Priors on exchangeable directed graphs

TL;DR

This paper develops a Bayesian nonparametric framework for modeling exchangeable directed graphs using digraphons, enabling flexible priors and inference for various graph structures.

Contribution

It introduces the infinite relational digraphon model (di-IRM), a novel nonparametric prior for exchangeable directed graphs, extending the structural theory to practical Bayesian modeling.

Findings

Constructed models for various exchangeable directed graph structures.

Developed the di-IRM for Bayesian nonparametric priors.

Demonstrated inference capabilities on synthetic data.

Abstract

Directed graphs occur throughout statistical modeling of networks, and exchangeability is a natural assumption when the ordering of vertices does not matter. There is a deep structural theory for exchangeable undirected graphs, which extends to the directed case via measurable objects known as digraphons. Using digraphons, we first show how to construct models for exchangeable directed graphs, including special cases such as tournaments, linear orderings, directed acyclic graphs, and partial orderings. We then show how to construct priors on digraphons via the infinite relational digraphon model (di-IRM), a new Bayesian nonparametric block model for exchangeable directed graphs, and demonstrate inference on synthetic data.