pytorch搭建简单神经网络

一个基本的神经网络结构如图1和图2所示。图1是只有一个神经元的示意图，图2是一个含有隐藏层的简单神经网络。

如图1所示，当我们有一系列特征（input signals）为x1, x2, …xm，我们为其赋予对应的权重wk1,wk2,…xkm，对应相乘再相加，得到了x1wk1 + x2wk2 + x3wk3 + ... + xmwkm。我们再加上一个偏置（bias），得到一个总和sum。然后将这个值代入一个激活函数（比如sigmoid/relu等），得到最终值，输出。

图2是在图1的基础上，加入了隐藏层。我们对于LayerL1中的输入，赋予多组权重，计算可以得到Layer L2中的值，再对其中的值赋予权重a1, a2, a3，求出sum值，经过激活函数激活，输出。

图1 图2

以下用pytorch实现一个简单网络：

import torch
import numpy as np
from sklearn import datasets
import pandas as pd
# data
boston = datasets.load_boston()

housing_data = pd.DataFrame(boston.data)
housing_data.columns = boston.feature_names
# housing_data["Price"] = boston.target
housing_data.head(5)

from sklearn.model_selection import train_test_split
X_train, X_test, y_train, y_test = train_test_split(housing_data, boston.target, random_state = 1, test_size = 0.1)

class Net(torch.nn.Module):
    def __init__(self, n_feature, n_output):
        super(Net, self).__init__()
        self.hidden = torch.nn.Linear(n_feature, 100)
        self.predict = torch.nn.Linear(100, n_output)
    
    def forward(self,x):
        out = self.hidden(x)
        out = torch.relu(out)
        out = self.predict(out)
        return out
    
net = Net(13, 1) # 输入13个特征，输出1
    
# 定义loss
loss_func = torch.nn.MSELoss()

# 优化函数
optimizer = torch.optim.Adam(net.parameters(), lr=0.01)

#训练
x_train = torch.Tensor(np.array(X_train))
y_train = torch.Tensor(np.array(y_train))
x_test = torch.Tensor(np.array(X_test))
y_test = torch.Tensor(np.array(y_test))

loss_train_list = []
loss_test_list = []

for i in range(1000):    
    pred = net.forward(x_train)
    pred = torch.squeeze(pred)
    loss_train = loss_func(pred, y_train)

    optimizer.zero_grad() # 将梯度设为0
    loss_train.backward() # 反向传播
    optimizer.step()

    loss_train_list.append(loss_train)
    # test
    pred = net.forward(x_test)
    pred = torch.squeeze(pred)
    loss_test = loss_func(pred, y_test)
    loss_test_list.append(loss_test)

print('end!')

我们看看loss的分布：

import matplotlib.pyplot as plt
plt.plot(np.log(np.array(loss_train_list)), label='train')
plt.plot(np.log(np.array(loss_test_list)), label = 'test')
plt.legend(prop = {'size':18})
plt.show()