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Sure independence screening for ultra-high dimensional feature space (2006)
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BibTeX
@TECHREPORT{Fan06sureindependence,
author = {Jianqing Fan and Jinchi Lv},
title = {Sure independence screening for ultra-high dimensional feature space},
institution = {},
year = {2006}
}
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Abstract
Variable selection plays an important role in high dimensional statistical modeling which nowa-days appears in many areas and is key to various scientific discoveries. For problems of large scale or dimensionality p, estimation accuracy and computational cost are two top concerns. In a recent paper, Candes and Tao (2007) propose the Dantzig selector using L1 regularization and show that it achieves the ideal risk up to a logarithmic factor log p. Their innovative procedure and remarkable result are challenged when the dimensionality is ultra high as the factor log p can be large and their uniform uncertainty principle can fail. Motivated by these concerns, we introduce the concept of sure screening and propose a sure screening method based on a correlation learning, called the Sure Independence Screening (SIS), to reduce dimensionality from high to a moderate scale that is below sample size. In a fairly general asymptotic framework, the SIS is shown to have the sure screening property for even exponentially growing dimensionality. As a methodological extension, an iterative SIS (ISIS) is also proposed to enhance its finite sample performance. With dimension reduced accurately from high to below sample size, variable selection can be improved on both speed and accuracy, and can then be ac-
Keyphrases
ultra-high dimensional feature space sure independence sample size variable selection important role high dimensional statistical top concern moderate scale remarkable result ideal risk various scientific discovery methodological extension estimation accuracy l1 regularization general asymptotic framework uniform uncertainty principle factor log dantzig selector many area logarithmic factor log computational cost finite sample performance sure independence screening sure screening large scale innovative procedure recent paper correlation learning iterative si
