本來以為自動編碼器是很簡單的東西，但是也是看了好多資料仍然不太懂它的原理。先把程式碼記錄下來，有時間好好研究。

這個例子是用MNIST資料集生成為例子。

# -*- coding: utf-8 -*-
"""
Created on Fri Oct 12 11:42:19 2018

@author: www
"""

import os

import torch
from torch.autograd import Variable
import torch.nn.functional as F
from torch import nn
from torch.utils.data import DataLoader

from torchvision.datasets import MNIST
from torchvision import transforms as tfs
from torchvision.utils import save_image


im_tfs = tfs.Compose([
    tfs.ToTensor(),
    tfs.Normalize([0.5, 0.5, 0.5], [0.5, 0.5, 0.5]) # 標準化
])

train_set = MNIST('E:\data', transform=im_tfs)
train_data = DataLoader(train_set, batch_size=128, shuffle=True)

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

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

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

    def reparametrize(self, mu, logvar):
        std = logvar.mul(0.5).exp_()
        eps = torch.FloatTensor(std.size()).normal_()
        if torch.cuda.is_available():
            eps = Variable(eps.cuda())
        else:
            eps = Variable(eps)
        return eps.mul(std).add_(mu)

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

    def forward(self, x):
        mu, logvar = self.encode(x) # 編碼
        z = self.reparametrize(mu, logvar) # 重新引數化成正態分佈
        return self.decode(z), mu, logvar # 解碼，同時輸出均值方差


net = VAE() # 例項化網路
if torch.cuda.is_available():
    net = net.cuda()
    
x, _ = train_set[0]
x = x.view(x.shape[0], -1)
if torch.cuda.is_available():
    x = x.cuda()
x = Variable(x)
_, mu, var = net(x)

print(mu)

#可以看到，對於輸入，網路可以輸出隱含變數的均值和方差，這裡的均值方差還沒有訓練

#下面開始訓練

reconstruction_function = nn.MSELoss(size_average=False)

def loss_function(recon_x, x, mu, logvar):
    """
    recon_x: generating images
    x: origin images
    mu: latent mean
    logvar: latent log variance
    """
    MSE = reconstruction_function(recon_x, x)
    # loss = 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)
    # KL divergence
    return MSE + KLD

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

def to_img(x):
    '''
    定義一個函式將最後的結果轉換回圖片
    '''
    x = 0.5 * (x + 1.)
    x = x.clamp(0, 1)
    x = x.view(x.shape[0], 1, 28, 28)
    return x

for e in range(100):
    for im, _ in train_data:
        im = im.view(im.shape[0], -1)
        im = Variable(im)
        if torch.cuda.is_available():
            im = im.cuda()
        recon_im, mu, logvar = net(im)
        loss = loss_function(recon_im, im, mu, logvar) / im.shape[0] # 將 loss 平均
        optimizer.zero_grad()
        loss.backward()
        optimizer.step()

    if (e + 1) % 20 == 0:
        print('epoch: {}, Loss: {:.4f}'.format(e + 1, loss.item()))
        save = to_img(recon_im.cpu().data)
        if not os.path.exists('./vae_img'):
            os.mkdir('./vae_img')
        save_image(save, './vae_img/image_{}.png'.format(e + 1))