Covariance-regularized regression and classification for high dimensional problems Export

@article{citeulike:4718193, abstract = {Summary. 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.}, address = {Stanford University, USA}, author = {Witten, Daniela M. and Tibshirani, Robert}, citeulike-article-id = {4718193}, citeulike-linkout-0 = {http://dx.doi.org/10.1111/j.1467-9868.2009.00699.x}, citeulike-linkout-1 = {http://www.ingentaconnect.com/content/bpl/rssb/2009/00000071/00000003/art00003}, citeulike-linkout-2 = {http://www3.interscience.wiley.com/cgi-bin/abstract/122210830/ABSTRACT}, doi = {10.1111/j.1467-9868.2009.00699.x}, journal = {Journal of the Royal Statistical Society: Series B (Statistical Methodology)}, keywords = {shrinkage}, number = {3}, pages = {615--636}, posted-at = {2009-06-02 13:29:47}, priority = {4}, title = {Covariance-regularized regression and classification for high dimensional problems}, url = {http://dx.doi.org/10.1111/j.1467-9868.2009.00699.x}, volume = {71}, year = {2009} }

TY - JOUR ID - citeulike:4718193 L3 - citeulike-article-id:4718193 N2 - Summary. 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. IS - 3 JF - Journal of the Royal Statistical Society: Series B (Statistical Methodology) AD - Stanford University, USA EP - 636 TI - Covariance-regularized regression and classification for high dimensional problems VL - 71 SP - 615 KW - shrinkage AU - Witten, Daniela AU - Tibshirani, Robert PY - 2009/// UR - http://dx.doi.org/10.1111/j.1467-9868.2009.00699.x ER -