Distribution-free and Model-free Multivariate Feature Screening via Multivariate Rank Distance Correlation

Abstract

Feature screening approaches are effective in selecting active features from data with ultrahigh dimensionality and increasing complexity; however, the majority of existing feature screening approaches are either restricted to a univariate response or rely on some distribution or model assumptions. In this article, we propose a novel sure independence screening approach based on the multivariate rank distance correlation (MrDc-SIS). The MrDc-SIS achieves multiple desirable properties such as being distribution-free, completely nonparametric, scale-free, robust for outliers or heavy tails, and sensitive for hidden structures. Moreover, the MrDc-SIS can be used to screen either univariate or multivariate responses and either one dimensional or multi-dimensional predictors. We establish the asymptotic sure screening consistency property of the MrDc-SIS under a mild condition by lifting previous assumptions about the finite moments. Simulation studies demonstrate that MrDc-SIS outperforms three other closely relevant approaches under various settings. We also apply the MrDc-SIS approach to a multi-omics ovarian carcinoma data downloaded from The Cancer Genome Atlas (TCGA).

Deep Feature Screening: Feature Selection for Ultra High-Dimensional Data via Deep Neural Networks

“…which generates the abstract features from the original high dimensional data and will be used later in the second step. The feature screening procedure via multivariate rank distance correlation has been proved to be of asymptotic sure screening consistency by Zhao and Fu (2021). For the sake of convenience, in what follows, we recapitulate the multivariate rank distance correlation of Deb and Sen (2021).…”