线性回归 李沐

简介

采用传统的梯度下降进行线性回归，线性函数 一般为 $$y = <w,x> + b$$ 的形式

code

import random
import torch
from d2l import torch as d2l



# 人造数据集
def synthetic_data(w, b, num_example):
    """生成 y=Xw+b+噪声"""
    X = torch.normal(0, 1, (num_example, len(w))) # 生成均值为0,方差为1的随即数， num_example 个样本， 列数为 w 的长度
    y = torch.matmul(X, w) + b
    y += torch.normal(0, 0.01, y.shape) # 加入正态分布的噪音
    return X, y.reshape((-1, 1)) # y 从行向量转为列向量

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


# 读数据集
def data_iter(batch_size, features, labels):
    num_examples = len(features)
    indices = list(range(num_examples))
    random.shuffle(indices) # 将序列的元素随即打乱
    for i in range(0, num_examples, batch_size): # i 从0 开始 然后
        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:", X, '\n y:', y)
    break;

# 初始化模型参数
w = torch.normal(0, 0.01, size=(2, 1), requires_grad = True) # requres_grad = True 表明需要计算梯度
b = torch.zeros(1, requires_grad = True) # 偏差 b 直接赋值为0, 标量

# 定义模型
def linreg(X, w, b):
    """现行回归模型"""
    return torch.matmul(X, w) + b

# 定义损失函数
def squared_loss(y_hat, y):
    """均方损失"""
    return (y_hat - y.reshape(y_hat.shape)) ** 2 / 2

# 定义优化算法
# param: [w, b], lr 即学习率
def sgd(params, lr, batch_size):
    """小批量随即梯度下降(mini-batch stochastic gradient descent)"""
    with torch.no_grad():
        for param in params:
            param -= lr * param.grad / batch_size
            param.grad.zero_()

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) # 因为 l 形状是 (batch_size, 1), 而不是一个标量
        l.sum().backward() # https://blog.csdn.net/qq_42750982/article/details/125023492 偏导数求和计算
        #  https://img-blog.csdnimg.cn/008c9c1f7b4b47ddac40a25b46439131.jpeg#pic_center  如何将l 关于 w 和b的偏导数  传递到 sgd 函数 猜测，应该存储在了 param.grad
        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}') # https://zhuanlan.zhihu.com/p/541191036  格式化输出


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}')
print("w ", w, " b ", b)d

简易实现

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):
    """构造一个Pyorch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))

from torch import nn
net = nn.Sequential(nn.Linear(2, 1))

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

loss = nn.MSELoss()

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 {l:f}')

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