ARK：基于耦合的稳健 Knockoffs 推断
ARK: Robust Knockoffs Inference with Coupling
AI总结：
针对特征分布错误设定或估计时 model-X knockoffs 框架的稳健性问题，提出 approximate knockoffs（ARK）过程，通过耦合技术证明其能实现渐近 FDR 和 $k$-FWER 控制，并验证了框架的稳健性。
摘要：
我们研究了 model-X knockoffs 框架在特征分布被错误设定或估计时的稳健性。我们通过在错误发现率（FDR）和 $k$-族错误率（$k$-FWER）度量下，理论分析一种实际应用的 knockoffs 算法的特征选择性能来实现这一目标，我们将该算法命名为 approximate knockoffs（ARK）过程。该过程与 model-X knockoffs 过程的唯一区别在于前者使用了错误设定或估计的特征分布。我们理论分析中的一项关键技术是将 approximate knockoffs 过程与 model-X knockoffs 过程进行耦合，使得这两个过程中的随机变量在实现上可以相互接近。我们证明，如果存在这样的耦合 model-X knockoffs 过程，approximate knockoffs 过程就能在目标水平上实现渐近的 FDR 或 $k$-FWER 控制。我们展示了此类耦合 model-X knockoff 变量的三种具体构造，验证了它们的存在性，并证明了 model-X knockoffs 框架的稳健性。此外，我们将 knockoff 变量耦合的概念与一种 Wasserstein 距离建立了正式联系。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
