Feature screening for ultrahigh-dimensional data via the adapted sliced Wasserstein correlation coefficient

Various methods including model-based and model-free feature screening procedures have beendeveloped to detect active predictors for ultrahigh-dimensional data. The existing feature screening procedures mainly focus on the association between the scalar predictor and the response variable, and are not available for detecting the association between two probability measures, which are commonly encountered in various fields. To address this issue, we propose a novel model-free feature screening procedure for ultrahigh-dimensional data based on the Wasserstein correlation coefficient. Its key merits include that (i) it can be applied to various types of covariates and response variables including univariate and multivariate discrete, categorical and continuous variables; (ii) it is robust to outliers or heavy-tailed data because of only distribution functions involved in evaluating the Wasserstein distance; (iii) it works well for the linear or nonlinear relationship between response variables and predictors. Under some mild conditions, we establish sure screening and rank consistency properties for the proposed screening procedure without imposing any moment conditions on the covariates. Simulation studies are implemented to assess the finite sample performance of the proposed method.A real-world example is used to illustrate the proposed procedure.