Binary Maximal Correlation Bounds and Isoperimetric Inequalities via Anti-Concentration

Dror Drach, Or Ordentlich, Ofer Shayevitz

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

This paper establishes a dimension-independent upper bound on the maximal correlation between Boolean functions of dependent random variables, in terms of the second and third singular values in their spectral decomposition, and the anti-concentration properties of the second singular vectors. This result has notable consequences, among which are: A strengthening of Witsenhausen's lower bound on the probability of disagreement between Boolean functions; a Poincaré inequality for bounded-cardinality functions; and improved lower bounds on the isoperimetric constant of Markov chains.

Original languageAmerican English
Title of host publication2021 IEEE International Symposium on Information Theory, ISIT 2021 - Proceedings
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages1284-1289
Number of pages6
ISBN (Electronic)9781538682098
DOIs
StatePublished - 12 Jul 2021
Event2021 IEEE International Symposium on Information Theory, ISIT 2021 - Virtual, Melbourne, Australia
Duration: 12 Jul 202120 Jul 2021

Publication series

NameIEEE International Symposium on Information Theory - Proceedings
Volume2021-July
ISSN (Print)2157-8095

Conference

Conference2021 IEEE International Symposium on Information Theory, ISIT 2021
Country/TerritoryAustralia
CityVirtual, Melbourne
Period12/07/2120/07/21

Bibliographical note

Publisher Copyright:
© 2021 IEEE.

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