Binary Maximal Correlation Bounds and Isoperimetric Inequalities via Anti-Concentration

Dror Drach; Or Ordentlich; Ofer Shayevitz

doi:10.1109/isit45174.2021.9517829

Binary Maximal Correlation Bounds and Isoperimetric Inequalities via Anti-Concentration

Dror Drach
, Or Ordentlich
, Ofer Shayevitz

The Rachel and Selim Benin School of Engineering and Computer Science

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-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 language	English
Title of host publication	2021 IEEE International Symposium on Information Theory, ISIT 2021 - Proceedings
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	1284-1289
Number of pages	6
ISBN (Electronic)	9781538682098
DOIs	https://doi.org/10.1109/isit45174.2021.9517829
State	Published - 12 Jul 2021
Event	2021 IEEE International Symposium on Information Theory, ISIT 2021 - Virtual, Melbourne, Australia Duration: 12 Jul 2021 → 20 Jul 2021

Publication series

Name	IEEE International Symposium on Information Theory - Proceedings
Volume	2021-July
ISSN (Print)	2157-8095

Conference

Conference	2021 IEEE International Symposium on Information Theory, ISIT 2021
Country/Territory	Australia
City	Virtual, Melbourne
Period	12/07/21 → 20/07/21

Bibliographical note

Publisher Copyright:
© 2021 IEEE.

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10.1109/isit45174.2021.9517829

Cite this

Drach, D., Ordentlich, O., & Shayevitz, O. (2021). Binary Maximal Correlation Bounds and Isoperimetric Inequalities via Anti-Concentration. In 2021 IEEE International Symposium on Information Theory, ISIT 2021 - Proceedings (pp. 1284-1289). (IEEE International Symposium on Information Theory - Proceedings; Vol. 2021-July). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/isit45174.2021.9517829

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Drach, D, Ordentlich, O & Shayevitz, O 2021, Binary Maximal Correlation Bounds and Isoperimetric Inequalities via Anti-Concentration. in 2021 IEEE International Symposium on Information Theory, ISIT 2021 - Proceedings. IEEE International Symposium on Information Theory - Proceedings, vol. 2021-July, Institute of Electrical and Electronics Engineers Inc., pp. 1284-1289, 2021 IEEE International Symposium on Information Theory, ISIT 2021, Virtual, Melbourne, Australia, 12/07/21. https://doi.org/10.1109/isit45174.2021.9517829

Binary Maximal Correlation Bounds and Isoperimetric Inequalities via Anti-Concentration. / Drach, Dror; Ordentlich, Or; Shayevitz, Ofer.
2021 IEEE International Symposium on Information Theory, ISIT 2021 - Proceedings. Institute of Electrical and Electronics Engineers Inc., 2021. p. 1284-1289 (IEEE International Symposium on Information Theory - Proceedings; Vol. 2021-July).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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Drach D, Ordentlich O, Shayevitz O. Binary Maximal Correlation Bounds and Isoperimetric Inequalities via Anti-Concentration. In 2021 IEEE International Symposium on Information Theory, ISIT 2021 - Proceedings. Institute of Electrical and Electronics Engineers Inc. 2021. p. 1284-1289. (IEEE International Symposium on Information Theory - Proceedings). doi: 10.1109/isit45174.2021.9517829

Binary Maximal Correlation Bounds and Isoperimetric Inequalities via Anti-Concentration

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