Smoothing Graphons for Modelling Exchangeable Relational Data

Modelling exchangeable relational data can be described by \textit{graphon theory}. Most Bayesian methods for modelling exchangeable relational data can be attributed to this framework by exploiting different forms of graphons. However, the graphons adopted by existing Bayesian methods are either piecewise-constant functions, which are insufficiently flexible for accurate modelling of the relational data, or are complicated continuous functions, which incur heavy computational costs for inference. In this work, we introduce a smoothing procedure to piecewise-constant graphons to form {\em smoothing graphons}, which permit continuous intensity values for describing relations, but without impractically increasing computational costs. In particular, we focus on the Bayesian Stochastic Block Model (SBM) and demonstrate how to adapt the piecewise-constant SBM graphon to the smoothed version. We initially propose the Integrated Smoothing Graphon (ISG) which introduces one smoothing parameter to the SBM graphon to generate continuous relational intensity values. We then develop the Latent Feature Smoothing Graphon (LFSG), which improves on the ISG by introducing auxiliary hidden labels to decompose the calculation of the ISG intensity and enable efficient inference. Experimental results on real-world data sets validate the advantages of applying smoothing strategies to the Stochastic Block Model, demonstrating that smoothing graphons can greatly improve AUC and precision for link prediction without increasing computational complexity.

Recurrent Dirichlet Belief Networks for Interpretable Dynamic Relational Data Modelling

The Dirichlet Belief Network~(DirBN) has been recently proposed as a promising approach in learning interpretable deep latent representations for objects. In this work, we leverage its interpretable modelling architecture and propose a deep dynamic probabilistic framework -- the Recurrent Dirichlet Belief Network~(Recurrent-DBN) -- to study interpretable hidden structures from dynamic relational data. The proposed Recurrent-DBN has the following merits: (1) it infers interpretable and organised hierarchical latent structures for objects within and across time steps; (2) it enables recurrent long-term temporal dependence modelling, which outperforms the one-order Markov descriptions in most of the dynamic probabilistic frameworks. In addition, we develop a new inference strategy, which first upward-and-backward propagates latent counts and then downward-and-forward samples variables, to enable efficient Gibbs sampling for the Recurrent-DBN. We apply the Recurrent-DBN to dynamic relational data problems. The extensive experiment results on real-world data validate the advantages of the Recurrent-DBN over the state-of-the-art models in interpretable latent structure discovery and improved link prediction performance.