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On the local and global properties of information manifolds
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 R...
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| Format: | Thesis |
| Language: | Eng |
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Department of Mathematics and Applied Mathematics
2016
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| _version_ | 1867613807975596032 |
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| access_status_str | Open Access |
| author | Clingman, Tslil |
| author2 | Murugan, Jeffrey |
| author_browse | Clingman, Tslil Murugan, Jeffrey |
| author_facet | Murugan, Jeffrey Clingman, Tslil |
| author_sort | Clingman, Tslil |
| collection | Thesis |
| description | 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. |
| format | Thesis |
| id | oai:open.uct.ac.za:11427/19950 |
| institution | University of Cape Town (South Africa) |
| language | Eng |
| last_indexed | 2026-06-10T12:42:01.632Z |
| license_str | Not specified — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from UCTD — University of Cape Town Open Access Repository |
| publishDate | 2016 |
| publishDateRange | 2016 |
| publishDateSort | 2016 |
| publisher | Department of Mathematics and Applied Mathematics |
| publisherStr | Department of Mathematics and Applied Mathematics |
| record_format | dspace |
| source_str | UCTD — University of Cape Town Open Access Repository |
| spelling | oai:open.uct.ac.za:11427/19950 On the local and global properties of information manifolds Clingman, Tslil Murugan, Jeffrey Applied Mathematics 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. 2016-06-09T11:08:34Z 2016-06-09T11:08:34Z 2015 Master Thesis Masters MSc http://hdl.handle.net/11427/19950 Eng application/pdf Department of Mathematics and Applied Mathematics Faculty of Science University of Cape Town |
| spellingShingle | Applied Mathematics Clingman, Tslil On the local and global properties of information manifolds |
| thesis_degree_str | Master's |
| title | On the local and global properties of information manifolds |
| title_full | On the local and global properties of information manifolds |
| title_fullStr | On the local and global properties of information manifolds |
| title_full_unstemmed | On the local and global properties of information manifolds |
| title_short | On the local and global properties of information manifolds |
| title_sort | on the local and global properties of information manifolds |
| topic | Applied Mathematics |
| url | http://hdl.handle.net/11427/19950 |
| work_keys_str_mv | AT clingmantslil onthelocalandglobalpropertiesofinformationmanifolds |