# Learning Optimal Fair Scoring Systems for Multi-Class Classification

arXiv: https://arxiv.org/abs/2304.05023 · HTML: https://mlsanity.com/paper/2304.05023/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 39 references that are in the map.
- First posted on arXiv 11 Apr 2023.

## Builds on (most cited first, 16 of 16)

- [Equality of Opportunity in Supervised Learning](https://mlsanity.com/paper/1610.02413/) (2016)
- [Towards A Rigorous Science of Interpretable Machine Learning](https://mlsanity.com/paper/1702.08608/) (2017)
- [A Survey Of Methods For Explaining Black Box Models](https://mlsanity.com/paper/1802.01933/) (2018)
- [The Mythos of Model Interpretability](https://mlsanity.com/paper/1606.03490/) (2016)
- [Fair prediction with disparate impact: A study of bias in recidivism prediction instruments](https://mlsanity.com/paper/1610.07524/) (2016)
- [Retiring Adult: New Datasets for Fair Machine Learning](https://mlsanity.com/paper/2108.04884/) (2021)
- [Fairness in Machine Learning: A Survey](https://mlsanity.com/paper/2010.04053/) (2020)
- [Metrics for Multi-Class Classification: an Overview](https://mlsanity.com/paper/2008.05756/) (2020)
- [Fairwashing: the risk of rationalization](https://mlsanity.com/paper/1901.09749/) (2019)
- [Supersparse Linear Integer Models for Optimized Medical Scoring Systems](https://mlsanity.com/paper/1502.04269/) (2015)
- [Achieving Equalized Odds by Resampling Sensitive Attributes](https://mlsanity.com/paper/2006.04292/) (2020)
- [Beyond Adult and COMPAS: Fairness in Multi-Class Prediction](https://mlsanity.com/paper/2206.07801/) (2022)
- [Blackbox Post-Processing for Multiclass Fairness](https://mlsanity.com/paper/2201.04461/) (2022)
- [Fairness with Overlapping Groups](https://mlsanity.com/paper/2006.13485/) (2020)
- [Unbiased Subdata Selection for Fair Classification: A Unified Framework and Scalable Algorithms](https://mlsanity.com/paper/2012.12356/) (2020)
- [A Reduction to Binary Approach for Debiasing Multiclass Datasets](https://mlsanity.com/paper/2205.15860/) (2022)

## Built on by (most cited first, 8 of 8)

- [A Generic Framework for Conformal Fairness](https://mlsanity.com/paper/2505.16115/) (2025)
- [Unveiling the Impact of Local Homophily on GNN Fairness: In-Depth Analysis and New Benchmarks](https://mlsanity.com/paper/2410.04287/) (2024)
- [Evaluating Model Bias Requires Characterizing its Mistakes](https://mlsanity.com/paper/2407.10633/) (2024)
- [Learning Social Fairness Preferences from Non-Expert Stakeholder Opinions in Kidney Placement](https://mlsanity.com/paper/2404.03800/) (2024)
- [Fair Decentralized Learning](https://mlsanity.com/paper/2410.02541/) (2024)
- [MISS: Multiclass Interpretable Scoring Systems](https://mlsanity.com/paper/2401.05069/) (2024)
- [Fairness Risks for Group-conditionally Missing Demographics](https://mlsanity.com/paper/2402.13393/) (2024)
- [Happiness as a Measure of Fairness](https://mlsanity.com/paper/2511.01069/) (2025)

## Abstract (arXiv)

Machine Learning models are increasingly used for decision making, in particular in high-stakes applications such as credit scoring, medicine or recidivism prediction. However, there are growing concerns about these models with respect to their lack of interpretability and the undesirable biases they can generate or reproduce. While the concepts of interpretability and fairness have been extensively studied by the scientific community in recent years, few works have tackled the general multi-class classification problem under fairness constraints, and none of them proposes to generate fair and interpretable models for multi-class classification. In this paper, we use Mixed-Integer Linear Programming (MILP) techniques to produce inherently interpretable scoring systems under sparsity and fairness constraints, for the general multi-class classification setup. Our work generalizes the SLIM (Supersparse Linear Integer Models) framework that was proposed by Rudin and Ustun to learn optimal scoring systems for binary classification. The use of MILP techniques allows for an easy integration of diverse operational constraints (such as, but not restricted to, fairness or sparsity), but also for the building of certifiably optimal models (or sub-optimal models with bounded optimality gap).