Counterfactually Fair Regression via Optimal Transport

• URL: http://arxiv.org/abs/2605.28251v1
• Date: Wed, 27 May 2026 10:00:54 GMT
• Title: Counterfactually Fair Regression via Optimal Transport
• Abstract summary: We focus on obtaining theoretical fairness guarantees for a new post-processing estimator.<n>We provide a matching lower bound on the excess risk of almost fair predictions.<n>We validate our approach on real-world and synthetic data.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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