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

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-divergen...

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Autores:
Quiceno, H. R.
Loaiza, Gabriel
Tipo de recurso:
Fecha de publicación:
2013
Institución:
Universidad EAFIT
Repositorio:
Repositorio EAFIT
Idioma:
eng
OAI Identifier:
oai:repository.eafit.edu.co:10784/4401
Acceso en línea:
http://hdl.handle.net/10784/4401
Palabra clave:
q-Exponential
Banach Manifold
Geometry
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License
Acceso restringido
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spelling 2014-11-07T20:31:52Z20132014-11-07T20:31:52Zhttp://hdl.handle.net/10784/4401For 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.engSpringerGrupo de Investigación Análisis Funcional y AplicacionesEscuela de Ciencias y HumanidadesGeometric Science of Information: Lecture Notes in Computer Science Volume 8085, 2013, pp 737-742http://dx.doi.org/10.1007/978-3-642-40020-9_82A Riemannian Geometry in the q-Exponential Banach Manifold induced by q-Divergences.bookPartinfo:eu-repo/semantics/bookPartCapítulo o parte de un libroObra publicadapublishedVersionhttp://purl.org/coar/version/c_970fb48d4fbd8a85http://purl.org/coar/resource_type/c_3248Acceso restringidohttp://purl.org/coar/access_right/c_16ecq-ExponentialBanach ManifoldGeometryUniversidad EAFIT. Escuela de Ciencias y Humanidades. Grupo de Investigación Análisis Funcional y AplicacionesGabriel Loaiza (gloaiza@eafit.edu.co)Quiceno, H. R.Loaiza, GabrielLICENSElicense.txtlicense.txttext/plain; charset=utf-82556https://repository.eafit.edu.co/bitstreams/08a69995-ba2a-48d2-94c7-79162f95b6c4/download76025f86b095439b7ac65b367055d40cMD51ORIGINAL978-3-642-40020-9_82.pdf978-3-642-40020-9_82.pdfTexto completoapplication/pdf140821https://repository.eafit.edu.co/bitstreams/fccd7059-48d8-49b9-be75-cf9178481fca/downloadb666677b9e4d3d7c65c51f395d8fd7c8MD5210784/4401oai:repository.eafit.edu.co:10784/44012014-11-07 15:32:58.465restrictedhttps://repository.eafit.edu.coRepositorio Institucional Universidad EAFITrepositorio@eafit.edu.co
dc.title.spa.fl_str_mv A Riemannian Geometry in the q-Exponential Banach Manifold induced by q-Divergences.
title A Riemannian Geometry in the q-Exponential Banach Manifold induced by q-Divergences.
spellingShingle A Riemannian Geometry in the q-Exponential Banach Manifold induced by q-Divergences.
q-Exponential
Banach Manifold
Geometry
title_short A Riemannian Geometry in the q-Exponential Banach Manifold induced by q-Divergences.
title_full A Riemannian Geometry in the q-Exponential Banach Manifold induced by q-Divergences.
title_fullStr A Riemannian Geometry in the q-Exponential Banach Manifold induced by q-Divergences.
title_full_unstemmed A Riemannian Geometry in the q-Exponential Banach Manifold induced by q-Divergences.
title_sort A Riemannian Geometry in the q-Exponential Banach Manifold induced by q-Divergences.
dc.creator.fl_str_mv Quiceno, H. R.
Loaiza, Gabriel
dc.contributor.department.none.fl_str_mv Universidad EAFIT. Escuela de Ciencias y Humanidades. Grupo de Investigación Análisis Funcional y Aplicaciones
dc.contributor.eafitauthor.spa.fl_str_mv Gabriel Loaiza (gloaiza@eafit.edu.co)
dc.contributor.author.none.fl_str_mv Quiceno, H. R.
Loaiza, Gabriel
dc.subject.keyword.spa.fl_str_mv q-Exponential
Banach Manifold
Geometry
topic q-Exponential
Banach Manifold
Geometry
description 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.
publishDate 2013
dc.date.issued.none.fl_str_mv 2013
dc.date.available.none.fl_str_mv 2014-11-07T20:31:52Z
dc.date.accessioned.none.fl_str_mv 2014-11-07T20:31:52Z
dc.type.eng.fl_str_mv bookPart
dc.type.none.fl_str_mv info:eu-repo/semantics/bookPart
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dc.type.coar.fl_str_mv http://purl.org/coar/resource_type/c_3248
dc.type.local.spa.fl_str_mv Capítulo o parte de un libro
dc.type.hasVersion.spa.fl_str_mv Obra publicada
publishedVersion
dc.identifier.uri.none.fl_str_mv http://hdl.handle.net/10784/4401
url http://hdl.handle.net/10784/4401
dc.language.iso.eng.fl_str_mv eng
language eng
dc.relation.ispartof.spa.fl_str_mv Geometric Science of Information: Lecture Notes in Computer Science Volume 8085, 2013, pp 737-742
dc.relation.isversionof.spa.fl_str_mv http://dx.doi.org/10.1007/978-3-642-40020-9_82
dc.rights.coar.fl_str_mv http://purl.org/coar/access_right/c_16ec
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rights_invalid_str_mv Acceso restringido
http://purl.org/coar/access_right/c_16ec
dc.publisher.spa.fl_str_mv Springer
dc.publisher.program.spa.fl_str_mv Grupo de Investigación Análisis Funcional y Aplicaciones
dc.publisher.department.spa.fl_str_mv Escuela de Ciencias y Humanidades
institution Universidad EAFIT
bitstream.url.fl_str_mv https://repository.eafit.edu.co/bitstreams/08a69995-ba2a-48d2-94c7-79162f95b6c4/download
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