An empirical Bayes Approach to stochastic blockmodels and graphons: shrinkage estimation and model selection

TL;DR

This paper introduces an empirical Bayes method for estimating the graphon function and selecting the number of communities in stochastic block models, improving accuracy over existing methods.

Contribution

It develops a hierarchical Binomial model and a novel empirical Bayes estimator for the connectivity matrix, along with a model selection criterion for community number.

Findings

Superior estimation accuracy demonstrated in simulations

Effective model selection for the number of communities

Outperforms existing approaches in social network analysis

Abstract

The graphon (W-graph), including the stochastic block model as a special case, has been widely used in modeling and analyzing network data. This random graph model is well-characterized by its graphon function, and estimation of the graphon function has gained a lot of recent research interests. Most existing works focus on community detection in the latent space of the model, while adopting simple maximum likelihood or Bayesian estimates for the graphon or connectivity parameters given the identified communities. In this work, we propose a hierarchical Binomial model and develop a novel empirical Bayes estimate of the connectivity matrix of a stochastic block model to approximate the graphon function. Based on the likelihood of our hierarchical model, we further introduce a model selection criterion for choosing the number of communities. Numerical results on extensive simulations and two well-annotated social networks demonstrate the superiority of our approach in terms of estimation accuracy and model selection.