深度学习——线性回归（一）

一、线性回归实现（从零开始）

数据生成

python">import random
import torch
import matplotlib.pyplot as plt#***************** 1.数据生成函数 *****************
def synthetic_data(w = torch.tensor([2, -3.4]), b = 4.2, num_examples = 1000):x = torch.normal(0, 1, (num_examples, len(w)))y = torch.matmul(x, w) + by += torch.normal(0 , 0.01, y.shape)return x, y.reshape(-1, 1)

读取数据集

python">
#***************** 2.读取数据集 *****************
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]def data_iter_test():batch_size = 10x , y = synthetic_data(); for x, y in data_iter(batch_size, x, y):print(x, '\n', y)
data_iter_test()

初始化模型参数

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

定义线性回归模型

python">def Line_regression(x, w, b):""" 线性回归模型 """return torch .matmul(x, w) + b

损失函数

python">def squared_loss(y_predict, y):"""" 均方损失函数 """return (y_predict - y.reshape(y_predict.shape)) ** 2 / 2

优化算法

python">def sgd(params, lr, batch_size):"""" 小批量随机梯度下降 """with torch.no_grad():for param in params:param -= lr * param.grad / batch_sizeparam.grad.zero_()

模型训练

python">lr = 0.02
num_epochs = 4
batch_size = 10net = Line_regression
loss = squared_losstrue_w = w
true_b = b
def Model_train():train_x , train_y = synthetic_data(); for epoch in range(num_epochs):for x, y in data_iter(batch_size, features=train_x, label=train_y):l = loss(net(x, w, b), y)         # 小批量损失l.sum().backward()sgd([w, b], lr, batch_size)with torch.no_grad():train_l = loss(net(train_x, w ,b), train_y)print(f'epoch {epoch + 1}, loss {float(train_l.mean()):f}')print(f'w的估计误差: {(true_w - w)}')print(f'b的估计误差: {true_b - b}')
Model_train()

二、线性回归实现（调用torch库实现）

获取数据

python">import numpy as np
import torch
from torch.utils import data
# 数据生成
true_w = torch.tensor([2, -3.4])
true_b = 4.2
features, labels = synthetic_data(true_w, true_b, 1000)# 获取数据
def load_array(data_arrays, batch_size, is_train = True):dataset = data.TensorDataset(*data_arrays)return data.DataLoader(dataset=dataset, batch_size=batch_size, shuffle=is_train)batch_size = 10
data_iter = load_array((features, labels), batch_size)print(next(iter(data_iter)))

线性模型建立

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。下面建立一个一层的全连接层，并对参数进行初始化

python">from torch import nn
net = nn.Sequential(nn.Linear(2,1))net[0].weight.data.normal_(0, 0.01)        #初始权值w
net[0].bias.data.fill_(0)                  #初始偏置b

定义损失函数

损失函数有很多种，其中常用的有平方损失、均方损失、L1范数、L2范数等L1Loss：平均绝对误差 (MAE)NLLLoss：The negative log likelihood lossPoissonNLLLoss：Negative log likelihood loss with Poisson distribution of targetGaussianNLLLoss：Gaussian negative log likelihood lossKLDivLoss：The Kullback-Leibler divergence lossMSELoss： the mean squared error (squared L2 norm)BCELoss：Creates a criterion that measures the Binary Cross Entropy between the target and the input probabilities

python">loss = nn.MSELoss()
# 优化算法
trainer = torch.optim.SGD(net.parameters(), lr = 0.03)

训练模型

python">num_epochs = 3
print(f'w:{net[0].weight},b:{net[0].bias}')
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(f'w:{net[0].weight},b:{net[0].bias}')