منابع مشابه
Algorithmic Statistics
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 (or probability distribution) where the data sample typically came from. The statistical theory based...
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The mission of statistics is to provide adequate statistical hypotheses (models) for observed data. But what is an “adequate” model? To answer this question, one needs to use the notions of algorithmic information theory. It turns out that for every data string x one can naturally define “stochasticity profile”, a curve that represents a trade-off between complexity of a model and its adequacy....
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Algorithmic statistics has two different (and almost orthogonal) motivations. From the philosophical point of view, it tries to formalize how the statistics works and why some statistical models are better than others. After this notion of a “good model” is introduced, a natural question arises: it is possible that for some piece of data there is no good model? If yes, how often these bad (non-...
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The notion of a strong sufficient statistic was introduced in [N. Vereshchagin, Algorithmic Minimal Sufficient Statistic Revisited. Proc. 5th Conference on Computability in Europe, CiE 2009, LNCS 5635, pp. 478-487]. In this paper, we give a survey of fine properties of strong sufficient statistics and show that there are strings for which complexity of every strong sufficient statistic is much ...
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We express some criticism about the definition of an algorithmic sufficient statistic and, in particular, of an algorithmic minimal sufficient statistic. We propose another definition, which has better properties.
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ژورنال
عنوان ژورنال: IEEE Transactions on Information Theory
سال: 2001
ISSN: 0018-9448
DOI: 10.1109/18.945257