The knockoff filter of Barber and Candes (arXiv:1404.5609) is a flexible framework for multiple testing in supervised learning models, based on introducing synthetic predictor variables to control the false discovery rate (FDR). Using the conditional calibration framework of Fithian and Lei (arXiv:2007.10438), we introduce the calibrated knockoff procedure, a method that uniformly improves the power of any fixed-X or model-X knockoff procedure. We show theoretically and empirically that the improvement is especially notable in two contexts where knockoff methods can be nearly powerless: when the rejection set is small, and when the structure of the design matrix in fixed-X knockoffs prevents us from constructing good knockoff variables. In these contexts, calibrated knockoffs even outperform competing FDR-controlling methods like the (dependence-adjusted) procedure Benjamini-Hochberg in many scenarios.

翻译：Barber与Candès提出的Knockoff滤波器（arXiv:1404.5609）是一种基于合成预测变量构建的监督学习模型多重检验框架，用于控制错误发现率。基于Fithian与Lei的条件校准框架（arXiv:2007.10438），本文提出校准Knockoff方法，该方法能一致提升任意固定-X或模型-X Knockoff流程的检验功效。理论与实证研究表明，该方法在两种Knockoff方法可能近乎失效的场景中提升尤为显著：当拒绝集规模较小时，以及当固定-X Knockoff中的设计矩阵结构导致无法构建优质Knockoff变量时。在这些场景中，校准Knockoff方法在多数情况下甚至优于其他FDR控制方法（如Benjamini-Hochberg及其依赖调整版本）。