Robust Dual-Regularized Variable Selection under Outlier Contamination

2026-09-18

AI Summary

本文提出了一种两阶段的稀疏中位数外积梯度(smOPG)方法，用于在存在异常值的情况下进行单指标模型的变量选择，通过结合中位数回归和局部加权来提高鲁棒性。

Abstract

Real data often contain unusual observations that can exert disproportionate effects on variable selection, especially in complex predictor settings. We propose a two-stage {\it sparse median outer product of gradients (smOPG)} method for variable selection in single index models with outlier contamination. We first estimate sparse local gradients via \(\ell_1\)-penalized local median regression and then recover the active predictor set from a rank-one sparse approximation of the resulting gradient matrix using regularized singular value decomposition. The combination of median regression and local weighting provides robustness to both response outliers and leverage points. Extensive simulations across varying dimensions and contamination mechanisms demonstrate the favorable variable selection performance of smOPG relative to existing methods. Applications to air pollution and genomic data demonstrate practical utility, while theory establishes active-set recovery without requiring selection consistency of individual local regressions.

Problem

• outlier contamination
• variable selection
• robustness

Innovation

• sparse median outer product of gradients (smOPG)
• outlier contamination
• variable selection
• robustness
• regularized singular value decomposition