Asymptotically minimax regret by Bayes mixtures for non-exponential families

Junnichi Takeuchi, Andrew R. Barron

研究成果: Chapter in Book/Report/Conference proceedingConference contribution

5 被引用数 (Scopus)

抄録

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.

本文言語英語
ホスト出版物のタイトル2013 IEEE Information Theory Workshop, ITW 2013
DOI
出版ステータス出版済み - 12 1 2013
イベント2013 IEEE Information Theory Workshop, ITW 2013 - Seville, スペイン
継続期間: 9 9 20139 13 2013

出版物シリーズ

名前2013 IEEE Information Theory Workshop, ITW 2013

その他

その他2013 IEEE Information Theory Workshop, ITW 2013
Countryスペイン
CitySeville
Period9/9/139/13/13

All Science Journal Classification (ASJC) codes

  • Information Systems

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