线性回归两种实现方式

方式1-自构造

%matplotlib inline
import random
import torch
from d2l import torch as d2l

根据带有噪声的线性模型构造一个人造数据集，我们使用线性模型参数w =[2,-3.4].T、b=4.2和噪声向e生成数据集及其标签：y = Xw+b+e

def synthetic_data(w,b,num_examples):
    X = torch.normal(0,1,(num_examples,len(w)))
    y = torch.matmul(X,w)+b
    y += torch.normal(0,0.01,y.shape)
    return X , y.reshape((-1,1))
true_w = torch.tensor([2,-3.4])
true_b = 4.2
features,labels = synthetic_data(true_w,true_b,1000)
print('features:',features[0],'\nlabel:',labels[0])

features: tensor([ 1.2775, -0.2630])
label: tensor([7.6531])

d2l库 可换成matplotlib库

d2l.set_figsize()
d2l.plt.scatter(features[:,1].detach().numpy(),labels.detach().numpy(),1)  #detach出来才能转到numpy里面去

定义一个data_iter函数，该函数接收批量大小，特征矩阵和标签向量作为输入，生成大小为batch_size的小批量

def data_iter(batch_size,features,labels):
    num_examples = len(features)
    indices = list(range(num_examples))
    #这些样本随机读取，没有特定顺序
    random.shuffle(indices)#下标随机打乱
    for i in range(0,num_examples,batch_size):
        batch_indices = torch.tensor(indices[i:min(i+batch_size,num_examples)])
        
        yield features[batch_indices],labels[batch_indices] #产生随机index的特征和标号
batch_size = 10
for X , y in data_iter(batch_size,features,labels):
    print(X, '\n', y )
    break

定义初始化模型参数

w = torch.normal(0,0.01,size=(2,1),requires_grad = True)
b = torch.zeros(1,requires_grad=True)

定义模型

def linereg(X,w,b):
    return torch.matmul(X,w)+b

定义损失函数

def squared_loss(y_hat,y):
    return(y_hat - y.reshape(y_hat.shape))**2 / 2  #y.reshape(y_hat.shape)) y reshape 成 y_hat 的 shape

定义优化算法

def sgd(params,lr,batch_size):
    '''小批量sgd'''
    with torch.no_grad():
        for param in params:
            param -= lr*param.grad / batch_size
            param.grad.zero_()  #手动梯度置为0，防止下一次计算的梯度与上一次计算的梯度相关

训练

lr = 0.01
num_epochs = 10
net = linereg
loss = squared_loss
for epoch in range(num_epochs):
    for X , y in data_iter(batch_size,features,labels):
        l = loss(net(X,w,b),y)#‘X’和‘y’的小批量损失
        #因为‘l’形状是（batch_size,1）,不是一个标量
        l.sum().backward()#求和
        sgd([w,b],lr,batch_size)#使用参数的梯度更新参数
    with torch.no_grad():
        train_l = loss(net(features,w,b),labels)
        print(f'epoch {epoch + 1},loss {float(train_l.mean()):f}')

方式2-调torch.nn

import numpy as np
import torch
from torch.utils import data
from d2l import torch as d2l
ture_w = torch.tensor([2,-3.4])
ture_b = 4.2
features, labels = d2l.synthetic_data(ture_w,ture_b,10000)

构造数据迭代器

def load_array(data_arrays,batch_size,is_train=True):
    '''构造一个Pytorch数据迭代器'''
    dataset = data.TensorDataset(*data_arrays)
    return data.DataLoader(dataset,batch_size, shuffle = is_train)
batch_size = 10
data_iter = load_array((features,labels),batch_size)
next = (iter(data_iter))

回归网络 （回归相当于单层全连接网络）

from torch import nn
net  = nn.Sequential(nn.Linear(2,1))
net[0].weight.data.normal_(0,0.01)  #normal_   用正态分布替换data的值
net[0].bias.data.fill_(0)

MSE损失

loss = nn.MSELoss()

实例化SGD

trainer = torch.optim.SGD(net.parameters(),lr=0.03)
num_epochs = 3

for epoch in range(num_epochs):
    for X , y in data_iter:
        l = loss(net(X),y)
        trainer.zero_grad()
        l.backward()
        trainer.step()
    l = loss(net(features),labels)

    print(f'epoch {epoch + 1},loss {float(train_l.mean()):f}')