  The variational autoencoder (VAE) is a popular deep latent variable model
used to analyse high-dimensional datasets by learning a low-dimensional latent
representation of the data. It simultaneously learns a generative model and an
inference network to perform approximate posterior inference. Recently proposed
extensions to VAEs that can handle temporal and longitudinal data have
applications in healthcare, behavioural modelling, and predictive maintenance.
However, these extensions do not account for heterogeneous data (i.e., data
comprising of continuous and discrete attributes), which is common in many
real-life applications. In this work, we propose the heterogeneous longitudinal
VAE (HL-VAE) that extends the existing temporal and longitudinal VAEs to
heterogeneous data. HL-VAE provides efficient inference for high-dimensional
datasets and includes likelihood models for continuous, count, categorical, and
ordinal data while accounting for missing observations. We demonstrate our
model's efficacy through simulated as well as clinical datasets, and show that
our proposed model achieves competitive performance in missing value imputation
and predictive accuracy.
