Learning Correlated Latent Representations with Adaptive Priors

Variational Auto-Encoders (VAEs) have been widely applied for learning compact low-dimensional latent representations for high-dimensional data. When the correlation structure among data points is available, previous work proposed Correlated Variational Auto-Encoders (CVAEs) which employ a structured mixture model as prior and a structured variational posterior for each mixture component to enforce the learned latent representations to follow the same correlation structure. However, as we demonstrate in this paper, such a choice can not guarantee that CVAEs can capture all of the correlations. Furthermore, it prevents us from obtaining a tractable joint and marginal variational distribution. To address these issues, we propose Adaptive Correlated Variational Auto-Encoders (ACVAEs), which apply an adaptive prior distribution that can be adjusted during training, and learn a tractable joint distribution via a saddle-point optimization procedure. Its tractable form also enables further refinement with belief propagation. Experimental results on two real datasets show that ACVAEs outperform other benchmarks significantly.