Longitudinal Variational Autoencoder

Longitudinal datasets measured repeatedly over time from individual subjects, arise in many biomedical, psychological, social, and other studies. Such multivariate time-series are often high-dimensional and contain missing values. A common approach to analyse this kind of data is to learn a low-dimensional representation using variational autoencoders (VAEs). However, standard VAEs assume that the learned representations are i.i.d., and fail to capture the correlations between the data samples. We propose a novel deep generative model, Longitudinal VAE (L-VAE), that uses a multi-output additive Gaussian process (GP) prior to extend the VAE's capability to learn structured low-dimensional representations imposed by auxiliary covariate information, and also derive a new divergence upper bound for such GPs. Our approach can simultaneously accommodate both time-varying shared and random effects, produce structured low-dimensional representations, disentangle effects of individual covariates or their interactions, and achieve highly accurate predictive performance. We compare our model against previous methods on synthetic and clinical datasets, and demonstrate the state-of-the-art performance in data imputation, reconstruction, and long-term prediction tasks.