# Enforcing Fair Predicted Scores on Intervals of Percentiles by Difference-of-Convex Constraints

arXiv: https://arxiv.org/abs/2505.12530 · HTML: https://mlsanity.com/paper/2505.12530/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 36 of its 95 references that are in the map.
- First posted on arXiv 18 May 2025.

## Builds on (most cited first, 30 of 36)

- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [Equality of Opportunity in Supervised Learning](https://mlsanity.com/paper/1610.02413/) (2016)
- [Counterfactual Fairness](https://mlsanity.com/paper/1703.06856/) (2017)
- [Fair prediction with disparate impact: A study of bias in recidivism prediction instruments](https://mlsanity.com/paper/1610.07524/) (2016)
- [A Reductions Approach to Fair Classification](https://mlsanity.com/paper/1803.02453/) (2018)
- [Retiring Adult: New Datasets for Fair Machine Learning](https://mlsanity.com/paper/2108.04884/) (2021)
- [Nuanced Metrics for Measuring Unintended Bias with Real Data for Text Classification](https://mlsanity.com/paper/1903.04561/) (2019)
- [Empirical Risk Minimization under Fairness Constraints](https://mlsanity.com/paper/1802.08626/) (2018)
- [Fairness in Recommendation Ranking through Pairwise Comparisons](https://mlsanity.com/paper/1903.00780/) (2019)
- [Fair Regression with Wasserstein Barycenters](https://mlsanity.com/paper/2006.07286/) (2020)
- [Online Convex Optimization with Stochastic Constraints](https://mlsanity.com/paper/1708.03741/) (2017)
- [Satisfying Real-world Goals with Dataset Constraints](https://mlsanity.com/paper/1606.07558/) (2016)
- [Pairwise Fairness for Ranking and Regression](https://mlsanity.com/paper/1906.05330/) (2019)
- [Fair and Optimal Classification via Post-Processing](https://mlsanity.com/paper/2211.01528/) (2022)
- [The Fairness of Risk Scores Beyond Classification: Bipartite Ranking and the xAUC Metric](https://mlsanity.com/paper/1902.05826/) (2019)
- [Factors Influencing Perceived Fairness in Algorithmic Decision-Making: Algorithm Outcomes, Development Procedures, and Individual Differences](https://mlsanity.com/paper/2001.09604/) (2020)
- [Stochastic First-order Methods for Convex and Nonconvex Functional Constrained Optimization](https://mlsanity.com/paper/1908.02734/) (2019)
- [Quadratically Regularized Subgradient Methods for Weakly Convex Optimization with Weakly Convex Constraints](https://mlsanity.com/paper/1908.01871/) (2019)
- [First-Order Methods for Nonsmooth Nonconvex Functional Constrained Optimization with or without Slater Points](https://mlsanity.com/paper/2212.00927/) (2022)
- [Stochastic Optimization for DC Functions and Non-smooth Non-convex Regularizers with Non-asymptotic Convergence](https://mlsanity.com/paper/1811.11829/) (2018)
- [Improving Fairness and Privacy in Selection Problems](https://mlsanity.com/paper/2012.03812/) (2020)
- [Minimax AUC Fairness: Efficient Algorithm with Provable Convergence](https://mlsanity.com/paper/2208.10451/) (2022)
- [Convergence guarantees for a class of non-convex and non-smooth optimization problems](https://mlsanity.com/paper/1804.09629/) (2018)
- [Large-scale Optimization of Partial AUC in a Range of False Positive Rates](https://mlsanity.com/paper/2203.01505/) (2022)
- [Wasserstein-based fairness interpretability framework for machine learning models](https://mlsanity.com/paper/2011.03156/) (2020)
- [Computing B-Stationary Points of Nonsmooth DC Programs](https://mlsanity.com/paper/1511.01796/) (2015)
- [Oracle Complexity of Single-Loop Switching Subgradient Methods for Non-Smooth Weakly Convex Functional Constrained Optimization](https://mlsanity.com/paper/2301.13314/) (2023)
- [On the rate of convergence of the Difference-of-Convex Algorithm (DCA)](https://mlsanity.com/paper/2109.13566/) (2021)
- [Stochastic Methods for AUC Optimization subject to AUC-based Fairness Constraints](https://mlsanity.com/paper/2212.12603/) (2022)
- [Accelerating the DC algorithm for smooth functions](https://mlsanity.com/paper/1507.07375/) (2015)

## Built on by (most cited first, 2 of 2)

- [Fair regression under localized demographic parity constraints](https://mlsanity.com/paper/2603.25224/) (2026)
- [Demographic Parity Tails for Regression](https://mlsanity.com/paper/2604.02017/) (2026)

## Abstract (arXiv)

Fairness in machine learning has become a critical concern. Existing approaches often focus on achieving full fairness across all score ranges generated by predictive models, ensuring fairness in both high- and low-percentile populations. However, this stringent requirement can compromise predictive performance and may not align with the practical fairness concerns of stakeholders. In this work, we propose a novel framework for building partially fair machine learning models that enforce fairness only within a specific percentile interval of interest while maintaining flexibility in other regions. We introduce statistical metrics to evaluate partial fairness within a given percentile interval. To achieve partial fairness, we propose an in-processing method by formulating the model training problem as constrained optimization with difference-of-convex constraints, which can be solved by an inexact difference-of-convex algorithm (IDCA). We provide the complexity analysis of IDCA for finding a nearly KKT point. Through numerical experiments on real-world datasets, we demonstrate that our framework achieves high predictive performance while enforcing partial fairness where it matters most.