Information geometry of the space of probability measures and barycenter maps (2208.11861v2)

Published 25 Aug 2022 in math.DG

Abstract: In this article, we present recent developments of information geometry, namely, geometry of the Fisher metric, dualistic structures and divergences on the space of probability measures, particularly the theory of geodesics of the Fisher metric. Moreover, we consider several facts concerning the barycenter of probability measures on the ideal boundary of a Hadamard manifold from a viewpoint of the information geometry.

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