Learning an Interpretable Risk Scoring System for Maximizing Decision Net Benefit

arXiv:2604.04241v3 Announce Type: replace Abstract: Risk scoring systems are widely used in high-stakes domains to assist decision-making. However, existing approaches often focus on optimizing predictive accuracy or likelihood-based criteria, which may not align with the main goal of maximizing utility. In this paper, we propose a novel risk scoring system that directly optimizes net benefit over a range of decision thresholds. The model is formulated as a sparse integer linear programming problem which enables the construction of a transparent scoring system with integer coefficients, and hence, facilitates interpretation and practical application. We also establish fundamental relationships among net benefit, discrimination, and calibration. Specifically, we derive bounds relating the area under the net benefit curve to a ROC functional, both evaluated on a fixed threshold grid, and show that post-processing can achieve moderate calibration on the training data without decreasing the area under the net benefit curve on that grid. We evaluated our method on multiple public datasets as well as on a large-scale credit risk dataset. This computational study demonstrated that our interpretable method can effectively achieve high net benefit while maintaining competitive discrimination and calibration performance.

Abstract:Risk scoring systems are widely used in high-stakes domains to assist decision-making. However, existing approaches often focus on optimizing predictive accuracy or likelihood-based criteria, which may not align with the main goal of maximizing utility. In this paper, we propose a novel risk scoring system that directly optimizes net benefit over a range of decision thresholds. The model is formulated as a sparse integer linear programming problem which enables the construction of a transparent scoring system with integer coefficients, and hence, facilitates interpretation and practical application. We also establish fundamental relationships among net benefit, discrimination, and calibration. Specifically, we derive bounds relating the area under the net benefit curve to a ROC functional, both evaluated on a fixed threshold grid, and show that post-processing can achieve moderate calibration on the training data without decreasing the area under the net benefit curve on that grid. We evaluated our method on multiple public datasets as well as on a large-scale credit risk dataset. This computational study demonstrated that our interpretable method can effectively achieve high net benefit while maintaining competitive discrimination and calibration performance.

Machine Learning (cs.LG); Optimization and Control (math.OC)

arXiv:2604.04241 [cs.LG]

(or arXiv:2604.04241v3 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2604.04241 Focus to learn more arXiv-issued DOI via DataCite

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Learning an Interpretable Risk Scoring System for Maximizing Decision Net Benefit

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