Using distance covariance for improved variable selection with application to learning genetic risk models

Variable selection is of increasing importance to address the difficulties of high dimensionality in many scientific areas. In this paper, we demonstrate a property for distance covariance, which is incorporated in a novel feature screening procedure together with the use of distance correlation. The approach makes no distributional assumptions for the variables and does not require the specification of a regression model and hence is especially attractive in variable selection given an enormous number of candidate attributes without much information about the true model with the response. The method is applied to two genetic risk problems, where issues including uncertainty of variable selection via cross validation, subgroup of hard-to-classify cases, and the application of a reject option are discussed.