A characterization of statistical manifolds on which the relative entropy is a Bregman divergence

Abstract

It is well known that the relative entropy (Kullback-Leibler divergence) is represented in the form of Bregman divergence on exponential families and mixture families for some coordinate systems. We give a characterization of the class of statistical manifolds (smooth manifolds of probability mass functions on finite sample spaces) having coordinate systems for which the relative entropy is a Bregman divergence.