Fair Regression with Wasserstein Barycenters
This addresses fairness in regression for sensitive groups, offering a novel theoretical and practical solution with incremental improvements over existing methods.
The paper tackles fair regression under Demographic Parity by connecting it to optimal transport theory, deriving an optimal fair predictor as the Wasserstein barycenter of group distributions, and proposes a post-processing algorithm with proven guarantees and effective results in experiments, showing a relative error increase less than fairness gain.
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.