Advances in Network Clustering and Blockmodeling

11Bayesian Stochastic Blockmodeling

Tiago P. Peixoto

Department of Mathematical Sciences and Centre for Networks and Collective Behaviour, University of Bath, United Kingdom, and ISI Foundation, Turin, Italy

This chapter provides a self-contained introduction to the use of Bayesian inference to extract large-scale modular structures from network data, based on the stochastic blockmodel (SBM), as well as its degree-corrected and overlapping generalizations. We focus on nonparametric formulations that allow their inference in a manner that prevents overfitting and enables model selection. We discuss aspects of the choice of priors, in particular how to avoid underfitting via increased Bayesian hierarchies, and we contrast the task of sampling network partitions from the posterior distribution with finding the single point estimate that maximizes it, while describing efficient algorithms to perform either one. We also show how inferring the SBM can be used to predict missing and spurious links, and shed light on the fundamental limitations of the detectability of modular structures in networks.

11.1 Introduction

Over the past decade and a half there has been an ever-increasing demand to analyze network data, in particular those stemming from social, biological, and technological systems. Often these systems are very large, comprising millions or even billions of nodes and edges, such as the World Wide Web, and the global-level social interactions among humans. A particular ...