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 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 | |
| State | Published - Sep 2 2013 |
Publication series
| Name | Fields Institute Communications |
|---|---|
| Volume | 68 |
| ISSN (Print) | 1069-5265 |
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Keywords
- Affine surface area
- Relative entropy
- f-divergence
Cite this
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 proceeding › Chapter
}
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 -