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arXiv · 2110.03145

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

Shaofei Zhao·Guifang Fu
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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).

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Shaofei Zhao, Guifang Fu. 2021-10-07. Distribution-free and Model-free Multivariate Feature Screening via Multivariate Rank Distance Correlation. https://doi.org/10.1016/j.jmva.2022.105081

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