重学深度学习系列-回归

墨蓝 2023-01-16 09:56 182阅读 0赞

## 算法知识 ##

![20210425134400244.png_pic_center][] ![20210425134424150.png_pic_center][] ![20210425134519216.png_pic_center][]

计算一元线性回归的梯度  
     y=wx+b

![20210425133037189.png_pic_center][] ![20210425133733377.png_pic_center][]

import numpy as np
    import matplotlib.pyplot as plt
    from pylab import *
    mpl.rcParams['font.sans-serif'] = ['SimHei']
    mpl.rcParams['axes.unicode_minus'] = False
    #数据生成
    data = []
    for i in range(100):
        x = np.random.uniform(3., 12.)
        # mean=0, std=0.1
        eps = np.random.normal(0., 0.1)
        y = 1.477 * x + 0.089 + eps
        data.append([x, y])
    
    data = np.array(data)
    
    #统计误差
    # y = wx + b
    def compute_error_for_line_given_points(b, w, points):
        totalError = 0
        for i in range(0, len(points)):
            x = points[i, 0]
            y = points[i, 1]
            # computer mean-squared-error
            totalError += (y - (w * x + b)) ** 2
        # average loss for each point
        return totalError / float(len(points))
    
    
    #计算梯度
    def step_gradient(b_current, w_current, points, learningRate):
        b_gradient = 0
        w_gradient = 0
        N = float(len(points))
        for i in range(0, len(points)):
            x = points[i, 0]
            y = points[i, 1]
            # grad_b = 2(wx+b-y)
            b_gradient += (2/N) * ((w_current * x + b_current) - y)
            # grad_w = 2(wx+b-y)*x
            w_gradient += (2/N) * x * ((w_current * x + b_current) - y)
        # update w'
        new_b = b_current - (learningRate * b_gradient)
        new_w = w_current - (learningRate * w_gradient)
        return [new_b, new_w]
    
    #迭代更新
    def gradient_descent_runner(points, starting_b, starting_w, learning_rate, num_iterations):
        b = starting_b
        w = starting_w
        # update for several times
        for i in range(num_iterations):
            b, w = step_gradient(b, w, np.array(points), learning_rate)
        return [b, w]
    
    
    def run():
    
        learning_rate = 0.0001
        initial_b = 0  # initial y-intercept guess
        initial_w = 0  # initial slope guess
        num_iterations = 1000
        print("迭代前 b = {0}, w = {1}, error = {2}"
              .format(initial_b, initial_w,
                      compute_error_for_line_given_points(initial_b, initial_w, data))
              )
        print("Running...")
        [b, w] = gradient_descent_runner(data, initial_b, initial_w, learning_rate, num_iterations)
        print("第 {0} 次迭代结果 b = {1}, w = {2}, error = {3}".
              format(num_iterations, b, w,
                     compute_error_for_line_given_points(b, w, data))
              )
        plt.plot(data[:,0],data[:,1], color='r', marker='d', linestyle='--',label='true')
        plt.plot(data[:,0],w*data[:,0]+b,label='predict')
        plt.legend()
        plt.show()
    
    
    if __name__ == '__main__':
        run()

结果图  
![20210425140427882.png_pic_center][]

![202104251405210.png_pic_center][]

此系列博客为学习笔记  
![在这里插入图片描述][20210425140919405.jpg_pic_center]  
![20210425141023716.jpg_pic_center][]

[20210425134400244.png_pic_center]: https://img-blog.csdnimg.cn/20210425134400244.png#pic_center
[20210425134424150.png_pic_center]: https://img-blog.csdnimg.cn/20210425134424150.png#pic_center
[20210425134519216.png_pic_center]: /images/20221022/fc141901b23346f0b17405056301a5cd.png
[20210425133037189.png_pic_center]: https://img-blog.csdnimg.cn/20210425133037189.png#pic_center
[20210425133733377.png_pic_center]: /images/20221022/fdf4951a81f542ce9d8bdd82e7233a7e.png
[20210425140427882.png_pic_center]: /images/20221022/e114d0919b344bde8457aa26b825bb07.png
[202104251405210.png_pic_center]: /images/20221022/73ec960f083a4256a0050442bdb3702a.png
[20210425140919405.jpg_pic_center]: /images/20221022/7646a5a8016347fdbd8d669b816c7e47.png
[20210425141023716.jpg_pic_center]: /images/20221022/436d3198b37240f58cbc9f58f7d48c0d.png