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Relational exchangeability

Part of: Stochastic processes Operations research and management science

Published online by Cambridge University Press:  12 July 2019

Harry Crane  and
Walter Dempsey
Harry Crane*
Affiliation:
Rutgers University
Walter Dempsey*
Affiliation:
Harvard University
*
*Postal address: Department of Statistics & Biostatistics, Rutgers University, 110 Frelinghuysen Avenue, Piscataway, NJ 08854, USA. Email address: [email protected] Partially supported by NSF grants CNS-1523785 and CAREER DMS-1554092.
**Postal address: Department of Statistics, Harvard University, One Oxford Street, Cambridge, MA 02138, USA. Email address: [email protected]
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Abstract

A relationally exchangeable structure is a random combinatorial structure whose law is invariant with respect to relabeling its relations, as opposed to its elements. Historically, exchangeable random set partitions have been the best known examples of relationally exchangeable structures, but the concept now arises more broadly when modeling interaction data in modern network analysis. Aside from exchangeable random partitions, instances of relational exchangeability include edge exchangeable random graphs and hypergraphs, path exchangeable processes, and a range of other network-like structures. We motivate the general theory of relational exchangeability, with special emphasis on the alternative perspective it provides and its benefits in certain applied probability problems. We then prove a de Finetti-type structure theorem for the general class of relationally exchangeable structures.

Keywords

Edge exchangeable graphKingman’s correspondencepaintbox processexchangeable random partition

MSC classification

Primary: 60G09: Exchangeability
Secondary: 90B15: Network models, stochastic
Type
Research Papers
Information
Journal of Applied Probability , Volume 56 , Issue 1 , March 2019 , pp. 192 - 208
Copyright
© Applied Probability Trust 2019 

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