Bayesian nonparametric modeling of heterogeneous populations of networks

TL;DR

This paper introduces a Bayesian nonparametric model for clustering heterogeneous network populations, effectively capturing connectivity patterns and demonstrating superior performance through simulations and real brain network data analysis.

Contribution

It proposes a novel Dirichlet process mixture model for networks, with a scalable inference scheme and proven theoretical properties, advancing network clustering methods.

Findings

Model has full support and is strongly consistent.

Outperforms existing methods in simulations.

Successfully applied to human brain network data.

Abstract

The increasing availability of multiple network data has highlighted the need for statistical models for heterogeneous populations of networks. A convenient framework makes use of metrics to measure similarity between networks. In this context, we propose a novel Bayesian nonparametric model that identifies clusters of networks characterized by similar connectivity patterns. Our approach relies on a location-scale Dirichlet process mixture of centered Erd\H{o}s--R\'enyi kernels, with components parametrized by a unique network representative, or mode, and a univariate measure of dispersion around the mode. We demonstrate that this model has full support in the Kullback--Leibler sense and is strongly consistent. An efficient Markov chain Monte Carlo scheme is proposed for posterior inference and clustering of multiple network data. The performance of the model is validated through extensive simulation studies, showing improvements over state-of-the-art methods. Additionally, we present an effective strategy to extend the application of the proposed model to datasets with a large number of nodes. We illustrate our approach with the analysis of human brain network data.