de Finetti reductions for partially exchangeable probability distributions

TL;DR

This paper develops a unified framework for de Finetti reductions applicable to various partially exchangeable probability distributions, using combinatorial techniques based on the BEST theorem to derive explicit results for different exchangeability notions.

Contribution

It introduces a general combinatorial approach to de Finetti reductions for partially exchangeable distributions, extending existing results to broader cases.

Findings

Explicit de Finetti reduction statements for exchangeability and Markov exchangeability.

Application of the BEST theorem to enumerate Eulerian cycles in multigraphs.

Framework generalizes to various notions of partial exchangeability.

Abstract

We introduce a general framework for de Finetti reduction results, applicable to various notions of partially exchangeable probability distributions. Explicit statements are derived for the cases of exchangeability, Markov exchangeability, and some generalizations of these. Our techniques are combinatorial and rely on the "BEST" theorem, enumerating the Eulerian cycles of a multigraph.