Asymptotically minimax regret for models with hidden variables

Junnichi Takeuchi, Andrew R. Barron

Research output: Chapter in Book/Report/Conference proceedingConference contribution

3 Citations (Scopus)

Abstract

We study the problems of data compression, gambling and prediction of a string xn = x1x2...xn from an alphabet X, in terms of regret with respect to models with hidden variables including general mixture families. When the target class is a non-exponential family, a modification of Jeffreys prior which has measure outside the given family of densities was introduced to achieve the minimax regret [8], under certain regularity conditions. In this paper, we show that the models with hidden variables satisfy those regularity conditions, when the hidden variables' model is an exponential family. In paticular, we do not have to restrict the class of data strings so that the MLE is in the interior of the parameter space for the case of the general mixture family.

Original languageEnglish
Title of host publication2014 IEEE International Symposium on Information Theory, ISIT 2014
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages3037-3041
Number of pages5
ISBN (Print)9781479951864
DOIs
Publication statusPublished - Jan 1 2014
Event2014 IEEE International Symposium on Information Theory, ISIT 2014 - Honolulu, HI, United States
Duration: Jun 29 2014Jul 4 2014

Publication series

NameIEEE International Symposium on Information Theory - Proceedings
ISSN (Print)2157-8095

Other

Other2014 IEEE International Symposium on Information Theory, ISIT 2014
CountryUnited States
CityHonolulu, HI
Period6/29/147/4/14

Fingerprint

Hidden Variables
Regret
Minimax
Regularity Conditions
Strings
Maximum likelihood estimation
Data compression
Gambling
Jeffreys Prior
Exponential Family
Data Compression
Model
Parameter Space
Interior
Target
Family
Prediction
Class

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Information Systems
  • Modelling and Simulation
  • Applied Mathematics

Cite this

Takeuchi, J., & Barron, A. R. (2014). Asymptotically minimax regret for models with hidden variables. In 2014 IEEE International Symposium on Information Theory, ISIT 2014 (pp. 3037-3041). [6875392] (IEEE International Symposium on Information Theory - Proceedings). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ISIT.2014.6875392

Asymptotically minimax regret for models with hidden variables. / Takeuchi, Junnichi; Barron, Andrew R.

2014 IEEE International Symposium on Information Theory, ISIT 2014. Institute of Electrical and Electronics Engineers Inc., 2014. p. 3037-3041 6875392 (IEEE International Symposium on Information Theory - Proceedings).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Takeuchi, J & Barron, AR 2014, Asymptotically minimax regret for models with hidden variables. in 2014 IEEE International Symposium on Information Theory, ISIT 2014., 6875392, IEEE International Symposium on Information Theory - Proceedings, Institute of Electrical and Electronics Engineers Inc., pp. 3037-3041, 2014 IEEE International Symposium on Information Theory, ISIT 2014, Honolulu, HI, United States, 6/29/14. https://doi.org/10.1109/ISIT.2014.6875392
Takeuchi J, Barron AR. Asymptotically minimax regret for models with hidden variables. In 2014 IEEE International Symposium on Information Theory, ISIT 2014. Institute of Electrical and Electronics Engineers Inc. 2014. p. 3037-3041. 6875392. (IEEE International Symposium on Information Theory - Proceedings). https://doi.org/10.1109/ISIT.2014.6875392
Takeuchi, Junnichi ; Barron, Andrew R. / Asymptotically minimax regret for models with hidden variables. 2014 IEEE International Symposium on Information Theory, ISIT 2014. Institute of Electrical and Electronics Engineers Inc., 2014. pp. 3037-3041 (IEEE International Symposium on Information Theory - Proceedings).
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