Mutual Information in Community Detection with Covariate Information and Correlated Networks

TL;DR

This paper investigates community detection in networks with covariate data and multiple correlated networks, providing theoretical bounds and analysis of information measures to understand the combined effects of different information sources.

Contribution

It offers the first asymptotic bounds on mutual information and MMSE matrix for community detection with covariates and correlated networks, linking these effects to low-dimensional Gaussian estimation.

Findings

Derived asymptotic upper bounds on per-node mutual information.

Provided heuristic analysis of the MMSE matrix in this context.

Supported results with numerical simulations.

Abstract

We study the problem of community detection when there is covariate information about the node labels and one observes multiple correlated networks. We provide an asymptotic upper bound on the per-node mutual information as well as a heuristic analysis of a multivariate performance measure called the MMSE matrix. These results show that the combined effects of seemingly very different types of information can be characterized explicitly in terms of formulas involving low-dimensional estimation problems in additive Gaussian noise. Our analysis is supported by numerical simulations.