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2016 Priors on exchangeable directed graphs
Diana Cai, Nathanael Ackerman, Cameron Freer
Electron. J. Statist. 10(2): 3490-3515 (2016). DOI: 10.1214/16-EJS1185

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.

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Diana Cai. Nathanael Ackerman. Cameron Freer. "Priors on exchangeable directed graphs." Electron. J. Statist. 10 (2) 3490 - 3515, 2016. https://doi.org/10.1214/16-EJS1185

Information

Received: 1 January 2016; Published: 2016
First available in Project Euclid: 16 November 2016

zbMATH: 1355.60041
MathSciNet: MR3572857
Digital Object Identifier: 10.1214/16-EJS1185

Subjects:
Primary: 05C20‎ , 60G09
Secondary: 62F15 , 62G05

Keywords: block model , digraphon , Directed graph , exchangeable graph , graphon , network model , nonparametric prior

Rights: Copyright © 2016 The Institute of Mathematical Statistics and the Bernoulli Society

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Vol.10 • No. 2 • 2016
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