Electronic Journal of Statistics

Priors on exchangeable directed graphs

Diana Cai, Nathanael Ackerman, and Cameron Freer

Full-text: Open access

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.

Article information

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

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

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1479287229

Digital Object Identifier
doi:10.1214/16-EJS1185

Mathematical Reviews number (MathSciNet)
MR3572857

Zentralblatt MATH identifier
1355.60041

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

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

Citation

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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