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            <idno type="halRefHtml">&lt;i&gt;AISTATS 2020 - 23rd International Conference on Artificial Intelligence and Statistics&lt;/i&gt;, Aug 2020, Palermo /Online, Italy. pp.3186-3196</idno>
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              <p>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.</p>
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