Model-Free Conditional Feature Screening with FDR Control

Abstract

In this article, we propose a model-free conditional feature screening method with false discovery rate (FDR) control for ultra-high dimensional data. The proposed method is built upon a new measure of conditional independence. Thus, the new method does not require a specific functional form of the regression function and is robust to heavy-tailed responses and predictors. The variables to be conditional on are allowed to be multivariate. The proposed method enjoys sure screening and ranking consistency properties under mild regularity conditions. To control the FDR, we apply the Reflection via Data Splitting method and prove its theoretical guarantee using martingale theory and empirical process techniques. Simulated examples and real data analysis show that the proposed method performs very well compared with existing works. Supplementary materials for this article are available online.

Keywords:

• False discovery rate control
• Ranking consistency
• Sure screening
• Ultra-high dimensional data analysis

Supplementary Materials

The supplementary materials contain technical lemmas and proof of other theorems.

Acknowledgments

The authors would like to thank the AE and reviewers for their constructive comments, which leads to a significant improvement of this work.

Additional information

Funding

Tong and Li’s research was supported by National Science Foundation DMS-1820702.