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：我们提出了一种基于稳定性原理的广义去偏Lasso估计量。当设计矩阵的某一列受到扰动时，该估计量允许通过一个简单更新公式从原始解中计算得到。在协方差矩阵良态的子高斯设计下，该近似在比例增长机制中对于除坐标零测集以外的所有坐标均具有渐近精确性。证明过程利用集中性与反集中性参数控制误差项与符号变化。相比之下，在类似假设下建立可比较的分布极限（例如高斯性）仍是一个开放性问题。作为应用，我们证明该近似能够显著降低基于重抽样的变量选择过程（包括条件随机化检验与局部knockoff滤波器）的计算代价。