Information-theoretic inequalities for contoured probability distributions

Research output: Contribution to journalArticle

Abstract

We show that for a special class of probability distributions that we call contoured distributions, information-theoretic invariants and inequalities are equivalent to geometric invariants and inequalities of bodies in Euclidean space associated with the distributions. Using this, we obtain characterizations of contoured distributions with extremal Shannon and Renyi entropy. We also obtain a new reverse information-theoretic inequality for contoured distributions.

Original languageEnglish (US)
Pages (from-to)2377-2383
Number of pages7
JournalIEEE Transactions on Information Theory
Volume48
Issue number8
DOIs
StatePublished - Aug 2002

Fingerprint

Probability distributions
Entropy
entropy

Keywords

  • Brunn-Minkowski
  • Convex bodies
  • Elliptically contoured
  • Entropy
  • Fisher information
  • Inequalities
  • Isoperimetric inequalities

ASJC Scopus subject areas

  • Electrical and Electronic Engineering
  • Information Systems

Cite this

Information-theoretic inequalities for contoured probability distributions. / Guleryuz, Onur G.; Lutwak, Erwin; Yang, Deane; Zhang, Gaoyong.

In: IEEE Transactions on Information Theory, Vol. 48, No. 8, 08.2002, p. 2377-2383.

Research output: Contribution to journalArticle

@article{4e16a15fd850444e8b05582f77777a13,
title = "Information-theoretic inequalities for contoured probability distributions",
abstract = "We show that for a special class of probability distributions that we call contoured distributions, information-theoretic invariants and inequalities are equivalent to geometric invariants and inequalities of bodies in Euclidean space associated with the distributions. Using this, we obtain characterizations of contoured distributions with extremal Shannon and Renyi entropy. We also obtain a new reverse information-theoretic inequality for contoured distributions.",
keywords = "Brunn-Minkowski, Convex bodies, Elliptically contoured, Entropy, Fisher information, Inequalities, Isoperimetric inequalities",
author = "Guleryuz, {Onur G.} and Erwin Lutwak and Deane Yang and Gaoyong Zhang",
year = "2002",
month = "8",
doi = "10.1109/TIT.2002.800496",
language = "English (US)",
volume = "48",
pages = "2377--2383",
journal = "IEEE Transactions on Information Theory",
issn = "0018-9448",
publisher = "Institute of Electrical and Electronics Engineers Inc.",
number = "8",

}

TY - JOUR

T1 - Information-theoretic inequalities for contoured probability distributions

AU - Guleryuz, Onur G.

AU - Lutwak, Erwin

AU - Yang, Deane

AU - Zhang, Gaoyong

PY - 2002/8

Y1 - 2002/8

N2 - We show that for a special class of probability distributions that we call contoured distributions, information-theoretic invariants and inequalities are equivalent to geometric invariants and inequalities of bodies in Euclidean space associated with the distributions. Using this, we obtain characterizations of contoured distributions with extremal Shannon and Renyi entropy. We also obtain a new reverse information-theoretic inequality for contoured distributions.

AB - We show that for a special class of probability distributions that we call contoured distributions, information-theoretic invariants and inequalities are equivalent to geometric invariants and inequalities of bodies in Euclidean space associated with the distributions. Using this, we obtain characterizations of contoured distributions with extremal Shannon and Renyi entropy. We also obtain a new reverse information-theoretic inequality for contoured distributions.

KW - Brunn-Minkowski

KW - Convex bodies

KW - Elliptically contoured

KW - Entropy

KW - Fisher information

KW - Inequalities

KW - Isoperimetric inequalities

UR - http://www.scopus.com/inward/record.url?scp=0036671994&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0036671994&partnerID=8YFLogxK

U2 - 10.1109/TIT.2002.800496

DO - 10.1109/TIT.2002.800496

M3 - Article

VL - 48

SP - 2377

EP - 2383

JO - IEEE Transactions on Information Theory

JF - IEEE Transactions on Information Theory

SN - 0018-9448

IS - 8

ER -