Optimal Transport for Fairness in Machine Learning

• Activity Number: 79 - Measure Transportation-Based Statistical Inference
• Type: Topic-Contributed
• Date/Time: Monday, August 9, 2021 : 10:00 AM to 11:50 AM
• Sponsor: IMS
• Author(s): jean michel loubes*
• Companies: University of Toulouse
• Keywords: Optimal Transport; Machine Learning; Bias; Barycenter

Abstract

Bias in Machine Learning are a key issue that has received a growing attention from the machine learning community. The presence of confounding variables or unbalanced sample may lead to algorithms whose behavior depend on such unwanted correlations and lead to disparate treatment of part of the population. We show that so-called fairness issues can be formulated as an optimal transport problem. In particular, the Wasserstein barycenter turns to be a candidate distribution that enables to post-process the outcome of an algorithm and ensure fair predictions. We procive upper and lower bound to control the accuracy of this new algorithm and define a price for fairness that balance the efficiency of an algorithm and its fairness. For this we will consider the problem of finding the barycenter between distributions as multi-marginal problem and define a projection onto a fair set that will prove to minimize the generalization error of the algorithm.