Measure Estimation in the Barycentric Coding Model. (arXiv:2201.12195v2 [stat.ML] UPDATED)

This paper considers the problem of measure estimation under the barycentric
coding model (BCM), in which an unknown measure is assumed to belong to the set
of Wasserstein-2 barycenters of a finite set of known measures. Estimating a
measure under this model is equivalent to estimating the unknown barycentric
coordinates. We provide novel geometrical, statistical, and computational
insights for measure estimation under the BCM, consisting of three main
results. Our first main result leverages the Riemannian geometry of
Wasserstein-2 space …

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