Les barycentres dans l'espace de Wasserstein constituent une manière naturelle d'interpoler entre plusieurs mesures de probabillité, utile dans différents domaines appliqués comme le traitement d'images ou l'apprentissage statistique. Nous conjecturons que ces barycentres obéissent à un théorème de la limite centrale que nous démontrons dans quelques cas (très) particuliers.
The notion of Wasserstein barycenters is a natural way to interpolate between several probability measures, useful in various applied settings like image processing or machine learning. We conjecture that such barycenters obey a central limit theorem which we prove in some (very) particular cases.
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@article{CRMATH_2017__355_7_812_0, author = {Agueh, Martial and Carlier, Guillaume}, title = {Vers un th\'eor\`eme de la limite centrale dans l'espace de {Wasserstein} ?}, journal = {Comptes Rendus. Math\'ematique}, pages = {812--818}, publisher = {Elsevier}, volume = {355}, number = {7}, year = {2017}, doi = {10.1016/j.crma.2017.05.010}, language = {fr}, url = {http://www.numdam.org/articles/10.1016/j.crma.2017.05.010/} }
TY - JOUR AU - Agueh, Martial AU - Carlier, Guillaume TI - Vers un théorème de la limite centrale dans l'espace de Wasserstein ? JO - Comptes Rendus. Mathématique PY - 2017 SP - 812 EP - 818 VL - 355 IS - 7 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2017.05.010/ DO - 10.1016/j.crma.2017.05.010 LA - fr ID - CRMATH_2017__355_7_812_0 ER -
%0 Journal Article %A Agueh, Martial %A Carlier, Guillaume %T Vers un théorème de la limite centrale dans l'espace de Wasserstein ? %J Comptes Rendus. Mathématique %D 2017 %P 812-818 %V 355 %N 7 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2017.05.010/ %R 10.1016/j.crma.2017.05.010 %G fr %F CRMATH_2017__355_7_812_0
Agueh, Martial; Carlier, Guillaume. Vers un théorème de la limite centrale dans l'espace de Wasserstein ?. Comptes Rendus. Mathématique, Tome 355 (2017) no. 7, pp. 812-818. doi : 10.1016/j.crma.2017.05.010. http://www.numdam.org/articles/10.1016/j.crma.2017.05.010/
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