# Wasserstein projection distance for fairness testing of regression models

arXiv: https://arxiv.org/abs/2510.04114 · HTML: https://mlsanity.com/paper/2510.04114/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 24 of its 65 references that are in the map.
- First posted on arXiv 5 Oct 2025.

## Builds on (most cited first, 24 of 24)

- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- [The Woman Worked as a Babysitter: On Biases in Language Generation](https://mlsanity.com/paper/1909.01326/) (2019)
- [BOLD: Dataset and Metrics for Measuring Biases in Open-Ended Language Generation](https://mlsanity.com/paper/2101.11718/) (2021)
- [Fair Regression: Quantitative Definitions and Reduction-based Algorithms](https://mlsanity.com/paper/1905.12843/) (2019)
- [A Convex Framework for Fair Regression](https://mlsanity.com/paper/1706.02409/) (2017)
- [Reducing Sentiment Bias in Language Models via Counterfactual Evaluation](https://mlsanity.com/paper/1911.03064/) (2019)
- [Fair Regression with Wasserstein Barycenters](https://mlsanity.com/paper/2006.07286/) (2020)
- [Does Gender Matter? Towards Fairness in Dialogue Systems](https://mlsanity.com/paper/1910.10486/) (2019)
- [Fairness Testing: A Comprehensive Survey and Analysis of Trends](https://mlsanity.com/paper/2207.10223/) (2022)
- [Probabilistic Verification of Fairness Properties via Concentration](https://mlsanity.com/paper/1812.02573/) (2018)
- [A Distributionally Robust Approach to Fair Classification](https://mlsanity.com/paper/2007.09530/) (2020)
- [Selective Regression Under Fairness Criteria](https://mlsanity.com/paper/2110.15403/) (2021)
- [A Statistical Test for Probabilistic Fairness](https://mlsanity.com/paper/2012.04800/) (2020)
- [Testing Group Fairness via Optimal Transport Projections](https://mlsanity.com/paper/2106.01070/) (2021)
- [Auditing ML Models for Individual Bias and Unfairness](https://mlsanity.com/paper/2003.05048/) (2020)
- [Understanding and Mitigating Accuracy Disparity in Regression](https://mlsanity.com/paper/2102.12013/) (2021)
- [Algorithmic Fairness Verification with Graphical Models](https://mlsanity.com/paper/2109.09447/) (2021)
- [Fairness Evaluation in Deepfake Detection Models using Metamorphic Testing](https://mlsanity.com/paper/2203.06825/) (2022)
- [A General Framework for Fair Regression](https://mlsanity.com/paper/1810.05041/) (2018)
- [Fairness Measures for Regression via Probabilistic Classification](https://mlsanity.com/paper/2001.06089/) (2020)
- [AequeVox: Automated Fairness Testing of Speech Recognition Systems](https://mlsanity.com/paper/2110.09843/) (2021)
- [Error Parity Fairness: Testing for Group Fairness in Regression Tasks](https://mlsanity.com/paper/2208.08279/) (2022)
- [Differentially Private Post-Processing for Fair Regression](https://mlsanity.com/paper/2405.04034/) (2024)
- [Intersectional Divergence: Measuring Fairness in Regression](https://mlsanity.com/paper/2505.00830/) (2025)

## Abstract (arXiv)

Fairness testing evaluates whether a model satisfies a specified fairness criterion across different groups, yet most research has focused on classification models, leaving regression models underexplored. This paper introduces a framework for fairness testing in regression models, leveraging Wasserstein distance to project data distribution and focusing on expectation-based criteria. Upon categorizing fairness criteria for regression, we derive a Wasserstein projection test statistic from dual reformulation, and derive asymptotic bounds and limiting distributions, allowing us to formulate both a hypothesis-testing procedure and an optimal data perturbation method to improve fairness while balancing accuracy. Experiments on synthetic data demonstrate that the proposed hypothesis-testing approach offers higher specificity compared to permutation-based tests. To illustrate its potential applications, we apply our framework to two case studies on real data, showing (1) statistically significant gender disparities that appear on student performance data across multiple models, and (2) significant unfairness between pollution areas under multiple fairness criteria affecting housing price data, robust to different group divisions, with feature-level analysis identifying spatial and socioeconomic drivers.