Equipping SBMs with RBMs: an interpretable approach for analysis of networks with covariates

Networks with node covariates offer two advantages to community detection methods, namely, (i) exploit covariates to improve the quality of communities, and more importantly, (ii) interpret the discovered communities by identifying the relative importance of different covariates in them. Recent methods have almost exclusively focused on the first point above. However, the quantitative improvements offered by them are often due to complex black-box models like deep neural networks at the expense of interpretability. Approaches that focus on the second point are either domain specific or have poor performance in practice. This article proposes interpretable, domain-independent statistical models for networks with node covariates that additionally offer good quantitative performance. The proposed models equip Stochastic Block Models with Restricted Boltzmann Machines to provide interpretable insights about the communities and they support both pure and mixed community memberships. Besides providing interpretability, our approach's main strength is that it does not explicitly assume a causal direction between community memberships and node covariates, making it applicable in diverse domains. We derive efficient inference procedures for our models, which can, in some cases, run in linear time in the number of nodes and edges. Experiments on several synthetic and real-world networks demonstrate that our models achieve close to state-of-the-art performance on community detection and link prediction tasks while also providing interpretations for the discovered communities.