Strongly Convex Divergences

Abstract

We consider a sub-class of the $f$-divergences satisfying a stronger convexity property, which we refer to as strongly convex, or $\kappa$-convex divergences. We derive new and old relationships, based on convexity arguments, between popular $f$-divergences.

Submitted to Entropy, special issue, Divergence Measures: Mathematical Foundations and Applications in Information-Theoretic and Statistical Problems, edited by Igal Sason