浅谈VAE

1 理论

假设后验分布p(z|x)是服从正态分布。
两个loss， 一个是重构误差，一个是p(z）分布和标准正态分布的散度（假定p(z)是服从标准正态分布）。

2 实践

x = Input(shape=(original_dim,))
h = Dense(intermediate_dim, activation='relu')(x)

# 算p(Z|X)的均值和方差
z_mean = Dense(latent_dim)(h)
z_log_var = Dense(latent_dim)(h)

# 重参数技巧
def sampling(args):
    z_mean, z_log_var = args
    epsilon = K.random_normal(shape=(K.shape(z_mean)[0], latent_dim), mean=0.,
                              stddev=epsilon_std)
    return z_mean + K.exp(z_log_var / 2) * epsilon

# 重参数层，相当于给输入加入噪声
z = Lambda(sampling, output_shape=(latent_dim,))([z_mean, z_log_var])

# 解码层，也就是生成器部分
decoder_h = Dense(intermediate_dim, activation='relu')
decoder_mean = Dense(original_dim, activation='sigmoid')
h_decoded = decoder_h(z)
x_decoded_mean = decoder_mean(h_decoded)

# 建立模型
vae = Model(x, x_decoded_mean)

# xent_loss是重构loss，kl_loss是KL loss
xent_loss = original_dim * metrics.binary_crossentropy(x, x_decoded_mean)
kl_loss = - 0.5 * K.sum(1 + z_log_var - K.square(z_mean) - K.exp(z_log_var), axis=-1)
vae_loss = K.mean(xent_loss + kl_loss)

# add_loss是新增的方法，用于更灵活地添加各种loss
vae.add_loss(vae_loss)
vae.compile(optimizer='rmsprop')
vae.summary()

vae.fit(x_train,
        shuffle=True,
        epochs=epochs,
        batch_size=batch_size,
        validation_data=(x_test, None))


# 构建encoder，然后观察各个数字在隐空间的分布
encoder = Model(x, z_mean)

x_test_encoded = encoder.predict(x_test, batch_size=batch_size)
plt.figure(figsize=(6, 6))
plt.scatter(x_test_encoded[:, 0], x_test_encoded[:, 1], c=y_test_)
plt.colorbar()
plt.show()

# 构建生成器
decoder_input = Input(shape=(latent_dim,))
_h_decoded = decoder_h(decoder_input)
_x_decoded_mean = decoder_mean(_h_decoded)
generator = Model(decoder_input, _x_decoded_mean)

参考：
1github vae.py;
2 blog vae;
3 mnist.npz