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This article is cited in 5 scientific papers (total in 5 papers)
Information Theory
On the maximum values of $f$-divergence and Rényi divergence under a given variational distance
V. V. Prelov Kharkevich Institute for Information Transmission Problems,
Russian Academy of Sciences, Moscow, Russia
Abstract:
We consider the problem of finding maximum values of $f$-divergences $D_f(P \parallel Q)$ of discrete probability distributions $P$ and $Q$ with values on a finite set under the condition that the variation distance $V(P, Q)$ between them and one of the distributions $P$ or $Q$ are given. We obtain exact expressions for such maxima of $f$-divergences, which in a number of cases allow to obtain both explicit formulas and upper bounds for them. As a consequence, we obtain explicit expressions for the maxima of $f$-divergences $D_f(P \parallel Q)$ given that, besides $V(P, Q)$, we only know the value of the maximum component of either $P$ or $Q$. Analogous results are also obtained for the Rényi divergence.
Keywords:
$f$-divergence, Rényi divergence, variation distance, discrete probability distributions.
Received: 28.01.2020 Revised: 28.01.2020 Accepted: 05.02.2020
Citation:
V. V. Prelov, “On the maximum values of $f$-divergence and Rényi divergence under a given variational distance”, Probl. Peredachi Inf., 56:1 (2020), 3–14; Problems Inform. Transmission, 56:1 (2020), 1–12
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https://www.mathnet.ru/eng/ppi2307 https://www.mathnet.ru/eng/ppi/v56/i1/p3
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