241013神经网络的线性回归模型

一.平方损失函数

#matplotlib inline
import random
import torch
from d2l import torch as d2l

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)

print('features:',features[0],'\nlablels:',labels[0])

d2l.set_figsize()
d2l.plt.scatter(features[:,1].detach().numpy(),
                labels.detach().numpy(),1);

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

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


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


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


def sgd(params, lr, batch_size):
    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=square_loss

for epoch in range(num_epochs):
    for x,y in data_iter(batch_size,features,labels):
        l=loss