手动实现一个线性回归

不念不忘少年蓝@ 2023-07-10 15:56 6阅读 0赞

# -*- coding: utf-8 -*-
    # @Time     :2020/3/1 11:38
    # @Author   :XiaoMa
    # @File     :5.py
    import torch as t
    from matplotlib import pyplot as plt
    #设置随机数种子
    t.manual_seed(1000)
    from IPython import display
    
    def get_fake_data(batch_size=8):
        '''产生随机数据：y=x*2+3，加上了一些噪声'''
        x=t.rand(batch_size,1)*20
        y=x*2+(1+t.randn(batch_size,1))*3
        return x,y
    
    # x,y=get_fake_data()
    # plt.scatter(x.squeeze().numpy(),y.squeeze().numpy())
    # plt.show()
    
    #随机初始化参数
    w=t.rand(1,1)
    b=t.zeros(1,1)
    lr=0.001
    for ii in range(20000):
        x,y=get_fake_data()
    
    
        #forward:计算loss
        y_pred=x.mm(w) + b.expand_as(y)
        loss=0.5*(y_pred-y)**2  #均方误差
        loss=loss.sum()
    
        #backward：手动计算梯度
        dloss=1
        dy_pred=dloss*(y_pred-y)
    
        dw=x.t().mm(dy_pred)
        db=dy_pred.sum()
    
        #更新参数
        w.sub_(lr*dw)
        b.sub_(lr*db)
    
        if ii %1000==0:
            #画图
            display.clear_output(True)
            x=t.arange(0,20).view(-1,1)
            y=x.float().mm(w) + b.expand_as(x)
            plt.plot(x.numpy(),y.numpy())   #预测值
    
            x2,y2=get_fake_data(batch_size=20)
            plt.scatter(x2.numpy(),y2.numpy())  #true data
    
            plt.xlim(0,20)
            plt.ylim(0,41)
            plt.show()
            plt.pause(0.5)
            print('w:',w.item(),'b',b.item())

程序学习的结果：

w: 1.59645676612854 b 0.14356936514377594
    w: 1.95401132106781 b 2.5674352645874023
    w: 1.9625165462493896 b 2.9557881355285645
    w: 1.8890539407730103 b 3.001418352127075
    w: 2.0090134143829346 b 2.9461421966552734
    w: 2.0715832710266113 b 3.1086935997009277
    w: 1.9367080926895142 b 2.9967336654663086
    w: 2.0456297397613525 b 2.9070372581481934
    w: 1.8773678541183472 b 2.946399450302124
    w: 2.1052446365356445 b 3.148202419281006
    w: 1.81801438331604 b 3.0318338871002197
    w: 2.119907855987549 b 2.948784351348877
    w: 2.113875150680542 b 3.1145777702331543
    w: 1.9084047079086304 b 2.946380376815796
    w: 2.09352970123291 b 2.8815550804138184
    w: 2.078930616378784 b 3.0505666732788086
    w: 1.9736963510513306 b 3.040769100189209
    w: 1.9155480861663818 b 2.9243123531341553
    w: 2.0103886127471924 b 3.0951311588287354
    w: 1.8826669454574585 b 3.0347161293029785

w接近2，b接近3。

拟合的结果：

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dlaXhpbl8zODY2NDIzMg_size_16_color_FFFFFF_t_70][]

[watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dlaXhpbl8zODY2NDIzMg_size_16_color_FFFFFF_t_70]: https://img-blog.csdnimg.cn/2020030320343818.png?x-oss-process=image/watermark,type_ZmFuZ3poZW5naGVpdGk,shadow_10,text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dlaXhpbl8zODY2NDIzMg==,size_16,color_FFFFFF,t_70