动手学深度学习 代码（二）：线性回归

文章目录

• • 线性回归的从零开始实现
  • 线性回归的简洁实现

线性回归的从零开始实现

#%%
import torch
import random
from d2l import torch as d2l
#%%
#生成数据集
def synthetic_data(w, b, num_examples): #@save
    X = torch.normal(0, 1, (num_examples, len(w)))
    y = torch.matmul(X, w) + b
    y += torch.normal(0, 0.01, y.shape) # 噪声
    return X, y.reshape((-1, 1)) # 标量转换为向量

true_w = torch.tensor([2, -3.4])
true_b = 4.2
features, labels = synthetic_data(true_w, true_b, 1000)
#%%
d2l.set_figsize()
d2l.plt.scatter(features[:, 1].detach().numpy(), labels.detach().numpy(), 1)
d2l.plt.show()
#%% 读取数据集
def data_iter(batch_size, features, labels):
    num_examples = len(features)
    indices = list(range(num_examples))
    random.shuffle(indices)
    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]  # 一个生成器

#%%
batch_size = 10

for X, y in data_iter(batch_size, features, labels):
    print(X, '\n', y)
    break
#%% 初始化权重
w = torch.normal(0,0.01,size = (2, 1), requires_grad = True)
b = torch.zeros(1, requires_grad = True)
#%% 定义模型
def linreg(X, w, b):
    return torch.matmul(X, w) + b
#%% 损失函数
def square_loss(y_hat, y):
    return (y_hat - y.reshape(y_hat.shape)) ** 2/2
#%% 优化算法
def sgd(params, lr, batch_size):
    with torch.no_grad():
        for param in params:
            param -= lr * param.grad/batch_size
            param.grad.zero_()

#%%
lr = 0.05
num_epochs = 3
net = linreg
loss = square_loss

for epoch in range(num_epochs):
    for X, y in data_iter(batch_size, features, labels):
        l = loss(net(X, w, b), y)
        l.sum().backward()
        sgd([w, b], lr, batch_size)
    with torch.no_grad():
        train_l = loss(net(features, w, b), labels)
        print(f'epoch {epoch + 1}, loss {float(train_l.mean()):f}')

print(f'w的估计误差: {true_w - w.reshape(true_w.shape)}')
print(f'b的估计误差: {true_b - b}')

线性回归的简洁实现

#%%
import numpy as np
import torch
from torch.utils import data
from d2l import torch as d2l

#%%
true_w = torch.tensor([2, -3.4])
true_b = 4.2
features, labels = d2l.synthetic_data(true_w, true_b, 1000)

def load_array(data_arrays, batch_size, is_train = True): #@save
    '''pytorch数据迭代器'''
    dataset = data.TensorDataset(*data_arrays) # 把输入的两类数据一一对应；*表示对list解开入参
    return data.DataLoader(dataset, batch_size, shuffle = is_train) # 重新排序

batch_size = 10
data_iter = load_array((features, labels), batch_size) # 和手动实现中data_iter使用方法相同

#%%
# 构造迭代器并验证data_iter的效果
next(iter(data_iter))  # 获得第一个batch的数据

#%% 定义模型
from torch import nn
net = nn.Sequential(nn.Linear(2, 1))  # Linear中两个参数一个表示输入形状一个表示输出形状
# sequential相当于一个存放各层数据的list，单层时也可以只用Linear

#%% 初始化模型参数
# 使用net[0]选择神经网络中的第一层
net[0].weight.data.normal_(0, 0.01) # 正态分布
net[0].bias.data.fill_(0)

#%% 定义损失函数
loss = torch.nn.MSELoss()
#%% 定义优化算法
trainer = torch.optim.SGD(net.parameters(), lr=0.03) # optim module中的SGD
#%% 训练
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 {l:f}')

#%% 查看误差
w = net[0].weight.data
print('w的估计误差：', true_w - w.reshape(true_w.shape))
b = net[0].bias.data
print('b的估计误差：', true_b - b)

#%% 损失函数换成HuberLoss
loss = torch.nn.HuberLoss()
#%% 自己写HuberLoss
import torch.nn as nn
import torch.nn.functional as F

class Huberloss(nn.Module):
    '''huberloss sigma=1时为SoftL1Loss'''
    def __init__(self, sigma):
        super(Huberloss, self).__init__()
        self.sigma = sigma
    def forward(self, y, y_hat):
        if F.l1_loss(y, y_hat) > self.sigma:
            loss = F.l1_loss(y, y_hat) - self.sigma/2
        else:
            loss = (1/(2*self.sigma))*F.mse_loss(y, y_hat)
        return loss