Entropy-regularized 2-Wasserstein distance between Gaussian measures

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