On Pairs of $f$-divergences and their Joint Range

TL;DR

This paper investigates the relationship between pairs of f-divergences, showing that their joint range is the convex hull of the range for two-point distributions, with applications demonstrated.

Contribution

It establishes a fundamental geometric property of f-divergences' joint ranges, providing new insights into their structure and applications.

Findings

Joint range of two f-divergences is convex hull of two-point distributions

Provides a geometric characterization of f-divergences

Includes applications demonstrating the theoretical results

Abstract

We compare two f-divergences and prove that their joint range is the convex hull of the joint range for distributions supported on only two points. Some applications of this result are given.