Efficient inference in stochastic block models with vertex labels

TL;DR

This paper analyzes a linearized belief propagation algorithm for stochastic block models with vertex labels, showing conditions for optimal community detection accuracy and how vertex label information influences algorithm performance.

Contribution

It introduces an analysis of a linearized belief propagation method in labeled stochastic block models, identifying conditions for optimality based on fixed points.

Findings

Belief propagation achieves optimal accuracy when a specific network parameter function has a unique fixed point.

Multiple fixed points can hinder the optimality of belief propagation.

Increasing label information can reduce fixed points, improving algorithm performance.

Abstract

We study the stochastic block model with two communities where vertices contain side information in the form of a vertex label. These vertex labels may have arbitrary label distributions, depending on the community memberships. We analyze a linearized version of the popular belief propagation algorithm. We show that this algorithm achieves the highest accuracy possible whenever a certain function of the network parameters has a unique fixed point. Whenever this function has multiple fixed points, the belief propagation algorithm may not perform optimally. We show that increasing the information in the vertex labels may reduce the number of fixed points and hence lead to optimality of belief propagation.