BCAM Scientific Seminar: Application of Optimal Transport Theory to Fair Learning

Abstract:
As machine learning is becoming more of an indispensable part of human life and activity over the last years, this question arises more frequently among the pop- ulation: do algorithmic decisions convey any type of discrimination against a person or minority group? Fairness is generally studied in a probabilistic framework where it is assumed that there exists a protected variable, which represents a discriminatory infor- mation that should not be used by the algorithm. Yet providing a definition of fairness or equity in machine learning is a complicated task and several propositions have been formulated. In this talk we focus on two of them, called Disparate Impact (DI) and Balanced Error Rate (BER). Both are based on the outcome of the algorithm across the different groups determined by the protected variable. The relationship between these two notions is also studied. Our goal is detecting when a binary classification rule lacks fairness and then trying to reduce the further impact in automatic decisions. This can be done by modifying either the classifier or the data itself. Our work falls into the second category and modifies the input data using optimal transport theory, where the use of such techniques is also justified. Finally, we provide a Central Limit Theorem for the Monge-Kantorovich distance between two empirical distributions with sizes n and m, Wp(Pn, Qm), p ≥ 1, for observations on the real line. In the case p > 1 our assumptions are sharp in terms of moments and smoothness. We prove results dealing with the choice of centering constants. We provide a consistent estimate of the asymptotic variance which enables to build two-sample tests and confidence intervals to certify the similarity between two distributions. These are then used to assess a new criterion of data set fairness in classification.

Joint work with Eustasio del Barrio (IMUVA, Universidad de Valladolid), Fabrice Gamboa (Institut de Mathématiques de Toulouse) & Jean-Michel Loubes (Institut de Mathématiques de Toulouse). 

The time of this seminar will be confirmed in the coming days.