Finite and Infinite Weighted Exchangeable Sequences
Wenpin Tang
Source abstract
Motivated by recent interest in predictive inference under distribution shifts, 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, recovering an instance of Barber, Candes, Ramdas and Tibshirani 1 (Bernoulli, 30 (2024), pp. 3004–3028) in the Polish space with bounded and continuous weights.
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