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Variable screening has been a useful research area that deals withultrahigh-dimensional data. When there exist both marginally and jointlydependent predictors to the response, existing methods such as conditionalscreening or iterative screening often suffer from instability against theselection of the conditional set or the computational burden, respectively. Inthis article, we propose a new independence measure, named conditionalmartingale difference divergence (CMDH), that can be treated as either aconditional or a marginal independence measure. Under regularity conditions, weshow that the sure screening property of CMDH holds for both marginally andjointly active variables. Based on this measure, we propose a kernel-basedmodel-free variable screening method, which is efficient, flexible, and stableagainst high correlation among predictors and heterogeneity of the response. Inaddition, we provide a data-driven method to select the conditional set. Insimulations and real data applications, we demonstrate the superior performanceof the proposed method.

High-dimensional Variable Screening via Conditional Martingale Difference Divergence