Priors on exchangeable directed graphs
This work provides a framework for statistical modeling of networks where vertex order is irrelevant, applicable to domains like tournaments and partial orderings, but it appears incremental as it extends existing undirected graph methods to directed cases.
The authors tackled the problem of modeling exchangeable directed graphs by leveraging digraphons, a measurable object from structural theory, and introduced the infinite relational digraphon model (di-IRM) as a Bayesian nonparametric block model for this purpose, demonstrating inference on synthetic data.
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.