  Variational autoencoders (VAEs), as well as other generative models, have
been shown to be efficient and accurate for capturing the latent structure of
vast amounts of complex high-dimensional data. However, existing VAEs can still
not directly handle data that are heterogenous (mixed continuous and discrete)
or incomplete (with missing data at random), which is indeed common in
real-world applications. In this paper, we propose a general framework to
design VAEs suitable for fitting incomplete heterogenous data. The proposed
HI-VAE includes likelihood models for real-valued, positive real valued,
interval, categorical, ordinal and count data, and allows accurate estimation
(and potentially imputation) of missing data. Furthermore, HI-VAE presents
competitive predictive performance in supervised tasks, outperforming
supervised models when trained on incomplete data.
