[Towards a central limit theorem in the Wasserstein space?]
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.
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.
Accepted:
Published online:
Martial Agueh 1; Guillaume Carlier 2, 3
@article{CRMATH_2017__355_7_812_0, author = {Martial Agueh and Guillaume Carlier}, 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}, }
Martial Agueh; Guillaume Carlier. Vers un théorème de la limite centrale dans l'espace de Wasserstein ?. Comptes Rendus. Mathématique, Volume 355 (2017) no. 7, pp. 812-818. doi : 10.1016/j.crma.2017.05.010. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2017.05.010/
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