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MDL convergence speed for Bernoulli sequences

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タイトル: MDL convergence speed for Bernoulli sequences
著者: Poland, Jan 著作を一覧する
Hutter, Marcus 著作を一覧する
発行日: 2006年 6月
出版者: Springer
誌名: Statistics and Computing
巻: 16
号: 2
開始ページ: 161
終了ページ: 175
出版社 DOI: 10.1007/s11222-006-6746-3
抄録: The Minimum Description Length principle for online sequence estimation/prediction in a proper learning setup is studied. If the underlying model class is discrete, then the total expected square loss is a particularly interesting performance measure: (a) this quantity is finitely bounded, implying convergence with probability one, and (b) it additionally specifies the convergence speed. For MDL, in general one can only have loss bounds which are finite but exponentially larger than those for Bayes mixtures. We show that this is even the case if the model class contains only Bernoulli distributions. We derive a new upper bound on the prediction error for countable Bernoulli classes. This implies a small bound (comparable to the one for Bayes mixtures) for certain important model classes. We discuss the application to Machine Learning tasks such as classification and hypothesis testing, and generalization to countable classes of i.i.d. models.
Rights: The original publication is available at
資料タイプ: article (author version)
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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