Fair Regression via Plug-in Estimator and Recalibration With Statistical Guarantees

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

1 CELESTE - Statistique mathématique et apprentissage
2 LMO - Laboratoire de Mathématiques d'Orsay
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 an optimal regression function subject to a fairness constraint. It requires that, conditionally on the sensitive feature, the distribution of the function output remains the same. This constraint naturally extends the notion of demographic parity, often used in classification, to the regression setting. We tackle this problem by leveraging on a proxy-discretized version, for which we derive an explicit expression of the optimal fair predictor. This result naturally suggests a two stage approach, in which we first estimate the (unconstrained) regression function from a set of labeled data and then we recalibrate it with another set of unlabeled data. The recalibration step can be efficiently performed via a smooth optimization. We derive rates of convergence of the proposed estimator to the optimal fair predictor both in terms of the risk and fairness constraint. Finally, we present numerical experiments illustrating that the proposed method is often superior or competitive with state-of-the-art methods.

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

Evgenii Chzhen, Christophe Denis, Mohamed Hebiri, Luca Oneto, Massimiliano Pontil. Fair Regression via Plug-in Estimator and Recalibration With Statistical Guarantees. NeurIPS 2020 - 34th Conference on Neural Information Processing Systems, Dec 2020, Vancouver / Virtuel, Canada. ⟨hal-02501190⟩