Ellipsoidal buffered area under the curve maximization model with variable selection in credit risk estimation

In 2019, a buffered AUC (bAUC) maximization model with the linear classifier was developed to maximize the area under the curve (AUC), a popular statistic for evaluating classification performance. Previous studies have recently used the bAUC for different problems. We propose a new bAUC maximization model, including the ellipsoidal classifier and the variable selection constraint, to enhance classification performance. However, the proposed model is hard to solve because it is formulated as a mixed-integer semidefinite programming (MISDP) problem with numerous constraints. Several algorithms have been proposed to solve MISDP, but no algorithm has been proposed that can quickly solve a problem of this size. Tanaka and Yamamoto (Int J Financ Eng, 2022. https://doi.org/10.1142/S2424786321500420 specifically suggested a heuristic algorithm for solving MISDP under hundreds of constraints, but it might not be effective for problems in this study. Therefore, we enhance the heuristic algorithm in Tanaka and Yamamoto (Int J Financ Eng, 2022. https://doi.org/10.1142/S2424786321500420 to quickly attain solutions to our suggested MISDP and show that the proposed heuristic algorithm derives superior solutions to existing algorithms. Furthermore, we demonstrate that for a classification problem related to credit risk estimation using real-world corporate rating data, the tailored bAUC maximization model outperforms the existing bAUC maximization and standard machine learning models in terms of generalization performance.