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- W2127789717 abstract "$f$-divergences are a general class of divergences between probability measures which include as special cases many commonly used divergences in probability, mathematical statistics and information theory such as Kullback-Leibler divergence, chi-squared divergence, squared Hellinger distance, total variation distance etc. In this paper, we study the problem of maximizing or minimizing an $f$-divergence between two probability measures subject to a finite number of constraints on other $f$-divergences. We show that these infinite-dimensional optimization problems can all be reduced to optimization problems over small finite dimensional spaces which are tractable. Our results lead to a comprehensive and unified treatment of the problem of obtaining sharp inequalities between $f$-divergences. We demonstrate that many of the existing results on inequalities between $f$-divergences can be obtained as special cases of our results and we also improve on some existing non-sharp inequalities." @default.
- W2127789717 created "2016-06-24" @default.
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- W2127789717 date "2013-02-02" @default.
- W2127789717 modified "2023-09-27" @default.
- W2127789717 title "Sharp Inequalities for $f$-divergences" @default.
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