Pytorch:多维线性回归

1.目标

拟合函数$ f(x) = 5.0x_1+4.0x_2+3.0x_3+3 $

2.理论

和一维线性回归大同小异。

3.实现

3.0 环境

python == 3.6
torch == 1.4

3.1 必要的包

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

3.2 创造数据并转换形式

# f(x)=5x1+4x2+3x3+3
x_train = np.array([[1,3,4],[2,4,2],[7,5,9], [2,5,6], [6,4,2],[8,2,7],[9,3,6],[1,6,8], [5,3,6],[3,7,3]], dtype=np.float32)
y_train = x_train[:,0]*5+x_train[:,1]*4+3*x_train[:,2]+3
y_train = y_train.reshape((10,1))

x_train = torch.from_numpy(x_train)
y_train = torch.from_numpy(y_train)

3.3 构造模型并创建对象

class MultiLinearRegression(nn.Module):
    def __init__(self):
        super(MultiLinearRegression, self).__init__()
        self.linear = nn.Linear(3,1)  # 因为3个变量映射1个输出
        
    def forward(self,x):
        out = self.linear(x)
        return out

model = MultiLinearRegression()

3.4 检查CUDA

if torch.cuda.is_available():
    model = model.cuda()
    x_train = x_train.cuda()
    y_train = y_train.cuda()

3.5 选择优化器

这里使用均方误差，学习率为0.001

criterion = nn.MSELoss()
optimizer = optim.SGD(model.parameters(), lr=1e-3)

3.6 开始训练

epoch = 0
while True:
    output = model(x_train)  # 前向传播
    loss = criterion(output, y_train)  # 损失计算
    loss_value = loss.data.cpu().numpy()  # 获取损失值
    optimizer.zero_grad()  # 梯度置零
    loss.backward()  # 反向传播
    optimizer.step()  # 更新梯度
    
    epoch += 1
    if epoch % 100 == 0:  # 每100步打印一次损失
        print('Epoch:{}, loss:{:.6f}'.format(epoch, loss_value))
    if loss_value <= 1e-3:
        break

3.7 查看结果

w = model.linear.weight.data.cpu().numpy()
b = model.linear.bias.data.cpu().numpy()
print('w:{},b:{}'.format(w,b))

# 结果为
w:[[5.0077577 4.0204782 3.004031 ]],b:[2.851891]

4.建议意见欢迎留言