A Riemannian Geometry in the q-Exponential Banach Manifold induced by q-Divergences.

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dc.contributor.authorQuiceno, H. R.
dc.contributor.authorLoaiza, Gabriel
dc.contributor.departmentUniversidad EAFIT. Escuela de Ciencias y Humanidades. Grupo de Investigación Análisis Funcional y Aplicaciones
dc.contributor.eafitauthorGabriel Loaiza (gloaiza@eafit.edu.co)spa
dc.date.accessioned2014-11-07T20:31:52Z
dc.date.available2014-11-07T20:31:52Z
dc.date.issued2013
dc.description.abstractFor 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.spa
dc.identifier.urihttp://hdl.handle.net/10784/4401
dc.language.isoengeng
dc.publisherSpringerspa
dc.publisher.departmentEscuela de Ciencias y Humanidadesspa
dc.publisher.programGrupo de Investigación Análisis Funcional y Aplicacionesspa
dc.relation.ispartofGeometric Science of Information: Lecture Notes in Computer Science Volume 8085, 2013, pp 737-742spa
dc.relation.isversionofhttp://dx.doi.org/10.1007/978-3-642-40020-9_82spa
dc.rights.accessrightsinfo:eu-repo/semantics/restrictedAccessspa
dc.rights.localAcceso restringidospa
dc.subject.keywordq-Exponentialspa
dc.subject.keywordBanach Manifoldspa
dc.subject.keywordGeometryspa
dc.titleA Riemannian Geometry in the q-Exponential Banach Manifold induced by q-Divergences.spa
dc.typebookParteng
dc.type.hasVersionObra publicadaspa
dc.type.localCapítulo o parte de un librospa

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