Wasserstein Riemannian Geometry on Statistical Manifold

Authors : Carlos OGOUYANDJOU, Nestor WADAGNI

Pages : 144-151

Doi:10.36890/iejg.689702

View : 11 | Download : 6

Publication Date : 2020-10-15

Article Type : Research Paper

Abstract :In this paper, we study some geometric properties of statistical manifold equipped with the Riemannian Otto metric which is related to the L 2 -Wasserstein distance of optimal mass transport. We construct some α -connections on such manifold and we prove that the proposed connections are torsion-free and coincide with the Levi-Civita connection when α = 0 . In addition, the exponentialy families and the mixture families are shown to be respectively insert ignore into journalissuearticles values(1); -flat and insert ignore into journalissuearticles values(−1); -flat.                                                                                                                                             ..............................................
Keywords : Statistical manifold, Riemannian metric, Otto metric, α connections, Wasserstein Riemannian space, flatness