TY - GEN
T1 - Binary Maximal Correlation Bounds and Isoperimetric Inequalities via Anti-Concentration
AU - Drach, Dror
AU - Ordentlich, Or
AU - Shayevitz, Ofer
N1 - Publisher Copyright:
© 2021 IEEE.
PY - 2021/7/12
Y1 - 2021/7/12
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85115064519&partnerID=8YFLogxK
U2 - 10.1109/ISIT45174.2021.9517829
DO - 10.1109/ISIT45174.2021.9517829
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AN - SCOPUS:85115064519
T3 - IEEE International Symposium on Information Theory - Proceedings
SP - 1284
EP - 1289
BT - 2021 IEEE International Symposium on Information Theory, ISIT 2021 - Proceedings
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 2021 IEEE International Symposium on Information Theory, ISIT 2021
Y2 - 12 July 2021 through 20 July 2021
ER -