A Multilayer Probit Network Model for Community Detection with Dependent Edges and Layers

TL;DR

This paper introduces a novel multilayer probit network model that captures complex inter-layer and intra-layer dependencies for improved community detection in multilayer networks.

Contribution

It combines a multilayer stochastic block model with a multivariate probit model and develops a constrained pairwise likelihood estimation method.

Findings

Accurately detects communities in dependent multilayer networks

Demonstrates robustness through simulations and real-world data

Provides theoretical insights into dependence effects on estimation

Abstract

Community detection in multilayer networks, which aims to identify groups of nodes exhibiting similar connectivity patterns across multiple network layers, has attracted considerable attention in recent years. Most existing methods are based on the assumption that different layers are either independent or follow specific dependence structures, and edges within the same layer are independent. In this article, we propose a novel method for community detection in multilayer networks that accounts for a broad range of inter-layer and intra-layer dependence structures. The proposed method integrates the multilayer stochastic block model for community detection with a multivariate probit model to capture the structures of inter-layer dependence, which also allows intra-layer dependence. To facilitate parameter estimation, we develop a constrained pairwise likelihood method coupled with an efficient alternating updating algorithm. The asymptotic properties of the proposed method are also established, with a focus on examining the influence of inter-layer and intra-layer dependences on the accuracy of both parameter estimation and community detection. The theoretical results are supported by extensive numerical experiments on both simulated networks and a real-world multilayer trade network.