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- Kolmogorov_structure_function abstract "In 1973 Kolmogorov proposed a non-probabilistic approach to statistics and model selection. Let each data be a finite binary string and models be finite sets of binary strings. Consider model classes consisting of models of given maximal Kolmogorov complexity.The Kolmogorov structure function of an individual data string expresses the relation between the complexity level constraint on a model class and the least log-cardinality of a model in the class containing the data. The structure function determines all stochastic properties of the individual data string: for every constrained model class it determines the individual best-fitting model in the class irrespective of whether the true model is in the model class considered or not. In the classical case we talk about a set of data with a probability distribution, and the properties are those of the expectations. In contrast, here we deal with individual data strings and the properties of the individual string focussed on. In this setting, a property holds with certainty rather than with high probability as in the classical case. The Kolmogorov structure function precisely quantify the goodness-of-fit of an individual model with respect to individual data.The Kolmogorov structure function is used in the algorithmic information theory, also known as the theory of Kolmogorov complexity, for describing the structure of a string by use of models of increasing complexity.".
- Kolmogorov_structure_function thumbnail Kolm_complexity_lect.jpg?width=300.
- Kolmogorov_structure_function wikiPageExternalLink 294.full.pdf+html.
- Kolmogorov_structure_function wikiPageExternalLink 340.full.pdf+htm.
- Kolmogorov_structure_function wikiPageExternalLink p389_s1.
- Kolmogorov_structure_function wikiPageID "18010343".
- Kolmogorov_structure_function wikiPageRevisionID "572821025".
- Kolmogorov_structure_function hasPhotoCollection Kolmogorov_structure_function.
- Kolmogorov_structure_function subject Category:Algorithmic_information_theory.
- Kolmogorov_structure_function comment "In 1973 Kolmogorov proposed a non-probabilistic approach to statistics and model selection. Let each data be a finite binary string and models be finite sets of binary strings. Consider model classes consisting of models of given maximal Kolmogorov complexity.The Kolmogorov structure function of an individual data string expresses the relation between the complexity level constraint on a model class and the least log-cardinality of a model in the class containing the data.".
- Kolmogorov_structure_function label "Kolmogorov structure function".
- Kolmogorov_structure_function sameAs m.047t3gq.
- Kolmogorov_structure_function sameAs Q5805968.
- Kolmogorov_structure_function sameAs Q5805968.
- Kolmogorov_structure_function wasDerivedFrom Kolmogorov_structure_function?oldid=572821025.
- Kolmogorov_structure_function depiction Kolm_complexity_lect.jpg.
- Kolmogorov_structure_function isPrimaryTopicOf Kolmogorov_structure_function.
