Joint Range of f-divergences

TL;DR

This paper introduces a general method to evaluate the joint range of f-divergences for different functions, using topological arguments to characterize the range and derive inequalities relevant to information theory and statistics.

Contribution

It provides a novel topological approach to determine the joint range of f-divergences, simplifying analysis by reducing to two-element distributions.

Findings

Joint range equals convex hull of two-element set distributions.

Provides inequalities between different f-divergences.

Applicable in information theory and statistical analysis.

Abstract

We provide a general method for evaluation of the joint range of f-divergences for two different functions f. Via topological arguments we prove that the joint range for general distributions equals the convex hull of the joint range achieved by the distributions on a two-element set. The joint range technique provides important inequalities between different f-divergences with various applications in information theory and statistics.