A1 Vertaisarvioitu alkuperäisartikkeli tieteellisessä lehdessä
Boundary problem and overfitting reduction in convex regression
Tekijät: Liao, Zhiqiang; Dai, Sheng; Lim, Eunji; Kuosmanen, Timo
Kustantaja: Elsevier BV
Julkaisuvuosi: 2026
Lehti: European Journal of Operational Research
Vuosikerta: 333
Numero: 2
Aloitussivu: 555
Lopetussivu: 566
ISSN: 0377-2217
eISSN: 1872-6860
DOI: https://doi.org/10.1016/j.ejor.2026.04.009
Julkaisun avoimuus kirjaamishetkellä: Ei avoimesti saatavilla
Julkaisukanavan avoimuus : Osittain avoin julkaisukanava
Verkko-osoite: https://doi.org/10.1016/j.ejor.2026.04.009
Rinnakkaistallenteen osoite: https://research.utu.fi/converis/portal/detail/Publication/523239733
Rinnakkaistallenteen lisenssi: CC BY NC ND
Rinnakkaistallennetun julkaisun versio: Final draft
Convex regression is a nonparametric approach for estimating a convex or concave function from observed data. It is widely used in operations research, economics, machine learning, and related fields. However, empirical evidence has shown that convex regression can yield excessively large subgradients on the boundary. In this paper, we provide theoretical evidence of this boundary problem. To address such a problem, we propose two new estimators by placing a bound on the subgradients of the convex function. We further prove that they converge to the underlying true convex function and that their subgradients converge to the gradient of the underlying function, both uniformly over the domain with probability one as the sample size increases to infinity. The proposed methods also help to reduce overfitting in finite samples: Monte Carlo simulations and empirical illustrations with large-scale datasets confirm the superior performance of the proposed estimators in predictive power over the existing methods.
Julkaisussa olevat rahoitustiedot:
Zhiqiang Liao gratefully acknowledges financial support from the BNBU Start-up Research Fund [grant no. UICR0700139-26]. Sheng Dai gratefully acknowledges financial support from the National Natural Science Foundation of China [grant no. 72501303].
