Mixture Models and Networks -- Overview of Stochastic Blockmodelling

TL;DR

This paper reviews stochastic blockmodels for network data, discussing their variants, estimation methods, and applications to real datasets, highlighting advantages and challenges of different approaches.

Contribution

It provides a comprehensive overview of stochastic blockmodels, surveys existing estimation methods, and introduces an alternative approach with practical applications.

Findings

Different estimation methods have varying advantages and limitations.

Stochastic blockmodels effectively identify community structures in networks.

Application to real datasets demonstrates practical utility and challenges.

Abstract

Mixture models are probabilistic models aimed at uncovering and representing latent subgroups within a population. In the realm of network data analysis, the latent subgroups of nodes are typically identified by their connectivity behaviour, with nodes behaving similarly belonging to the same community. In this context, mixture modelling is pursued through stochastic blockmodelling. We consider stochastic blockmodels and some of their variants and extensions from a mixture modelling perspective. We also survey some of the main classes of estimation methods available, and propose an alternative approach. In addition to the discussion of inferential properties and estimating procedures, we focus on the application of the models to several real-world network datasets, showcasing the advantages and pitfalls of different approaches.