Exchangeable Random Measures for Sparse and Modular Graphs with Overlapping Communities
This work addresses the challenge of analyzing large, sparse real-world networks with overlapping communities, which is incremental as it builds on existing probabilistic models.
The authors tackled the problem of modeling sparse networks with overlapping community structure by proposing a novel statistical model based on exchangeable point processes and completely random measures, which generalizes existing probabilistic models to the sparse regime and can handle graphs with thousands of nodes and tens of thousands of edges.
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.