  Variable selection is a difficult problem that is particularly challenging in
the analysis of high-dimensional genomic data. Here, we introduce the CAR
score, a novel and highly effective criterion for variable ranking in linear
regression based on Mahalanobis-decorrelation of the explanatory variables. The
CAR score provides a canonical ordering that encourages grouping of correlated
predictors and down-weights antagonistic variables. It decomposes the
proportion of variance explained and it is an intermediate between marginal
correlation and the standardized regression coefficient. As a population
quantity, any preferred inference scheme can be applied for its estimation.
Using simulations we demonstrate that variable selection by CAR scores is very
effective and yields prediction errors and true and false positive rates that
compare favorably with modern regression techniques such as elastic net and
boosting. We illustrate our approach by analyzing data concerned with diabetes
progression and with the effect of aging on gene expression in the human brain.
The R package "care" implementing CAR score regression is available from CRAN.
