sklearn正规方程和梯度下降 岭回归

一。sklearnAPI 正规方程和梯度下降

from sklearn.datasets import load_boston
from sklearn.model_selection import train_test_split
from sklearn.preprocessing import StandardScaler
from sklearn.linear_model import LinearRegression,SGDRegressor #正规方程，梯度下降
from sklearn.metrics import mean_squared_error #均方误差
def linear1():
    """
    正规方程对波士顿房价进行预测
    :return:
    """
    #1.导入数据
    boston=load_boston()
    #print(boston)
    #2.划分数据集
    x_train,x_test,y_train,y_test=train_test_split(boston.data,boston.target,random_state=22)
    #3.特征工程：标准化
    transfer=StandardScaler()
    x_train=transfer.fit_transform(x_train)
    x_test=transfer.transform(x_test)
    #4.预估器
    estimator=LinearRegression()
    estimator.fit(x_train,y_train)
    #5.得出模型
    print("正规方程权重系数：
",estimator.coef_)
    print("正规方程偏置：
",estimator.intercept_)
    #6.模型评估
    y_predict=estimator.predict(x_test)
    error = mean_squared_error(y_test,y_predict)
    print("正规方程均方误差：
：",error)

def linear2():
    """
    梯度下降对波士顿房价进行预测
    :return:
    """
    #1.导入数据
    boston=load_boston()
    #print(boston)
    #2.划分数据集
    x_train,x_test,y_train,y_test=train_test_split(boston.data,boston.target,random_state=22)
    #3.特征工程：标准化
    transfer=StandardScaler()
    x_train=transfer.fit_transform(x_train)
    x_test=transfer.transform(x_test)
    #4.预估器
    estimator=SGDRegressor(learning_rate="constant",eta0=0.001,max_iter=10000)
    estimator.fit(x_train,y_train)
    #5.得出模型
    print("梯度下降权重系数：
",estimator.coef_)
    print("梯度下降偏置：
",estimator.intercept_)
    #6.模型评估
    y_predict=estimator.predict(x_test)
    error = mean_squared_error(y_test,y_predict)
    print("梯度下降均方误差：
：",error)
if __name__ == "__main__":
    linear1()
    linear2()

二。 岭回归-带L2正则化的线性回归 

在建立回归方程时加上正则化，解决过拟合问题。

from sklearn.linear_model import LinearRegression,SGDRegressor,Ridge #正规方程，梯度下降、

def linear3():
    """
    岭回归对波士顿房价进行预测
    :return:
    """
    #1.导入数据
    boston=load_boston()
    #print(boston)
    #2.划分数据集
    x_train,x_test,y_train,y_test=train_test_split(boston.data,boston.target,random_state=22)
    #3.特征工程：标准化
    transfer=StandardScaler()
    x_train=transfer.fit_transform(x_train)
    x_test=transfer.transform(x_test)
    #4.预估器
    estimator=Ridge()
    estimator.fit(x_train,y_train)
    #5.得出模型
    print("岭回归权重系数：
",estimator.coef_)
    print("岭回归偏置：
",estimator.intercept_)
    #6.模型评估
    y_predict=estimator.predict(x_test)
    error = mean_squared_error(y_test,y_predict)
    print("岭回归均方误差：
：",error)