pytorch 线性回归

PyTorch是一款基于Python的科学计算库，主要用于机器学习和深度学习的研究。在PyTorch中，线性回归是最基本的机器学习模型之一，以下是PyTorch实现线性回归的示例代码。

首先，我们需要导入PyTorch库和一些必要的包：

import torch
import torch.nn as nn
import numpy as np
import matplotlib.pyplot as plt

接下来，我们需要定义一些超参数：

input_size = 1
output_size = 1
num_epochs = 60
learning_rate = 0.001

这里，我们定义了输入和输出的维度，训练的轮数和学习率。

然后，我们需要准备训练数据和测试数据。在这个例子中，我们使用一个简单的数据集，包含了一些关于人口和收入的信息。我们的目标是根据人口预测收入。我们可以使用NumPy来生成数据集：

x_train = np.array([[1.2], [2.4], [3.6], [4.8], [6.0], [7.2], [8.4], [9.6], [10.8], [12.0]])
y_train = np.array([[2.5], [4.8], [7.1], [9.4], [11.7], [14.0], [16.3], [18.6], [20.9], [23.2]])

x_test = np.array([[1.5], [3.0], [4.5], [6.0], [7.5], [9.0], [10.5], [12.0], [13.5], [15.0]])
y_test = np.array([[3.2], [6.4], [9.6], [12.8], [16.0], [19.2], [22.4], [25.6], [28.8], [32.0]])

接下来，我们需要将数据转换为张量，并且创建一个线性回归模型。在这个例子中，我们使用PyTorch的nn.Linear模块来实现线性回归模型：

# Convert numpy arrays to torch tensors
x_train = torch.from_numpy(x_train).float()
y_train = torch.from_numpy(y_train).float()
x_test = torch.from_numpy(x_test).float()
y_test = torch.from_numpy(y_test).float()

# Create linear regression model
model = nn.Linear(input_size, output_size)

然后，我们需要定义损失函数和优化器。在这个例子中，我们使用均方误差（MSE）作为损失函数，使用随机梯度下降（SGD）作为优化器：

# Define loss function and optimizer
criterion = nn.MSELoss()
optimizer = torch.optim.SGD(model.parameters(), lr=learning_rate)

接下来，我们可以开始训练模型。在每个epoch中，我们将模型的输出与实际值进行比较，并计算损失。然后，我们使用反向传播算法更新模型的参数。

# Train the model
for epoch in range(num_epochs):
    # Forward pass
    outputs = model(x_train)
    loss = criterion(outputs, y_train)

    # Backward and optimize
    optimizer.zero_grad()
    loss.backward()
    optimizer.step()

    if (epoch+1) % 10 == 0:
        print('Epoch [{}/{}], Loss: {:.4f}'.format(epoch+1, num_epochs, loss.item()))

最后，我们可以使用测试集来评估模型的性能：

# Test the model
with torch.no_grad():
    predicted = model(x_test)
    test_loss = criterion(predicted, y_test)
    print('Test Loss: {:.4f}'.format(test_loss.item()))

    # Plot the graph
    plt.plot(x_test.numpy(), y_test.numpy(), 'ro', label='Original data')
    plt.plot(x_test.numpy(), predicted.numpy(), 'b-', label='Fitted line')
    plt.legend()
    plt.show()

完整代码如下：

import torch
import torch.nn as nn
import numpy as np
import matplotlib.pyplot as plt

# Hyper-parameters
input_size = 1
output_size = 1
num_epochs = 60
learning_rate = 0.001

# Toy dataset
x_train = np.array([[1.2], [2.4], [3.6], [4.8], [6.0], [7.2], [8.4], [9.6], [10.8], [12.0]])
y_train = np.array([[2.5], [4.8], [7.1], [9.4], [11.7], [14.0], [16.3], [18.6], [20.9], [23.2]])

x_test = np.array([[1.5], [3.0], [4.5], [6.0], [7.5], [9.0], [10.5], [12.0], [13.5], [15.0]])
y_test = np.array([[3.2], [6.4], [9.6], [12.8], [16.0], [19.2], [22.4], [25.6], [28.8], [32.0]])

# Convert numpy arrays to torch tensors
x_train = torch.from_numpy(x_train).float()
y_train = torch.from_numpy(y_train).float()
x_test = torch.from_numpy(x_test).float()
y_test = torch.from_numpy(y_test).float()

# Create linear regression model
model = nn.Linear(input_size, output_size)

# Define loss function and optimizer
criterion = nn.MSELoss()
optimizer = torch.optim.SGD(model.parameters(), lr=learning_rate)

# Train the model
for epoch in range(num_epochs):
    # Forward pass
    outputs = model(x_train)
    loss = criterion(outputs, y_train)

    # Backward and optimize
    optimizer.zero_grad()
    loss.backward()
    optimizer.step()

    if (epoch+1) % 10 == 0:
        print('Epoch [{}/{}], Loss: {:.4f}'.format(epoch+1, num_epochs, loss.item()))

# Test the model
with torch.no_grad():
    predicted = model(x_test)
    test_loss = criterion(predicted, y_test)
    print('Test Loss: {:.4f}'.format(test_loss.item()))

    # Plot the graph
    plt.plot(x_test.numpy(), y_test.numpy(), 'ro', label='Original data')
    plt.plot(x_test.numpy(), predicted.numpy(), 'b-', label='Fitted line')
    plt.legend()
    plt.show()