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Robust Dual-Regularized Variable Selection under Outlier Contamination

arXiv · AI, language, vision and robotics · article · Sep 18, 2026 · UTC

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

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