Journal
JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
Volume 71, Issue -, Pages 615-636Publisher
WILEY
DOI: 10.1111/j.1467-9868.2009.00699.x
Keywords
Classification; Covariance regularization; n < p; Regression; Variable selection
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Funding
- National Defense Science and Engineering Graduate Fellowship
- National Science Foundation [DMS-9971405]
- National Institutes of Health [N01-HV-28183]
- NATIONAL HEART, LUNG, AND BLOOD INSTITUTE [R01HL028183] Funding Source: NIH RePORTER
- NATIONAL INSTITUTE OF BIOMEDICAL IMAGING AND BIOENGINEERING [R01EB001988] Funding Source: NIH RePORTER
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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.
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