正规方程与线性回归对象API介绍

from sklearn.linear_model import LinearRegression, SGDRegressor
from sklearn.metrics import mean_absolute_error, mean_squared_error
from sklearn.model_selection import train_test_split
from sklearn.preprocessing import StandardScaler
from sklearn.datasets import fetch_california_housing

# 加载数据集（使用加州房价替代波士顿房价）
housing = fetch_california_housing()
X = housing.data
Y = housing.target

# 划分训练集和测试集
X_train, X_test, y_train, y_test = train_test_split(X, Y, test_size=0.2, random_state=42)

# 特征标准化
scaler = StandardScaler()
X_train_scaled = scaler.fit_transform(X_train)
X_test_scaled = scaler.transform(X_test)

# 1. 正规方程（LinearRegression）
lr = LinearRegression()
lr.fit(X_train_scaled, y_train)

print("=== LinearRegression（正规方程）===")
print("回归系数W:", lr.coef_)
print("偏置B:", lr.intercept_)

y_pred_lr = lr.predict(X_test_scaled)
print("MAE:", mean_absolute_error(y_test, y_pred_lr))
print("MSE:", mean_squared_error(y_test, y_pred_lr))
print("RMSE:", mean_squared_error(y_test, y_pred_lr, squared=False))

# 2. 随机梯度下降（SGDRegressor）
sgd = SGDRegressor(loss='squared_loss', learning_rate='constant', eta0=0.01, max_iter=1000)
sgd.fit(X_train_scaled, y_train)

print("\n=== SGDRegressor（随机梯度下降）===")
print("回归系数W:", sgd.coef_)
print("偏置B:", sgd.intercept_)

y_pred_sgd = sgd.predict(X_test_scaled)
print("MAE:", mean_absolute_error(y_test, y_pred_sgd))
print("MSE:", mean_squared_error(y_test, y_pred_sgd))
print("RMSE:", mean_squared_error(y_test, y_pred_sgd, squared=False))