Day 09-实战：线性回归-灵析社区

本节重点：

• 基于numpy实现线性回归算法
• 参考视频：
https://www.bilibili.com/video/BV1oD4y1u7U8/?spm_id_from=333.999.0.0&vd_source=ea41ada76e180cf6c5af0f913147e4c0

一、线性回归：

表达式:
损失函数：

梯度更新： notion image lr为学习率，w和b的梯度就是对loss function的求导【这里为手动求解导数后，放入公式，也用diff进行计算】

二、numpy实现线性回归

数据准备

import numpy as np
import matplotlib.pyplot as plt
x = np.random.randint(2,200, size = 100)
y =  np.linspace(0.4, 0.500, num=100)* x + np.random.randint(1,3,size=100)
plt.plot(x,y,'o')
plt.show()

predict

def count_y_prediction(X, w, b):
    y_pred = np.add(np.multiply(w,X) , b)
    # y_pred = np.add(np.dot(w,x) ,b)
    # print(y_pred)
    return y_pred

损失函数

def compete_error_for_given_points(y, y_pred):
    error = np.power(np.subtract(y, y_pred) , 2)
    error = np.sum(error) / y.shape[0]
    # print(error)
    return error

梯度更新

def compete_gradient_and_update(x, w, b, lr):
    w_gradient = 0
    b_gradient = 0
    N = x.shape[0]
    w_gradient = 2*np.multiply(np.subtract(np.add(np.multiply(self.w,x),b),y),x)
    w_gradient_sum = np.sum(w_gradient)
    b_gradient = 2*np.subtract(np.add(np.multiply(self.w,x),b),y)
    b_gradient_sum = np.sum(b_gradient)
    w -= lr * w_gradient_sum / N
    b -= lr * b_gradient_sum / N
    return w,b

画图

def draw(X, y, y_pred,final=True):
    # plt.ion()
    plt.clf()
    plt.scatter(X, y, c="red")
    plt.plot(X, y_pred, c="blue")
    if final:
        plt.pause(0.2) 
        # plt.close()
    else:
        plt.show()

三、代码封装

#简单线性回归
class SimpleRegress(object):
    def __init__(self):
        self.b = np.linspace(1, 3, num=100)
        self.w = np.ones((100,))
        self.lr = 0.003
        return
	
    #梯度更新
    def compete_gradient_and_update(self,x,y):
        w_gradient = 0
        b_gradient = 0
        N = x.shape[0]
        w_gradient = 2*np.multiply(np.subtract(np.add(np.multiply(self.w,x),self.b),y),x)
        w_gradient_sum = np.sum(w_gradient)
        b_gradient = 2*np.subtract(np.add(np.multiply(self.w,x),self.b),y)
        b_gradient_sum = np.sum(b_gradient)
        self.w -= self.lr * w_gradient_sum / N
        self.b -= self.lr * b_gradient_sum / N
        return self.w,self.b
    
    #求损失函数
    def compete_error_for_given_points(self,y, y_pred):
        error = np.power(np.subtract(y , y_pred) , 2)
        error = np.sum(error)/ error.shape[0]
        # print(error)
        return error
    
    #计算多少个epoch
    def gradient_desent_runner(self,times,x,y):
        for i in range(times):
            self.w,self.b = self.compete_gradient_and_update(x,y)
        return [self.w,self.b]
    
    #推理
    def count_y_prediction(self,X):
        y_pred = np.add(np.multiply(self.w,X) ,self.b)
        # print(y_pred)
        return y_pred		
    
    #画图
    def draw(self,X, y, y_pred,final=True):
        # plt.ion()
        plt.clf()
        plt.plot(X, y, 'o')
        plt.plot(X, y_pred, c="blue")
        if final:
            plt.pause(0.2) 
            # plt.close()
        else:
            plt.show()

#数据
x_data = np.random.randint(2,200, size = 100)
y_data = np.linspace(0.4, 0.450, num=100)* x_data 

times = 50 # epoch次数
test_data = list([16]) #测试数据
sr = SimpleRegress()
# 预测
y_pred = sr.count_y_prediction(x_data) 

# 记录原始值
print("Starting Giadient desent at w ={0},b ={1},error={2}"
        .format(sr.w,sr.b,sr.compete_error_for_given_points(y_data,y_pred)))
print("Running:")

# 梯度更新求解
[w,b] = sr.gradient_desent_runner(times,x_data,y_data)

# 最新预测值
y_pred = sr.count_y_prediction(x_data)
print("After {0} times w = {1},b = {2},error = {3}"
        .format(times,w,b,sr.compete_error_for_given_points(y_data,y_pred)))

>
Starting Giadient desent at w =[1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.
 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.
 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.
 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.
 1. 1. 1. 1.],b =[1.         1.02020202 1.04040404 1.06060606 1.08080808 1.1010101
 1.12121212 1.14141414 1.16161616 1.18181818 1.2020202  1.22222222
 1.24242424 1.26262626 1.28282828 1.3030303  1.32323232 1.34343434
 1.36363636 1.38383838 1.4040404  1.42424242 1.44444444 1.46464646
 1.48484848 1.50505051 1.52525253 1.54545455 1.56565657 1.58585859
 1.60606061 1.62626263 1.64646465 1.66666667 1.68686869 1.70707071
 1.72727273 1.74747475 1.76767677 1.78787879 1.80808081 1.82828283
 1.84848485 1.86868687 1.88888889 1.90909091 1.92929293 1.94949495
 1.96969697 1.98989899 2.01010101 2.03030303 2.05050505 2.07070707
 2.09090909 2.11111111 2.13131313 2.15151515 2.17171717 2.19191919
 2.21212121 2.23232323 2.25252525 2.27272727 2.29292929 2.31313131
 2.33333333 2.35353535 2.37373737 2.39393939 2.41414141 2.43434343
 2.45454545 2.47474747 2.49494949 2.51515152 2.53535354 2.55555556
 2.57575758 2.5959596  2.61616162 2.63636364 2.65656566 2.67676768
 2.6969697  2.71717172 2.73737374 2.75757576 2.77777778 2.7979798
 2.81818182 2.83838384 2.85858586 2.87878788 2.8989899  2.91919192
 2.93939394 2.95959596 2.97979798 3.        ],error=4217.362019403632
Running:
After 50 times w = [3.37361812e+92 3.37361812e+92 3.37361812e+92 3.37361812e+92
 3.37361812e+92 3.37361812e+92 3.37361812e+92 3.37361812e+92
 3.37361812e+92 3.37361812e+92 3.37361812e+92 3.37361812e+92
...
 2.6302579e+90 2.6302579e+90 2.6302579e+90 2.6302579e+90 2.6302579e+90
 2.6302579e+90 2.6302579e+90 2.6302579e+90 2.6302579e+90 2.6302579e+90
 2.6302579e+90 2.6302579e+90 2.6302579e+90 2.6302579e+90 2.6302579e+90
 2.6302579e+90 2.6302579e+90 2.6302579e+90 2.6302579e+90 2.6302579e+90],error = 1.3779443376053316e+189

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