线性回归模型实现——pytorch版

import random
import torch
from d2l import torch as d2l

def synthetic_data(w,b,num_examples):
    """生成y=Xw+b+噪声"""
    x = torch.normal(0,1,(num_examples,len(w))) #0 1 正态分布，num_examples个样本，len(w)列
    print('len是：'+str(len(w)))
    # 生成y
    y = torch.matmul(x,w) + b
    # 加入正态分布0 0.01的和y相等列的噪音
    y += torch.normal(0,0.01,y.shape)
    # -1代表自动计算维度，1代表一列
    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],'\nlabel:',labels[0])

# d2l.set_figsize()
# 画第一列和labels
# d2l.plt.scatter(features[:,(1)].detach().numpy(),labels.detach().numpy(),1)

def data_iter(batch_size,features,labels):
    # 查看一共有多少个样本
    num_examples = len(features)
    #获取样本索引
    indices = list(range(num_examples))
    # 把样本索引打乱
    random.shuffle(indices)
    for i in range(0,num_examples,batch_size):
        batch_indices = torch.tensor(
            # 从头开始按索引取值，防止去过头加了验证条件
            indices[i:min(i+batch_size,num_examples)]
        )
        # 随机顺序的特征和标号
        yield features[batch_indices],labels[batch_indices],

batch_size = 10
for x,y in data_iter(batch_size,features,labels):
    # x是10x1的tensor，y是10x1的向量
    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):
    """线性回归模型"""
    return torch.matmul(x,w)+b

def squared_loss(y_hat,y):
    """均方损失"""
    # 让预测值和真实值格式统一，做均方损失
    return (y_hat - y.reshape(y_hat.shape))**2/2

# 定义优化算法
def sgd(params,lr,batch_size):
    """小批量随机梯度下降"""
    with torch.no_grad():   #不更新梯度
        for param in params:
            # 对每个参数做梯度下降
            param -= lr*param.grad/batch_size
            # 梯度清零
            param.grad.zero_()

# 学习率
lr = 0.03
# 将模型扫3遍
num_epochs = 3
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
        l = loss(net(x,w,b),y)
        # 因为l的形状是(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()
        # 使用参数的梯度更新参数
        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的估计误差:{true_w-w.reshape(true_w.shape)}')
print(f'b的估计误差:{true_b-b}')

运行结果

len是：2
features: tensor([-0.2004, -2.0049]) 
label: tensor([10.6152])
tensor([[ 1.0884, -0.9585],
        [-0.1686,  0.4229],
        [-0.3642, -0.7151],
        [ 1.2426, -1.3948],
        [ 0.7473, -0.0862],
        [ 0.6056, -1.4912],
        [ 0.8237,  1.2756],
        [-0.0991, -1.0443],
        [-1.0252,  0.6845],
        [ 0.1991, -0.4367]]) 
 tensor([[ 9.6328],
        [ 2.4175],
        [ 5.9022],
        [11.4402],
        [ 5.9788],
        [10.4812],
        [ 1.5190],
        [ 7.5556],
        [-0.1732],
        [ 6.0907]])
epoch1,loss0.032279
epoch2,loss0.000108
epoch3,loss0.000048
w的估计误差:tensor([-0.0004,  0.0002], grad_fn=<SubBackward0>)
b的估计误差:tensor([0.0003], grad_fn=<RsubBackward1>)