Wasserstein Riemannian Geometry on Statistical Manifold - OGOUYANDJOU, KOLADÉ SIMPLICE EPHREM CARLOS; WADAGNI, Nestor; WADAGNI, Nestor (My University, 2020)
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 (1) -flat and (−1) -flat.
Keywords: Statistical manifold; Riemannian metric; Otto metric; α-connections; Wasserstein Riemannian space; flatness.