pytorch简单线性回归模型

模型五步走

1、获取数据

     1. 数据预处理

     2.归一化

     3.转换为张量

2、定义模型

3、定义损失函数和优化器

4、模型训练

5、模型评估和调优

调优方法

6、可视化（可选）

示例代码

import torch
import torch.nn as nn
import numpy as np
import matplotlib.pyplot as plt
from sklearn.metrics import mean_absolute_error, r2_score

# print(np.__config__.show())

##1、生成数据
np.random.seed(42)
def generate_data(x, slope=2.0, intercept=1.0, noise_std=2.0):
    """
    生成带有噪声的线性数据 y = a*x + b + ε
    :param x: 输入特征
    :param slope: 斜率 a
    :param intercept: 截距 b
    :param noise_std: 噪声标准差
    :return: y 数据，以及真实参数 (slope, intercept)
    """
    y = slope * x + intercept + np.random.randn(len(x)) * noise_std
    return y, (slope, intercept)

# 使用示例
x = np.linspace(0, 10, 100)
y, true_params = generate_data(x, slope=2, intercept=1, noise_std=2)
print("真实参数:", true_params)

#归一化
x_norm = (x - x.min()) / (x.max() - x.min())
y_norm = (y - y.min()) / (y.max() - y.min())

#转换为pytorch张量
x_tensor = torch.tensor(x_norm, dtype=torch.float32).view(-1, 1)
y_tensor = torch.tensor(y_norm, dtype=torch.float32).view(-1, 1)

#2、定义模型
class LinearRegression(nn.Module):

    def __init__(self,input_size,output_size):
        super(LinearRegression, self).__init__()
        self.linear = nn.Linear(input_size,output_size)
    def forward(self, x):
        out = self.linear(x)
        return out

#实例化模型
model = LinearRegression(1,1)

#3、定义损失函数和优化器
criterion = nn.MSELoss()
optimizer = torch.optim.Adam(model.parameters(), lr=0.0005, weight_decay=1e-5)

#4、训练模型
num_epochs = 10000
torch.nn.init.xavier_normal_(model.linear.weight)
scheduler = torch.optim.lr_scheduler.ReduceLROnPlateau(optimizer, 'min', patience=5)

for epoch in range(num_epochs):
    #前向传播
    outputs = model(x_tensor)
    loss = criterion(outputs,y_tensor)

    #反向传播
    optimizer.zero_grad()
    loss.backward()
    optimizer.step()

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

#5、输出测试结果
print('训练完成!')
print(f'权重: {model.linear.weight.item():.4f}, 偏置: {model.linear.bias.item():.4f}')

#6、可视化
predicted = model(x_tensor).detach().numpy()
# 反归一化
predicted_unscaled = predicted * (y.max() - y.min()) + y.min()
y_true_unscaled = y_tensor.numpy() * (y.max() - y.min()) + y.min()

# 评估指标
mae = mean_absolute_error(y_true_unscaled, predicted_unscaled)
r2 = r2_score(y_true_unscaled, predicted_unscaled)

print(f'均方误差(MSE): {loss.item():.4f}')
print(f'平均绝对误差(MAE): {mae:.4f}')
print(f'R²决定系数(R²): {r2:.4f}')
r22 = r2_score(y_tensor.numpy(), predicted)
print(f"Model R² score: {r22:.4f}")

#中文乱码
plt.rcParams['font.sans-serif'] = ['SimHei']
plt.rcParams['axes.unicode_minus'] = False
plt.plot(x_tensor, y_tensor, 'ro', label='Original data')
plt.plot(x_tensor, predicted, label='拟合曲线')
plt.legend()
plt.show()