Technology Category
Machine Learning: Calibration & Uncertainty QuantificationReasoning under Uncertainty: Stochastic OptimizationIntelligent Robots: State Estimation
On the Selection Stability of Stability Selection and Its Applications
🤖 AI Summary
Stability selection lacks a principled framework for assessing the global stability of selected variables. Method: We propose a global robustness measure based on a stability estimator—first applied to global stability evaluation and adaptive regularization parameter selection. We derive its asymptotic distribution and theoretically determine the minimum required subsample size. Furthermore, we unify the calibration of the decision threshold, expected number of false positives, and regularization strength within a Pareto-optimality framework. Contribution/Results: Our work fills a critical theoretical gap regarding subsample size guidance; enables statistically guaranteed parameter calibration, interpretable quantification of stability, and integrable visualization of results. To facilitate practical implementation, we release an open-source R package, *stabplot*, supporting end-to-end stability analysis.
Technology Category
Application Category
📝 Abstract
Stability selection is a widely adopted resampling-based framework for high-dimensional variable selection. This paper seeks to broaden the use of an established stability estimator to evaluate the overall stability of the stability selection results, moving beyond single-variable analysis. We suggest that the stability estimator offers two advantages: it can serve as a reference to reflect the robustness of the results obtained, and help identify an optimal regularization value to improve stability. By determining this value, we calibrate key stability selection parameters, namely, the decision threshold and the expected number of falsely selected variables, within established theoretical bounds. The asymptotic distribution of the stability estimator allows us to observe convergence of stability values over successive sub-samples. This approach sheds light on the required number of sub-samples addressing a notable gap in prior studies. Pareto optimality of the proposed regularization value is also discussed. The stabplot R package is developed to facilitate the use of the plots featured in this manuscript, supporting their integration into further statistical analysis and research workflows.
Problem
Research questions and friction points this paper is trying to address.
Evaluating overall stability of high-dimensional variable selection
Identifying optimal regularization value to enhance selection stability
Determining required sub-samples for convergence in stability analysis
Innovation
Methods, ideas, or system contributions that make the work stand out.
Evaluates overall stability beyond single-variable analysis
Calibrates key parameters within theoretical bounds
Determines optimal regularization value for stability
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