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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 Rademacher complexity ： ウィキペディア英語版 Rademacher complexity In computational learning theory (machine learning and theory of computation), Rademacher complexity, named after Hans Rademacher, measures richness of a class of real-valued functions with respect to a probability distribution. Given a training sample $S=(z\_1,\; z\_2,\; \backslash dots,\; z\_m)\; \backslash in\; Z^m$, and a class $\backslash mathcal$ of real-valued functions defined on a domain space $Z$, the empirical Rademacher complexity of $\backslash mathcal$ is defined as: $$ \widehat) = \frac \mathbb \left( \sup_^m \sigma_i h(z_i) \right| \ \bigg| \ S \right ) where $\backslash sigma\_1,\; \backslash sigma\_2,\; \backslash dots,\; \backslash sigma\_m$ are independent random variables drawn from the Rademacher distribution i.e. $\backslash Pr(\backslash sigma\_i\; =\; +1)\; =\; \backslash Pr(\backslash sigma\_i\; =\; -1)\; =\; 1/2$ for $i=1,2,\backslash dots,m$. Let $P$ be a probability distribution over $Z$. The Rademacher complexity of the function class $\backslash mathcal$ with respect to $P$ for sample size $m$ is: $$ \mathcal_m(\mathcal) = \mathbb \left(\widehat) \right ) where the above expectation is taken over an identically independently distributed (i.i.d.) sample $S=(z\_1,\; z\_2,\; \backslash dots,\; z\_m)$ generated according to $P$. One can show, for example, that there exists a constant $C$, such that any class of $\backslash$-indicator functions with Vapnik-Chervonenkis dimension $d$ has Rademacher complexity upper-bounded by $C\backslash sqrt\}$. ==Gaussian complexity== Gaussian complexity is a similar complexity with similar physical meanings, and can be obtained from the previous complexity using the random variables $g\_i$ instead of $\backslash sigma\_i$, where $g\_i$ are Gaussian i.i.d. random variables with zero-mean and variance 1, i.e. $g\_i\; \backslash sim\; \backslash mathcal\; \backslash left(\; 0,\; 1\; \backslash right)$. 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「Rademacher complexity」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.