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Autoencoder 的基本概念

机器学习中包含监督学习和非监督学习，其中非监督学习简单来说就是学习人类没有标记过的数据。

对于没有标记的数据最常见的应用就是通过聚类(Clustering)的方式将数据进行分类。对于这些数据来说通常有非常多的维度或者说Features。如何降低这些数据的维度或者说“压缩”数据，从而减轻模型学习的负担，我们就要用到Autoencoder了。

ae.py

import torchvisionimport torchfrom torch import nnclass AE(nn.Module):    def __init__(self):        super(AE, self).__init__()        # [b, 784] => [b, 20]        self.encoder = nn.Sequential(            nn.Linear(784, 256),            nn.ReLU(),            nn.Linear(256, 64),            nn.ReLU(),            nn.Linear(64, 20),            nn.ReLU()        )        # [b, 20] => [b, 784]        self.decoder = nn.Sequential(            nn.Linear(20, 64),            nn.ReLU(),            nn.Linear(64, 256),            nn.ReLU(),            nn.Linear(256, 784),            nn.Sigmoid()        )    def forward(self, x):        # param x: [b, 1, 28, 28]        batchsz = x.size(0)        x = x.view(batchsz, 784)        x = self.encoder(x)        x = self.decoder(x)        x = x.view(batchsz, 1, 28, 28)        return x, None

main_ae.py

import torchfrom torch.utils.data import DataLoaderfrom torch import nn, optimfrom torchvision import transforms, datasetsfrom ae import AEimport visdomdef main():    mnist_train = datasets.MNIST('mnist_data', train=True, transform=transforms.Compose([        transforms.ToTensor()    ]), download=True)    mnist_train = DataLoader(mnist_train, batch_size=32, shuffle=True)    mnist_test = datasets.MNIST('mnist_data', train=False, transform=transforms.Compose([        transforms.ToTensor()    ]), download=True)    mnist_test = DataLoader(mnist_test, batch_size=32, shuffle=True)    x, _ = next(iter(mnist_train))    print('x:', x.shape)    # 训练    model = AE()    criteon = nn.MSELoss()    optimizer = optim.Adam(model.parameters(), lr=1e-3)    viz = visdom.Visdom()    print(model)    for epoch in range(1000):        for batchid, (x, _) in enumerate(mnist_train):            x_hat, kld = model(x)            loss = criteon(x_hat, x)            optimizer.zero_grad()            loss.backward()            optimizer.step()        print(epoch, 'loss', loss.item())        x, _ = next(iter(mnist_test))        print('好奇next(iter(mnist_test)) 后的x什么样子 print x: ', x)        # 看来 next(iter(mnist_test)) 是一下都装完呀        with torch.no_grad():            x_hat, kld = model(x)        viz.images(x, nrow=8, win='x', opts=dict(title='x'))        viz.images(x_hat, nrow=8, win='x_hat', opts=dict(title='x_hat'))if __name__ == '__main__':    main()

结果展示

VAE 的基本概念

KL divergence所表达的就是如果我们用一套最优的压缩机制(compression scheme)来储存Q的分布

相对熵，又称 KL散度( Kullback–Leibler divergence)，是描述两个概率分布P和Q差异的一种方法。它是非对称的，这意味着D(P||Q) ≠ D(Q||P)。

所谓KL散度，是指当某分布q(x)被用于近似p(x)时的信息损失。

vae.py

import torchvisionimport torchfrom torch import nnclass VAE(nn.Module):    def __init__(self):        super(VAE, self).__init__()        # [b, 784] => [b, 20]        self.encoder = nn.Sequential(            nn.Linear(784, 256),            nn.ReLU(),            nn.Linear(256, 64),            nn.ReLU(),            nn.Linear(64, 20),            nn.ReLU()        )        # [b, 20] => [b, 784]        self.decoder = nn.Sequential(            nn.Linear(10, 64),            nn.ReLU(),            nn.Linear(64, 256),            nn.ReLU(),            nn.Linear(256, 784),            nn.Sigmoid()        )    def forward(self, x):        # param x: [b, 1, 28, 28]        batchsz = x.size(0)        # flatten        x = x.view(batchsz, 784)        # encoder        h_ = self.encoder(x)    # [b, 20], including mean and sigma        mu, sigma = h_.chunk(2, dim=1)  # 把encoder后的东西 拆分，[b, 20] => [b, 10] and [b, 10]        h = mu + sigma * torch.randn_like(sigma)     # reparametrize trick, epison~N(0, 1)        # decoder        x_hat = self.decoder(h)        # reshape        x_hat = x_hat.view(batchsz, 1, 28, 28)        kld = 0.5 * torch.sum(            torch.pow(mu, 2) +            torch.pow(sigma, 2) -            torch.log(1e-8 + torch.pow(sigma, 2)) - 1        ) / (batchsz * 28 * 28)        return x_hat, kld

main_vae.py

import torchfrom torch.utils.data import DataLoaderfrom torch import nn, optimfrom torchvision import transforms, datasets# from    ae import AEfrom vae import VAEimport visdomdef main():    mnist_train = datasets.MNIST('mnist_data', train=True, transform=transforms.Compose([        transforms.ToTensor()    ]), download=True)    mnist_train = DataLoader(mnist_train, batch_size=32, shuffle=True)    mnist_test = datasets.MNIST('mnist_data', train=False, transform=transforms.Compose([        transforms.ToTensor()    ]), download=True)    mnist_test = DataLoader(mnist_test, batch_size=32, shuffle=True)    x, _ = next(iter(mnist_train))    print('x:', x.shape)    # 训练    # model = AE()    model = VAE()    criteon = nn.MSELoss()    optimizer = optim.Adam(model.parameters(), lr=1e-3)    viz = visdom.Visdom()    print(model)    for epoch in range(1000):        for batchid, (x, _) in enumerate(mnist_train):            x_hat, kld = model(x)            loss = criteon(x_hat, x)            if kld is not None:                elbo = - loss - 1.0 * kld                loss = - elbo            optimizer.zero_grad()            loss.backward()            optimizer.step()        print(epoch, 'loss', loss.item(), kld.item())        x, _ = next(iter(mnist_test))        # print('好奇next(iter(mnist_test)) 后的x什么样子 print x: ', x)        # 看来 next(iter(mnist_test)) 是一下都装完呀        with torch.no_grad():            x_hat, kld = model(x)        viz.images(x, nrow=8, win='x', opts=dict(title='x'))        viz.images(x_hat, nrow=8, win='x_hat', opts=dict(title='x_hat'))if __name__ == '__main__':    main()

结果展示

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