Convex support vector regression

• Published in: European journal of operational research Vol. 313; no. 3; pp. 858 - 870
• Main Authors: Liao, Zhiqiang, Dai, Sheng, Kuosmanen, Timo
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 16-03-2024
• Subjects: Convex regression; Overfitting; Regularization; Robustness and sensitivity analysis; Support vector regression; Convex regression; Support vector regression; Robustness and sensitivity analysis; Regularization; Overfitting
• ISSN: 0377-2217; 1872-6860
• DOI: 10.1016/j.ejor.2023.05.009

•The convex support vector regression (CSVR) approach is developed.•CSVR inherits the appealing features of convex regression and SVR.•CSVR has been extended to two Lasso CVSR approaches.•The Monte Carlo study confirms the effectiveness of CSVR in avoiding overfitting.•Four real-world applications have demonstrated the superior performance of CSVR.
Nonparametric regression subject to convexity or concavity constraints is increasingly popular in economics, finance, operations research, machine learning, and statistics. However, the conventional convex regression based on the least squares loss function often suffers from overfitting and outliers. This paper proposes to address these two issues by introducing the convex support vector regression (CSVR) method, which effectively combines the key elements of convex regression and support vector regression. Numerical experiments demonstrate the performance of CSVR in prediction accuracy and robustness that compares favorably with other state-of-the-art methods.