具有一个变量的线性回归

Question

虽然在线性回归中实施梯度下降算法，但是我的算法所做的预测以及所得的回归线以错误的输出形式出现。有人可以看看我的实施情况并为我提供帮助吗？另外，请指导我如何知道特定回归问题中要选择的“学习率”和“迭代次数”的值？

theta0 = 0                               #first parameter
theta1 = 0                               #second parameter
alpha = 0.001                             #learning rate (denoted by alpha)
num_of_iterations = 100                #total number of iterations performed by Gradient Descent
m = float(len(X))                         #total number of training examples

for i in range(num_of_iterations):
    y_predicted = theta0 + theta1 * X
    derivative_theta0 = (1/m) * sum(y_predicted - Y)
    derivative_theta1 = (1/m) * sum(X * (y_predicted - Y))
    temp0 = theta0 - alpha * derivative_theta0
    temp1 = theta1 - alpha * derivative_theta1
    theta0 = temp0
    theta1 = temp1
print(theta0, theta1)

y_predicted = theta0 + theta1 * X
plt.scatter(X,Y)
plt.plot(X, y_predicted, color = 'red')
plt.show()

Resulting regression line about which I need some help

Answer 1

您的学习率很高，我通过将学习率降低到alpha = 0.0001使它起作用。