Relational exchangeability

TL;DR

This paper introduces a general framework for relational exchangeability, proving a de Finetti-type theorem that applies to various network-like structures such as graphs, hypergraphs, and processes, highlighting their invariance under relabeling.

Contribution

It establishes a unifying de Finetti-type representation theorem for relationally exchangeable structures, extending exchangeability concepts to complex network models.

Findings

Proves a general de Finetti-type theorem for relational exchangeability

Includes applications to graphs, hypergraphs, and network processes

Provides a theoretical foundation for invariance under relabeling in complex structures

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. Aside from exchangeable random partitions, examples include edge exchangeable random graphs and hypergraphs, path exchangeable processes, and a range of other network-like structures that arise in statistical applications. We prove a de Finetti-type structure theorem for the general class of relationally exchangeable structures.