Buffered AUC maximization for scoring systems via mixed-integer optimization

TL;DR

This paper introduces a mixed-integer optimization framework for creating interpretable scoring systems that directly maximize buffered AUC, leading to superior classification performance on real-world datasets.

Contribution

It develops a novel MILO model that directly maximizes buffered AUC with a sparsity constraint, advancing MIO techniques for interpretable scoring systems.

Findings

MILO-based scoring systems outperform baseline methods in AUC.

The approach yields highly interpretable models with competitive accuracy.

Computational experiments validate the effectiveness of the proposed method.

Abstract

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.