线性回归从零开始（麻雀虽小五脏俱全）

目录

• 构造数据集
• 初始化模型参数
• 定义模型
• 定义损失函数
• 定义优化算法
• 训练过程
• 线性回归的简洁实现
  • 读取数据
  • 使用框架预定义好的层
  • 初始化模型参数
  • 误差
  • 实例化SGD
  • 训练过程

线性回归是一个很好能理解深度学习的模型，麻雀虽小五脏俱全。

构造数据集

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)

定义一个获取小批量数据集的函数

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]
batch_size = 10

for X, y in data_iter(batch_size, features, labels):
    print(X, '\n', y)
    break

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 linreg(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

定义优化算法

def sgd(params, lr, batch_size):
  with torch.no_grad():
    for param in params:
      param -= lr * param.grad / batch_size
      param.grad.zero_()

训练过程

lr = 0.03
num_epochs = 3
net = linreg
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)
    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}')

线性回归的简洁实现

读取数据

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):
  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))

使用框架预定义好的层

from torch import nn

net = nn.Sequential(nn.Linear(2, 1))

初始化模型参数

net[0].weight.data.normal_(0, 0.01)
net[0].bias.data.fill_(0)

误差

loss = nn.MSELoss()

实例化SGD

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

训练过程

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}')