A Central Limit Theorem for $L_p$ transportation cost with applications to Fairness Assessment in Machine Learning
Statistics Theory
2018-07-19 v1 Statistics Theory
Abstract
We provide a Central Limit Theorem for the Monge-Kantorovich distance between two empirical distributions with size and , for 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.
Keywords
Cite
@article{arxiv.1807.06796,
title = {A Central Limit Theorem for $L_p$ transportation cost with applications to Fairness Assessment in Machine Learning},
author = {Eustasio del Barrio and Paula Gordaliza and Jean-Michel Loubes},
journal= {arXiv preprint arXiv:1807.06796},
year = {2018}
}