机器学习--线性回归

理论依据是吴恩达的视频：

import matplotlib.pyplot as plt
import numpy as np
import random

def linear_reg(x, y):

    theta_0, theta_1, alpha = 0, 0, 0.01
    J_pre = (1/len(x)) * sum(y)
    x_ = np.linspace(1,200)/10
    plt.scatter(x, y)
    while True:
        h = theta_0 + theta_1 * x
        J_cur = (1 / (2 * len(x))) * sum(pow(h - y,2))
        if abs(J_cur - J_pre) >= 1e-7 :
            temp0 = theta_0 - alpha * (1/len(x)) * sum(h-y)
            temp1 = theta_1 - alpha * (1/len(x)) * sum((h-y) * x)
            theta_0 = temp0
            theta_1 = temp1
            J_pre = J_cur
        else:
            break


    print('Theta_0:{}'.format(theta_0))
    print('Theta_1:{}'.format(theta_1))
    plt.plot(x_, theta_0 + theta_1 * x_)
    plt.show()
    return theta_0, theta_1

def generate_data():
    """取一个直线上的一些点，并且加上随机数来作为噪声，原方程y=8-2x"""
    data_list = [ ]
    x = [ ]
    num = 1
    test = []
    for i in range(200):
        if i < 170 and i > 40 and random.randint(1,10) > 3:
            if num < 80:
                x.append(i+random.randint(2,5)/10)
                data_list.append((80 - 2 * i+random.randint(2,5)/10)+random.randint(-45,45))
                num += 1
            else:
                break
        else:
            pass

    x = np.array(x)/10
    y = np.array(data_list)/10

    return x,y, test
if __name__ == '__main__':
    x, y, test= generate_data()
    the0, the1 = linear_reg(x,y)