Thinning and information projections

P Harremoes; Oliver T Johnson; I Kontoyiannis

doi:10.1109/ISIT.2008.4595471

Thinning and information projections

P Harremoes, Oliver T Johnson, I Kontoyiannis

Research output: Chapter in Book/Report/Conference proceeding › Conference Contribution (Conference Proceeding)

3 Citations (Scopus)

Abstract

The law of thin numbers is a Poisson approximation theorem related to the thinning operation. We use information projections to derive lower bounds on the information divergence from a thinned distribution to a Poisson distribution. Conditions for the existence of projections are given. If an information projection exists it must be an element of the associated exponential family. Exponential families are used to derive lower bounds on information divergence and lower bounds on the rate of convergence in the law of thin numbers. A method of translating results related to Poisson distributions into results related to Gaussian distributions is developed and used to prove a new non-trivial result related to the central limit theorem.

Translated title of the contribution	Thinning and information projections
Original language	English
Title of host publication	2008 IEEE International Symposium on Information Theory Proceedings
Subtitle of host publication	Proceedings of a meeting held 6-11 July 2008, Toronto, Ontario, Canada
Publisher	Institute of Electrical and Electronics Engineers (IEEE)
Pages	2644-2648
Number of pages	5
ISBN (Electronic)	9781424422579
ISBN (Print)	9781424422562
DOIs	https://doi.org/10.1109/ISIT.2008.4595471
Publication status	Published - Nov 2008
Event	IEEE International Symposium on Information Theory - Ontario, Canada, Toronto, Canada Duration: 6 Jul 2008 → 11 Jul 2008

Conference

Conference	IEEE International Symposium on Information Theory
Country/Territory	Canada
City	Toronto
Period	6/07/08 → 11/07/08

Keywords

Gaussian distributions
Poisson approximation theorem
central limit theorem
information divergence
information projections

Access to Document

10.1109/ISIT.2008.4595471

Cite this

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title = "Thinning and information projections",

abstract = "The law of thin numbers is a Poisson approximation theorem related to the thinning operation. We use information projections to derive lower bounds on the information divergence from a thinned distribution to a Poisson distribution. Conditions for the existence of projections are given. If an information projection exists it must be an element of the associated exponential family. Exponential families are used to derive lower bounds on information divergence and lower bounds on the rate of convergence in the law of thin numbers. A method of translating results related to Poisson distributions into results related to Gaussian distributions is developed and used to prove a new non-trivial result related to the central limit theorem.",

keywords = "Gaussian distributions, Poisson approximation theorem, central limit theorem, information divergence, information projections",

author = "P Harremoes and Johnson, {Oliver T} and I Kontoyiannis",

year = "2008",

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doi = "10.1109/ISIT.2008.4595471",

language = "English",

isbn = "9781424422562",

pages = "2644--2648",

booktitle = "2008 IEEE International Symposium on Information Theory Proceedings",

publisher = "Institute of Electrical and Electronics Engineers (IEEE)",

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note = "IEEE International Symposium on Information Theory ; Conference date: 06-07-2008 Through 11-07-2008",

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Harremoes, P, Johnson, OT & Kontoyiannis, I 2008, Thinning and information projections. in 2008 IEEE International Symposium on Information Theory Proceedings: Proceedings of a meeting held 6-11 July 2008, Toronto, Ontario, Canada. Institute of Electrical and Electronics Engineers (IEEE), pp. 2644-2648, IEEE International Symposium on Information Theory, Toronto, Canada, 6/07/08. https://doi.org/10.1109/ISIT.2008.4595471

Thinning and information projections. / Harremoes, P; Johnson, Oliver T; Kontoyiannis, I.

2008 IEEE International Symposium on Information Theory Proceedings: Proceedings of a meeting held 6-11 July 2008, Toronto, Ontario, Canada. Institute of Electrical and Electronics Engineers (IEEE), 2008. p. 2644-2648.

Research output: Chapter in Book/Report/Conference proceeding › Conference Contribution (Conference Proceeding)

TY - GEN

T1 - Thinning and information projections

AU - Harremoes, P

AU - Johnson, Oliver T

AU - Kontoyiannis, I

PY - 2008/11

Y1 - 2008/11

N2 - The law of thin numbers is a Poisson approximation theorem related to the thinning operation. We use information projections to derive lower bounds on the information divergence from a thinned distribution to a Poisson distribution. Conditions for the existence of projections are given. If an information projection exists it must be an element of the associated exponential family. Exponential families are used to derive lower bounds on information divergence and lower bounds on the rate of convergence in the law of thin numbers. A method of translating results related to Poisson distributions into results related to Gaussian distributions is developed and used to prove a new non-trivial result related to the central limit theorem.

AB - The law of thin numbers is a Poisson approximation theorem related to the thinning operation. We use information projections to derive lower bounds on the information divergence from a thinned distribution to a Poisson distribution. Conditions for the existence of projections are given. If an information projection exists it must be an element of the associated exponential family. Exponential families are used to derive lower bounds on information divergence and lower bounds on the rate of convergence in the law of thin numbers. A method of translating results related to Poisson distributions into results related to Gaussian distributions is developed and used to prove a new non-trivial result related to the central limit theorem.

KW - Gaussian distributions

KW - Poisson approximation theorem

KW - central limit theorem

KW - information divergence

KW - information projections

U2 - 10.1109/ISIT.2008.4595471

DO - 10.1109/ISIT.2008.4595471

M3 - Conference Contribution (Conference Proceeding)

SN - 9781424422562

SP - 2644

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BT - 2008 IEEE International Symposium on Information Theory Proceedings

PB - Institute of Electrical and Electronics Engineers (IEEE)

T2 - IEEE International Symposium on Information Theory

Y2 - 6 July 2008 through 11 July 2008

ER -

Thinning and information projections

Abstract

Conference

Keywords

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