Can Linear Algebra Create Perfect Knockoffs?

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 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.