f-Divergence for Convex Bodies

Elisabeth M. Werner

doi:10.1007/978-1-4614-6406-8_18

f-Divergence for Convex Bodies

Elisabeth M. Werner

Institute for Mathematics and its Applications

Research output: Chapter in Book/Report/Conference proceeding › Chapter

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 L_paffine surface area from the L_pBrunn Minkowski theory are special cases of f-divergences.

Original language	English (US)
Title of host publication	Asymptotic Geometric Analysis
Subtitle of host publication	Proceedings of the Fall 2010 Fields Institute Thematic Program
Editors	Monika Ludwig, Vladimir Pestov, Vitali Milman, Nicole Tomczak-Jaegermann
Pages	381-395
Number of pages	15
DOIs	https://doi.org/10.1007/978-1-4614-6406-8_18
State	Published - Sep 2 2013

Publication series

Name	Fields Institute Communications
Volume	68
ISSN (Print)	1069-5265

Keywords

Affine surface area
Relative entropy
f-divergence

Access

10.1007/978-1-4614-6406-8_18

Fingerprint Dive into the research topics of 'f-Divergence for Convex Bodies'. Together they form a unique fingerprint.

Cite this

@inbook{5eeef6aba06c4b82ae1c638953037dad,

title = "f-Divergence for Convex Bodies",

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.",

keywords = "Affine surface area, Relative entropy, f-divergence",

author = "Werner, {Elisabeth M.}",

year = "2013",

month = sep,

day = "2",

doi = "10.1007/978-1-4614-6406-8_18",

language = "English (US)",

isbn = "9781461464051",

series = "Fields Institute Communications",

pages = "381--395",

editor = "Monika Ludwig and Vladimir Pestov and Vitali Milman and Nicole Tomczak-Jaegermann",

booktitle = "Asymptotic Geometric Analysis",

}

TY - CHAP

T1 - f-Divergence for Convex Bodies

AU - Werner, Elisabeth M.

PY - 2013/9/2

Y1 - 2013/9/2

N2 - 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.

AB - 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.

KW - Affine surface area

KW - Relative entropy

KW - f-divergence

UR - http://www.scopus.com/inward/record.url?scp=84883104167&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84883104167&partnerID=8YFLogxK

U2 - 10.1007/978-1-4614-6406-8_18

DO - 10.1007/978-1-4614-6406-8_18

M3 - Chapter

AN - SCOPUS:84883104167

SN - 9781461464051

T3 - Fields Institute Communications

SP - 381

EP - 395

BT - Asymptotic Geometric Analysis

A2 - Ludwig, Monika

A2 - Pestov, Vladimir

A2 - Milman, Vitali

A2 - Tomczak-Jaegermann, Nicole

ER -