1 导入所需要的包
import numpy as np import torch from torch import nn import matplotlib.pyplot as plt from IPython import display from torch.utils.data import TensorDataset ,DataLoader from sklearn.model_selection import train_test_split
2 自定义数据
要求：
1、生成单个数据集。
2、数据集的大小为10000且训练集大小为7000，测试集大小为3000。
3、数据集的样本特征维度p为500，且服从如下的高维线性函数：$y=0.028+\sum \limits _{i=1}^{p} 0.0056 x_{i}+\epsilon$
num_input,num_example = 500,10000 true_w = torch.tensor(np.ones((num_input,1)),dtype = torch.float32)*0.0056
# true_w = torch.ones(500,1)*0.0056
true_b = 0.028 x_data = torch.tensor(np.random.randn(num_example,num_input),dtype = torch.float32) y_data = torch.mm(x_data ,true_w)+true_b y_data += torch.normal(mean = 0,std = 0.001,size=y_data.size()) # y_dat += torch.tensor(np.random.normal(0, 0.01, size=y_data.size()), dtype=torch.float)
train_x,test_x,train_y,test_y = train_test_split(x_data,y_data,shuffle=True,test_size=0.3) print(train_x.shape) print(train_y.shape) print(test_x.shape) print(test_y.shape)
3 读取数据
batch_size = 50 train_datasets = TensorDataset(train_x,train_y) train_iter = DataLoader( dataset = train_datasets, batch_size = batch_size, shuffle = True, num_workers = 0 ) test_datasets = TensorDataset(test_x,test_y) test_iter = DataLoader( dataset = test_datasets, batch_size = batch_size, shuffle = True, num_workers = 0 )
4 初始化参数
num_hiddens , num_output = 256,1 w1 = torch.normal(mean = 0,std = 0.001,size = (num_hiddens,num_input), dtype=torch.float32) b1 = torch.ones(1,dtype = torch.float32) w2 = torch.normal(mean = 0,std = 0.001,size = (num_output,num_hiddens), dtype=torch.float32) b2 = torch.ones(1,dtype = torch.float32) params = [w1,w2,b1,b2] for param in params: param.requires_grad_(requires_grad=True)
5 定义隐藏层的激活函数
def ReLU(X): return torch.max(X,other = torch.tensor(0.0))
6 定义模型
def DNN(x): H = ReLU(torch.matmul(x,w1.t())+b1) H = ReLU(torch.matmul(H,w2.t())+b2) return H
7 定义最小化均方误差以及随机梯度下降法
loss = torch.nn.MSELoss() def SGD(paras,lr,batch_size): for param in params: param.data -= lr*param.grad/batch_size
8 定义训练函数
def train(model,train_iter,loss,num_epochs,batch_size,lr,optimizer =None): train_ls ,test_ls = [],[] for epoch in range(num_epochs): train_ls_sum,train_acc_num,n = 0,0,0 for x ,y in train_iter: y_pred = model(x) l = loss(y_pred,y) if params is not None and params[0].grad is not None: for param in params: param.grad.data.zero_() l.backward() SGD(params,lr,batch_size) train_ls.append(loss(model(train_x),train_y).item()) test_ls.append(loss(model(test_x),test_y).item()) print('epoch %d, train_loss %.6f,test_loss %f'%(epoch+1, train_ls[epoch],test_ls[epoch])) return train_ls,test_ls
9 训练
lr = 0.001 num_epochs = 500 train_loss ,test_lss =train(DNN,train_iter,loss,num_epochs,batch_size,lr)
10 可视化
x = np.linspace(0,len(train_loss),len(train_loss)) plt.plot(x,train_loss,label="train_loss",linewidth=1.5) plt.plot(x,test_loss,label="test_loss",linewidth=1.5) plt.xlabel("epoch") plt.ylabel("loss") plt.legend() plt.show()