From Fragile to Certified: Wasserstein Audits of Group Fairness Under Distribution Shift

• URL: http://arxiv.org/abs/2509.26241v1
• Date: Tue, 30 Sep 2025 13:35:50 GMT
• Title: From Fragile to Certified: Wasserstein Audits of Group Fairness Under Distribution Shift
• Abstract summary: Group-fairness metrics can vary sharply across resamples and are especially brittle under distribution shift.<n>We propose a Wasserstein distributionally robust framework that certifies worst-case group fairness over a ball of plausible test distributions centered at the empirical law.
• Score: 21.387312729118364
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Group-fairness metrics (e.g., equalized odds) can vary sharply across resamples and are especially brittle under distribution shift, undermining reliable audits. We propose a Wasserstein distributionally robust framework that certifies worst-case group fairness over a ball of plausible test distributions centered at the empirical law. Our formulation unifies common group fairness notions via a generic conditional-probability functional and defines $\varepsilon$-Wasserstein Distributional Fairness ($\varepsilon$-WDF) as the audit target. Leveraging strong duality, we derive tractable reformulations and an efficient estimator (DRUNE) for $\varepsilon$-WDF. We prove feasibility and consistency and establish finite-sample certification guarantees for auditing fairness, along with quantitative bounds under smoothness and margin conditions. Across standard benchmarks and classifiers, $\varepsilon$-WDF delivers stable fairness assessments under distribution shift, providing a principled basis for auditing and certifying group fairness beyond observational data.

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