Thanks to its fine balance between model flexibility and interpretability, the nonparametric additive model has been widely used, and variable selection for this type of model has received constant attention. However, none of the existing solutions can control the false discovery rate (FDR) under the finite sample setting. The knockoffs framework is a recent proposal that can effectively control the FDR with a finite sample size, but few knockoffs solutions are applicable to nonparametric models. In this article, we propose a novel kernel knockoffs selection procedure for the nonparametric additive model. We integrate three key components: the knockoffs, the subsampling for stability, and the random feature mapping for nonparametric function approximation. We show that the proposed method is guaranteed to control the FDR under any finite sample size, and achieves a power that approaches one as the sample size tends to infinity. We demonstrate the efficacy of our method through intensive numerical analyses and comparisons with the alternative solutions. Our proposal thus makes useful contributions to the methodology of nonparametric variable selection, FDR-based inference, as well as knockoffs.
翻译:由于在模型灵活性和可解释性之间保持了细微的平衡,非参数添加模型被广泛使用,这种模型的可变选择一直受到注意。然而,现有的解决方案没有一个能够控制在有限样本设置下的虚假发现率(FDR),击倒框架是最近提出的一项提案,它能够以有限的样本规模有效控制FDR,但很少有击倒解决方案适用于非参数模型。在本条中,我们为非参数添加模型提出了一个新的内核取舍选择程序。我们整合了三个关键组成部分:击落、稳定性子取样和非参数近似的随机特征绘图。我们表明,拟议方法保证在任何有限的样本规模下控制FDR,并取得一种作为样本规模的接近于无限性的力量。我们通过密集的数值分析和与替代解决方案的比较来展示我们的方法的有效性。我们的提案因此为非参数变量选择方法、基于FDR的推论以及敲倒作出了有益的贡献。