Empirical Bayes Estimation for the Stochastic Blockmodel

TL;DR

This paper introduces an empirical Bayes approach for estimating block memberships in stochastic blockmodels, leveraging spectral graph theory and Bayesian inference, with demonstrated effectiveness on simulated and real-world network data.

Contribution

It develops a novel empirical Bayes methodology for stochastic blockmodel inference using spectral embedding and Bayesian posterior sampling, advancing network community detection techniques.

Findings

Effective block membership estimation demonstrated on simulations

Bayesian approach improves inference accuracy

Method applied successfully to Wikipedia network data

Abstract

Inference for the stochastic blockmodel is currently of burgeoning interest in the statistical community, as well as in various application domains as diverse as social networks, citation networks, brain connectivity networks (connectomics), etc. Recent theoretical developments have shown that spectral embedding of graphs yields tractable distributional results; in particular, a random dot product latent position graph formulation of the stochastic blockmodel informs a mixture of normal distributions for the adjacency spectral embedding. We employ this new theory to provide an empirical Bayes methodology for estimation of block memberships of vertices in a random graph drawn from the stochastic blockmodel, and demonstrate its practical utility. The posterior inference is conducted using a Metropolis-within-Gibbs algorithm. The theory and methods are illustrated through Monte Carlo simulation studies, both within the stochastic blockmodel and beyond, and experimental results on a Wikipedia data set are presented.