Concentration of the information in data with log-concave distributions

Sergey Bobkov; Mokshay Madiman

doi:10.1214/10-AOP592

Concentration of the information in data with log-concave distributions

Sergey Bobkov
, Mokshay Madiman

School of Mathematics

Research output: Contribution to journal › Article › peer-review

63 Scopus citations

Abstract

A concentration property of the functional - log f(X) is demonstrated, when a random vector X has a log-concave density f on Rⁿ. This concentration property implies in particular an extension of the Shannon-McMillan-Breiman strong ergodic theorem to the class of discrete-time stochastic processes with log-concave marginals.

Original language	English (US)
Pages (from-to)	1528-1543
Number of pages	16
Journal	Annals of Probability
Volume	39
Issue number	4
DOIs	https://doi.org/10.1214/10-AOP592
State	Published - Jul 2011

Keywords

Asymptotic equipartition property
Concentration
Entropy
Log-concave distributions
Shannon-Mcmillan-Breiman theorem

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10.1214/10-AOP592

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abstract = "A concentration property of the functional - log f(X) is demonstrated, when a random vector X has a log-concave density f on Rn. This concentration property implies in particular an extension of the Shannon-McMillan-Breiman strong ergodic theorem to the class of discrete-time stochastic processes with log-concave marginals.",

keywords = "Asymptotic equipartition property, Concentration, Entropy, Log-concave distributions, Shannon-Mcmillan-Breiman theorem",

author = "Sergey Bobkov and Mokshay Madiman",

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AU - Madiman, Mokshay

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AB - A concentration property of the functional - log f(X) is demonstrated, when a random vector X has a log-concave density f on Rn. This concentration property implies in particular an extension of the Shannon-McMillan-Breiman strong ergodic theorem to the class of discrete-time stochastic processes with log-concave marginals.

KW - Asymptotic equipartition property

KW - Concentration

KW - Entropy

KW - Log-concave distributions

KW - Shannon-Mcmillan-Breiman theorem

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JO - Annals of Probability

JF - Annals of Probability

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ER -

Concentration of the information in data with log-concave distributions

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Keywords

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