Quantitative stability of optimal transport maps and linearization of the 2Wasserstein space
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Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics, PMLR 108:31863196, 2020.
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 2Wasserstein space and is shown to be biHölder continuous. It enables the direct use of generic supervised and unsupervised learning algorithms on measure data consistently w.r.t. the Wasserstein geometry.
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