AISTATS 2020poster70 citations
Quantitative stability of optimal transport maps and linearization of the 2-Wasserstein space
Quentin Mérigot, Alex Delalande, Frederic Chazal
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 is shown to be bi-Hölder continuous. It enables the direct use of generic supervised and unsupervised learning algorithms on measure data consistently w.r.t. the Wasserstein geometry.
BibTeX
@InProceedings{pmlr-v108-merigot20a,
title = {Quantitative stability of optimal transport maps and linearization of the 2-Wasserstein space},
author = {M\'erigot, Quentin and Delalande, Alex and Chazal, Frederic},
booktitle = {Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics},
pages = {3186--3196},
year = {2020},
editor = {Chiappa, Silvia and Calandra, Roberto},
volume = {108},
series = {Proceedings of Machine Learning Research},
month = {26--28 Aug},
publisher = {PMLR},
pdf = {http://proceedings.mlr.press/v108/merigot20a/merigot20a.pdf},
url = {https://proceedings.mlr.press/v108/merigot20a.html},
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 is shown to be bi-Hölder continuous. It enables the direct use of generic supervised and unsupervised learning algorithms on measure data consistently w.r.t. the Wasserstein geometry.}
}