A Pseudo Knockoff Filter for Correlated Features

TL;DR

This paper introduces a pseudo-knockoff filter that offers greater flexibility and potentially higher power in variable selection while controlling the false discovery rate, inspired by the original knockoff filter.

Contribution

It proposes a new pseudo-knockoff filter method with improved construction flexibility and analyzes its FDR control properties, supported by numerical experiments.

Findings

Pseudo-knockoff filter with half Lasso statistic controls FDR in simulations.

The pseudo-knockoff filter demonstrates higher power than the original in tested scenarios.

Partial theoretical guarantees are provided for the pseudo-knockoff filter.

Abstract

In 2015, Barber and Candes introduced a new variable selection procedure called the knockoff filter to control the false discovery rate (FDR) and prove that this method achieves exact FDR control. Inspired by the work of Barber and Candes (2015), we propose and analyze a pseudo-knockoff filter that inherits some advantages of the original knockoff filter and has more flexibility in constructing its knockoff matrix. Moreover, we perform a number of numerical experiments that seem to suggest that the pseudo knockoff filter with the half Lasso statistic has FDR control and offers more power than the original knockoff filter with the Lasso Path or the half Lasso Statistic for the numerical examples that we consider in this paper. Although we cannot establish rigorous FDR control for the pseudo knockoff filter, we provide some partial analysis of the pseudo knockoff filter with the half Lasso statistic and establish a uniform FDP bound and an expectation inequality.