Mixed f-divergence for multiple pairs of measures

Elisabeth Werner, Deping Ye

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)641-654
Number of pages14
JournalCanadian Mathematical Bulletin
Volume60
Issue number3
DOIs
StatePublished - Sep 2017

Bibliographical note

Funding Information:
Partially supported by an NSF grant. Supported by an NSERC grant and a start-up grant from Memorial University of Newfoundland.

Publisher Copyright:
© Canadian Mathematical Society 2016.

Keywords

  • Alexandrov-Fenchel inequality
  • F-dissimilarity
  • F-divergence
  • Isoperimetric inequality

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