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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 Leave one out error ： ウィキペディア英語版 Leave-one-out error * Leave-one-out cross-validation (CVloo) Stability An algorithm f has CVloo stability β with respect to the loss function V if the following holds: $\backslash forall\; i\backslash in\backslash ,\; \backslash mathbb\_S\backslash \},z\_i)|\backslash leq\backslash beta\_\backslash \}\backslash geq1-\backslash delta\_$ * Expected-to-leave-one-out error ($Eloo\_$) Stability An algorithm f has $Eloo\_$ stability if for each n there exists a$\backslash beta\_^m$ and a $\backslash delta\_^m$ such that: $\backslash forall\; i\backslash in\backslash ,\; \backslash mathbb\_S\backslash \backslash sum\_^m\; V(f\_^m\backslash \}\backslash geq1-\backslash delta\_^m$, with $\backslash beta\_^m$and $\backslash delta\_^m$ going to zero for $n\backslash rightarrow\backslash inf$ ==Preliminary Notations== X and Y ⊂ R being respectively an input and an output space, we consider a training set $S\; =\; \backslash$ of size m in $Z\; =\; X\; \backslash times\; Y$ drawn i.i.d. from an unknown distribution D. A learning algorithm is a function $f$ from $Z\_m$ into $F\; \backslash subset\; YX$which maps a learning set S onto a function $f\_S$ from X to Y. To avoid complex notation, we consider only deterministic algorithms. It is also assumed that the algorithm $f$ is symmetric with respect to S, i.e. it does not depend on the order of the elements in the training set. Furthermore, we assume that all functions are measurable and all sets are countable which does not limit the interest of the results presented here. The loss of an hypothesis f with respect to an example $z\; =\; (x,y)$ is then defined as $V(f,z)\; =\; V(f(x),y)$. The empirical error of f is $I\_S()\; =\; \backslash frac\backslash sum\; V(f,z\_i)$. The true error of f is $I()\; =\; \backslash mathbb\_z\; V(f,z)$ Given a training set S of size m, we will build, for all i = 1....,m, modified training sets as follows: * By removing the i-th element $S^\; =\; \backslash ,...,\backslash \; z\_m\backslash \}$ * By replacing the i-th element $S^i\; =\; \backslash ,...,\backslash \; z\_m\backslash \}$ 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「Leave-one-out error」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.