Buffered AUC maximization for scoring systems via mixed-integer optimization
This work addresses the need for highly interpretable classification models in domains requiring manual calculations, though it is incremental as it builds on existing MIO techniques by focusing on AUC optimization.
The paper tackled the problem of constructing interpretable scoring systems for binary classification by directly maximizing the buffered AUC (bAUC) using mixed-integer linear optimization (MILO), resulting in scoring systems with superior AUC values compared to baseline methods like regularization and stepwise regression on real-world datasets.
A scoring system is a linear classifier composed of a small number of explanatory variables, each assigned a small integer coefficient. This system is highly interpretable and allows predictions to be made with simple manual calculations without the need for a calculator. Several previous studies have used mixed-integer optimization (MIO) techniques to develop scoring systems for binary classification; however, they have not focused on directly maximizing AUC (i.e., area under the receiver operating characteristic curve), even though AUC is recognized as an essential evaluation metric for scoring systems. Our goal herein is to establish an effective MIO framework for constructing scoring systems that directly maximize the buffered AUC (bAUC) as the tightest concave lower bound on AUC. Our optimization model is formulated as a mixed-integer linear optimization (MILO) problem that maximizes bAUC subject to a group sparsity constraint for limiting the number of questions in the scoring system. Computational experiments using publicly available real-world datasets demonstrate that our MILO method can build scoring systems with superior AUC values compared to the baseline methods based on regularization and stepwise regression. This research contributes to the advancement of MIO techniques for developing highly interpretable classification models.