# Stability of a Generalized Debiased Lasso with Applications to Resampling-Based Variable Selection

arXiv: https://arxiv.org/abs/2405.03063 · HTML: https://mlsanity.com/paper/2405.03063/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 62 references that are in the map.
- First posted on arXiv 5 May 2024.

## Builds on (most cited first, 25 of 25)

- [Panning for Gold: Model-X Knockoffs for High-dimensional Controlled Variable Selection](https://mlsanity.com/paper/1610.02351/) (2016)
- [Controlling the false discovery rate via knockoffs](https://mlsanity.com/paper/1404.5609/) (2014)
- [Confidence Intervals and Hypothesis Testing for High-Dimensional Regression](https://mlsanity.com/paper/1306.3171/) (2013)
- [Universality of empirical risk minimization](https://mlsanity.com/paper/2202.08832/) (2022)
- [Noisy Matrix Completion: Understanding Statistical Guarantees for Convex Relaxation via Nonconvex Optimization](https://mlsanity.com/paper/1902.07698/) (2019)
- [Generalization error in high-dimensional perceptrons: Approaching Bayes error with convex optimization](https://mlsanity.com/paper/2006.06560/) (2020)
- [The Lasso with general Gaussian designs with applications to hypothesis testing](https://mlsanity.com/paper/2007.13716/) (2020)
- [De-biasing the Lasso: Optimal Sample Size for Gaussian Designs](https://mlsanity.com/paper/1508.02757/) (2015)
- [Approximate Message Passing algorithms for rotationally invariant matrices](https://mlsanity.com/paper/2008.11892/) (2020)
- [A knockoff filter for high-dimensional selective inference](https://mlsanity.com/paper/1602.03574/) (2016)
- [Fast and Powerful Conditional Randomization Testing via Distillation](https://mlsanity.com/paper/2006.03980/) (2020)
- [Hypothesis Testing in High-Dimensional Regression under the Gaussian Random Design Model: Asymptotic Theory](https://mlsanity.com/paper/1301.4240/) (2013)
- [Approximate Message Passing for orthogonally invariant ensembles: Multivariate non-linearities and spectral initialization](https://mlsanity.com/paper/2110.02318/) (2021)
- [Estimation in Rotationally Invariant Generalized Linear Models via Approximate Message Passing](https://mlsanity.com/paper/2112.04330/) (2021)
- [Robust inference with knockoffs](https://mlsanity.com/paper/1801.03896/) (2018)
- [Black-box tests for algorithmic stability](https://mlsanity.com/paper/2111.15546/) (2021)
- [De-Biasing The Lasso With Degrees-of-Freedom Adjustment](https://mlsanity.com/paper/1902.08885/) (2019)
- [Controlling False Discovery Rate Using Gaussian Mirrors](https://mlsanity.com/paper/1911.09761/) (2019)
- [Causal Inference in Genetic Trio Studies](https://mlsanity.com/paper/2002.09644/) (2020)
- [Spectrum-Aware Debiasing: A Modern Inference Framework with Applications to Principal Components Regression](https://mlsanity.com/paper/2309.07810/) (2023)
- [A Power and Prediction Analysis for Knockoffs with Lasso Statistics](https://mlsanity.com/paper/1712.06465/) (2017)
- [IPAD: Stable Interpretable Forecasting with Knockoffs Inference](https://mlsanity.com/paper/1809.05032/) (2018)
- [A Flexible Framework for Hypothesis Testing in High-dimensions](https://mlsanity.com/paper/1704.07971/) (2017)
- [A non-asymptotic distributional theory of approximate message passing for sparse and robust regression](https://mlsanity.com/paper/2401.03923/) (2024)
- [Power analysis of knockoff filters for correlated designs](https://mlsanity.com/paper/1910.12428/) (2019)

## Built on by (most cited first, 1 of 1)

- [Accelerating Conformal Prediction via Approximate Leave-One-Out](https://mlsanity.com/paper/2606.31915/) (2026)

## Abstract (arXiv)

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.