Bound on extended f -divergences for a variety of classes

Pietro Cerone; Sever Silvestru Dragomir; Ferdinand Österreicher

Kybernetika (2004)

  • Volume: 40, Issue: 6, page [745]-756
  • ISSN: 0023-5954

Abstract

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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 , ∞ ) . 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 χ α -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 χ α -divergences and four further classes of f -divergences are used in order to investigate limitations and strengths of the inequalities derived.

How to cite

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Cerone, Pietro, Dragomir, Sever Silvestru, and Österreicher, Ferdinand. "Bound on extended $f$-divergences for a variety of classes." Kybernetika 40.6 (2004): [745]-756. <http://eudml.org/doc/33733>.

@article{Cerone2004,
abstract = {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.},
author = {Cerone, Pietro, Dragomir, Sever Silvestru, Österreicher, Ferdinand},
journal = {Kybernetika},
keywords = {$f$-divergences; bounds; Ostrowki’s inequality; Ostrowki's inequality},
language = {eng},
number = {6},
pages = {[745]-756},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Bound on extended $f$-divergences for a variety of classes},
url = {http://eudml.org/doc/33733},
volume = {40},
year = {2004},
}

TY - JOUR
AU - Cerone, Pietro
AU - Dragomir, Sever Silvestru
AU - Österreicher, Ferdinand
TI - Bound on extended $f$-divergences for a variety of classes
JO - Kybernetika
PY - 2004
PB - Institute of Information Theory and Automation AS CR
VL - 40
IS - 6
SP - [745]
EP - 756
AB - 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.
LA - eng
KW - $f$-divergences; bounds; Ostrowki’s inequality; Ostrowki's inequality
UR - http://eudml.org/doc/33733
ER -

References

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  8. Österreicher F., Vajda I., 10.1007/BF02517812, Ann. Inst. Statist. Math. 55 (2003), 3, 639–653 Zbl1052.62002MR2007803DOI10.1007/BF02517812
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