从零实现线性回归

生成数据

import torch
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(0,0.1,y.shape)
    return X,y.reshape((-1,1))
true_w=torch.tensor([2,-3.4]).reshape(2,1)
true_b=4.2
features,label=synthetic_data(true_w,true_b,500)
print(f'features的值{features[0]},label的值{label[0]}')

可视化

import matplotlib.pyplot as plt
# 创建三维坐标系
fig = plt.figure()
ax = fig.add_subplot(projection='3d')
ax.scatter(features[:,0],features[:,1],label)

plt.scatter(features[:,0],label)

plt.scatter(features[:,1],label)

读取数据集

import random
def data_iter(batch_size,features,label):
    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],label[batch_indices]
for x,y in data_iter(10,features,label):
    print(x,y)
    break

搭建模型

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

损失函数

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

随机梯度下降

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

w=torch.normal(0,0.01,size=(2,1),requires_grad=True)
b=torch.tensor(1.0,requires_grad=True)
lr=0.03
num_epochs=5
batch_size=5
net=linreg
loss=squared_loss
for epoch in range(num_epochs):
    for x,y in data_iter(batch_size,features,label):
        l=loss(net(x,w,b),y)
        l.sum().backward()
        sgd([w,b],lr,batch_size)
    with torch.no_grad():
        train_l=loss(net(features,w,b),label)
        print(f'第{epoch+1}轮损失为{train_l.mean()}')

w-true_w,b-true_b

线性回归简明实现

读取数据

from torch.utils import data
def data_iter(data_array,batch_size,is_train=True):
    datasets=data.TensorDataset(*data_array)
    return data.DataLoader(datasets,batch_size,shuffle=is_train)

神经网络

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)

损失函数

loss=nn.MSELoss()

优化器

trainer=torch.optim.SGD(net.parameters(),lr=0.03)

训练

epochs_num=5
for epoch in range(epochs_num):
    for x,y in data_iter((features,label),batch_size):
        l=loss(net(x),y)
        trainer.zero_grad()
        l.backward()
        trainer.step()
    l=loss(net(features),label)
    print(f'第{epoch+1}轮损失为{l}')

net[0].weight.data.reshape(true_w.shape)-true_w,net[0].bias.data-true_b