A categorical characterization of relative entropy on standard Borel spaces
We give a categorical treatment, in the spirit of Baez and Fritz, of relative entropy for probability distributions defined on standard Borel spaces. We define a category suitable for reasoning about statistical inference on standard Borel spaces. We define relative entropy as a functor into Lawvere...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Logical Methods in Computer Science e.V.
2023-11-01
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| Series: | Logical Methods in Computer Science |
| Subjects: | |
| Online Access: | https://lmcs.episciences.org/7621/pdf |
| _version_ | 1797268488374452224 |
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| author | Nicolas Gagne Prakash Panangaden |
| author_facet | Nicolas Gagne Prakash Panangaden |
| author_sort | Nicolas Gagne |
| collection | DOAJ |
| description | We give a categorical treatment, in the spirit of Baez and Fritz, of relative
entropy for probability distributions defined on standard Borel spaces. We
define a category suitable for reasoning about statistical inference on
standard Borel spaces. We define relative entropy as a functor into Lawvere's
category and we show convexity, lower semicontinuity and uniqueness. |
| first_indexed | 2024-04-25T01:33:17Z |
| format | Article |
| id | doaj.art-44bc10822a164830b277348a53165f0e |
| institution | Directory Open Access Journal |
| issn | 1860-5974 |
| language | English |
| last_indexed | 2024-04-25T01:33:17Z |
| publishDate | 2023-11-01 |
| publisher | Logical Methods in Computer Science e.V. |
| record_format | Article |
| series | Logical Methods in Computer Science |
| spelling | doaj.art-44bc10822a164830b277348a53165f0e2024-03-08T10:43:58ZengLogical Methods in Computer Science e.V.Logical Methods in Computer Science1860-59742023-11-01Volume 19, Issue 410.46298/lmcs-19(4:10)20237621A categorical characterization of relative entropy on standard Borel spacesNicolas GagnePrakash PanangadenWe give a categorical treatment, in the spirit of Baez and Fritz, of relative entropy for probability distributions defined on standard Borel spaces. We define a category suitable for reasoning about statistical inference on standard Borel spaces. We define relative entropy as a functor into Lawvere's category and we show convexity, lower semicontinuity and uniqueness.https://lmcs.episciences.org/7621/pdfcomputer science - information theory |
| spellingShingle | Nicolas Gagne Prakash Panangaden A categorical characterization of relative entropy on standard Borel spaces Logical Methods in Computer Science computer science - information theory |
| title | A categorical characterization of relative entropy on standard Borel spaces |
| title_full | A categorical characterization of relative entropy on standard Borel spaces |
| title_fullStr | A categorical characterization of relative entropy on standard Borel spaces |
| title_full_unstemmed | A categorical characterization of relative entropy on standard Borel spaces |
| title_short | A categorical characterization of relative entropy on standard Borel spaces |
| title_sort | categorical characterization of relative entropy on standard borel spaces |
| topic | computer science - information theory |
| url | https://lmcs.episciences.org/7621/pdf |
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