Robust subset selection

Ryan Thompson

Computational Statistics & Data Analysis, 2022, vol. 169, issue C

Abstract: The best subset selection (or “best subsets”) estimator is a classic tool for sparse regression, and developments in mathematical optimization over the past decade have made it more computationally tractable than ever. Notwithstanding its desirable statistical properties, the best subsets estimator is susceptible to outliers and can break down in the presence of a single contaminated data point. To address this issue, a robust adaption of best subsets is proposed that is highly resistant to contamination in both the response and the predictors. The adapted estimator generalizes the notion of subset selection to both predictors and observations, thereby achieving robustness in addition to sparsity. This procedure, referred to as “robust subset selection” (or “robust subsets”), is defined by a combinatorial optimization problem for which modern discrete optimization methods are applied. The robustness of the estimator in terms of the finite-sample breakdown point of its objective value is formally established. In support of this result, experiments on synthetic and real data are reported that demonstrate the superiority of robust subsets over best subsets in the presence of contamination. Importantly, robust subsets fares competitively across several metrics compared with popular robust adaptions of continuous shrinkage estimators.

Keywords: Best subset selection; Least trimmed squares; Sparse regression; Robust regression; Discrete optimization; Mixed-integer optimization (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:csdana:v:169:y:2022:i:c:s0167947321002498

DOI: 10.1016/j.csda.2021.107415

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