Bayesian Deep Generative Models for Multiplex Networks with Multiscale Overlapping Clusters

TL;DR

This paper introduces a Bayesian hierarchical model for multiplex network data that infers hierarchical node structures and multi-resolution clusters, supported by theoretical guarantees and demonstrated on real data.

Contribution

It presents a novel Bayesian model with theoretical identifiability and consistency results, along with efficient computational methods for multiplex network analysis.

Findings

Model successfully infers hierarchical structures in multiplex networks.

Theoretical guarantees ensure model identifiability and posterior consistency.

Application to brain connectome data demonstrates practical utility.

Abstract

Our interest is in multiplex network data with multiple network samples observed across the same set of nodes. Examples originate from a variety of fields, including brain connectivity, international trade networks, and social networks, among others. Our goal is to infer a hierarchical structure of the nodes at a population level, while performing multi-resolution clustering of the individual replicates. To accomplish this, we propose a Bayesian hierarchical model, provide theoretical support in terms of identifiability and posterior consistency, and design efficient methods for posterior computation. We provide novel technical tools for proving model identifiability, which are of independent interest. Our proposed methodology is demonstrated through numerical simulation and an application to brain connectome data.