[HTML][HTML] A fixed-point approach to barycenters in Wasserstein space
PC Álvarez-Esteban, E Del Barrio… - Journal of Mathematical …, 2016 - Elsevier
Let P 2, ac be the set of Borel probabilities on R d with finite second moment and absolutely
continuous with respect to Lebesgue measure. We consider the problem of finding the …
continuous with respect to Lebesgue measure. We consider the problem of finding the …
Existence and consistency of Wasserstein barycenters
T Le Gouic, JM Loubes - Probability Theory and Related Fields, 2017 - Springer
Based on the Fréchet mean, we define a notion of barycenter corresponding to a usual
notion of statistical mean. We prove the existence of Wasserstein barycenters of random …
notion of statistical mean. We prove the existence of Wasserstein barycenters of random …
Statistical inference for Bures–Wasserstein barycenters
A Kroshnin, V Spokoiny… - The Annals of Applied …, 2021 - projecteuclid.org
In this work we introduce the concept of Bures–Wasserstein barycenter Q∗, that is
essentially a Fréchet mean of some distribution P supported on a subspace of positive semi …
essentially a Fréchet mean of some distribution P supported on a subspace of positive semi …
Penalization of barycenters in the Wasserstein space
In this paper, a regularization of Wasserstein barycenters for random measures supported
on R^d is introduced via convex penalization. The existence and uniqueness of such …
on R^d is introduced via convex penalization. The existence and uniqueness of such …
A novel notion of barycenter for probability distributions based on optimal weak mass transport
We introduce weak barycenters of a family of probability distributions, based on the recently
developed notion of optimal weak transport of mass by Gozlan et al.(2017) and Backhoff …
developed notion of optimal weak transport of mass by Gozlan et al.(2017) and Backhoff …
Gaussian processes with multidimensional distribution inputs via optimal transport and Hilbertian embedding
In this work, we propose a way to construct Gaussian processes indexed by
multidimensional distributions. More precisely, we tackle the problem of defining positive …
multidimensional distributions. More precisely, we tackle the problem of defining positive …
Construction of non-asymptotic confidence sets in 2-Wasserstein space
J Ebert, V Spokoiny, A Suvorikova - arXiv preprint arXiv:1703.03658, 2017 - arxiv.org
In this paper, we consider a probabilistic setting where the probability measures are
considered to be random objects. We propose a procedure of construction non-asymptotic …
considered to be random objects. We propose a procedure of construction non-asymptotic …
Distribution regression model with a Reproducing Kernel Hilbert Space approach
In this paper, we introduce a new distribution regression model for probability distributions.
This model is based on a Reproducing Kernel Hilbert Space (RKHS) regression framework …
This model is based on a Reproducing Kernel Hilbert Space (RKHS) regression framework …
Distribution regression model with a Reproducing Kernel Hilbert Space approach
In this paper, we introduce a new distribution regression model for probability distributions.
This model is based on a Reproducing Kernel Hilbert Space (RKHS) regression framework …
This model is based on a Reproducing Kernel Hilbert Space (RKHS) regression framework …
Machine learning and optimal transport: some statistical and algorithmic tools
E Cazelles - ESAIM: Proceedings and Surveys, 2023 - esaim-proc.org
In this paper, we focus on the analysis of data that can be described by probability measures
supported on a Euclidean space, by way of optimal transport. Our main objective is to …
supported on a Euclidean space, by way of optimal transport. Our main objective is to …