A Central Limit Theorem for L_p transportation cost with applications to Fairness Assessment in Machine Learning

07/18/2018

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by   Eustasio del Barrio, et al.

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We provide a Central Limit Theorem for the Monge-Kantorovich distance between two empirical distributions with size n and m, W_p(P_n,Q_m) for p>1 for observations on the real line, using a minimal amount of assumptions. We provide an estimate of the asymptotic variance which enables to build a two sample test to assess the similarity between two distributions. This test is then used to provide a new criterion to assess the notion of fairness of a classification algorithm.