# 2D Stability Selection: Design Jittering for Doubly Stable Feature Selection

arXiv: https://arxiv.org/abs/2605.02205 · HTML: https://mlsanity.com/paper/2605.02205/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 34 references that are in the map.
- First posted on arXiv 4 May 2026.

## Builds on (most cited first, 13 of 13)

- [Deep Stable Learning for Out-Of-Distribution Generalization](https://mlsanity.com/paper/2104.07876/) (2021)
- [Stable Learning via Sample Reweighting](https://mlsanity.com/paper/1911.12580/) (2019)
- [Stabilizing Variable Selection and Regression](https://mlsanity.com/paper/1911.01850/) (2019)
- [Random-projection ensemble classification](https://mlsanity.com/paper/1504.04595/) (2015)
- [Bagging Provides Assumption-free Stability](https://mlsanity.com/paper/2301.12600/) (2023)
- [Independently Interpretable Lasso: A New Regularizer for Sparse Regression with Uncorrelated Variables](https://mlsanity.com/paper/1711.01796/) (2017)
- [Calibrated inference: statistical inference that accounts for both sampling uncertainty and distributional uncertainty](https://mlsanity.com/paper/2202.11886/) (2022)
- [Causality-oriented robustness: exploiting general noise interventions](https://mlsanity.com/paper/2307.10299/) (2023)
- [Cluster Stability Selection](https://mlsanity.com/paper/2201.00494/) (2022)
- [Bayesian Stability Selection and Inference on Selection Probabilities](https://mlsanity.com/paper/2410.21914/) (2024)
- [Estimation in linear errors-in-variables models with unknown error distribution](https://mlsanity.com/paper/1812.00492/) (2018)
- [A Linear Errors-in-Variables Model with Unknown Heteroscedastic Measurement Errors](https://mlsanity.com/paper/2310.13874/) (2023)
- [Data-Adaptive Automatic Threshold Calibration for Stability Selection](https://mlsanity.com/paper/2505.22012/) (2025)

## Abstract (arXiv)

We study feature selection in high-dimensional regression under two distinct sources of instability: sampling variability and measurement error in the design matrix. Stability Selection addresses the former through sub-sampling and aggregation, but does not explicitly stress-test robustness to noisy predictors. We introduce doubly stable feature selection, a perturb-and-aggregate framework that targets features whose inclusion is stable both across randomization and across increasing levels of design noise. The method injects controlled additive noise into the design matrix, fits a fixed base selector such as the Lasso on the perturbed data, and aggregates selection frequencies. Sweeping over a grid of noise levels yields a stability path that summarizes robustness to measurement error while using the full sample size and isolating the effect of design perturbations. On the theory side, we show that classical model-selection conditions are preserved under sufficiently small perturbations, with a high-probability extension for Gaussian noise. Empirically, experiments on synthetic and real datasets show improved robustness compared with Stability Selection and standard base selectors.