# Auditing and Enforcing Conditional Fairness via Optimal Transport

arXiv: https://arxiv.org/abs/2410.14029 · HTML: https://mlsanity.com/paper/2410.14029/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 34 of its 85 references that are in the map.
- First posted on arXiv 17 Oct 2024.

## Builds on (most cited first, 30 of 34)

- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [Equality of Opportunity in Supervised Learning](https://mlsanity.com/paper/1610.02413/) (2016)
- [Certifying and removing disparate impact](https://mlsanity.com/paper/1412.3756/) (2014)
- [Mitigating Unwanted Biases with Adversarial Learning](https://mlsanity.com/paper/1801.07593/) (2018)
- [Algorithmic decision making and the cost of fairness](https://mlsanity.com/paper/1701.08230/) (2017)
- [Fair Regression: Quantitative Definitions and Reduction-based Algorithms](https://mlsanity.com/paper/1905.12843/) (2019)
- [Inherent Tradeoffs in Learning Fair Representations](https://mlsanity.com/paper/1906.08386/) (2019)
- [Wasserstein Fair Classification](https://mlsanity.com/paper/1907.12059/) (2019)
- [Bias Mitigation for Machine Learning Classifiers: A Comprehensive Survey](https://mlsanity.com/paper/2207.07068/) (2022)
- [Improving GANs Using Optimal Transport](https://mlsanity.com/paper/1803.05573/) (2018)
- [Fair Regression with Wasserstein Barycenters](https://mlsanity.com/paper/2006.07286/) (2020)
- [COT-GAN: Generating Sequential Data via Causal Optimal Transport](https://mlsanity.com/paper/2006.08571/) (2020)
- [Characterizing Fairness Over the Set of Good Models Under Selective Labels](https://mlsanity.com/paper/2101.00352/) (2021)
- [Differential Properties of Sinkhorn Approximation for Learning with Wasserstein Distance](https://mlsanity.com/paper/1805.11897/) (2018)
- [FlipTest: Fairness Testing via Optimal Transport](https://mlsanity.com/paper/1906.09218/) (2019)
- [Achieving Equalized Odds by Resampling Sensitive Attributes](https://mlsanity.com/paper/2006.04292/) (2020)
- [All of the Fairness for Edge Prediction with Optimal Transport](https://mlsanity.com/paper/2010.16326/) (2020)
- [Testing Group Fairness via Optimal Transport Projections](https://mlsanity.com/paper/2106.01070/) (2021)
- [Synthetic Data Applications in Finance](https://mlsanity.com/paper/2401.00081/) (2023)
- [Causal transport in discrete time and applications](https://mlsanity.com/paper/1606.04062/) (2016)
- [On the Convergence Rate of Sinkhorn's Algorithm](https://mlsanity.com/paper/2212.06000/) (2022)
- [Algorithmic Decision Making with Conditional Fairness](https://mlsanity.com/paper/2006.10483/) (2020)
- [FADE: FAir Double Ensemble Learning for Observable and Counterfactual Outcomes](https://mlsanity.com/paper/2109.00173/) (2021)
- [Causal optimal transport and its links to enlargement of filtrations and continuous-time stochastic optimization](https://mlsanity.com/paper/1611.02610/) (2016)
- [On conditional parity as a notion of non-discrimination in machine learning](https://mlsanity.com/paper/1706.08519/) (2017)
- [Fairness with Continuous Optimal Transport](https://mlsanity.com/paper/2101.02084/) (2021)
- [Wasserstein Robust Classification with Fairness Constraints](https://mlsanity.com/paper/2103.06828/) (2021)
- [Obtaining Dyadic Fairness by Optimal Transport](https://mlsanity.com/paper/2202.04520/) (2022)
- [What Is Fairness? On the Role of Protected Attributes and Fictitious Worlds](https://mlsanity.com/paper/2205.09622/) (2022)
- [Demographic Parity Constrained Minimax Optimal Regression under Linear Model](https://mlsanity.com/paper/2206.11546/) (2022)

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

- [Cost Efficient Fairness Audit Under Partial Feedback](https://mlsanity.com/paper/2510.03734/) (2025)

## Abstract (arXiv)

Conditional demographic parity (CDP) is a measure of the demographic parity of a predictive model or decision process when conditioning on an additional feature or set of features. Many algorithmic fairness techniques exist to target demographic parity, but CDP is much harder to achieve, particularly when the conditioning variable has many levels and/or when the model outputs are continuous. The problem of auditing and enforcing CDP is understudied in the literature. In light of this, we propose novel measures of conditional demographic disparity (CDD) which rely on statistical distances borrowed from the optimal transport literature. We further design and evaluate regularization-based approaches based on these CDD measures. Our methods, fairbit and fairlp, allow us to target CDP even when the conditioning variable has many levels. When model outputs are continuous, our methods target full equality of the conditional distributions, unlike other methods that only consider first moments or related proxy quantities. We validate the efficacy of our approaches on real-world datasets.