Mixed f-divergence and inequalities for log-concave functions

Umut Caglar, Elisabeth M. Werner

Research output: Contribution to journalArticlepeer-review

11 Scopus citations

Abstract

Mixed f-divergences, a concept from information theory and statistics, measure the difference between multiple pairs of distributions. We introduce them for log-concave functions and establish some of their properties. Among them are affine invariant vector entropy inequalities, like new Alexandrov-Fenchel-type inequalities and an affine isoperimetric inequality for the vector form of the Kullback Leibler divergence for log-concave functions. Special cases of f-divergences are mixed L-λ-affine surface areas for log-concave functions. For those, we establish various affine isoperimetric inequalities as well as a vector Blaschke Santaló-type inequality.

Original languageEnglish (US)
Pages (from-to)271-290
Number of pages20
JournalProceedings of the London Mathematical Society
Volume110
Issue number2
DOIs
StatePublished - Dec 18 2012

Bibliographical note

Funding Information:
Received 27 January 2014; revised 31 July 2014; published online 12 November 2014. 2010 Mathematics Subject Classification 46B, 52A20, 60B. Elisabeth M. Werner was partially supported by an NSF grant.

Publisher Copyright:
© 2014 London Mathematical Society.

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