B0611
Title: ARK: robust knockoffs inference with coupling
Authors: Yingying Fan - University of Southern California (United States)
Lan Gao - University of Tennessee Knoxville (United States) [presenting]
Jinchi Lv - University of Southern California (United States)
Abstract: The robustness of the model-X knockoffs framework is investigated with respect to the misspecified or estimated feature distribution. Such a goal is achieved by theoretically studying the feature selection performance of a practically implemented knockoff algorithm, which is named the approximate knockoffs (ARK) procedure, under the measures of the false discovery rate (FDR) and family-wise error rate (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 the 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. It is proven that if such a coupled model-X knockoff procedure exists, the approximate knockoff procedure can achieve the asymptotic FDR or FWER control at the target level. Three specific constructions of such coupled model-X knockoff variables are showcased, verifying their existence and justifying the robustness of the model-X knockoff framework.
