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On $f$-Divergences: Integral Representations, Local Behavior, and Inequalities (1804.06334v3)
Published 17 Apr 2018 in cs.IT, math.IT, and math.PR
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.