Robust Dual-Regularized Variable Selection under Outlier Contamination
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 ℓ1-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.
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BibTeX
@misc{soale2026robust,
title = {{Robust Dual-Regularized Variable Selection under Outlier Contamination}},
author = {Abdul-Nasah Soale and Adewale F. Lukman and Essoham Ali},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.21342},
eprint = {2609.21342},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.21342},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Robust Dual-Regularized Variable Selection under Outlier Contamination
AU - Abdul-Nasah Soale
AU - Adewale F. Lukman
AU - Essoham Ali
PY - 2026
DA - 2026/09/18
PB - arXiv
DO - 10.48550/arxiv.2609.21342
UR - https://arxiv.org/abs/2609.21342
AB - 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 ℓ_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.
ER -