$f$-Divergence Inequalities via Functional Domination

TL;DR

This paper develops new inequalities for f-divergences using functional domination, providing bounds based on other divergences and relative information, applicable to arbitrary probability measures.

Contribution

It introduces novel bounds on f-divergences through functional domination, expanding the theoretical framework for divergence inequalities with broad applicability.

Findings

Bounds on f-divergences based on other divergences

Inequalities under boundedness assumptions on relative information

Applicability to arbitrary alphabets and probability measures

Abstract

This paper considers derivation of $f$-divergence inequalities via the approach of functional domination. Bounds on an $f$-divergence based on one or several other $f$-divergences are introduced, dealing with pairs of probability measures defined on arbitrary alphabets. In addition, a variety of bounds are shown to hold under boundedness assumptions on the relative information. The journal paper, which includes more approaches for the derivation of f-divergence inequalities and proofs, is available on the arXiv at https://arxiv.org/abs/1508.00335, and it has been published in the IEEE Trans. on Information Theory, vol. 62, no. 11, pp. 5973-6006, November 2016.