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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 Minimum message length ： ウィキペディア英語版 Minimum message length Minimum message length (MML) is a formal information theory restatement of Occam's Razor: even when models are not equal in goodness of fit accuracy to the observed data, the one generating the shortest overall message is more likely to be correct (where the message consists of a statement of the model, followed by a statement of data encoded concisely using that model). MML was invented by Chris Wallace, first appearing in the seminal Wallace and Boulton (1968). MML is intended not just as a theoretical construct, but as a technique that may be deployed in practice. It differs from the related concept of Kolmogorov complexity in that it does not require use of a Turing-complete language to model data. The relation between Strict MML (SMML) and Kolmogorov complexity is outlined in (Wallace and Dowe (1999a) ). Further, a variety of mathematical approximations to "Strict" MML can be used — see, e.g., (Chapters 4 and 5 ) of (Wallace (posthumous) 2005 ). ==Definition== Shannon's ''A Mathematical Theory of Communication'' (1949) states that in an optimal code, the message length (in binary) of an event $E$, $\backslash operatorname(E)$, where $E$ has probability $P(E)$, is given by $\backslash operatorname(E)\; =\; -\backslash log\_2(P(E))$. Bayes's theorem states that the probability of a (variable) hypothesis $H$ given fixed evidence $E$ is proportional to $P(E|H)\; P(H)$, which, by the definition of conditional probability, is equal to $P(H\; \backslash and\; E)$. We want the model (hypothesis) with the highest such ''posterior probability''. Suppose we encode a message which represents (describes) both model and data jointly. Since $\backslash operatorname(H\; \backslash and\; E)\; =\; -\backslash log\_2(P(H\; \backslash and\; E))$, the most probable model will have the shortest such message. The message breaks into two parts: $-\backslash log\_2(P(H\; \backslash and\; E))\; =\; -\backslash log\_2(P(H))\; +\; -\backslash log\_2(P(E|H))$. The first part encodes the model itself. The second part contains information (e.g., values of parameters, or initial conditions, etc.) that, when processed by the model, outputs the observed data. MML naturally and precisely trades model complexity for goodness of fit. A more complicated model takes longer to state (longer first part) but probably fits the data better (shorter second part). So, an MML metric won't choose a complicated model unless that model pays for itself. 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「Minimum message length」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.