Exchangeable Random Measures for Sparse and Modular Graphs with Overlapping Communities

TL;DR

This paper introduces a new exchangeable random measure model for sparse graphs with overlapping communities, enabling better interpretation and inference in large, complex networks.

Contribution

It generalizes existing models to the sparse regime using vectors of completely random measures, providing interpretable parameters and scalable inference methods.

Findings

Successfully recovers interpretable community structures

Handles large graphs with thousands of nodes

Provides effective simulation and inference techniques

Abstract

We propose a novel statistical model for sparse networks with overlapping community structure. The model is based on representing the graph as an exchangeable point process, and naturally generalizes existing probabilistic models with overlapping block-structure to the sparse regime. Our construction builds on vectors of completely random measures, and has interpretable parameters, each node being assigned a vector representing its level of affiliation to some latent communities. We develop methods for simulating this class of random graphs, as well as to perform posterior inference. We show that the proposed approach can recover interpretable structure from two real-world networks and can handle graphs with thousands of nodes and tens of thousands of edges.