Abstract
The variational autoencoder (VAE) is a generative model with continuous
latent variables where a pair of probabilistic encoder (bottom-up) and decoder
(top-down) is jointly learned by stochastic gradient variational Bayes. We
first elaborate Gaussian VAE, approximating the local covariance matrix of the
decoder as an outer product of the principal direction at a position determined
by a sample drawn from Gaussian distribution. We show that this model, referred
to as VAE-ROC, better captures the data manifold, compared to the standard
Gaussian VAE where independent multivariate Gaussian was used to model the
decoder. Then we extend the VAE-ROC to handle mixed categorical and continuous
data. To this end, we employ Gaussian copula to model the local dependency in
mixed categorical and continuous data, leading to Gaussian copula
variational autoencoder (GCVAE). As in VAE-ROC, we use the rank-one
approximation for the covariance in the Gaussian copula, to capture the local
dependency structure in the mixed data. Experiments on various datasets
demonstrate the useful behaviour of VAE-ROC and GCVAE, compared to the standard
VAE.
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