【PyTorch】正则化：L1范数，L2范数，Dropout

正则化
当数据集较小或者网络模型较简单，在进行一些处理的时候，很容易形成训练精度很高了，但是测试的误差仍然较大，为了解决这种过拟合的问题，需要进行正则化处理，有以下几种方式：

• 目标函数添加正则项：L1范数
• 目标函数添加正则项：L2f范数
• 当增强数据集后可使用dropout，获得更好的效果

正则化的详细的内容可参考：https://www.cnblogs.com/pinking/p/9310728.html
代码实现

L2正则化：

#高维线性回归
import torch
import torch.nn as nn
import numpy as np
import sys
import matplotlib.pyplot as plt
%matplotlib inline
n_train,n_test,num_inputs = 20,100,200
true_w,true_b = torch.ones(num_inputs,1)*0.01,0.05

features = torch.randn((n_train +n_test,num_inputs))
labels = torch.matmul(features,true_w)+true_b
labels += torch.tensor(np.random.normal(0,0.01,size = labels.size()),dtype = torch.float)
train_features ,test_features = features[:n_train,:],features[n_train:,:]
train_labels,test_labels = labels[:n_train],labels[n_train:]

#通过目标函数添加L2惩罚项来实现权重衰减
#初始化
def init_params():
    w = torch.randn((num_inputs,1),requires_grad = True)
    b = torch.zeros(1,requeires_grad = True)
    return [w,b]

#定义L2范数  1/2(w1+w2+..)^2
def l2_penaalty(w):
    return (w**2).sum()/2
#定义训练和测试模型  plt.semilogy对y轴使用了对数尺度
#x_vals：横坐标,y_vals：纵坐标 训练损失,x_label：横坐标的表头,y_label：纵坐标的表头,
#x2_vals=None,y2_vals=None 测试损失, legend=None：提示线型,figsize=(3.5,2.5）图像大小
def semilogy(x_vals,y_vals,x_label,y_label,x2_vals=None,y2_vals=None,
            legend=None,figsize=(3.5,2.5)):
    plt.xlabel(x_label)
    plt.ylabel(y_label)
    plt.semilogy(x_vals,y_vals)
    if x2_vals and y2_vals:
        plt.semilogy(x2_vals,y2_vals,linestyle=':')
        plt.legend(legend)

#定义训练和测试
batch_size, num_epochs, lr,loss = 1, 100, 0.003,torch.nn.MSELoss()
dataset = torch.utils.data.TensorDataset(train_features, train_labels)
train_iter = torch.utils.data.DataLoader(dataset, batch_size, shuffle=True)

def fit_and_plot_pytorch(wd):
    # 对权重参数衰减。权重名称一般是以weight结尾
    net = nn.Linear(num_inputs, 1)
    nn.init.normal_(net.weight, mean=0, std=1)
    nn.init.normal_(net.bias, mean=0, std=1)
    # 对权重参数衰减
    optimizer_w = torch.optim.SGD(params=[net.weight], lr=lr, weight_decay=wd)
    # 不对偏差参数衰减
    optimizer_b = torch.optim.SGD(params=[net.bias], lr=lr)  
    
    train_ls, test_ls = [], []
    for _ in range(num_epochs):
        for X, y in train_iter:
            #最小均方误差损失
            l = loss(net(X), y).mean()
            optimizer_w.zero_grad()
            optimizer_b.zero_grad()
            
            l.backward()
            
            # 对两个optimizer实例分别调用step函数，从而分别更新权重和偏差
            optimizer_w.step()
            optimizer_b.step()
        #将训练和测试损失添加到列表中
        train_ls.append(loss(net(train_features), train_labels).mean().item())
        test_ls.append(loss(net(test_features), test_labels).mean().item())
    semilogy(range(1, num_epochs + 1), train_ls, 'epochs', 'loss',
                 range(1, num_epochs + 1), test_ls, ['train', 'test'])
    print('L2 norm of w:', net.weight.data.norm().item())
#通过加大超参数 使得惩罚项的比重增大
fit_and_plot_pytorch(5)

Dropout

#dropout  不改变输入的期望值
import torch
import torch.nn as nn
import numpy as np
import sys
import torchvision
import torchvision.transforms as transforms

