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Asymptotics of Discrete MDL for Online Prediction

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タイトル: Asymptotics of Discrete MDL for Online Prediction
著者: Poland, Jan 著作を一覧する
Hutter, Marcus 著作を一覧する
キーワード: algorithmic information theory
discrete model class
loss bounds
minimum description length (MDL)
sequence prediction
universal induction
発行日: 2005年11月
出版者: IEEE
誌名: IEEE Transactions on Information Theory
巻: 51
号: 11
開始ページ: 3780
終了ページ: 3795
出版社 DOI: 10.1109/TIT.2005.856956
抄録: Minimum description length (MDL) is an important principle for induction and prediction, with strong relations to optimal Bayesian learning. This paper deals with learning processes which are not necessarily independent and identically distributed, by means of two-part MDL, where the underlying model class is countable. We consider the online learning framework, i.e., observations come in one by one, and the predictor is allowed to update its state of mind after each time step.We identify two ways of predicting by MDL for this setup, namely, a static and a dynamic one. (A third variant, hybrid MDL, will turn out inferior.)We will prove that under the only assumption that the data is generated by a distribution contained in the model class, the MDL predictions converge to the true values almost surely. This is accomplished by proving finite bounds on the quadratic, the Hellinger, and the KullbackLeibler loss of the MDL learner, which are, however, exponentially worse than for Bayesian prediction. We demonstrate that these bounds are sharp, even for model classes containing only Bernoulli distributions. We show how these bounds imply regret bounds for arbitrary loss functions. Our results apply to a wide range of setups, namely, sequence prediction, pattern classification, regression, and universal induction in the sense of algorithmic information theory among others.
記述: Erratum published: IEEE Transactions on Information Theory. Volume 52, Issue 3, March 2006, p.1279
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Rights: (c) 2005-2006 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.
資料タイプ: article
出現コレクション:雑誌発表論文等 (Peer-reviewed Journal Articles, etc)

提供者: Jan Poland


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