Thinning and information projections

P Harremoes, Oliver T Johnson, I Kontoyiannis

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

3 Citations (Scopus)


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 contributionThinning and information projections
Original languageEnglish
Title of host publication2008 IEEE International Symposium on Information Theory Proceedings
Subtitle of host publicationProceedings of a meeting held 6-11 July 2008, Toronto, Ontario, Canada
PublisherInstitute of Electrical and Electronics Engineers (IEEE)
Number of pages5
ISBN (Electronic)9781424422579
ISBN (Print)9781424422562
Publication statusPublished - Nov 2008
EventIEEE International Symposium on Information Theory - Ontario, Canada, Toronto, Canada
Duration: 6 Jul 200811 Jul 2008


ConferenceIEEE International Symposium on Information Theory


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


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