f-Divergence for Convex Bodies

Elisabeth M. Werner

Research output: Chapter in Book/Report/Conference proceedingChapter

5 Scopus citations

Abstract

We introduce f-divergence, a concept from information theory and statistics, for convex bodies in ℝn. We prove that f-divergences are SL(n) invariant valuations and we establish an affine isoperimetric inequality for these quantities. We show that generalized affine surface area and in particular the Lpaffine surface area from the LpBrunn Minkowski theory are special cases of f-divergences.

Original languageEnglish (US)
Title of host publicationAsymptotic Geometric Analysis
Subtitle of host publicationProceedings of the Fall 2010 Fields Institute Thematic Program
EditorsMonika Ludwig, Vladimir Pestov, Vitali Milman, Nicole Tomczak-Jaegermann
Pages381-395
Number of pages15
DOIs
StatePublished - Sep 2 2013

Publication series

NameFields Institute Communications
Volume68
ISSN (Print)1069-5265

Keywords

  • Affine surface area
  • Relative entropy
  • f-divergence

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