Python、GD和SGD在线性回归上的实现

import numpy as np

# 生成示例数据
X = np.array([[1, 1], [1, 2], [1, 3], [1, 4]])  # 特征矩阵
y = np.array([2, 3, 4, 5])  # 目标变量

# 使用梯度下降算法求解线性回归参数
def gradient_descent(X, y, learning_rate=0.01, num_iterations=1000):
    num_samples, num_features = X.shape
    theta = np.zeros(num_features)  # 初始化参数

    for _ in range(num_iterations):
        predictions = np.dot(X, theta)  # 预测值
        errors = predictions - y  # 误差
        gradient = np.dot(X.T, errors) / num_samples  # 梯度
        theta -= learning_rate * gradient  # 参数更新

    return theta

# 使用随机梯度下降算法求解线性回归参数
def stochastic_gradient_descent(X, y, learning_rate=0.01, num_iterations=1000):
    num_samples, num_features = X.shape
    theta = np.zeros(num_features)  # 初始化参数

    for _ in range(num_iterations):
        for i in range(num_samples):
            prediction = np.dot(X[i], theta)  # 单个样本的预测值
            error = prediction - y[i]  # 单个样本的误差
            gradient = X[i] * error  # 单个样本的梯度
            theta -= learning_rate * gradient  # 参数更新

    return theta

# 使用GD算法求解线性回归参数
gd_theta = gradient_descent(X, y)
print("GD算法求解的参数：", gd_theta)

# 使用SGD算法求解线性回归参数
sgd_theta = stochastic_gradient_descent(X, y)
print("SGD算法求解的参数：", sgd_theta)