python 线性回归 梯度下降法

版权声明：本文为博主原创文章，未经博主允许不得转载。 https://blog.csdn.net/sinat_36811967/article/details/84318449

公式：

代码：

# -*- coding:utf-8 -*-


def gradient_descent(xi, yi):
    theta0, theta1 = 0, 0  # 初始化
    m = len(xi)
    alpha = 0.01  # 学习率
    max_step = 20000  # 学习次数
    count = 0
    epsilon = 0.1  # 误差临界值
    while True:
        num1, num2 = 0, 0
        for i in range(m):
            num1 += theta0 + theta1 * xi[i] - yi[i]
            num2 += (theta0 + theta1 * xi[i] - yi[i]) * xi[i]

        # update theta
        theta0 = theta0 - alpha * num1 / m
        theta1 = theta1 - alpha * num2 / m
        # print('theta0', theta0)
        # print('theta1', theta1)

        error = 0
        for i in range(m):
            error += (theta0 + theta1 * xi[i] - yi[i]) ** 2
        if error <= epsilon:
            break

        count += 1
        if count > max_step:
            break

    return theta1, theta0, error


if __name__ == '__main__':
    xi = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
    yi = [10, 11.5, 12, 13, 14.5, 15.5, 16.8, 17.3, 18, 18.7]
    a, b, error = gradient_descent(xi, yi)
    print("y = %10.5fx + %10.5f" % (a, b))
    print("error: ", error)

Reference：
https://blog.csdn.net/troysps/article/details/80247320
https://blog.csdn.net/fenghuibian/article/details/52670806