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Entropy, compound poisson approximation, log-sobolev inequalities and measure concentration

Kontoyiannis, I and Madiman, M (2004) Entropy, compound poisson approximation, log-sobolev inequalities and measure concentration. In: UNSPECIFIED pp. 71-75..

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Abstract

The problem of approximating the distribution of a sum S n = Σ i=1n Y i of n discrete random variables Y i by a Poisson or a compound Poisson distribution arises naturally in many classical and current applications, such as statistical genetics, dynamical systems, the recurrence properties of Markov processes and reliability theory. Using information-theoretic ideas and techniques, we derive a family of new bounds for compound Poisson approximation. We take an approach similar to that of Kontoyiannis, Harremoës and Johnson (2003), and we generalize some of their Poisson approximation bounds to the compound Poisson case. Partly motivated by these results, we derive a new logarithmic Sobolev inequality for the compound Poisson measure and use it to prove measure-concentration bounds for a large class of discrete distributions. ©2004 IEEE.

Item Type: Conference or Workshop Item (UNSPECIFIED)
Subjects: UNSPECIFIED
Divisions: Div F > Signal Processing and Communications
Depositing User: Cron Job
Date Deposited: 08 Jan 2018 20:12
Last Modified: 18 Aug 2020 12:42
DOI: