线性回归

机器学习算法之一，用于预测一个连续值。回归分析方法，通过拟合线性函数预测输出。通过继承nn.Module类实现

\[ y=\Sigma_{i=1}^{n} \omega_i x_i+ \text{bias} \]

• y: 预测值（目标值）
• x: 输入特征
• w： 参数（待学习权重）
• bias：偏置项

Example

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

torch.manual_seed(42)

X = torch.randn(100, 2)
true_w = torch.tensor([2.0, 3.0])
true_b = 4.0
Y = X @ true_w + true_b + torch.randn(100) * 0.1 #加入噪声
print(X[:5])
print(Y[:5])

class LinearRegressionModel(nn.Module):
    def __init__(self):
        super(LinearRegressionModel, self).__init__()
        self.linear = nn.Linear(2, 1)

    def forward(self, x):
        return self.linear(x) #返回预测结果


model = LinearRegressionModel()

criterion = nn.MSELoss()
optimizer = torch.optim.SGD(model.parameters(), lr=0.01)

for epoch in range(1000):
    model.train() #设置训练模式

    predictions = model(X)
    loss = criterion(predictions.squeeze(), Y)
    optimizer.zero_grad()
    loss.backward()
    optimizer.step()

    if (epoch+1) % 100 == 0:
        print(f'epoch [{epoch+1}/1000], Loss: {loss.item():.4f}')

print(f'Predicted weight: {model.linear.weight.data.numpy()}')
print(f'Predicted bias: {model.linear.bias.data.numpy()}')

with torch.no_grad():  # 评估时不需要计算梯度
    predictions = model(X)

# 可视化预测与实际值
plt.scatter(X[:, 0], Y, color='blue', label='True values')
plt.scatter(X[:, 0], predictions, color='red', label='Predictions')
plt.legend()
plt.savefig('output.png')  # 保存图像到文件