# Learning Correlated Latent Representations with Adaptive Priors

## TL;DR

This paper introduces ACVAEs, an advanced VAE model with adaptive priors that better capture correlations in data, leading to improved performance in link prediction and clustering tasks.

## Contribution

We propose ACVAEs, which use adaptive priors to effectively learn correlated latent representations and enable tractable joint distributions, overcoming limitations of previous CVAEs.

## Key findings

- ACVAEs outperform CVAEs in link prediction.
- ACVAEs achieve better hierarchical clustering results.
- Adaptive priors improve correlation modeling.

## Abstract

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.