A note of feature screening via rank-based coefficient of correlation

TL;DR

This paper introduces a simple, rank-based feature screening method applicable to both continuous and discrete responses in ultrahigh-dimensional data, with proven theoretical guarantees and effective detection of nonlinear predictors.

Contribution

It extends Chatterjee's rank-based correlation to develop a versatile feature screening procedure suitable for various response types, overcoming previous limitations.

Findings

Successfully detects predictors with nonlinear and oscillatory trajectories

Demonstrates robustness across different response distributions

Establishes sure screening property for the proposed method

Abstract

Feature screening is useful and popular to detect informative predictors for ultrahigh-dimensional data before developing proceeding statistical analysis or constructing statistical models. While a large body of feature screening procedures has been developed, most of them are restricted on examining either continuous or discrete responses. Moreover, even though many model-free feature screening methods have been proposed, additional assumptions are imposed in those methods to ensure their theoretical results. To address those difficulties and provide simple implementation, in this paper we extend the rank-based coefficient of correlation proposed by Chatterjee (2020) to develop feature screening procedure. We show that this new screening criterion is able to deal with continuous and discrete responses. Theoretically, sure screening property is established to justify the proposed method. Simulation studies demonstrate that the predictors with nonlinear and oscillatory trajectory are successfully detected regardless of the distribution of the response.