High-dimensional variable screening through kernel-based conditional mean dependence

Abstract

This article proposes a model-free feature screening method for ultrahigh-dimensional data. The proposed method is built on the called kernel-based conditional mean dependence, which is defined based on the reproducing kernel embedding and the Hilbert–Schmidt norm of a tensor operator. Theoretically, both sure screening and rank consistency properties are established under weak assumptions. Through an extensive simulation study as well as a real data analysis, it is illustrated that the statistics generated by other kernels in distance kernel family are more sensitive to feature screening in ultra-high dimensions.