Finite and infinite weighted exchangeable sequences

Abstract

Motivated by recent interests in predictive inference under distribution shift, we study the problem of approximating finite weighted exchangeable sequences by a mixture of finite sequences with independent terms. Two different approaches are developed: a combinatorial approach and a probabilistic approach. Various bounds are derived in terms of weight functions, extending previous results on finite exchangeable sequences. As a byproduct, we obtain a version of de Finetti's theorem for infinite weighted exchangeable sequences.

arXiv comment14 pages. A new section of the probabilistic approach is added, and several errors are corrected