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A Riemannian Geometry in the q-Exponential Banach Manifold Induced by q-Divergences
(Springer Berlin Heidelberg, 2013) Loaiza Ossa, Gabriel Ignacio; Quiceno Echavarría, Héctor Román; Universidad EAFIT. Departamento de Ciencias; Análisis Funcional y Aplicaciones
For the family of non-parametric q-exponential statistical models, in a former paper, written by the same authors, a differentiable Banach manifold modelled on Lebesgue spaces of real random variables has been built. In this paper, the geometry induced on this manifold is characterized by q-divergence functionals. This geometry turns out to be a generalization of the geometry given by Fisher information metric and Levi-Civita connections. Moreover, the classical Amari’s α-connections appears as special case of the q −connections ∇ (q). The main result is the expected one, namely the zero curvature of the manifold. Loading... Geometric Science of InformationGeometric Science of Information Look Inside Chapter Metrics Downloads1K Provided by Bookmetrix Other actions Export citation About this Book Reprints and Permissions Add to Papers Share Share this content on Facebook Share this content on Twitter Share this content on LinkedIn