Reversal of Rényi Entropy Inequalities Under Log-Concavity

Reversal of Rényi Entropy Inequalities Under Log-Concavity

We establish a discrete analog of the Rényi entropy comparison due to Bobkov and Madiman. For log-concave variables on the integers, the min entropy is within \log e of the usual Shannon entropy. Additionally we investigate the entropic Rogers-Shephard inequality studied by Madiman and Kontoyannis...

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Veröffentlicht in:IEEE transactions on information theory 2021-01, Vol.67 (1), p.45-51
Hauptverfasser: Melbourne, James, Tkocz, Tomasz
Format: Artikel
Sprache:eng
Schlagworte:
Concavity
convex geometry
Density functional theory
Electronic mail
Entropy
Entropy (Information theory)
entropy power inequality
Geometry
Indexes
log-concave variables
Random variables
reversals
Rogers-Shephard
Rényi entropy
Uncertainty
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Zusammenfassung:We establish a discrete analog of the Rényi entropy comparison due to Bobkov and Madiman. For log-concave variables on the integers, the min entropy is within \log e of the usual Shannon entropy. Additionally we investigate the entropic Rogers-Shephard inequality studied by Madiman and Kontoyannis, and establish a sharp Rényi version for certain parameters in both the continuous and discrete cases.
ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2020.3024025