On the Convergence Speed of MDL Predictions for Bernoulli Sequences

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dc.creatorPoland, Jan
dc.creatorHutter, Marcus
dc.date2004-07-16
dc.date.accessioned2026-07-07T08:17:42Z
dc.date.available2026-07-07T08:17:42Z
dc.descriptionWe consider the Minimum Description Length principle for online sequence prediction. If the underlying model class is discrete, then the total expected square loss is a particularly interesting performance measure: (a) this quantity is bounded, implying convergence with probability one, and (b) it additionally specifies a `rate of convergence'. Generally, for MDL only exponential loss bounds hold, as opposed to the linear bounds for a Bayes mixture. 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. The results apply to many Machine Learning tasks including classification and hypothesis testing. We provide arguments that our theorems generalize to countable classes of i.i.d. models.
dc.description17 pages
dc.identifierhttps://arxiv.org/abs/cs/0407039
dc.identifierhttp://arxiv.org/abs/cs/0407039
dc.identifierProc. 15th International Conf. on Algorithmic Learning Theory (ALT-2004), pages 294-308
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/134180
dc.subjectMachine Learning
dc.subjectArtificial Intelligence
dc.subjectInformation Theory
dc.subjectProbability
dc.subjectI.2.6; E.4; G.3
dc.titleOn the Convergence Speed of MDL Predictions for Bernoulli Sequences
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