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.

该研究提出了基于相关变量分布的 CVAEs 方法来学习高维数据的潜在表示。通过对无向相关图的所有最大有向无环子图的可计算较低限的平均值来解决相关先验带来的不可计算问题，证明了该方法在公共基准评级数据集的匹配和链接预测，以及合成数据集上的谱聚类中的有效性。