Can linear algebra create perfect knockoffs?

TL;DR

This paper explores whether linear algebra can be used to construct near-perfect Model-X knockoffs efficiently, presenting methods to reduce computational costs while maintaining high-quality knockoffs.

Contribution

The paper demonstrates that linear algebra techniques can produce pseudo-perfect knockoffs and introduces methods to significantly reduce the computational complexity of the process.

Findings

Produced knockoffs with high mean absolute correlation to features

Developed algorithms to reduce computation time substantially

Achieved near-perfect knockoffs with improved efficiency

Abstract

As new Model-X knockoff construction techniques are developed, primarily concerned with determining the correct conditional distribution from which to sample, we focus less on deriving the correct multivariate distribution and instead ask if ``perfect'' knockoffs can be constructed using linear algebra. Using mean absolute correlation between knockoffs and features as a measure of quality, we do produce knockoffs that are pseudo-perfect, however, the optimization algorithm is computationally very expensive. We outline a series of methods to significantly reduce the computation time of the algorithm.