  Variational Auto-Encoders (VAEs) have been widely applied for learning
compact, low-dimensional latent representations of 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 that the learned latent representations
follow the same correlation structure. However, as we demonstrate in this work,
such a choice cannot guarantee that CVAEs capture all 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 can learn a tractable
joint variational distribution. Its tractable form also enables further
refinement with belief propagation. Experimental results on link prediction and
hierarchical clustering show that ACVAEs significantly outperform CVAEs among
other benchmarks.
