Redundancy of exchangeable estimators

Narayana P. Santhanam, Anand D. Sarwate, Jae Oh Woo

Research output: Contribution to journalArticlepeer-review

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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.

Original languageEnglish (US)
Pages (from-to)5339-5357
Number of pages19
JournalEntropy
Volume16
Issue number10
DOIs
StatePublished - 2014

All Science Journal Classification (ASJC) codes

  • Information Systems
  • Mathematical Physics
  • Physics and Astronomy (miscellaneous)
  • Electrical and Electronic Engineering

Keywords

  • Chinese restaurant process
  • Exchangeability
  • Pitman-Yor process
  • Random exchangeable partitions
  • Strong and weak universal compression

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