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. 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.

翻译：受近期分布偏移下预测推断研究的启发，我们探讨了用具有独立项的有限序列混合来近似有限加权可交换序列的问题。基于权重函数推导出多种界，拓展了先前关于有限可交换序列的结果。作为副产品，我们获得了无限加权可交换序列的德芬内蒂定理的一种版本。