# Joint Score-Threshold Optimization for Interpretable Risk Assessment

arXiv: https://arxiv.org/abs/2510.21934 · HTML: https://mlsanity.com/paper/2510.21934/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 36 references that are in the map.
- First posted on arXiv 24 Oct 2025.

## Builds on (most cited first, 7 of 7)

- [Rank consistent ordinal regression for neural networks with application to age estimation](https://mlsanity.com/paper/1901.07884/) (2019)
- [What do we need to build explainable AI systems for the medical domain?](https://mlsanity.com/paper/1712.09923/) (2017)
- [Progressive Identification of True Labels for Partial-Label Learning](https://mlsanity.com/paper/2002.08053/) (2020)
- [Provably Consistent Partial-Label Learning](https://mlsanity.com/paper/2007.08929/) (2020)
- [Learning Optimized Risk Scores](https://mlsanity.com/paper/1610.00168/) (2016)
- [Learning Sparse Classifiers: Continuous and Mixed Integer Optimization Perspectives](https://mlsanity.com/paper/2001.06471/) (2020)
- [Tailored Bayes: a risk modelling framework under unequal misclassification costs](https://mlsanity.com/paper/2104.01822/) (2021)

## Built on by (most cited first, 1 of 1)

- [An interpretable data-driven approach to optimizing clinical fall risk assessment](https://mlsanity.com/paper/2601.05194/) (2026)

## Abstract (arXiv)

Risk assessment tools in healthcare commonly employ point-based scoring systems that map patients to ordinal risk categories via thresholds. While electronic health record (EHR) data presents opportunities for data-driven optimization of these tools, two fundamental challenges impede standard supervised learning: (1) labels are often available only for extreme risk categories due to intervention-censored outcomes, and (2) misclassification cost is asymmetric and increases with ordinal distance. We propose a mixed-integer programming (MIP) framework that jointly optimizes scoring weights and category thresholds in the face of these challenges. Our approach prevents label-scarce category collapse via threshold constraints, and utilizes an asymmetric, distance-aware objective. The MIP framework supports governance constraints, including sign restrictions, sparsity, and minimal modifications to incumbent tools, ensuring practical deployability in clinical workflows. We further develop a continuous relaxation of the MIP problem to provide warm-start solutions for more efficient MIP optimization. We apply the proposed score optimization framework to a case study of inpatient falls risk assessment using the Johns Hopkins Fall Risk Assessment Tool.