Fair Regression with Wasserstein Barycenters

Evgenii Chzhen (1, 2) , Christophe Denis (3) , Mohamed Hebiri (3) , Luca Oneto (4) , Massimiliano Pontil (5, 6)

1 LMO - Laboratoire de Mathématiques d'Orsay
2 CELESTE - Statistique mathématique et apprentissage
3 LAMA - Laboratoire Analyse et de Mathématiques Appliquées
4 DIBRIS - Dipartimento di Informatica, Bioingegneria, Robotica e Ingegneria dei Sistemi [Genova]
5 UCL - University College of London [London]
6 IIT - Instituto Italiano di Tecnologia

We study the problem of learning a real-valued function that satisfies the Demographic Parity constraint. It demands the distribution of the predicted output to be independent of the sensitive attribute. We consider the case that the sensitive attribute is available for prediction. We establish a connection between fair regression and optimal transport theory, based on which we derive a close form expression for the optimal fair predictor. Specifically, we show that the distribution of this optimum is the Wasserstein barycenter of the distributions induced by the standard regression function on the sensitive groups. This result offers an intuitive interpretation of the optimal fair prediction and suggests a simple post-processing algorithm to achieve fairness. We establish risk and distribution-free fairness guarantees for this procedure. Numerical experiments indicate that our method is very effective in learning fair models, with a relative increase in error rate that is inferior to the relative gain in fairness.

Domaines: Statistiques [stat]; Théorie [stat.TH]; Machine Learning [stat.ML]

Evgenii Chzhen, Christophe Denis, Mohamed Hebiri, Luca Oneto, Massimiliano Pontil. Fair Regression with Wasserstein Barycenters. NeurIPS 2020 - 34th Conference on Neural Information Processing Systems, Dec 2020, Vancouver / Virtuel, Canada. ⟨hal-02866811⟩