Fréchet barycenters in the Monge-Kantorovich spaces

Content Provider	Semantic Scholar
Author	Kroshnin, Alexey
Copyright Year	2017
Abstract	We consider the space $\mathcal{P}(X)$ of probability measures on arbitrary Radon space $X$ endowed with a transportation cost $J(\mu, \nu)$ generated by a nonnegative continuous cost function. For a probability distribution on $\mathcal{P}(X)$ we formulate a notion of average with respect to this transportation cost, called here the Fr\'echet barycenter, prove a version of the law of large numbers for Fr\'echet barycenters, and discuss the structure of $\mathcal{P}(X)$ related to the transportation cost $J$.
File Format	PDF HTM / HTML
Alternate Webpage(s)	https://arxiv.org/pdf/1702.05740v1.pdf
Language	English
Access Restriction	Open
Content Type	Text
Resource Type	Article