# Intersectional Divergence: Measuring Fairness in Regression

arXiv: https://arxiv.org/abs/2505.00830 · HTML: https://mlsanity.com/paper/2505.00830/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 30 of its 55 references that are in the map.
- First posted on arXiv 1 May 2025.

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

- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- [Equality of Opportunity in Supervised Learning](https://mlsanity.com/paper/1610.02413/) (2016)
- [A Reductions Approach to Fair Classification](https://mlsanity.com/paper/1803.02453/) (2018)
- [Linear Convergence of Gradient and Proximal-Gradient Methods Under the Polyak-Lojasiewicz Condition](https://mlsanity.com/paper/1608.04636/) (2016)
- [Fairness in Machine Learning: A Survey](https://mlsanity.com/paper/2010.04053/) (2020)
- [Fair Regression: Quantitative Definitions and Reduction-based Algorithms](https://mlsanity.com/paper/1905.12843/) (2019)
- [A survey on datasets for fairness-aware machine learning](https://mlsanity.com/paper/2110.00530/) (2021)
- [A Convex Framework for Fair Regression](https://mlsanity.com/paper/1706.02409/) (2017)
- [An Intersectional Definition of Fairness](https://mlsanity.com/paper/1807.08362/) (2018)
- [Fair Regression with Wasserstein Barycenters](https://mlsanity.com/paper/2006.07286/) (2020)
- [Bias in Machine Learning Software: Why? How? What to do?](https://mlsanity.com/paper/2105.12195/) (2021)
- [Fairness Testing: A Comprehensive Survey and Analysis of Trends](https://mlsanity.com/paper/2207.10223/) (2022)
- [A Survey on Intersectional Fairness in Machine Learning: Notions, Mitigation, and Challenges](https://mlsanity.com/paper/2305.06969/) (2023)
- [Fair Kernel Learning](https://mlsanity.com/paper/1710.05578/) (2017)
- [Auditing and Achieving Intersectional Fairness in Classification Problems](https://mlsanity.com/paper/1911.01468/) (2019)
- [Rank-Based Multi-task Learning for Fair Regression](https://mlsanity.com/paper/2009.11405/) (2020)
- [FairMask: Better Fairness via Model-based Rebalancing of Protected Attributes](https://mlsanity.com/paper/2110.01109/) (2021)
- [Understanding and Mitigating Accuracy Disparity in Regression](https://mlsanity.com/paper/2102.12013/) (2021)
- [Multi-dimensional discrimination in Law and Machine Learning -- A comparative overview](https://mlsanity.com/paper/2302.05995/) (2023)
- [Fair Risk Control: A Generalized Framework for Calibrating Multi-group Fairness Risks](https://mlsanity.com/paper/2405.02225/) (2024)
- [A General Framework for Fair Regression](https://mlsanity.com/paper/1810.05041/) (2018)
- [A structured regression approach for evaluating model performance across intersectional subgroups](https://mlsanity.com/paper/2401.14893/) (2024)
- [Model Optimization in Imbalanced Regression](https://mlsanity.com/paper/2206.09991/) (2022)
- [Fair Oversampling Technique using Heterogeneous Clusters](https://mlsanity.com/paper/2305.13875/) (2023)
- [Multi-fairness under class-imbalance](https://mlsanity.com/paper/2104.13312/) (2021)
- [Normalise for Fairness: A Simple Normalisation Technique for Fairness in Regression Machine Learning Problems](https://mlsanity.com/paper/2202.00993/) (2022)
- [Monotone Individual Fairness](https://mlsanity.com/paper/2403.06812/) (2024)
- [Individual Fairness in Graph Decomposition](https://mlsanity.com/paper/2406.00213/) (2024)
- [Towards Fairness and Privacy: A Novel Data Pre-processing Optimization Framework for Non-binary Protected Attributes](https://mlsanity.com/paper/2410.00836/) (2024)
- [Counterfactual Situation Testing: From Single to Multidimensional Discrimination](https://mlsanity.com/paper/2502.01267/) (2025)

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

- [Wasserstein projection distance for fairness testing of regression models](https://mlsanity.com/paper/2510.04114/) (2025)

## Abstract (arXiv)

Fairness in machine learning research is commonly framed in the context of classification tasks, leaving critical gaps in regression. In this paper, we propose a novel approach to measure intersectional fairness in regression tasks, going beyond the focus on single protected attributes from existing work to consider combinations of all protected attributes. Furthermore, we contend that it is insufficient to measure the average error of groups without regard for imbalanced domain preferences. Accordingly, we propose Intersectional Divergence (ID) as the first fairness measure for regression tasks that 1) describes fair model behavior across multiple protected attributes and 2) differentiates the impact of predictions in target ranges most relevant to users. We extend our proposal demonstrating how ID can be adapted into a loss function, IDLoss, that satisfies convergence guarantees and has piecewise smooth properties that enable practical optimization. Through an extensive experimental evaluation, we demonstrate how ID allows unique insights into model behavior and fairness, and how incorporating IDLoss into optimization can considerably improve single-attribute and intersectional model fairness while maintaining a competitive balance in predictive performance.