# Model-free Feature Screening and FDR Control with Knockoff Features

## TL;DR

This paper introduces a model-free, data-adaptive feature screening method for high-dimensional data using projection correlation, with an innovative two-step FDR control approach leveraging knockoff features, demonstrating strong empirical results.

## Contribution

It develops a novel model-free screening method based on projection correlation and a two-step FDR control procedure using knockoff features, applicable to complex data scenarios.

## Key findings

- Method achieves sure screening and rank consistency.
- FDR control is effective when FDR level ≥ 1/s.
- Numerical experiments show superior empirical performance.

## Abstract

This paper proposes a model-free and data-adaptive feature screening method for ultra-high dimensional datasets. The proposed method is based on the projection correlation which measures the dependence between two random vectors. This projection correlation based method does not require specifying a regression model and applies to the data in the presence of heavy-tailed errors and multivariate response. It enjoys both sure screening and rank consistency properties under weak assumptions. Further, a two-step approach is proposed to control the false discovery rate (FDR) in feature screening with the help of knockoff features. It can be shown that the proposed two-step approach enjoys both sure screening and FDR control if the pre-specified FDR level $\alpha$ is greater or equal to $1/s$, where $s$ is the number of active features. The superior empirical performance of the proposed methods is justified by various numerical experiments and real data applications.