Priors on exchangeable directed graphs

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.

Publication
Electronic Journal of Statistics

Preliminary version in the NIPS Workshop on Bayesian Nonparametrics, 2015.

Avatar
Diana Cai

I am broadly interested in machine learning and statistics, and in particular, developing robust and reliable methods for modeling and inference.