Quantitative Stability of Optimal Transport Maps and Linearization of the 2-Wasserstein Space
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.
Cite
Text
Mérigot et al. "Quantitative Stability of Optimal Transport Maps and Linearization of the 2-Wasserstein Space." Artificial Intelligence and Statistics, 2020.Markdown
[Mérigot et al. "Quantitative Stability of Optimal Transport Maps and Linearization of the 2-Wasserstein Space." Artificial Intelligence and Statistics, 2020.](https://mlanthology.org/aistats/2020/merigot2020aistats-quantitative/)BibTeX
@inproceedings{merigot2020aistats-quantitative,
title = {{Quantitative Stability of Optimal Transport Maps and Linearization of the 2-Wasserstein Space}},
author = {Mérigot, Quentin and Delalande, Alex and Chazal, Frederic},
booktitle = {Artificial Intelligence and Statistics},
year = {2020},
pages = {3186-3196},
volume = {108},
url = {https://mlanthology.org/aistats/2020/merigot2020aistats-quantitative/}
}