MDL convergence speed for Bernoulli sequences

Jan Poland*, Marcus Hutter

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

13 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)161-175
Number of pages15
JournalStatistics and Computing
Volume16
Issue number2
DOIs
Publication statusPublished - Jun 2006
Externally publishedYes

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