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 |
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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 | |
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 |
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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