared_error(y_test, y1_predict)   # 1.3394026201341973

plot_model(lasso_reg1)    # 绘制模型拟合结果，相对顺滑的曲线

"""LASSO回归调参：提高超参数，增大惩罚力度"""
    """alpha=0.1"""
lasso_reg2 = LassoRegression(degree=30, alpha=0.1)
lasso_reg2.fit(X_train, y_train)
y2_predict = lasso_reg2.predict(X_test)
mean_squared_error(y_test, y2_predict)   # 1.2224470338258882，MSE减小
    plot_model(lasso_reg2)    # 绘制模型拟合结果，更加顺滑的曲线，接近二次曲线

    """alpha=10"""
lasso_reg3 = LassoRegression(30,10)
lasso_reg3.fit(X_train,y_train)
y3_predict=lasso_reg3.predict(X_test)
mean_squared_error(y_test,y3_predict)   # 12.626654141939536，MSE反弹增大
plot_model(lasso_reg3)   # 绘制模型拟合结果，成为一条直线


"""L2正则化：RIDGE回归"""
from sklearn.linear_model import Ridge   # 封装lasso回归的pipeline

def RidgeRegression(degree, alpha):
    return Pipeline([
            ('poly', PolynomialFeatures(degree=degree)),
            ('std_scaler', StandardScaler()),
            ('ridge_reg', Ridge(alpha=alpha))
            ])

ridge1_reg = RidgeRegression(degree=30, alpha=0.0001)
ridge1_reg.fit(X_train, y_train)
y1_predict = ridge1_reg.predict(X_test)
mean_squared_error(y_test, y1_predict)   # 1.2975253949535803

plot_model(ridge1_reg)   # 绘制模型拟合结果，相对顺滑的曲线


"""RIDGE回归调参：提高超参数，增大惩罚力度"""
ridge2_reg = RidgeRegression(degree=30, alpha=1)
ridge2_reg.fit(X_train, y_train)
y2_predict = ridge2_reg.predict(X_test)
mean_squared_error(y_test, y2_predict)   # 1.1533633669392716

plot_model(ridge2_reg)   # 绘制模型拟合结果，更加顺滑的曲线，接近二次曲线