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hih_ihi(i=1,…,5i=1, \ldots, 5i=1,…,5)的计算表达式为:
hi=ϕ(x1w1i+x2w2i+x3w3i+x4w4i+bi)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\phiϕ是激活函数,x1,…,x4x_1, \ldots, x_4x1,…,x4是输入,隐藏单元iii的权重参数为w1i,…,w4iw_{1i}, \ldots, w_{4i}w1i,…,w4i,偏差参数为bib_ibi。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ppp,那么有ppp的概率hih_ihi会被清零,有1−p1-p1−p的概率hih_ihi会除以1−p1-p1−p做拉伸。丢弃概率是丢弃法的超参数。具体来说,设随机变量ξi\xi_iξi为0和1的概率分别为ppp和1−p1-p1−p。使用丢弃法时我们计算新的隐藏单元hi′h_i'hi′
hi′=ξi1−phih_i' = \frac{\xi_i}{1-p} h_i hi′=1−pξihi
(这个公式就表示 hi′h_i'hi′有1−p1-p1−p的概率为hih_ihi)
由于E(ξi)=1−pE(\xi_i) = 1-pE(ξi)=1−p,因此
E(hi′)=E(ξi)1−phi=hiE(h_i') = \frac{E(\xi_i)}{1-p}h_i = h_i E(hi′)=1−pE(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h2h_2h2和h5h_5h5被清零。这时输出值的计算不再依赖h2h_2h2和h5h_5h5,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h1,…,h5h_1, \ldots, h_5h1,…,h5都有可能被清零,输出层的计算无法过度依赖h1,…,h5h_1, \ldots, h_5h1,…,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 inlineimport torchimport torch.nn as nnimport numpy as npdef dropout(X, drop_prob):X = X.float()assert 0 <= drop_prob <= 1keep_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, 256W1 = 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激活函数ReLU串起来,并对每个激活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, 0.5def 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) + b3def evaluate_accuracy(data_iter, net):acc_sum, n = 0.0, 0for X, y in data_iter:if isinstance(net, torch.nn.Module):net.eval() # 评估模式, 这会关闭dropoutacc_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Falseacc_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, 256loss = 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 = pose(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 = 4train_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_iterdef 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, 0for 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)
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