Asymptotic analysis of the optimal cost in some transportation problems with random locations

On the asymptotics of Ajtai-Komlós-Tusnády statistics

“…Matchings on the Euclidean ball were investigated in [3]. The paper [13] investigates the rate of convergence in abstract settings. An investigation of different types of matchings was given in [6].…”

Fair Learning: an optimal transport based approach

“…Methods in the first family consist in pre-processing the data or in extracting representations that do not contain undesired biases (see e.g. Beutel et al [2017], , Calmon et al [2017], Chierichetti et al [2017], Edwards and Storkey [2015], Feldman [2015], , Fish and Lelkes [2015], Gordaliza et al [2019], Johndrow et al [2019], , 2012, Madras et al [2018a], Song et al [2018], Zemel et al [2013]), which can then be used as input to a standard machine learning model.…”

“…Further details on recent developments in the area of transport inequalities could be found in Gozlan and Léonard [2010]. Also a generalization of the moderate deviation principle in Ganesh and O'Connell [2007] to general Polish spaces was proposed in Torrisi [2012]. In this comprehensive work, results on almost sure convergence, large and moderate deviation principles are proved under various assumptions on the reference samples X i s, Y i s and the cost function, as well as expressions for the large deviation rate functions in terms of infinite-dimensional variational problems.…”