Exchangeable Random Measures for Sparse and Modular Graphs with Overlapping Communities

Adrien Todeschini (1, 2) , Francois Caron (3)

1 IMB - Institut de Mathématiques de Bordeaux
2 CQFD - Quality control and dynamic reliability
3 Department of Statistics [Oxford]

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.

Mots clés: Networks; Random Graphs; Multiview Networks; Multigraphs; Completely Random Measures; Lévy measure; Multivariate Subordinator; Sparsity; Non-Negative Factorization; Exchangeability; Point Processes

Domaines: Méthodologie [stat.ME]; Machine Learning [stat.ML]; Réseaux sociaux et d'information [cs.SI]; Physique et Société [physics.soc-ph]

Adrien Todeschini, Francois Caron. Exchangeable Random Measures for Sparse and Modular Graphs with Overlapping Communities. 2016. ⟨hal-01270854⟩