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

Igal Sason

doi:10.3390/e20050383

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arXiv · 1804.06334

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

Igal Sason

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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.

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Igal Sason. 2018-04-17. On $f$-Divergences: Integral Representations, Local Behavior, and Inequalities. https://doi.org/10.3390/e20050383

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