生成欠拟合模型:

import torch
import torch.optim as optim
from study.torchData import tensorDataGenRe,mse_cla,fit,split_loader
import torch.nn as nn
import matplotlib.pyplot as plt

features,labels = tensorDataGenRe(w=[2,-1],bias=False,bag=2)

train,test = split_loader(features,labels)

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

    def forward(self,x):
        out = self.linear(x)
        return out

Lr = LR()

torch.manual_seed(929)
train_mse = []
test_mse = []
num_epochs = 10

for epochs in range(num_epochs):

    fit(net=Lr,epochs=epochs,criterion=nn.MSELoss(),optimizer=optim.SGD(Lr.parameters(),lr=0.03),batchdata=train)
    train_mse.append(mse_cla(train,Lr).detach().numpy())
    test_mse.append(mse_cla(test,Lr).detach().numpy())

if __name__ == __main__:
    print(train_mse)
    print(test_mse)
    # plt.plot(list(range(num_epochs)),train_mse)

优化:

增加网络复杂度(不增加激活函数):

class LR_1(nn.Module):
    def __init__(self,in_features=2,n_hidden=4,out_features=1):
        super(LR_1, self).__init__()
        self.linear = nn.Linear(in_features,n_hidden)
        self.linear = nn.Linear(n_hidden,out_features)

    def forward(self,x):
        zhat = self.linear(x)
        out = self.linear(zhat)
        return out

可以画图观察到，对于loss来说没有显著的提升，但是稳定性得以提高。所以加入简单的线性层并不能达到拟合高此项的目的，后续我们加入激活函数

带入激活函数:

class LR_1(nn.Module):
    def __init__(self,in_features=2,n_hidden=4,out_features=1):
        super(LR_1, self).__init__()
        self.linear1 = nn.Linear(in_features,n_hidden)
        self.linear2 = nn.Linear(n_hidden,out_features)

    def forward(self,x):
        zhat = self.linear1(x)
        out = self.linear2(zhat)
        return out

class sigmoid_LR(nn.Module):
    def __init__(self,in_features=2,n_hidden=4,out_features=1):
        super(sigmoid_LR, self).__init__()
        self.linear1 = nn.Linear(in_features, n_hidden)
        self.linear2 = nn.Linear(n_hidden, out_features)

    def forward(self, x):
        zhat = torch.sigmoid(self.linear1(x))
        out = self.linear2(zhat)
        return out
class tanh_LR(nn.Module):
    def __init__(self,in_features=2,n_hidden=4,out_features=1):
        super(tanh_LR, self).__init__()
        self.linear1 = nn.Linear(in_features, n_hidden)
        self.linear2 = nn.Linear(n_hidden, out_features)

    def forward(self, x):
        zhat = torch.tanh(self.linear1(x))
        out = self.linear2(zhat)
        return out
class relu_LR(nn.Module):
    def __init__(self,in_features=2,n_hidden=4,out_features=1):
        super(relu_LR, self).__init__()
        self.linear1 = nn.Linear(in_features, n_hidden)
        self.linear2 = nn.Linear(n_hidden, out_features)

    def forward(self, x):
        zhat = torch.relu(self.linear1(x))
        out = self.linear2(zhat)
        return out

sigmoid_LR = sigmoid_LR()
relu_LR = relu_LR()
tanh_LR = tanh_LR()
Lr = LR_1()
model_list = [Lr,sigmoid_LR,relu_LR,tanh_LR]
num_epochs = 20
torch.manual_seed(929)
train_mse = torch.zeros(len(model_list),num_epochs)
test_mse = torch.zeros(len(model_list),num_epochs)

for epochs in range(num_epochs):
    for i,model in enumerate(model_list):
        fit(net=model,epochs=epochs,criterion=nn.MSELoss(),optimizer=optim.SGD(Lr.parameters(),lr=0.03),batchdata=train)
        train_mse[i][epochs] = mse_cla(train,model).detach()
        test_mse[i][epochs] = mse_cla(test,model).detach()

对比之后可以确定的是，有relu激活函数的模型最稳定，且效果相对最好

后续在添加relu函数的神经元，效果反而会下降，称为’神经元坏死‘