ARK: Robust knockoffs inference with coupling

The Annals of Statistics · 2025 · Volume 53 · Issue 2

Abstract

We investigate the robustness of the model-X knockoffs framework with respect to the misspecified or estimated feature distribution. We achieve such a goal by theoretically studying the feature selection performance of a practically implemented knockoffs algorithm, which we name as the approximate knockoffs (ARK) procedure, under the measures of the false discovery rate (FDR) and k-familywise error rate (k-FWER). The approximate knockoffs procedure differs from the model-X knockoffs procedure only in that the former uses the misspecified or estimated feature distribution. A key technique in our theoretical analyses is to couple the approximate knockoffs procedure with the model-X knockoffs procedure so that random variables in these two procedures can be close in realizations. We prove that if such coupled model-X knockoffs procedure exists, the approximate knockoffs procedure can achieve the asymptotic FDR or k-FWER control at the target level. We showcase three specific constructions of such coupled model-X knockoff variables, verifying their existence and justifying the robustness of the model-X knockoffs framework. Additionally, we formally connect our concept of knockoff variable coupling to a type of Wasserstein distance.

Keywords

62E17, 62F07, 62F35, 62G10, 62G35, coupling, false discovery rate control, familywise error rate control, high dimensionality, Knockoffs inference, robustness, Wasserstein distance

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