MDL Convergence Speed for Bernoulli Sequences

Simple item page
dc.creatorPoland, Jan
dc.creatorHutter, Marcus
dc.date2006-02-22
dc.date.accessioned2026-07-07T08:18:17Z
dc.date.available2026-07-07T08:18:17Z
dc.descriptionThe 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.
dc.description28 pages
dc.identifierhttps://arxiv.org/abs/math/0602505
dc.identifierhttp://arxiv.org/abs/math/0602505
dc.identifierStatistics and Computing, 16 (2006) pages 161-175
dc.identifierdoi:10.1007/s11222-006-6746-3
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/134378
dc.subjectStatistics Theory
dc.subjectInformation Theory
dc.subjectMachine Learning
dc.subjectProbability
dc.titleMDL Convergence Speed for Bernoulli Sequences
dc.typetext

Files

Collections

arXiv