A Riemannian geometry in the q-exponential Banach manifold induced by q-divergences
| dc.contributor.author | Loaiza, G. | |
| dc.contributor.author | Quiceno, H.R. | |
| dc.contributor.department | Universidad EAFIT. Departamento de Ciencias | spa |
| dc.contributor.researchgroup | Matemáticas y Aplicaciones | spa |
| dc.creator | Loaiza, G. | |
| dc.creator | Quiceno, H.R. | |
| dc.date.accessioned | 2021-04-12T13:55:40Z | |
| dc.date.available | 2021-04-12T13:55:40Z | |
| dc.date.issued | 2013-01-01 | |
| dc.description.abstract | 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 a-connections appears as special case of the q-connections ?(q). The main result is the expected one, namely the zero curvature of the manifold. © 2013 Springer-Verlag. | eng |
| dc.identifier | https://eafit.fundanetsuite.com/Publicaciones/ProdCientif/PublicacionFrw.aspx?id=1718 | |
| dc.identifier.doi | 10.1007/978-3-642-40020-9_82 | |
| dc.identifier.issn | 03029743 | |
| dc.identifier.issn | 16113349 | |
| dc.identifier.other | SCOPUS;2-s2.0-84884972071 | |
| dc.identifier.uri | http://hdl.handle.net/10784/27665 | |
| dc.language.iso | eng | eng |
| dc.publisher | SPRINGER | |
| dc.relation.uri | https://www.scopus.com/inward/record.uri?eid=2-s2.0-84884972071&doi=10.1007%2f978-3-642-40020-9_82&partnerID=40&md5=1669c3e28c8f09fc21b385c034cfd875 | |
| dc.rights | https://v2.sherpa.ac.uk/id/publication/issn/0302-9743 | |
| dc.source | Lecture Notes In Computer Science | |
| dc.subject.keyword | Fisher information metric | eng |
| dc.subject.keyword | Functionals | eng |
| dc.subject.keyword | Lebesgue space | eng |
| dc.subject.keyword | Non-parametric | eng |
| dc.subject.keyword | Riemannian geometry | eng |
| dc.subject.keyword | Banach spaces | eng |
| dc.subject.keyword | Fisher information matrix | eng |
| dc.subject.keyword | Information science | eng |
| dc.subject.keyword | Geometry | eng |
| dc.title | A Riemannian geometry in the q-exponential Banach manifold induced by q-divergences | eng |
| dc.type | info:eu-repo/semantics/conferencePaper | eng |
| dc.type | conferencePaper | eng |
| dc.type | info:eu-repo/semantics/publishedVersion | eng |
| dc.type | publishedVersion | eng |
| dc.type.local | Documento de conferencia | spa |