Strongly Convex Divergences

TL;DR

This paper introduces a subclass of $f$-divergences called strongly convex divergences, establishing new relationships among them based on convexity properties.

Contribution

It defines strongly convex ($$-convex) $f$-divergences and derives novel and existing relationships among these divergences using convexity arguments.

Findings

New class of strongly convex divergences introduced

Relationships between $f$-divergences established using convexity

Theoretical framework for analyzing divergence properties

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.