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A Central Limit Theorem for $L_p$ transportation cost with applications to Fairness Assessment in Machine Learning. (arXiv:1807.06796v1 [math.ST])

来源于:arXiv
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. 查看全文>>