Minimum Description Length Induction, Bayesianism, and Kolmogorov Complexity

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dc.creatorVitanyi, Paul
dc.creatorLi, Ming
dc.date1999-01-27
dc.date.accessioned2026-07-07T08:18:06Z
dc.date.available2026-07-07T08:18:06Z
dc.descriptionThe relationship between the Bayesian approach and the minimum description length approach is established. We sharpen and clarify the general modeling principles MDL and MML, abstracted as the ideal MDL principle and defined from Bayes's rule by means of Kolmogorov complexity. The basic condition under which the ideal principle should be applied is encapsulated as the Fundamental Inequality, which in broad terms states that the principle is valid when the data are random, relative to every contemplated hypothesis and also these hypotheses are random relative to the (universal) prior. Basically, the ideal principle states that the prior probability associated with the hypothesis should be given by the algorithmic universal probability, and the sum of the log universal probability of the model plus the log of the probability of the data given the model should be minimized. If we restrict the model class to the finite sets then application of the ideal principle turns into Kolmogorov's minimal sufficient statistic. In general we show that data compression is almost always the best strategy, both in hypothesis identification and prediction.
dc.description35 pages, Latex. Submitted IEEE Trans. Inform. Theory
dc.identifierhttps://arxiv.org/abs/cs/9901014
dc.identifierhttp://arxiv.org/abs/cs/9901014
dc.identifierIEEE Transactions on Information Theory, 46:2(2000), 446-464
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/134320
dc.subjectMachine Learning
dc.subjectArtificial Intelligence
dc.subjectComputational Complexity
dc.subjectInformation Theory
dc.subjectLogic in Computer Science
dc.subjectProbability
dc.subjectData Analysis, Statistics and Probability
dc.subjectE.4,F.2,H.3,I.2,I.5,I.7
dc.titleMinimum Description Length Induction, Bayesianism, and Kolmogorov Complexity
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