Following the procedure described in this SO question, I am trying to transform my (greatly performing) convolutional Autoencoder into a Variational version of the same Autoencoder. As explained in the cited post, this essentially boils down to adding the KL divergence in the loss and to adding a layer for the sampling.

My data is composed of 1D time series.

This is my code:

from __future__ import division
import numpy as np
import matplotlib.pyplot as plt
from keras.layers import Input, Dense, Lambda, Reshape, Conv1D, MaxPooling1D, UpSampling1D, Flatten
from keras.models import Model
from keras import backend as K
from keras import losses
from keras.callbacks import Callback

X_train = np.loadtxt(..)# here I load my data
X_test = np.loadtxt(..)

# dimension of input 
n_x = X_train.shape[1]

X_train = np.reshape(X_train, [1500, n_x, 1])
X_test = np.reshape(X_test, [500, n_x, 1])

# dimension of latent space (batch size by latent dim)
batch_size = 100
latent_dim = 2

x = Input(shape=(n_x, 1))
conv_1 = Conv1D(8, kernel_size=16,
                padding='valid', activation='tanh')(x)
maxp1 = MaxPooling1D(2)(conv_1)
conv_2 = Conv1D(16, kernel_size=64,
                padding='valid', activation='tanh')(maxp1)
maxp2 = MaxPooling1D(2)(conv_2)
flatten = Flatten()(maxp2)
hidden = Dense(700, activation='tanh')(flatten)
hidden2 = Dense(400, activation='tanh')(hidden)

z_mean = Dense(latent_dim)(hidden2)
z_log_var = Dense(latent_dim)(hidden2)

epsilon_std = 1.0
def sampling(args):
    z_mean, z_log_var = args
    epsilon = K.random_normal(shape=(batch_size, latent_dim), 
                              mean=0., stddev=epsilon_std)
    return(z_mean + K.exp(z_log_var/2) * epsilon)

z = Lambda(sampling, output_shape=(latent_dim,))([z_mean, z_log_var])

decoder = Dense(700, activation='tanh')(z)
decoder = Reshape((700, 1))(decoder)
de_conv_1 = Conv1D(16, kernel_size=64, 
                   padding='valid', activation='tanh')(decoder)
upsamp = UpSampling1D(2)(de_conv_1)
de_conv_2 = Conv1D(8, kernel_size=16,
                   padding='valid', activation='tanh')(upsamp)
upsamp = UpSampling1D(2)(de_conv_2)
flatten = Flatten()(upsamp)
x_decoded_mean = Dense(n_x)(flatten)
x_decoded_mean = Reshape([n_x, 1])(x_decoded_mean)

epochs = 200

vae = Model(x, x_decoded_mean)

## define loss (sum of reconstruction and KL divergence)
def vae_loss(y_true, y_pred):
    # E[log P(X|z)]
    recon = K.sum(K.square(y_true - y_pred), axis=[1, 2])
    # D_KL(Q(z|X) || P(z|X))
    kl = K.exp(z_log_var) + K.square(z_mean) - 1. - z_log_var
    kl = 0.5 * K.sum(kl, axis=-1)
    return K.mean(recon + kl)
def KL_loss(y_true, y_pred):
    return(0.5 * K.sum(K.exp(z_log_var) + K.square(z_mean) - 1. - z_log_var, axis=-1))
def recon_loss(y_true, y_pred):
    return K.sum(K.square(y_true - y_pred), axis=[1, 2])
# compile and fit
vae.compile(optimizer='adam', loss=vae_loss, metrics = [KL_loss, recon_loss])
vae_hist = vae.fit(X_train, X_train, batch_size=batch_size, epochs=epochs,
                            validation_data = (X_test, X_test))

This results in horrible reconstructions. I am wondering if this has to do with the balance between KL and reconstruction loss, which is a notorious problem in Variational Autoencoder. However, even trying with different variations of using mean, sum etc in the definition of the KL and Reconstruction losses, the performance remains very poor. I have also tried with KL divergence Annealing, as explained e.g. here, but basically the problem I face in that case is that once the KL loss kicks in, the total loss stops decreasing.



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