torch神经网络--线性回归

简单线性回归

y = 2*x + 1

import numpy as np
import torch
import torch.nn as nn


class LinearRegressionModel(nn.Module):
    def __init__(self, input_dim, output_dim):
        super(LinearRegressionModel, self).__init__()
        self.linear = nn.Linear(input_dim, output_dim)

    def forward(self, x):
        out = self.linear(x)
        return out


x_values = [i for i in range(11)]
x_train = np.array(x_values, dtype=np.float32)
x_train = x_train.reshape(-1, 1)
x_train.shape

y_values = [2*i+1 for i in x_values]
y_train = np.array(y_values, dtype=np.float32)
y_train = y_train.reshape(-1, 1)
y_train.shape
input_dim = 1
output_dim = 1
model = LinearRegressionModel(input_dim, output_dim)

# 如果使用GPU训练,增加以下两行代码
# device = torch.device('cuda:0' if torch.cuda.is_available() else 'cpu')
# model.to(device)


# 指定好参数和损失函数
epochs = 1000
learning_rate = 0.01
optimizer = torch.optim.SGD(model.parameters(), lr=learning_rate)
criterion = nn.MSELoss()

# 训练模型
for epoch in range(epochs):
    epoch += 1
    # 使用cpu时，注意转行成tensor
    inputs = torch.from_numpy(x_train)
    labels = torch.from_numpy(y_train)
    # 如果使用GPU训练,将以上两行代码修改为
    # inputs = torch.from_numpy(x_train).to(device)
    # labels = torch.from_numpy(y_train).to(device)

    # 梯度要清零每一次迭代
    optimizer.zero_grad()
    # 前向传播
    outputs = model(inputs)
    # 计算损失
    loss = criterion(outputs, labels)
    # 反向传播
    loss.backward()
    # 更新权重参数
    optimizer.step()

    # 打印
    if epoch % 50 == 0:
        print('epoch {}, loss {}'.format(epoch, loss.item()))


# CPU测试模型预测结果
predicted = model(torch.from_numpy(x_train).requires_grad_()).data.numpy()

# 模型的保存
torch.save(model.state_dict(), 'model.pkl')
# 模型读取
model.load_state_dict(torch.load('model.pkl'))

实例二：手写线性回归

import random
import torch
from d2l import torch as d2l


def synthetic_data(w, b, num_examples=100):
    """
    生成数据 y = Xw + b + 噪声 随机
    :param w:
    :param b:
    :param num_examples:
    :return:
    """
    # w = torch.tensor([2, -3.4])
    # b = 4.2
    # num_examples = 1000

    X = torch.normal(0,                          # 均值
                     1,                          # 方差
                     (num_examples, len(w)))     # 生成一个1000行，2列的矩阵
    y = torch.matmul(X, w) + b

    # 噪音
    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], '\nlabel:', labels[0])

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


def data_iter(batch_size, features, labels):
    """
    # 定义一个data_iter函数，该函数接收批量大小，特征矩阵和标签向量作为输入，生成大小为batch_size的小批量
    :param batch_size:
    :param features:
    :param labels:
    :return:
    """
    num_examples = len(features)
    # num_examples = 1000
    # batch_size = 32
    indices = list(range(num_examples))
    # 这些样本是随机读取的，没有特定顺序
    random.shuffle(indices)
    for i in range(0, num_examples, batch_size):
        # i = 1
        batch_indices = torch.tensor(indices[i:min(i+batch_size, num_examples)])
        yield features[batch_indices], labels[batch_indices]


# 初始化模型参数
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


# 定义损失函数
def squared_loss(y_hat, y):
    """均方损失"""
    return (y_hat - y.reshape(y_hat.shape)) ** 2 / 2

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


batch_size = 10
lr = 0.03
num_epochs = 3
net = linreg
loss = squared_loss

for epoch in range(num_epochs):
    for X, y in data_iter(batch_size, features, labels):
        l = loss(net(X, w, b), y)  # X和y的小批量损失
        # 因为l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()
        sgd([w, b], lr, batch_size)  # 使用参数的梯度更新参数
    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}')

print(f'w的估计值: {w}')
print(f'b的估计值: {b}')

实例三：线性回归调用torch

import random
import torch
from torch.utils import data    # 数据处理模块
from d2l import torch as d2l


def synthetic_data(w, b, num_examples=100):
    """
    生成数据 y = Xw + b + 噪声 随机
    :param w:
    :param b:
    :param num_examples:
    :return:
    """
    # w = torch.tensor([2, -3.4])
    # b = 4.2
    # num_examples = 1000

    X = torch.normal(0,                          # 均值
                     1,                          # 方差
                     (num_examples, len(w)))     # 生成一个1000行，2列的矩阵
    y = torch.matmul(X, w) + b

    # 噪音
    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], '\nlabel:', labels[0])

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


def load_array(data_arrays, batch_size, is_train=True):
    """
    构造一个pytorch数据迭代器
    :param data_arrays:
    :param batch_size:
    :param is_train:
    :return:
    """
    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)
next(iter(data_iter))

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

# nn是神经网络的缩写, 模型定义
from torch import nn
net = nn.Sequential(nn.Linear(2, 1))

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


# 定义损失函数
loss = nn.MSELoss()

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

# 训练
num_epochs = 3
for epoch in range(num_epochs):
    for X, y in data_iter:
        l = loss(net(X), y)
        opt.zero_grad()
        l.backward()
        opt.step()
    l = loss(net(features), labels)
    print(f'epoch {epoch + 1}, loss {l:f}')

w = net[0].weight.data
print('w的估计误差：', true_w - w.reshape(true_w.shape))
b = net[0].bias.data
print('b的估计误差：', true_b - b)

print(f'w的估计值: {w}')
print(f'b的估计值: {b}')