Quantitative stability of optimal transport maps and linearization of the 2-Wasserstein space
From MaRDI portal
Publication:6327127
arXiv1910.05954MaRDI QIDQ6327127
Author name not available (Why is that?)
Publication date: 14 October 2019
Abstract: This work studies an explicit embedding of the set of probability measures into a Hilbert space, defined using optimal transport maps from a reference probability density. This embedding linearizes to some extent the 2-Wasserstein space, and enables the direct use of generic supervised and unsupervised learning algorithms on measure data. Our main result is that the embedding is (bi-)H"older continuous, when the reference density is uniform over a convex set, and can be equivalently phrased as a dimension-independent H"older-stability results for optimal transport maps.
Has companion code repository: https://github.com/AlxDel/stability_ot_maps_and_linearization_wasserstein_space
This page was built for publication: Quantitative stability of optimal transport maps and linearization of the 2-Wasserstein space
Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q6327127)
