一、VAE的具体结构

二、VAE的pytorch实现

1加载并规范化MNIST

 import相关类：

from __future__ import print_function
import argparse
import torch
import torch.utils.data
import torch.nn as nn
import torch.optim as optim
from torch.autograd import Variable
from torchvision import datasets, transforms

 设置参数：

parser = argparse.ArgumentParser(description='PyTorch MNIST Example')
parser.add_argument('--batch-size', type=int, default=128, metavar='N',
                    help='input batch size for training (default: 128)')
parser.add_argument('--epochs', type=int, default=10, metavar='N',
                    help='number of epochs to train (default: 10)')
parser.add_argument('--no-cuda', action='store_true', default=False,
                    help='enables CUDA training')
parser.add_argument('--seed', type=int, default=1, metavar='S',
                    help='random seed (default: 1)')
parser.add_argument('--log-interval', type=int, default=10, metavar='N',
                    help='how many batches to wait before logging training status')
args = parser.parse_args()
args.cuda = not args.no_cuda and torch.cuda.is_available()
print(args)

#Sets the seed for generating random numbers. And returns a torch._C.Generator object.
torch.manual_seed(args.seed)
if args.cuda:
    torch.cuda.manual_seed(args.seed)    

输出结果：

Namespace(batch_size=128, cuda=True, epochs=10, log_interval=10, no_cuda=False, seed=1)

下载数据集到./data/目录下：

kwargs = {'num_workers': 1, 'pin_memory': True} if args.cuda else {}
trainset = datasets.MNIST('../data', train=True, download=True,transform=transforms.ToTensor())
train_loader = torch.utils.data.DataLoader(
    trainset,
    batch_size=args.batch_size, shuffle=True, **kwargs)
testset= datasets.MNIST('../data', train=False, transform=transforms.ToTensor())
test_loader = torch.utils.data.DataLoader(
    testset,
    batch_size=args.batch_size, shuffle=True, **kwargs)
image, label = trainset[0]  
print(len(trainset))
print(image.size())
image, label = testset[0]  
print(len(testset))
print(image.size())

输出结果：

60000
torch.Size([1, 28, 28])
10000
torch.Size([1, 28, 28])

2定义VAE

首先我们介绍x.view方法：

x = torch.randn(4, 4)y = x.view(16)z = x.view(-1, 16)  # the size -1 is inferred from other dimensions
print(x)
print(y)
print(z)

输出结果：

 1.6154  1.1792  0.6450  1.2078
-0.4741  1.2145  0.8381  2.3532
 0.2070 -0.9054  0.9262  0.6758
 1.2613  0.5196 -1.7125 -0.0519
[torch.FloatTensor of size 4x4]
 1.6154
 1.1792
 0.6450
 1.2078
-0.4741
 1.2145
 0.8381
 2.3532
 0.2070
-0.9054
 0.9262
 0.6758
 1.2613
 0.5196
-1.7125
-0.0519
[torch.FloatTensor of size 16]
Columns 0 to 9 
 1.6154  1.1792  0.6450  1.2078 -0.4741  1.2145  0.8381  2.3532  0.2070 -0.9054

Columns 10 to 15 
 0.9262  0.6758  1.2613  0.5196 -1.7125 -0.0519
[torch.FloatTensor of size 1x16]

然后建立VAE模型

class VAE(nn.Module):
    def __init__(self):
        super(VAE, self).__init__()

        self.fc1 = nn.Linear(784, 400)
        self.fc21 = nn.Linear(400, 20)
        self.fc22 = nn.Linear(400, 20)
        self.fc3 = nn.Linear(20, 400)
        self.fc4 = nn.Linear(400, 784)

        self.relu = nn.ReLU()
        self.sigmoid = nn.Sigmoid()

    def encode(self, x):
        h1 = self.relu(self.fc1(x))
        return self.fc21(h1), self.fc22(h1)

    def reparametrize(self, mu, logvar):
        std = logvar.mul(0.5).exp_()
        eps = Variable(std.data.new(std.size()).normal_())
        return eps.mul(std).add_(mu)

    def decode(self, z):
        h3 = self.relu(self.fc3(z))
        return self.sigmoid(self.fc4(h3))

    def forward(self, x):
        mu, logvar = self.encode(x.view(-1, 784))
        z = self.reparametrize(mu, logvar)
        return self.decode(z), mu, logvar

model = VAE()
if args.cuda:
    model.cuda()

3.定义一个损失函数

reconstruction_function = nn.BCELoss()
reconstruction_function.size_average = False

def loss_function(recon_x, x, mu, logvar):
    BCE = reconstruction_function(recon_x, x.view(-1, 784))

    # see Appendix B from VAE paper:
    # Kingma and Welling. Auto-Encoding Variational Bayes. ICLR, 2014
    # https://arxiv.org/abs/1312.6114
    # 0.5 * sum(1 + log(sigma^2) - mu^2 - sigma^2)
    KLD_element = mu.pow(2).add_(logvar.exp()).mul_(-1).add_(1).add_(logvar)
    KLD = torch.sum(KLD_element).mul_(-0.5)

    return BCE + KLD


optimizer = optim.Adam(model.parameters(), lr=1e-3)

4.在训练数据上训练神经网络

我们只需要对数据迭代器进行循环，并将输入反馈到网络并进行优化。

for epoch in range(1, args.epochs + 1):
    train(epoch)
    test(epoch)

其中 

def train(epoch):
    model.train()
    train_loss = 0
    for batch_idx, (data, _) in enumerate(train_loader):
        data = Variable(data)
        if args.cuda:
            data = data.cuda()
        optimizer.zero_grad()
        recon_batch, mu, logvar = model(data)
        loss = loss_function(recon_batch, data, mu, logvar)
        loss.backward()
        train_loss += loss.data[0]
        optimizer.step()
        if batch_idx % args.log_interval == 0:
            print('Train Epoch: {} [{}/{} ({:.0f}%)]\tLoss: {:.6f}'.format(
                epoch, batch_idx * len(data), len(train_loader.dataset),
                100. * batch_idx / len(train_loader),
                loss.data[0] / len(data)))
            

    print('====> Epoch: {} Average loss: {:.4f}'.format(
          epoch, train_loss / len(train_loader.dataset)))


def test(epoch):
    model.eval()
    test_loss = 0
    for data, _ in test_loader:
        if args.cuda:
            data = data.cuda()
        data = Variable(data, volatile=True)
        recon_batch, mu, logvar = model(data)
        test_loss += loss_function(recon_batch, data, mu, logvar).data[0]

    test_loss /= len(test_loader.dataset)
    print('====> Test set loss: {:.4f}'.format(test_loss))

 Tips：

1.直接运行pytorch examples里的代码发现library not initialized at /pytorch/torch/lib/THC/THCGeneral.c错误

解决方案：sudo rm -r ~/.nv

2.该源码实现的论文为https://arxiv.org/pdf/1312.6114.pdf