Geodesic
Bound on extended $f$-divergences for a variety of classes
Kybernetika, Tome 40 (2004) no. 6, pp. 745-756 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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The concept of $f$-divergences was introduced by Csiszár in 1963 as measures of the ‘hardness’ of a testing problem depending on a convex real valued function $f$ on the interval $[0,\infty )$. The choice of this parameter $f$ can be adjusted so as to match the needs for specific applications. The definition and some of the most basic properties of $f$-divergences are given and the class of $\chi ^{\alpha }$-divergences is presented. Ostrowski’s inequality and a Trapezoid inequality are utilized in order to prove bounds for an extension of the set of $f$-divergences. The class of $\chi ^{\alpha }$-divergences and four further classes of $f$-divergences are used in order to investigate limitations and strengths of the inequalities derived.
The concept of $f$-divergences was introduced by Csiszár in 1963 as measures of the ‘hardness’ of a testing problem depending on a convex real valued function $f$ on the interval $[0,\infty )$. The choice of this parameter $f$ can be adjusted so as to match the needs for specific applications. The definition and some of the most basic properties of $f$-divergences are given and the class of $\chi ^{\alpha }$-divergences is presented. Ostrowski’s inequality and a Trapezoid inequality are utilized in order to prove bounds for an extension of the set of $f$-divergences. The class of $\chi ^{\alpha }$-divergences and four further classes of $f$-divergences are used in order to investigate limitations and strengths of the inequalities derived.
Classification : 62B10, 62E99, 94A17
Keywords: $f$-divergences; bounds; Ostrowki’s inequality 
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Cerone, Pietro; Dragomir, Sever S.; Österreicher, Ferdinand. Bound on extended $f$-divergences for a variety of classes. Kybernetika, Tome 40 (2004) no. 6, pp. 745-756. http://geodesic.mathdoc.fr/item/KYB_2004_40_6_a7/

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