線性迴歸之正則化的模型

一、普通的線性模型

import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
from sklearn.linear_model import LinearRegression
from sklearn.model_selection import train_test_split
from sklearn.preprocessing import StandardScaler
from sklearn import metrics
%matplotlib inline

data = pd.read_csv('Advertising.csv',index_col=0)#第一列爲index
data.head()

#切分訓練集和測試集
x = data.values[:,:3]
y = data.values[:,3]
x_train,x_test,y_train,y_test = train_test_split(x,y,train_size=0.7,random_state=0)
#標準化處理
sc = StandardScaler()
x_train_std = sc.fit_transform(x_train)
x_test_std = sc.transform(x_test)
#訓練模型
linreg = LinearRegression()
linreg.fit(x_train_std,y_train)
y_pred = linreg.predict(x_test_std)
#檢驗模型結果
mse = np.average((y_pred-y_test)**2)
metrics.mean_squared_error(y_pred,y_test)  #這個也是均方誤差
r2 = metrics.r2_score(y_test,y_pred)  #R2值，注意參數，前面的是實際值，後面的是預測值
mse,r2
#計算R2
def calculater2(y_pred,y_test):
    RSS = ((y_pred-y_test)**2).sum()
    TSS = (((y_test-np.average(y_test))**2)).sum()
    return 1-(RSS/TSS)
calculater2(y_pred,y_test)
#畫圖
fig = plt.figure(figsize=(10,6))
plt.plot(y_test)
plt.plot(y_pred)

二、加入正則化的模型

Ridge迴歸

from sklearn.linear_model import RidgeCV,LassoCV   #用這個自帶交叉驗證參數
from sklearn.model_selection import GridSearchCV   #如果使用RidgeCV就不用GridSearchCV這個API了
#使用RidgeCV來建立參數
alpha = np.logspace(-3,2,10)    #生成超參數，10的-3次方到10的2次方的等差數列
ridge = RidgeCV(alpha,cv=5)
ridge.fit(x_train_std,y_train)
ridge.alpha_   #輸出超參數的值
#使用Ridge配合GridSearchCV來做
from sklearn.linear_model import Ridge,Lasso
ridge_model = GridSearchCV(Ridge(),param_grid={'alpha':alpha},cv=5)
ridge_model.fit(x_train_std,y_train)
ridge_model.best_params_
#驗證模型效果
y_pred_ridge = ridge.predict(x_test_std)
mse_ridge = metrics.mean_squared_error(y_test,y_pred_ridge)
r2_ridge = metrics.r2_score(y_test,y_pred_ridge)
mse_ridge,r2_ridge

Lasso迴歸

#建立模型
lasso = LassoCV(alphas=alpha,cv=5)
lasso.fit(x_train_std,y_train)
lasso.alpha_
#驗證模型效果
y_pred_lasso = lasso.predict(x_test_std)
mse_lasso = metrics.mean_squared_error(y_test,y_pred_lasso)
r2_lasso = metrics.r2_score(y_test,y_pred_lasso)
mse_lasso,r2_lasso