Electronic Journal of Statistics

Priors on exchangeable directed graphs

Diana Cai, Nathanael Ackerman, and Cameron Freer

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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.

Article information

Electron. J. Statist., Volume 10, Number 2 (2016), 3490-3515.

Received: January 2016
First available in Project Euclid: 16 November 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60G09: Exchangeability 05C20: Directed graphs (digraphs), tournaments
Secondary: 62F15: Bayesian inference 62G05: Estimation

Graphon digraphon directed graph exchangeable graph nonparametric prior network model block model


Cai, Diana; Ackerman, Nathanael; Freer, Cameron. Priors on exchangeable directed graphs. Electron. J. Statist. 10 (2016), no. 2, 3490--3515. doi:10.1214/16-EJS1185. https://projecteuclid.org/euclid.ejs/1479287229

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