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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Kolmogorov structure function ： ウィキペディア英語版 Kolmogorov structure function 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's definition== The structure function was originally proposed by Kolmogorov in 1973 at a Soviet Information Theory symposium in Tallinn, but these results were not published 〔 p. 182. But the results were announced in 〔(Abstract of a talk for the Moscow Mathematical Society in Uspekhi Mat. Nauk Volume 29, Issue 4(178) in the Communications of the Moscow Mathematical Society page 155 (in the Russian edition, not translated into English) )〕 in 1974, the only written record by Kolmogorov himself. One of his last scientific statements is (translated from the original Russian by L.A. Levin): 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Kolmogorov structure function」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.