1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
| import matplotlib.pyplot as plt
import random
import torch
import pandas as pd
import numpy as np
def synthetic_data(w, b, num_examples):
"""生成y = wX+b+噪声"""
X = torch.normal(0, 1, (num_examples, len(w)))
"""X是一个均值为0,方差为1的随机数,(num_examples, len(w))是样本量和样本长度"""
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)
"""以房价为例：label是真实售价；feature是预测label的两个因素。"""
print(features[0], labels[0])
plt.scatter(features[:, 1], labels, 1)
plt.show()
def data_iter(batch_size, features, labels):
"""定义一个data_iter函数,该函数接受批量大小,特征矩阵features和标签向量labels作为输入,生成大小为batch_size的小批量"""
num_example = len(features)
indices = list(range(num_example))
"""随机读取数据"""
random.shuffle(indices)
for i in range(0, num_example, batch_size):
batch_indices = torch.tensor(indices[i:min(i + batch_size, num_example)])
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
"""定义初始化模型"""
w = torch.normal(0, 0.01, size=(2, 1), requires_grad=True)
"""requires_grad=True 的作用是让 backward 可以追踪这个参数并且计算它的梯度"""
b = torch.zeros(1, requires_grad=True)
"""定义模型"""
def linreg(X, w, b):
""""线性回归"""
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"""
def sgd(params, lr, batch_size):
"""params是一个参数里面包含了w和d,lr为学习率"""
"""小批量梯度下降"""
with torch.no_grad():
for params in params:
params -= lr * params.grad / batch_size
params.grad.zero_()
print('_____________________________________________________________________________')
"""训练过程"""
lr = 0.01
num_epochs = 10
net = linreg
loss = squared_loss
for epoch in range(num_epochs):
"""先把数据扫一遍"""
for X, y in data_iter(batch_size, features, labels):
"""再拿出一个批量大小的x和y"""
l = loss(net(X,w,b),y)
"""把下x,w,b放在模型中做预测,把预测值与真实值y来做损失"""
"""x,y是小批量损失,l的形状是(batch_size,1),而不是一个标量"""
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的误差值:{true_w-w.reshape(true_w.shape)}')
print(f'b的误差值:{true_b-b}')
|
