Sparse covariance thresholding for high-dimensional variable selection

X. Jessie Jeng, Zhongyin J Daye

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

In high dimensions, variable selection methods such as the lasso are oftenlimited by excessive variability and rank deficiency of the sample covariancematrix. Covariance sparsity is a natural phenomenon in such high-dimensional applications as microarray analysis, image processing, etc., in which a large number of predictors are independent or weakly correlated. In this paper, we propose thecovariance-thresholded lasso, a new class of regression methods that can utilize covariance sparsity to improve variable selection. We establish theoretical results, under the random design setting, that relate covariance sparsity to variable selection. Data and simulations indicate that our method can be useful in improving variable selection performances.

Original languageEnglish (US)
Pages (from-to)625-657
Number of pages33
JournalStatistica Sinica
Volume21
Issue number2
StatePublished - Apr 2011
Externally publishedYes

Fingerprint

Variable Selection
Thresholding
High-dimensional
Sparsity
Lasso
Random Design
Microarray Analysis
Higher Dimensions
Predictors
Image Processing
Regression
Variable selection
Simulation

Keywords

  • Consistency
  • Covariance sparsity
  • Large p small n
  • Random design
  • Regression
  • Regularization

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Cite this

Sparse covariance thresholding for high-dimensional variable selection. / Jeng, X. Jessie; Daye, Zhongyin J.

In: Statistica Sinica, Vol. 21, No. 2, 04.2011, p. 625-657.

Research output: Contribution to journalArticle

@article{c7bce0eb681b4211883958d6af40df73,
title = "Sparse covariance thresholding for high-dimensional variable selection",
abstract = "In high dimensions, variable selection methods such as the lasso are oftenlimited by excessive variability and rank deficiency of the sample covariancematrix. Covariance sparsity is a natural phenomenon in such high-dimensional applications as microarray analysis, image processing, etc., in which a large number of predictors are independent or weakly correlated. In this paper, we propose thecovariance-thresholded lasso, a new class of regression methods that can utilize covariance sparsity to improve variable selection. We establish theoretical results, under the random design setting, that relate covariance sparsity to variable selection. Data and simulations indicate that our method can be useful in improving variable selection performances.",
keywords = "Consistency, Covariance sparsity, Large p small n, Random design, Regression, Regularization",
author = "Jeng, {X. Jessie} and Daye, {Zhongyin J}",
year = "2011",
month = "4",
language = "English (US)",
volume = "21",
pages = "625--657",
journal = "Statistica Sinica",
issn = "1017-0405",
publisher = "Institute of Statistical Science",
number = "2",

}

TY - JOUR

T1 - Sparse covariance thresholding for high-dimensional variable selection

AU - Jeng, X. Jessie

AU - Daye, Zhongyin J

PY - 2011/4

Y1 - 2011/4

N2 - In high dimensions, variable selection methods such as the lasso are oftenlimited by excessive variability and rank deficiency of the sample covariancematrix. Covariance sparsity is a natural phenomenon in such high-dimensional applications as microarray analysis, image processing, etc., in which a large number of predictors are independent or weakly correlated. In this paper, we propose thecovariance-thresholded lasso, a new class of regression methods that can utilize covariance sparsity to improve variable selection. We establish theoretical results, under the random design setting, that relate covariance sparsity to variable selection. Data and simulations indicate that our method can be useful in improving variable selection performances.

AB - In high dimensions, variable selection methods such as the lasso are oftenlimited by excessive variability and rank deficiency of the sample covariancematrix. Covariance sparsity is a natural phenomenon in such high-dimensional applications as microarray analysis, image processing, etc., in which a large number of predictors are independent or weakly correlated. In this paper, we propose thecovariance-thresholded lasso, a new class of regression methods that can utilize covariance sparsity to improve variable selection. We establish theoretical results, under the random design setting, that relate covariance sparsity to variable selection. Data and simulations indicate that our method can be useful in improving variable selection performances.

KW - Consistency

KW - Covariance sparsity

KW - Large p small n

KW - Random design

KW - Regression

KW - Regularization

UR - http://www.scopus.com/inward/record.url?scp=79952611724&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79952611724&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:79952611724

VL - 21

SP - 625

EP - 657

JO - Statistica Sinica

JF - Statistica Sinica

SN - 1017-0405

IS - 2

ER -