基于PyTorch的线性回归算法

1. 基于PyTorch使用Jupyter Notebook环境实现线性回归算法；
2. 使用均方差作为损失函数；
3. 使用随机批梯度下降作为参数优化算法；
4. 动画显示模型拟合数据的过程；
5. 序列化模型参数；

from __future__ import print_function
import torch
import torch.nn as nn
import numpy as np
import matplotlib.pyplot as plt

import time
%matplotlib inline
from IPython import display

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

# Toy dataset
x_train = np.array([[3.3], [4.4], [5.5], [6.71], [6.93], [4.168], 
                    [9.779], [6.182], [7.59], [2.167], [7.042], 
                    [10.791], [5.313], [7.997], [3.1]], dtype=np.float32)

y_train = np.array([[1.7], [2.76], [2.09], [3.19], [1.694], [1.573], 
                    [3.366], [2.596], [2.53], [1.221], [2.827], 
                    [3.465], [1.65], [2.904], [1.3]], dtype=np.float32)

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

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

# Train the model
for epoch in range(num_epochs):
    # Convert numpy arrays to torch tensors
    inputs = torch.from_numpy(x_train)
    targets = torch.from_numpy(y_train)

    # Forward pass
    outputs = model(inputs)
    loss = criterion(outputs, targets)
    
    # Backward and optimize
    optimizer.zero_grad()
    loss.backward()
    optimizer.step()
    
    if (epoch+1) % 5 == 0:
        predicted = model(torch.from_numpy(x_train)).detach().numpy()
        plt.plot(x_train, y_train, 'ro', label='Original data')
        plt.plot(x_train, predicted, label='Fitted line')
        plt.xlim((0,12))
        plt.ylim((-2,8))
        plt.legend()
        plt.show()
        display.clear_output(wait=True)
        plt.pause(1)
        #print ('Epoch [{}/{}], Loss: {:.4f}'.format(epoch+1, num_epochs, loss.item()))

# Plot the graph
predicted = model(torch.from_numpy(x_train)).detach().numpy()
plt.plot(x_train, y_train, 'ro', label='Original data')
plt.plot(x_train, predicted, label='Fitted line')
plt.legend()
plt.show()

# Save the model checkpoint
torch.save(model.state_dict(), 'model.ckpt')