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(pytorch-深度学习系列)pytorch避免过拟合-dropout丢弃法的实现-学习笔记

程序员文章站 2022-07-13 09:58:27
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pytorch避免过拟合-dropout丢弃法的实现

对于一个单隐藏层的多层感知机,其中输入个数为4,隐藏单元个数为5,且隐藏单元 h i h_i hi i = 1 , … , 5 i=1, \ldots, 5 i=1,,5)的计算表达式为:
h i = ϕ ( x 1 w 1 i + x 2 w 2 i + x 3 w 3 i + x 4 w 4 i + b i ) h_i = \phi\left(x_1 w_{1i} + x_2 w_{2i} + x_3 w_{3i} + x_4 w_{4i} + b_i\right) hi=ϕ(x1w1i+x2w2i+x3w3i+x4w4i+bi)
这里 ϕ \phi ϕ是**函数, x 1 , … , x 4 x_1, \ldots, x_4 x1,,x4是输入,隐藏单元 i i i的权重参数为 w 1 i , … , w 4 i w_{1i}, \ldots, w_{4i} w1i,,w4i,偏差参数为 b i b_i bi。当对该隐藏层使用丢弃法时,该层的隐藏单元将有一定概率被丢弃掉。设丢弃概率为 p p p,那么有 p p p的概率 h i h_i hi会被清零,有 1 − p 1-p 1p的概率 h i h_i hi会除以 1 − p 1-p 1p做拉伸。丢弃概率是丢弃法的超参数。具体来说,设随机变量 ξ i \xi_i ξi为0和1的概率分别为 p p p 1 − p 1-p 1p。使用丢弃法时我们计算新的隐藏单元 h i ′ h_i' hi
h i ′ = ξ i 1 − p h i h_i' = \frac{\xi_i}{1-p} h_i hi=1pξihi
(这个公式就表示 h i ′ h_i' hi 1 − p 1-p 1p的概率为 h i h_i hi

由于 E ( ξ i ) = 1 − p E(\xi_i) = 1-p E(ξi)=1p,因此

E ( h i ′ ) = E ( ξ i ) 1 − p h i = h i E(h_i') = \frac{E(\xi_i)}{1-p}h_i = h_i E(hi)=1pE(ξi)hi=hi
即丢弃法不改变其输入的期望值。我们对隐藏层使用丢弃法,一种可能的结果是 h 2 h_2 h2 h 5 h_5 h5被清零。这时输出值的计算不再依赖 h 2 h_2 h2 h 5 h_5 h5,在反向传播时,与这两个隐藏单元相关的权重的梯度均为0。由于在训练中隐藏层神经元的丢弃是随机的,即 h 1 , … , h 5 h_1, \ldots, h_5 h1,,h5都有可能被清零,输出层的计算无法过度依赖 h 1 , … , h 5 h_1, \ldots, h_5 h1,,h5中的任一个,从而在训练模型时起到正则化的作用,并可以用来应对过拟合。在测试模型时,我们为了拿到更加确定性的结果,一般不使用丢弃法。

开始实现drop丢弃法避免过拟合

定义dropout函数:

%matplotlib inline
import torch
import torch.nn as nn
import numpy as np

def dropout(X, drop_prob):
    X = X.float()
    assert 0 <= drop_prob <= 1
    keep_prob = 1 - drop_prob
    # 这种情况下把全部元素都丢弃
    if keep_prob == 0:
        return torch.zeros_like(X)
    mask = (torch.rand(X.shape) < keep_prob).float()

    return mask * X / keep_prob

定义模型参数:

num_inputs, num_outputs, num_hiddens1, num_hiddens2 = 784, 10, 256, 256

W1 = torch.tensor(np.random.normal(0, 0.01, size=(num_inputs, num_hiddens1)), dtype=torch.float, requires_grad=True)
b1 = torch.zeros(num_hiddens1, requires_grad=True)
W2 = torch.tensor(np.random.normal(0, 0.01, size=(num_hiddens1, num_hiddens2)), dtype=torch.float, requires_grad=True)
b2 = torch.zeros(num_hiddens2, requires_grad=True)
W3 = torch.tensor(np.random.normal(0, 0.01, size=(num_hiddens2, num_outputs)), dtype=torch.float, requires_grad=True)
b3 = torch.zeros(num_outputs, requires_grad=True)

params = [W1, b1, W2, b2, W3, b3]

定义模型将全连接层和**函数ReLU串起来,并对每个**函数的输出使用丢弃法。分别设置各个层的丢弃概率。通常的建议是把靠近输入层的丢弃概率设得小一点。在这个实验中,我们把第一个隐藏层的丢弃概率设为0.2,把第二个隐藏层的丢弃概率设为0.5。我们可以通过参数is_training来判断运行模式为训练还是测试,并只在训练模式下使用丢弃法。

drop_prob1, drop_prob2 = 0.2, 0.5

def net(X, is_training=True):
    X = X.view(-1, num_inputs)
    H1 = (torch.matmul(X, W1) + b1).relu()
    if is_training:  # 只在训练模型时使用丢弃法
        H1 = dropout(H1, drop_prob1)  # 在第一层全连接后添加丢弃层
    H2 = (torch.matmul(H1, W2) + b2).relu()
    if is_training:
        H2 = dropout(H2, drop_prob2)  # 在第二层全连接后添加丢弃层
    return torch.matmul(H2, W3) + b3

def evaluate_accuracy(data_iter, net):
    acc_sum, n = 0.0, 0
    for X, y in data_iter:
        if isinstance(net, torch.nn.Module):
            net.eval() # 评估模式, 这会关闭dropout
            acc_sum += (net(X).argmax(dim=1) == y).float().sum().item()
            net.train() # 改回训练模式
        else: # 自定义的模型
            if('is_training' in net.__code__.co_varnames): # 如果有is_training这个参数
                # 将is_training设置成False
                acc_sum += (net(X, is_training=False).argmax(dim=1) == y).float().sum().item() 
            else:
                acc_sum += (net(X).argmax(dim=1) == y).float().sum().item() 
        n += y.shape[0]
    return acc_sum / n

训练和测试模型:

num_epochs, lr, batch_size = 5, 100.0, 256
loss = torch.nn.CrossEntropyLoss()

def load_data_fashion_mnist(batch_size, resize=None, root='~/Datasets/FashionMNIST'):
    """Download the fashion mnist dataset and then load into memory."""
    trans = []
    if resize:
        trans.append(torchvision.transforms.Resize(size=resize))
    trans.append(torchvision.transforms.ToTensor())
    
    transform = torchvision.transforms.Compose(trans)
    mnist_train = torchvision.datasets.FashionMNIST(root=root, train=True, download=True, transform=transform)
    mnist_test = torchvision.datasets.FashionMNIST(root=root, train=False, download=True, transform=transform)
    if sys.platform.startswith('win'):
        num_workers = 0  # 0表示不用额外的进程来加速读取数据
    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=False, num_workers=num_workers)

    return train_iter, test_iter

def train_ch3(net, train_iter, test_iter, loss, num_epochs, batch_size,
              params=None, lr=None, optimizer=None):
    for epoch in range(num_epochs):
        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
            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()  # “softmax回归的简洁实现”一节将用到
            
            
            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))
train_iter, test_iter = load_data_fashion_mnist(batch_size)
train_ch3(net, train_iter, test_iter, loss, num_epochs, batch_size, params, lr)