On the local and global properties of information manifolds

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dc.contributor.advisorMurugan, Jeffreyen_ZA
dc.contributor.authorClingman, Tslilen_ZA
dc.date.accessioned2016-06-09T11:08:34Z
dc.date.available2016-06-09T11:08:34Z
dc.date.issued2015en_ZA
dc.description.abstractIn the first part of the work, we show a general relation between the spatially disjoint product of probability density functions and the sum of their Fisher information metric tensors. We then utilise this result to give a method for constructing the probability density functions for an arbitrary Riemannian Fisher information metric tensor given its associated Nash embedding. We note further that this construction is extremely unconstrained, depending only on certain continuity properties of the probability density functions and a select symmetry of their domains. In the second part of the work, with the aim of understanding the global, algebrao-topological nature of information manifolds, we exhibit some of the necessary category theory required to effect a discussion of homological algebra in a general setting.en_ZA
dc.identifier.apacitationClingman, T. (2015). <i>On the local and global properties of information manifolds</i>. (Thesis). University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics. Retrieved from http://hdl.handle.net/11427/19950en_ZA
dc.identifier.chicagocitationClingman, Tslil. <i>"On the local and global properties of information manifolds."</i> Thesis., University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics, 2015. http://hdl.handle.net/11427/19950en_ZA
dc.identifier.citationClingman, T. 2015. On the local and global properties of information manifolds. University of Cape Town.en_ZA
dc.identifier.ris TY - Thesis / Dissertation AU - Clingman, Tslil AB - In the first part of the work, we show a general relation between the spatially disjoint product of probability density functions and the sum of their Fisher information metric tensors. We then utilise this result to give a method for constructing the probability density functions for an arbitrary Riemannian Fisher information metric tensor given its associated Nash embedding. We note further that this construction is extremely unconstrained, depending only on certain continuity properties of the probability density functions and a select symmetry of their domains. In the second part of the work, with the aim of understanding the global, algebrao-topological nature of information manifolds, we exhibit some of the necessary category theory required to effect a discussion of homological algebra in a general setting. DA - 2015 DB - OpenUCT DP - University of Cape Town LK - https://open.uct.ac.za PB - University of Cape Town PY - 2015 T1 - On the local and global properties of information manifolds TI - On the local and global properties of information manifolds UR - http://hdl.handle.net/11427/19950 ER - en_ZA
dc.identifier.urihttp://hdl.handle.net/11427/19950
dc.identifier.vancouvercitationClingman T. On the local and global properties of information manifolds. [Thesis]. University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics, 2015 [cited yyyy month dd]. Available from: http://hdl.handle.net/11427/19950en_ZA
dc.language.isoEngen_ZA
dc.publisher.departmentDepartment of Mathematics and Applied Mathematicsen_ZA
dc.publisher.facultyFaculty of Scienceen_ZA
dc.publisher.institutionUniversity of Cape Town
dc.subject.otherApplied Mathematicsen_ZA
dc.titleOn the local and global properties of information manifoldsen_ZA
dc.typeMaster Thesis
dc.type.qualificationlevelMasters
dc.type.qualificationnameMScen_ZA
uct.type.filetypeText
uct.type.filetypeImage
uct.type.publicationResearchen_ZA
uct.type.resourceThesisen_ZA
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