鲁棒双正则化变量选择在外点污染下的应用
Robust Dual-Regularized Variable Selection under Outlier Contamination
- Case Western Reserve University（凯斯西储大学）
- University of North Dakota（北达科他大学）
- CNRS UMR 6205, Univ Bretagne Sud（法国国家科学研究中心联合研究实验室第6205号，南布列塔尼大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
针对外点污染下单指标模型的变量选择问题，提出两阶段稀疏中位数梯度外积（smOPG）方法，结合中位数回归与局部加权实现鲁棒性，模拟与实证均优于现有方法。
AI中文摘要：
真实数据中常含有异常观测值，这些观测值可能对变量选择产生不成比例的影响，尤其是在复杂的预测变量设置中。我们提出了一种两阶段的稀疏中位数梯度外积（smOPG）方法，用于在存在外点污染的单指标模型中进行变量选择。我们首先通过ℓ1惩罚的局部中位数回归估计稀疏的局部梯度，然后利用正则化奇异值分解，从所得梯度矩阵的秩一稀疏近似中恢复活跃预测变量集。中位数回归与局部加权的结合提供了对响应外点和杠杆点的鲁棒性。跨不同维度和污染机制的大量模拟表明，相对于现有方法，smOPG在变量选择性能上具有优势。对空气污染和基因组数据的应用展示了其实用性，而理论分析确立了在不要求单个局部回归具有选择一致性的情况下实现活跃集恢复。
英文摘要：
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.
