ARK: ROBUST KNOCKOFFS INFERENCE WITH COUPLING

• 成果类型: Article
• 署名作者: Fan, Yingying; Gao, Lan; Lv, Jinchi
• 署名单位: University of Southern California; University of Tennessee System; University of Tennessee Knoxville
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/24-AOS2480
• 发表日期: 2025
• 页码: 749-773
• 关键词: false discovery rate

摘要

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.