Adaptive conditional feature screening

When the correlation among the predictors is relatively strong and/or the model structures cannot be specified, the construction of adaptive feature screening remains a challenging issue. A general technique of conditional feature screening is proposed via combining a model-free feature screening with a predetermined set of predictors. The proposed centralization technique can remove the irrelevant part from the criterion of the model-free feature screening. Consequently, the new criterion can measure the marginal utilities of predictors conditional on the predetermined set of predictors. The conditional information about these predetermined predictors helps reducing the correlation among covariates and as a result the resulting method can reduce the false positive and the false negative rates in the variable selection procedure. Thus, our method is adaptive to both the correlation among the covariates and the model misspecification. The new procedures are computationally efficient and simple, and can be extended to other relevant methods. (C) 2015 Elsevier B.V. All rights reserved.