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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 Sample complexity ： ウィキペディア英語版 Sample complexity In machine learning, sample complexity is the number of examples needed for the estimate of a target function to be within a given error rate. The sample complexity of a machine learning algorithm characterizes its rate of consistency. ==Mathematical Setup== Given a sample $S\_n\; =\; \backslash$ drawn i.i.d. from a distribution $\backslash rho$ on some input space $\backslash mathcal\; X\; \backslash times\; \backslash mathcal\; Y$, a supervised learning algorithm chooses a function $f:\backslash mathcal\; X\; \backslash to\; \backslash mathcal\; Y$ from some hypothesis class $\backslash mathcal\; H$. A desirable property of the algorithm is that it chooses functions with small expected prediction error with respect to $\backslash rho$ and some loss function $V:\backslash mathcal\; Y\; \backslash times\; \backslash mathcal\; Y\; \backslash to\; \backslash mathbb\; R\_+$. Specifically, it is desirable to have a consistent algorithm, or an algorithm that generates functions whose expected loss or risk $$$$ \mathcal R(f) = \mathbb E_\rho(), converge to the best possible risk $$$$ \mathcal R^ *_\mathcal = \underset\mathcal R(f). Formally, let $f\_n$ be the functions generated by an algorithm as the number of data points $n$ grows. The algorithm is consistent if $$$$ \underset\mathbb P_(\mathcal R(f_n) - \mathcal R^ *_\mathcal > \epsilon) \to 0 for all $\backslash epsilon\; >\; 0$, where $\backslash mathbb\; P\_$ denotes the i.i.d. sampling measure $\backslash rho^n$. The consistency property is nice, but it says nothing about how fast the risks converge. Since in practice one always deals with finite data, it is important to answer the question of how large a sample is needed to achieve a risk that is close, in the $\backslash epsilon$ sense, to the best possible for the function class. The notion of sample complexity answers this question. The sample complexity of a learning algorithm is a function $n(\backslash rho,\backslash epsilon,\backslash delta)$ such that for all $n\; \backslash ge\; n(\backslash rho,\backslash epsilon,\backslash delta)$, $$$$ \mathbb P_(\mathcal R(f_n) - \mathcal R^ *_\mathcal > \epsilon) < \delta. In words, the sample complexity $n(\backslash rho,\backslash epsilon,\backslash delta)$ defines the rate of consistency of the algorithm: given a desired accuracy $\backslash epsilon$ and confidence $\backslash delta$, one needs to sample at most $n(\backslash rho,\backslash epsilon,\backslash delta)$ data points to guarantee that the risk of the output function is within $\backslash epsilon$ of the best possible, with probability at least $1-\backslash delta$. 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「Sample 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.