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# Mixed $f$-divergence for Multiple Pairs of Measures

Published:2016-09-08
Printed: Sep 2017
• Elisabeth Werner
• Deping Ye
 Format: LaTeX MathJax PDF

## Abstract

In this paper, the concept of the classical $f$-divergence for a pair of measures is extended to the mixed $f$-divergence for multiple pairs of measures. 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: Alexandrov-Fenchel inequality, $f$-dissimilarity, $f$-divergence, isoperimetric inequality
 MSC Classifications: 28-XX - unknown classification 28-XX52-XX - unknown classification 52-XX60-XX - unknown classification 60-XX

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