我在下面的代码中发现了一个错误，导致Thetas返回的是inf, inf。

def gradient_descent(x, y, t0, t1, alpha, num_iters):for i in range(num_iters):  t0_sum = 0  t1_sum = 0  for i in range(m_num): # 我感觉下面的偏导数可能有误    t0_sum += ((t1*x[i])+t0 - y[i])    t1_sum += (((t1*x[i])+t0 - y[i])*(x[i]))  t0 = t0 - ( alpha/m_num * (t0_sum) )  t1 = t1 - ( alpha/m_num * (t1_sum) )return t0, t1

谢谢

回答：

你的代码几乎是正确的。唯一的问题是：你在这两个循环中使用了相同的变量名。

只需将第一个循环中的i改为j，它就能正常工作了。

为了验证，你可以使用normal equation，它可以在不使用任何循环的情况下为问题提供最佳解决方案。

这是我的代码：

import numpy as npdef gradient_descent(x, y, t0, t1, alpha, num_iters):    m_num = len(x);    for j in range(num_iters):        t0_sum = 0        t1_sum = 0        for i in range(m_num):            t0_sum += ((t1*x[i])+t0 - y[i])            t1_sum += (((t1*x[i])+t0 - y[i])*(x[i]))        t0 = t0 - ( alpha/m_num * (t0_sum) )        t1 = t1 - ( alpha/m_num * (t1_sum) )    return t0, t1def norm_equation(x, y):    m = len(x);    x = np.asarray([x]).transpose()    y = np.asarray([y]).transpose()    x = np.hstack((np.ones((m, 1)), x))    t = np.dot(np.dot(np.linalg.pinv(np.dot(x.transpose(), x)), x.transpose()), y)    return tx = [6, 5, 8, 7, 5, 8, 7, 8, 6, 5, 5, 14]y = [17, 9, 13, 11, 6, 11, 4, 12, 6, 3, 3, 15]t0 = 0t1 = 0alpha = 0.008num_iters = 10000t0, t1 = gradient_descent(x, y, t0, t1, alpha, num_iters)print("Gradient descent:")print("t0 = " + str(t0) + "; t1 = " + str(t1))printt = norm_equation(x, y)print("Normal equation")print("t0 = " + str(t.item(0)) + "; t1 = " + str(t.item(1)))

结果：

Gradient descent:t0 = 1.56634355366; t1 = 1.08575561307Normal equationt0 = 1.56666666667; t1 = 1.08571428571