The recently proposed fixed-X knockoff is a powerful variable selection procedure that controls the false discovery rate (FDR) in any finite-sample setting, yet its theoretical insights are difficult to show beyond Gaussian linear models. In this paper, we make the first attempt to extend the fixed-X knockoff to partially linear models by using generalized knockoff features, and propose a new stability generalized knockoff (Stab-GKnock) procedure by incorporating selection probability as feature importance score. We provide FDR control and power guarantee under some regularity conditions. In addition, we propose a two-stage method under high dimensionality by introducing a new joint feature screening procedure, with guaranteed sure screening property. Extensive simulation studies are conducted to evaluate the finite-sample performance of the proposed method. A real data example is also provided for illustration.

翻译：近期提出的固定X-knockoff是一种强大的变量选择方法，可在任意有限样本场景下控制错误发现率(FDR)，但其理论见解难以推广至高斯线性模型之外。本文首次尝试通过使用广义knockoff特征将固定X-knockoff拓展至部分线性模型，并提出一种结合选择概率作为特征重要性评分的新型稳定性广义knockoff(Stab-GKnock)方法。我们在特定正则条件下提供了FDR控制与功效保证。此外，针对高维情形，我们引入一种新的联合特征筛选程序，提出两阶段方法，并保证了确定的筛选性质。我们开展了大量模拟研究以评估所提方法的有限样本性能，并给出了真实数据示例进行说明。