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Entropy 2014, 16(10), 5339-5357; doi:10.3390/e16105339

Redundancy of Exchangeable Estimators

1
Department of Electrical Engineering, University of Hawaii at Manoa, 2540 Dole Street, Honolulu, HI 96822, USA
2
Department of Electrical and Computer Engineering, Rutgers, The State University of New Jersey, 94 Brett Road, Piscataway, NJ 08854 , USA
3
Applied Mathematics Program, Yale University, 51 Prospect St, New Haven, CT 06511, USA
*
Authors to whom correspondence should be addressed.
Received: 19 July 2014 / Revised: 23 September 2014 / Accepted: 8 October 2014 / Published: 13 October 2014
(This article belongs to the Section Information Theory)
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Abstract

Exchangeable random partition processes are the basis for Bayesian approaches to statistical inference in large alphabet settings. On the other hand, the notion of the pattern of a sequence provides an information-theoretic framework for data compression in large alphabet scenarios. Because data compression and parameter estimation are intimately related, we study the redundancy of Bayes estimators coming from Poisson–Dirichlet priors (or “Chinese restaurant processes”) and the Pitman–Yor prior. This provides an understanding of these estimators in the setting of unknown discrete alphabets from the perspective of universal compression. In particular, we identify relations between alphabet sizes and sample sizes where the redundancy is small, thereby characterizing useful regimes for these estimators. View Full-Text
Keywords: exchangeability; random exchangeable partitions; Chinese restaurant process; Pitman–Yor process; strong and weak universal compression exchangeability; random exchangeable partitions; Chinese restaurant process; Pitman–Yor process; strong and weak universal compression
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Santhanam, N.P.; Sarwate, A.D.; Woo, J.O. Redundancy of Exchangeable Estimators. Entropy 2014, 16, 5339-5357.

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