Covariance-regularized regression and classification for high dimensional problems

Daniela M. Witten and Robert Tibshirani

Journal Of The Royal Statistical Society Series B, 2009, vol. 71, issue 3, pages 615-636

Abstract: We propose covariance-regularized regression, a family of methods for prediction in high dimensional settings that uses a shrunken estimate of the inverse covariance matrix of the features to achieve superior prediction. An estimate of the inverse covariance matrix is obtained by maximizing the log-likelihood of the data, under a multivariate normal model, subject to a penalty; it is then used to estimate coefficients for the regression of the response onto the features. We show that ridge regression, the lasso and the elastic net are special cases of covariance-regularized regression, and we demonstrate that certain previously unexplored forms of covariance-regularized regression can outperform existing methods in a range of situations. The covariance-regularized regression framework is extended to generalized linear models and linear discriminant analysis, and is used to analyse gene expression data sets with multiple class and survival outcomes. Copyright (c) 2009 Royal Statistical Society.

Date: 2009

Downloads: (external link)
http://www.blackwell-synergy.com/doi/abs/10.1111/j.1467-9868.2009.00699.x link to full text (text/html)
Access to full text is restricted to subscribers.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: http://EconPapers.repec.org/RePEc:bla:jorssb:v:71:y:2009:i:3:p:615-636

Ordering information: This journal article can be ordered from
http://www.blackwell ... bs.asp?ref=1369-7412

Access Statistics for this article

Journal Of The Royal Statistical Society Series B is edited by C. Robert and A. T. A. Wood

More articles in Journal Of The Royal Statistical Society Series B from Royal Statistical Society
Series data maintained by Christopher F. Baum ().