001.从0开始实现线性回归(pytorch)

000动手从0实现线性回归

0. 背景介绍

我们构造一个简单的人工训练数据集，它可以使我们能够直观比较学到的参数和真实的模型参数的区别。

设训练数据集样本数为1000，输入个数（特征数）为2。给定随机生成的批量样本特征 X∈R1000×2

X∈R 1000×2 ，我们使用线性回归模型真实权重 w= $2,-3.4$ ⊤ 和偏差 b=4.2以及一个随机噪声项 ϵϵ 来生成标签

python 复制代码

# 需要导入的包
import numpy as np
import torch
import random
from d2l import torch as d2l
from IPython import display
from matplotlib import pyplot as plt

1. 生成数据集合（待拟合）

使用python生成待拟合的数据

python 复制代码

num_input = 2
num_example = 1000
w_true = [2,-3.4]
b_true = 4.2
features = torch.randn(num_example,num_input)
print('features.shape = '+ str(features.shape) )
labels =  w_true[0] * features[:,0] + w_true[1] * features[:,1] + b_true
labels += torch.tensor(np.random.normal(0,0.01 , size = labels.size() ),dtype = torch.float32)
print(features[0],labels[0])

2.数据的分批量处理

python 复制代码

def data_iter(batch_size, features, labels):
    num_example = len(labels)
    indices = list(range(num_example))
    random.shuffle(indices)
    for i in range(0, num_example, batch_size):
        j = torch.tensor( indices[i:min(i+ batch_size,num_example)])
        yield features.index_select(0,j) ,labels.index_select(0,j)

3. 模型构建及训练

3.1 定义模型：

python 复制代码

def linreg(X, w, b):
    return torch.mm(X,w)+b

3.2 定义损失函数

python 复制代码

def square_loss(y, y_hat):
    return (y_hat - y.view(y_hat.size()))**2/2

3.3 定义优化算法

python 复制代码

def sgd(params , lr ,batch_size):
    for param in params:
        param.data  -= lr * param.grad / batch_size

3.4 模型训练

python 复制代码

# 设置超参数
lr = 0.03
num_epochs =5
net = linreg
loss = square_loss
batch_size = 10
for epoch in range(num_epochs):
    for X,y in data_iter(batch_size= batch_size,features=features,labels= labels):
        l = loss(net(X,w,b),y).sum()
        l.backward()
        sgd([w,b],lr,batch_size=batch_size)
        #梯度清零避免梯度累加
        w.grad.data.zero_()
        b.grad.data.zero_()
    train_l = loss(net(features,w,b),labels)
    print('epoch %d, loss %f' %(epoch +1 ,train_l.mean().item()))

epoch 1, loss 0.032550

epoch 2, loss 0.000133

epoch 3, loss 0.000053

epoch 4, loss 0.000053

epoch 5, loss 0.000053

基于pytorch的线性模型的实现

相关数据和初始化与上面构建相同
定义模型

python 复制代码

import torch
from torch import nn
class LinearNet(nn.Module):
    def __init__(self, n_feature):
        # 调用父类的初始化
        super(LinearNet,self).__init__()
        # Linear(输入特征数，输出特征的数量，是否含有偏置项)
        self.linera = nn.Linear(n_feature,1)

    def forward(self,x):
        y = self.linera(x)
        return y
#打印模型的结构：
net = LinearNet(num_input)
print(net) 
# LinearNet( (linera): Linear(in_features=2, out_features=1, bias=True)
)

初始化模型的参数

python 复制代码

from torch.nn import init
init.normal_(net.linera.weight,mean=0,std= 0.1)
init.constant_(net.linera.bias ,val=0)

定义损失函数

loss = nn.MSELoss()

5.定义优化算法

python 复制代码

import torch.optim as optim
optimizer =  optim.SGD(net.parameters(),lr = 0.03)
print(optimizer)

训练模型：

python 复制代码

num_epochs = 3
for epoch in range(1,num_epochs+1):
    for X,y in data_iter(batch_size= batch_size,features=features,labels= labels):
        output= net(X)
        l = loss(output,y.view(-1,1))
        optimizer.zero_grad()
        l.backward()
        optimizer.step()
    print('epoch %d ,loss: %f' %(epoch,l.item()) )

epoch 1 ,loss: 0.000159

epoch 2 ,loss: 0.000089

epoch 3 ,loss: 0.000066