#获取fashion_mnist数据集
mnist_train = torchvision.datasets.FashionMNIST(root='~/Desktop/OpenCV_demo/Datasets/FashionMNIST', train=True, download=False, transform=transforms.ToTensor())
mnist_test = torchvision.datasets.FashionMNIST(root='~/Desktop/OpenCV_demo/Datasets/FashionMNIST', train=False, download=False, transform=transforms.ToTensor())
#获得训练和测试数据
if sys.platform.startswith('win'):
    num_workers = 0
else:
    num_workers = 4
train_iter = torch.utils.data.DataLoader(
    mnist_train,batch_size = batch_size,shuffle = True,num_workers =  num_workers)
test_iter = torch.utils.data.DataLoader(
    mnist_test,batch_size = batch_size,shuffle = True,num_workers =  num_workers)
 #定义dropout
 def dropout(X,drop_prob):
    X = X.float()
    assert 0<=drop_prob<=1
    keep_prob = 1-drop_prob
    #全部元素都丢弃
    if keep_prob ==0:
        #返回原来的元素
        return torch.zeros_like(X)
    mask = (torch.rand(X.shape)<keep_prob).float()
    
    return mask *X/keep_prob
   
#对模型的精度进行评估
def evaluate_accuracy(data_iter,net):
    acc_sum,n = 0.0,0
    for X,y in data_iter:
        if isinstance(net,torch.nn.Module):
            # 评估模式, 这会关闭dropout
            net.eval()
            #判断行和最大的元素是否与类别相同，即计算准确的元素的个数
            acc_sum += (net(X).argmax(dim=1)==y).float().sum().item()
            net.train()
        else:
            if ('is_training' in net.__code__.co_varnames):
                acc_sum += (net(X,is_training = False).argmax(dim=1)==y).float().sum()
            else:
                acc_sum += (net(X).argmax(dim=1) == y).float().sum().item()
        n += y.shape[0]
    #返回准确的元素概率
    return acc_sum / n

num_epochs,lr,batch_size= 5,100,256

def train_softmax(net,train_iter,test_iter,loss,num_epochs,batch_size,
                  params=None, lr=None, optimizer=None):
    for epoch in range(num_epochs):
        #损失值、正确数量、总数 初始化
        train_l_sum,train_acc_sum,n = 0.0,0.0,0
        
        for X,y in train_iter:
            y_hat = net(X)
            l = loss(y_hat,y).sum()
            
             # 梯度清零 损失函数和优化函数梯度清零
            if optimizer is not None:
                optimizer.zero_grad()
            elif params is not None and params[0].grad is not None:
                for param in params:
                    param.grad.data.zero_()
                    
            l.backward()
            if optimizer is None:
                sgd(params, lr, batch_size)
            else:
                optimizer.step() 
            
            train_l_sum += l.item()
            train_acc_sum +=(y_hat.argmax(dim=1)==y).sum().item()
            n += y.shape[0]
            
        test_acc = evaluate_accuracy(test_iter,net)
        print('epoch %d, loss %.4f, train acc %.3f,test acc %.3f'

              %(epoch+1,train_l_sum/n,train_acc_sum/n,test_acc))
#定义网络模型 
class FlattenLayer(nn.Module):
    def __init__(self):
        super(FlattenLayer,self).__init__()
    def forward(self,x):
        return x.view(x.shape[0],-1)
        
drop_prob1,drop_prob2 = 0.2,0.5
num_inputs,num_outputs,num_hiddens1,num_hiddens2 = 784,10,256,256
net = nn.Sequential(
        FlattenLayer(),
        nn.Linear(num_inputs, num_hiddens1),
        nn.ReLU(),
        nn.Dropout(drop_prob1),
        nn.Linear(num_hiddens1, num_hiddens2), 
        nn.ReLU(),
        nn.Dropout(drop_prob2),
        nn.Linear(num_hiddens2, 10)
        )

for param in net.parameters():
    nn.init.normal_(param, mean=0, std=0.01)
#训练网络
optimizer = torch.optim.SGD(net.parameters(), lr=0.5)
loss = torch.nn.CrossEntropyLoss()
train_softmax(net, train_iter, test_iter, loss, num_epochs, batch_size, None, None, optimizer)