Entropy-regularized 2-Wasserstein distance between Gaussian measures

Anton Mallasto, Augusto Gerolin, Hà Quang Minh

Research output: Contribution to journalArticleScientificpeer-review

Abstract

Gaussian distributions are plentiful in applications dealing in uncertainty quantification and diffusivity. They furthermore stand as important special cases for frameworks providing geometries for probability measures, as the resulting geometry on Gaussians is often expressible in closed-form under the frameworks. In this work, we study the Gaussian geometry under the entropy-regularized 2-Wasserstein distance, by providing closed-form solutions for the distance and interpolations between elements. Furthermore, we provide a fixed-point characterization of a population barycenter when restricted to the manifold of Gaussians, which allows computations through the fixed-point iteration algorithm. As a consequence, the results yield closed-form expressions for the 2-Sinkhorn divergence. As the geometries change by varying the regularization magnitude, we study the limiting cases of vanishing and infinite magnitudes, reconfirming well-known results on the limits of the Sinkhorn divergence. Finally, we illustrate the resulting geometries with a numerical study.
Original languageEnglish
Number of pages35
JournalInformation Geometry
DOIs
Publication statusE-pub ahead of print - 16 Aug 2021
MoE publication typeA1 Journal article-refereed

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