  Variational Auto-Encoders (VAEs) are capable of learning latent
representations for high dimensional data. However, due to the i.i.d.
assumption, VAEs only optimize the singleton variational distributions and fail
to account for the correlations between data points, which might be crucial for
learning latent representations from dataset where a priori we know
correlations exist. We propose Correlated Variational Auto-Encoders (CVAEs)
that can take the correlation structure into consideration when learning latent
representations with VAEs. CVAEs apply a prior based on the correlation
structure. To address the intractability introduced by the correlated prior, we
develop an approximation by average of a set of tractable lower bounds over all
maximal acyclic subgraphs of the undirected correlation graph. Experimental
results on matching and link prediction on public benchmark rating datasets and
spectral clustering on a synthetic dataset show the effectiveness of the
proposed method over baseline algorithms.
