【线性回归】使用 PyTorch 手写一个线性回归从零开始的训练过程

博客地址：https://www.cnblogs.com/zylyehuo/

一. 数据准备阶段

1. 导入库

%matplotlib inline
import random
import matplotlib.pyplot as plt
import torch
from d2l import torch as d2l

2. 合成数据

def synthetic_data(w, b, num_examples):
    # 生成 y = Xw + b + 噪声
    X = torch.normal(0, 1, (num_examples, len(w)))  # 生成num_examples行、len(w)列的正态分布数据
    y = torch.matmul(X, w) + b
    # 加一点噪声
    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)

3. 可视化数据

plt.scatter(features[:, 1].detach().numpy(), labels.detach().numpy(), 1)
plt.show()

二. 定义批量读取函数 (mini-batch)

def data_iter(batch_size, features, labels):
    num_examples = len(features)
    indices = list(range(num_examples))  
    random.shuffle(indices)  # 将索引打乱，随机取样
    for i in range(0, num_examples, batch_size):
        batch_indices = torch.tensor(indices[i: i + batch_size])
        yield features[batch_indices], labels[batch_indices]

三. 模型定义与损失函数

1. 线性模型

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

2. 损失函数

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

3. 小批量随机梯度下降

def sgd(params, lr, batch_size):
    with torch.no_grad():  # 关闭求梯度的上下文
        for param in params:
            param -= lr * param.grad / batch_size
            param.grad.zero_()  # 梯度清零

四. 训练过程

lr = 0.03
num_epochs = 3
batch_size = 10

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

for epoch in range(num_epochs):
    for X, y in data_iter(batch_size, features, labels):
        # 1. 计算模型输出
        y_hat = linreg(X, w, b)
        # 2. 计算损失
        l = squared_loss(y_hat, y)
        # 3. 反向传播
        l.sum().backward()
        # 4. 参数更新
        sgd([w, b], lr, batch_size)
    # 每个epoch结束后，打印一下训练误差
    train_l = squared_loss(linreg(features, w, b), labels)
    print(f'epoch {epoch + 1}, loss {float(train_l.mean()):f}')

五. 结果查看

print(true_w, '\n', w)
print(true_b, '\n', b)

六. 整体流程图（示意）