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Pytorch构建神经网络多元线性回归模型

article 2024/9/21 13:20:09

1.模型线性方程y = W ∗ X + b

from torch import nn
import torch

#手动设置的W参数（待模型学习），这里设置为12个，自己随意设置

weight_set=torch.tensor([[1.5,2.38,4.22,6.5,7.2,3.21,4.44,6.55,2.48,-1.75,-3.26,4.78]])

#手动设置的偏置b
bias=torch.tensor([7.25])

#生成100个随机的12个特征的点
torch.random.manual_seed(100)
x=torch.randint(1,10,(100,12))
x=x.float()
#将参数转置
weight_set_trans=weight_set.transpose(0,1)
#y=w*x+b
y_true=torch.matmul(x,weight_set_trans)+bias

2.定义单层的网络结构

#定义模型

class linear_model(nn.Module):
    def __init__(self):
        super().__init__()
        self.layer = nn.Linear(12,1)
    def forward (self, x):
        y = self.layer(x)
        return y
model=linear_model()
h=model(x)
for name ,param in model.named_parameters():
    print(f"{name}:{param}")

output:

layer.weight:Parameter containing:
tensor([[ 0.2429,  0.0523, -0.2873,  0.2485,  0.1396, -0.0960,  0.2534,  0.2423,
          0.0123, -0.2309, -0.2212,  0.0499]], requires_grad=True)
layer.bias:Parameter containing:
tensor([0.0503], requires_grad=True)

可以看到模型初始化的参数与设置的参数相差很大

3.模型训练

#定义优化器
optimizer=torch.optim.Adam(model.parameters(),lr=0.1)
#定义损失函数
criterion=nn.MSELoss()
#设置训练轮数
for epoch in range(5000):
    h=model(x)
    loss=criterion(h,y_true)
    #使用backward计算梯度
    loss.backward()
    #参数更新
    optimizer.step()
    optimizer.zero_grad() #梯度清零
    if epoch %100==0:
        print(f'after{epoch+1} iterations,train_loss:{loss.item():.3f}')
output:
after1 iterations,train_loss:36681.406
after101 iterations,train_loss:488.356
after201 iterations,train_loss:297.450
after301 iterations,train_loss:158.137
after401 iterations,train_loss:75.587
after501 iterations,train_loss:33.060
after601 iterations,train_loss:13.407
after701 iterations,train_loss:5.149
after801 iterations,train_loss:1.968
after901 iterations,train_loss:0.831
after1001 iterations,train_loss:0.445
after1101 iterations,train_loss:0.315
after1201 iterations,train_loss:0.268
after1301 iterations,train_loss:0.248
after1401 iterations,train_loss:0.236
after1501 iterations,train_loss:0.226
after1601 iterations,train_loss:0.218
after1701 iterations,train_loss:0.209
after1801 iterations,train_loss:0.200
after1901 iterations,train_loss:0.191


print(model.state_dict())

output:

OrderedDict({'layer.weight': tensor([[ 1.5698,  2.4342,  4.2689,  6.5287,  7.2732,  3.2440,  4.4685,  6.6003,
          2.5380, -1.7194, -3.2042,  4.8492]]), 'layer.bias': tensor([4.2708])})

#保存模型文件参数
torch.save(model.state_dict(),'lr.pth')


#模型预测

model_predict=linear_model()
#加载模型参数
model_predict.load_state_dict(torch.load('lr.pth'))

predict=model.predict(x)

可以看到经过1000次迭代之后，损失就很小了。最终模型训练的参数与开始设置的参数也比较接近。

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