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Mixed ƒ-divergence for Multiple Pairs of Measures

Published online by Cambridge University Press:  20 November 2018

Elisabeth Werner  and
Deping Ye
Elisabeth Werner
Affiliation:
Department of Mathematics, Case Western Reserve University, Cleveland, Ohio 100, USA e-mail: elisabeth.werner@case.edu
Deping Ye
Affiliation:
Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John's, Newfoundland A1C SS7 e-mail: deping.ye@mun.ca
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Abstract

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In this paper, the concept of the classical $f$ -divergence for a pair of measures is extended to the mixed $f$ -divergence formultiple pairs ofmeasures. The mixed $f$ -divergence provides a way to measure the difference between multiple pairs of (probability) measures. Properties for the mixed $f$ -divergence are established, such as permutation invariance and symmetry in distributions. An Alexandrov–Fenchel type inequality and an isoperimetric inequality for the mixed $f$ -divergence are proved.

Keywords

28-XX52-XX60-XXAlexandrov–Fenchel inequalityƒ-dissimilarityƒ-divergenceisoperimetric inequality

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 60 , Issue 3 , 01 September 2017 , pp. 641 - 654
Copyright
Copyright © Canadian Mathematical Society 2017

References

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