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Erschienen in:
2000 | OriginalPaper | Buchkapitel
Towards an Algorithmic Statistics
(Extended Abstract)
verfasst von : Peter Gács, John Tromp, Paul Vitányi
Erschienen in: Algorithmic Learning Theory
Verlag: Springer Berlin Heidelberg
Enthalten in: Professional Book Archive
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While Kolmogorov complexity is the accepted absolute measure of information content of an individual finite object, a similarly absolute notion is needed for the relation between an individual data sample and an individual model summarizing the information in the data, for example, a finite set where the data sample typically came from. The statistical theory based on such relations between individual objects can be called algorithmic statistics, in contrast to ordinary statistical theory that deals with relations between probabilistic ensembles. We develop a new algorithmic theory of typical statistic, sufficient statistic, and minimal suffcient statistic.