Relational topic models: Derived from the traditional topic models [12, 29], RTMs [14, 15] are introduced to jointly consider the generations of document contents and their relationships.

Following this trend, SIG-6 VAE is estimated to take at least 600GRAM on Cora with their original setting7 (K = 150,J = 2000),which isanormally unaffordable memory. We note a full matrix forU32 could provide extra flexibility to model stochastic equivalence/disassortativity (e.g., in protein-protein interaction33 network), while a diagonal one is more suitable to model an assortative relational network exhibiting homophily34 (e.g., co-author network)butnotnecessarily stochasticequivalence.

Although existing variational graph autoencoders (VGAEs) have been widely used for modeling and generating graph-structured data, most of them are still not flexible enough to approximate the sparse and skewed latent node representations, especially those of document relational networks (DRNs) with discrete observations. To analyze a collection of interconnected documents, a typical branch of Bayesian models, specifically relational topic models (RTMs), has proven their efficacy in describing both link structures and document contents of DRNs, which motives us to incorporate RTMs with existing VGAEs to alleviate their potential issues when modeling the generation of DRNs. In this paper, moving beyond the sophisticated approximate assumptions of traditional RTMs, we develop a graph Poisson factor analysis (GPFA), which provides analytic conditional posteriors to improve the inference accuracy, and extend GPFA to a multi-stochastic-layer version named graph Poisson gamma belief network (GPGBN) to capture the hierarchical document relationships at multiple semantic levels. Then, taking GPGBN as the decoder, we combine it with various Weibull-based graph inference networks, resulting in two variants of Weibull graph auto-encoder (WGAE), equipped with model inference algorithms. Experimental results demonstrate that our models can extract high-quality hierarchical latent document representations and achieve promising performance on various graph analytic tasks.