Finite de Finetti bounds in relative entropy

Lampros Gavalakis, Oliver Johnson, Ioannis Kontoyiannis

Published 2024-07-17Version 1

We review old and recent finite de Finetti theorems in total variation distance and in relative entropy, and we highlight their connections with bounds on the difference between sampling with and without replacement. We also establish two new finite de Finetti theorems for exchangeable random vectors taking values in arbitrary spaces. These bounds are tight, and they are independent of the size and the dimension of the underlying space.