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 knockoff procedure. We implement our method for fixed-X knockoffs and 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 prevents us from constructing good knockoff variables. In these contexts, calibrated knockoffs even outperform competing FDR-controlling methods like the (dependence-adjusted) Benjamini-Hochberg procedure in many scenarios.

翻译：Barber和Candes提出的knockoffs筛选器（arXiv:1404.5609）是监督学习模型中多重检验的灵活框架，其通过引入合成预测变量来控制错误发现率。基于Fithian与Lei建立的"条件校准"框架（arXiv:2007.10438），我们提出了校准knockoffs程序，该方法能显著提升任意knockoff程序的统计效力。我们在固定X型knockoffs上实现该方法，从理论与实证两个层面证明：在两类knockoffs方法几乎失效的典型场景中——即拒绝集规模较小，以及设计矩阵结构阻碍构建优质knockoff变量时——该方法改进效果尤为显著。在此类场景下，校准knockoffs甚至能在多数情况下超越（经相关性调整的）Benjamini-Hochberg程序等竞争性FDR控制方法。