# Counterfactually Fair Regression via Optimal Transport

arXiv: https://arxiv.org/abs/2605.28251 · HTML: https://mlsanity.com/paper/2605.28251/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 44 references that are in the map.
- First posted on arXiv 27 May 2026.

## Builds on (most cited first, 5 of 5)

- [Survey on Causal-based Machine Learning Fairness Notions](https://mlsanity.com/paper/2010.09553/) (2020)
- [Causal Fairness Analysis](https://mlsanity.com/paper/2207.11385/) (2022)
- [Fairness with Continuous Optimal Transport](https://mlsanity.com/paper/2101.02084/) (2021)
- [Projection to Fairness in Statistical Learning](https://mlsanity.com/paper/2005.11720/) (2020)
- [Counterfactual Fairness Is Not Demographic Parity, and Other Observations](https://mlsanity.com/paper/2402.02663/) (2024)

## Abstract (arXiv)

We consider the problem of learning a counterfactually fair regressor. We adopt a causal uncertainty view in which counterfactual fairness is defined with resampled noise. We focus on obtaining theoretical fairness guarantees for a new post-processing estimator. We begin by showing that counterfactual fairness is equivalent to satisfying demographic parity conditional on the latent variable. This allows us to provide a closed-form expression of the optimal fair regressor via a barycentric quantile map. In order to handle continuous latent variables, we propose a discretized post-processing method. Then, under mild regularity assumptions, we prove high-probability finite-sample fairness guarantees for our estimator, providing an unfairness decay at rate tilde O(n-1/3), and establishing a matching risk bound of order tilde O(n-1/3). We provide a matching lower bound on the excess risk of almost fair predictions. Finally, we extend our results to the setting of relaxed counterfactual fairness. We validate our approach on real-world and synthetic data.