Projection to Fairness in Statistical Learning

In the context of regression, we consider the fundamental question of making an estimator fair while preserving its prediction accuracy as much as possible. To that end, we define its projection to fairness as its closest fair estimator in a sense that reflects prediction accuracy. Our methodology leverages tools from optimal transport to construct efficiently the projection to fairness of any given estimator as a simple post-processing step. Moreover, our approach precisely quantifies the cost of fairness, measured in terms of prediction accuracy.