python
复制代码
%matplotlib inline
import random
import torch
from d2l import torch as d2l
# 生成数据集
def synthetic_data(w, b, num_examples): #@save
"""生成y=Xw+b+噪声"""
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)
# 读取数据集
def data_iter(batch_size, features, labels):
# 获取x中特征的长度，转换成列表，通过for循环进行批量生成
num_examples = len(features)
indices = list(range(num_examples))
# 这些样本是随机读取的，没有特定的顺序
random.shuffle(indices)
for i in range(0, num_examples, batch_size):
# 此时获取的是向量了，最后如果不足批量大小取最后剩余的
batch_indices = torch.tensor(indices[i: min(i + batch_size, num_examples)])
yield features[batch_indices], labels[batch_indices]
# 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：线性回归模型
def linreg(X, w, b):
return torch.matmul(X, w) + b
# 定义优化算法sgd
# lr：学习率
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：
1、读取批量样本获取预测
2、计算损失，反向传播，存储每个参数的梯度
3、调用优化算法sgd来更新模型参数
4、输出每轮的损失
"""
lr = 0.03
num_epochs = 10
net = linreg
loss = squared_loss
for epoch in range(num_epochs):
for X, y in data_iter(batch_size, features, labels):
# X和y的小批量损失
# net()返回y=X*w+b，loss()返回(y'-y)^2/2
l = loss(net(X, w, b), y)\
# 因为l形状是(batch_size, 1)，而不是一个标量。L中的所有元素被加到一起
# 并以此计算关于[w, b]的梯度
l.sum().backward()
# sgd()：w = w - lr*w/batch_size
# 使用参数的梯度更新参数
sgd([w, b], lr, batch_size)
with torch.no_grad():
# loss(y_hat, y)
# net(features, w, b)相当于y_hat，labels相当于y
train_1 = loss(net(features, w, b), labels)
print(f'epoch {epoch + 1}, loss{float(train_1.mean()):f}')
# 输出w和b的估计误差
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}')