f-Divergence for Convex Bodies

Elisabeth M. Werner

Research output: Chapter in Book/Report/Conference proceedingChapter

4 Citations (Scopus)

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

Fingerprint

F-divergence
Convex Body
Surface area
Isoperimetric Inequality
Information Theory
Valuation
Statistics
Invariant

Keywords

  • Affine surface area
  • Relative entropy
  • f-divergence

Cite this

Werner, E. M. (2013). f-Divergence for Convex Bodies. In M. Ludwig, V. Pestov, V. Milman, & N. Tomczak-Jaegermann (Eds.), Asymptotic Geometric Analysis: Proceedings of the Fall 2010 Fields Institute Thematic Program (pp. 381-395). (Fields Institute Communications; Vol. 68). https://doi.org/10.1007/978-1-4614-6406-8_18

f-Divergence for Convex Bodies. / Werner, Elisabeth M.

Asymptotic Geometric Analysis: Proceedings of the Fall 2010 Fields Institute Thematic Program. ed. / Monika Ludwig; Vladimir Pestov; Vitali Milman; Nicole Tomczak-Jaegermann. 2013. p. 381-395 (Fields Institute Communications; Vol. 68).

Research output: Chapter in Book/Report/Conference proceedingChapter

Werner, EM 2013, f-Divergence for Convex Bodies. in M Ludwig, V Pestov, V Milman & N Tomczak-Jaegermann (eds), Asymptotic Geometric Analysis: Proceedings of the Fall 2010 Fields Institute Thematic Program. Fields Institute Communications, vol. 68, pp. 381-395. https://doi.org/10.1007/978-1-4614-6406-8_18
Werner EM. f-Divergence for Convex Bodies. In Ludwig M, Pestov V, Milman V, Tomczak-Jaegermann N, editors, Asymptotic Geometric Analysis: Proceedings of the Fall 2010 Fields Institute Thematic Program. 2013. p. 381-395. (Fields Institute Communications). https://doi.org/10.1007/978-1-4614-6406-8_18
Werner, Elisabeth M. / f-Divergence for Convex Bodies. Asymptotic Geometric Analysis: Proceedings of the Fall 2010 Fields Institute Thematic Program. editor / Monika Ludwig ; Vladimir Pestov ; Vitali Milman ; Nicole Tomczak-Jaegermann. 2013. pp. 381-395 (Fields Institute Communications).
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