Feature screening for ultrahigh-dimensional additive logistic models

Abstract

This paper introduces a sure screening method for ultrahigh-dimensional additive logistic models. With binary response variable, additive logistic model is very useful in social and biological research such as disease detection. The proposed feature screening procedure, ALNIS (nonparametric independence screening for additive logistic models), employs B-spline approximation to model the marginal effect, transforming nonparametric problems into parametric ones. This screening process ranks the nonparametric components according to their norms of the marginal likelihood estimate. Under appropriate conditions, the proposed method is shown to possess sure screening property with a vanishing false selection rate. In numerical studies, we use simulated data to compare the performance of the proposed approach with other seven methods that allow the existence of binary response. We further illustrate the proposed procedure by a real data analysis. Numerical comparison indicates that the proposed approach enjoys robustness and effectiveness under ultrahigh-dimensional additive logistic models.