【深度学习pytorch】线性回归

线性回归从零开始实现

利用张量和自动微分

import torch
import random

# 生成数据集
def synthetic_data(w, b, num_examples):  
    """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)

# 小批量读取数据集
def data_iter(features, labels, batch_size):
    example_nums = len(features)
    indices = list(range(example_nums))
    random.shuffle(indices)
    for i in range(0, example_nums, batch_size):
        batch_indices = torch.tensor(indices[i:min(i+batch_size, example_nums)])
        yield features[batch_indices], labels[batch_indices]

# 定义模型、损失函数、优化算法
def lin_reg(X, w, b):
    return torch.matmul(X, w) + b

def loss_fun(y_hat, y):
    return ((y_hat - y) ** 2 / 2).sum()

def sgd(paras, lr, batch_size):
    with torch.no_grad():
        for para in paras:
            para -= lr * para.grad / batch_size
            para.grad.zero_()
            
# 训练模型
def train(w, b, features, labels, lr, batch_size, epoches):
    for i in range(epoches):
        for X, y in data_iter(features, labels, batch_size):
            y_hat = lin_reg(X, w, b)
            loss = loss_fun(y, y_hat)
            loss.backward()
            sgd([w, b], lr, batch_size)
        loss = loss_fun(y, y_hat)
        print('epoch {0}: loss {1}'.format(i, loss))
    return w, b

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

w, b = train(w, b, features, labels, 0.03, 10, 3)
print(w)
print(b)

 线性回归简洁实现

使用深度学习框架

import torch
import random
import numpy as np
from torch.utils import data
from torch import nn

# 生成数据集
def synthetic_data(w, b, num_examples):  
    """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 load_array(data_arrays, batch_size, is_train=True):  
    """构造一个PyTorch数据迭代器"""
    dataset = data.TensorDataset(*data_arrays)
    return data.DataLoader(dataset, batch_size, shuffle=is_train)

batch_size = 10
data_iter = load_array((features, labels), batch_size)

# 定义模型
net = nn.Sequential(nn.Linear(2, 1))      # nn是神经网络的缩写
"""Sequential类将多个层串联在一起。 ...
   当给定输入数据时，Sequential实例将数据传入到第一层， 然后将第一层的输出作为第二层的输入，以此类推"""
"""nn.Linear第一个参数指定输入特征形状，第二个指定输出特征形状"""

# 初始化模型参数
net[0].weight.data.normal_(0, 0.01)
net[0].bias.data.fill_(0)

# 损失函数
loss = nn.MSELoss()    # L2， 返回所有样本损失的均值

# 优化算法
trainer = torch.optim.SGD(net.parameters(), lr=0.03)

# 训练模型
num_epochs = 5
for epoch in range(num_epochs):
    for X, y in data_iter:
        l = loss(net(X) ,y)
        trainer.zero_grad()
        l.backward()
        trainer.step()
    l = loss(net(features), labels)
    print(f'epoch {epoch + 1}, loss {l:f}')
    
print(w)
print(b)