On $f$-Divergences: Integral Representations, Local Behavior, and Inequalities

Abstract

This paper is focused on $f$-divergences, consisting of three main contributions. The first one introduces integral representations of a general $f$-divergence by means of the relative information spectrum. The second part provides a new approach for the derivation of $f$-divergence inequalities, and it exemplifies their utility in the setup of Bayesian binary hypothesis testing. The last part of this paper further studies the local behavior of $f$-divergences.

Final edits before publication. To appear in the Entropy journal, special issue on Entropy and Information Inequalities, May 2018

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