A CLT for Lp transportation cost on the real line with application to fairness assessment in machine learning

P. Gordaliza Pastor, E. Del Barrio, J. M. Loubes

We provide a Central Limit Theorem for the Monge-Kantorovich distance
between two empirical distributions with different sizes and cost
greater than or equal to 1, for observations on the real line. In the
case of cost 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.

Palabras clave: Optimal Transport Monge-Kantorovich distance Central Limit Theorem Fair Learning.

M. Lafuente Blasco, J. Asín Lafuente, A. C. Cebrián Guajardo, R. Gouet Bañares, F. J. López Lorente, G. Sanz Sáiz

J. Castillo-Mateo, A. C. Cebrián, M. Lafuente Blasco, G. Sanz, J. Abaurrea

J. J. Salamanca Jurado