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Entropic-Wasserstein Barycenters: PDE Characterization, Regularity, and CLT
SIAM Journal on Mathematical Analysis. 2021. Vol. 53. No. 5. P. 5880–5914.
Carlier G., Eichinger K., Kroshnin A.
In this paper, we investigate properties of entropy-penalized Wasserstein barycenters introduced in [J. Bigot, E. Cazelles, and N. Papadakis, SIAM J. Math. Anal., 51 (2019), pp. 2261--2285] as a regularization of Wasserstein barycenters [M. Agueh and G. Carlier, SIAM J. Math. Anal., 43 (2011), pp. 904--924]. After characterizing these barycenters in terms of a system of Monge--Ampère equations, we prove some global moment and Sobolev bounds as well as higher regularity properties. We finally establish a central limit theorem for entropic-Wasserstein barycenters.
Publication based on the results of:
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