Characterization of barycenters in the Wasserstein space by averaging optimal transport maps
KLEIN, Thierry
Institut de Mathématiques de Toulouse UMR5219 [IMT]
Ecole Nationale de l'Aviation Civile [ENAC]
Institut de Mathématiques de Toulouse UMR5219 [IMT]
Ecole Nationale de l'Aviation Civile [ENAC]
KLEIN, Thierry
Institut de Mathématiques de Toulouse UMR5219 [IMT]
Ecole Nationale de l'Aviation Civile [ENAC]
< Reduce
Institut de Mathématiques de Toulouse UMR5219 [IMT]
Ecole Nationale de l'Aviation Civile [ENAC]
Language
en
Article de revue
This item was published in
ESAIM: Probability and Statistics. 2018-11, vol. 22, p. 35 - 57
EDP Sciences
English Abstract
This paper is concerned by the study of barycenters for random probability measures in the Wasserstein space. Using a duality argument, we give a precise characterization of the population barycenter for various parametric ...Read more >
This paper is concerned by the study of barycenters for random probability measures in the Wasserstein space. Using a duality argument, we give a precise characterization of the population barycenter for various parametric classes of random probability measures with compact support. In particular, we make a connection between averaging in the Wasserstein space as introduced in Agueh and Carlier (2011), and taking the expectation of optimal transport maps with respect to a fixed reference measure. We also discuss the usefulness of this approach in statistics for the analysis of deformable models in signal and image processing. In this setting, the problem of estimating a population barycenter from n independent and identically distributed random probability measures is also considered.Read less <
English Keywords
Fréchet mean
Empirical and population barycenters
Wasserstein space
Deformable models AMS classifications: Primary 62G05
Optimal transport
Curve and image warping
Convergence of random variables
Deformable models
Duality
Origin
Hal imported