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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 Sufficient dimension reduction ： ウィキペディア英語版 Sufficient dimension reduction In statistics, sufficient dimension reduction (SDR) is a paradigm for analyzing data that combines the ideas of dimension reduction with the concept of sufficiency. Dimension reduction has long been a primary goal of regression analysis. Given a response variable ''y'' and a ''p''-dimensional predictor vector $\backslash textbf$, regression analysis aims to study the distribution of $y|\backslash textbf$, the conditional distribution of $y$ given $\backslash textbf$. A dimension reduction is a function $R(\backslash textbf)$ that maps $\backslash textbf$ to a subset of $\backslash mathbb^k$, ''k'' < ''p'', thereby reducing the dimension of $\backslash textbf$.〔Cook & Adragni (2009) (''Sufficient Dimension Reduction and Prediction in Regression'' ) In: ''Philosophical Transactions of the Royal Society A: Physical, Mathematical and Engineering Sciences'', 367(1906): 4385–4405〕 For example, $R(\backslash textbf)$ may be one or more linear combinations of $\backslash textbf$. A dimension reduction $R(\backslash textbf)$ is said to be sufficient if the distribution of $y|R(\backslash textbf)$ is the same as that of $y|\backslash textbf$. In other words, no information about the regression is lost in reducing the dimension of $\backslash textbf$ if the reduction is sufficient.〔 == Graphical motivation == In a regression setting, it is often useful to summarize the distribution of $y|\backslash textbf$ graphically. For instance, one may consider a scatter plot of $y$ versus one or more of the predictors. A scatter plot that contains all available regression information is called a sufficient summary plot. When $\backslash textbf$ is high-dimensional, particularly when $p\backslash geq\; 3$, it becomes increasingly challenging to construct and visually interpret sufficiency summary plots without reducing the data. Even three-dimensional scatter plots must be viewed via a computer program, and the third dimension can only be visualized by rotating the coordinate axes. However, if there exists a sufficient dimension reduction $R(\backslash textbf)$ with small enough dimension, a sufficient summary plot of $y$ versus $R(\backslash textbf)$ may be constructed and visually interpreted with relative ease. Hence sufficient dimension reduction allows for graphical intuition about the distribution of $y|\backslash textbf$, which might not have otherwise been available for high-dimensional data. Most graphical methodology focuses primarily on dimension reduction involving linear combinations of $\backslash textbf$. The rest of this article deals only with such reductions. 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「Sufficient dimension reduction」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.