We propose a generalized debiased Lasso estimator based on a stability principle. When a single column of the design matrix is perturbed, the estimator admits a simple update formula that can be computed from the original solution. Under sub-Gaussian designs with well-conditioned covariance, this approximation is asymptotically accurate for all but a vanishing fraction of coordinates in the proportional growth regime. The proof relies on concentration and anti-concentration arguments to control error terms and sign changes. In contrast, establishing comparable distributional limits (e.g., Gaussianity) under similar assumptions remains open. As an application, we show that the approximation significantly reduces the computational cost of resampling-based variable selection procedures, including the conditional randomization test and a local knockoff filter.

翻译：我们基于稳定性原理提出了一种广义去偏Lasso估计量。当设计矩阵的某一列受到扰动时，该估计量可基于原始解通过简单的更新公式计算得出。在协方差矩阵条件良好的亚高斯设计下，当比例增长机制中除有限坐标外，该近似在渐近意义下是精确的。证明过程利用集中与反集中论证来控制误差项和符号变化。相比之下，在相似假设下建立可比的分布极限（如高斯性）仍是开放性问题。作为应用实例，我们证明了该近似能够显著降低基于重采样的变量选择方法（包括条件随机化检验和局部敲除滤波器）的计算开销。