Asymptotically minimax regret by Bayes mixtures for non-exponential families

Junnichi Takeuchi, Andrew R. Barron

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

5 Citations (Scopus)

Abstract

We study the problems of data compression, gambling and prediction of a sequence xn = x1x2...xn from an alphabet X, in terms of regret with respect to various families of probability distributions. It is known that the regret of the Bayes mixture with respect to a general exponential families asymptotically achieves the minimax value when variants of Jeffreys prior are used, under the condition that the maximum likelihood estimate is in the interior of the parameter space. We discuss a modification of Jeffreys prior which has measure outside the given family of densities, to achieve minimax regret with respect to non-exponential type families, e.g. curved exponential families and mixture families. These results also provide characterization of Rissanen's stochastic complexity for those classes.

Original languageEnglish
Title of host publication2013 IEEE Information Theory Workshop, ITW 2013
DOIs
Publication statusPublished - Dec 1 2013
Event2013 IEEE Information Theory Workshop, ITW 2013 - Seville, Spain
Duration: Sep 9 2013Sep 13 2013

Publication series

Name2013 IEEE Information Theory Workshop, ITW 2013

Other

Other2013 IEEE Information Theory Workshop, ITW 2013
CountrySpain
CitySeville
Period9/9/139/13/13

All Science Journal Classification (ASJC) codes

  • Information Systems

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    Takeuchi, J., & Barron, A. R. (2013). Asymptotically minimax regret by Bayes mixtures for non-exponential families. In 2013 IEEE Information Theory Workshop, ITW 2013 [6691254] (2013 IEEE Information Theory Workshop, ITW 2013). https://doi.org/10.1109/ITW.2013.6691254