An Elementary Introduction to Information Geometry
In this survey, we describe the fundamental differential-geometric structures of information manifolds, state the fundamental theorem of information geometry, and illustrate some use cases of these information manifolds in information sciences. The exposition is self-contained by concisely introduci...
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-09-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/22/10/1100 |
| _version_ | 1797552259010134016 |
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| author | Frank Nielsen |
| author_facet | Frank Nielsen |
| author_sort | Frank Nielsen |
| collection | DOAJ |
| description | In this survey, we describe the fundamental differential-geometric structures of information manifolds, state the fundamental theorem of information geometry, and illustrate some use cases of these information manifolds in information sciences. The exposition is self-contained by concisely introducing the necessary concepts of differential geometry. Proofs are omitted for brevity. |
| first_indexed | 2024-03-10T15:57:28Z |
| format | Article |
| id | doaj.art-042ae0fc4d184c32919a3fb88adc8b9a |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-03-10T15:57:28Z |
| publishDate | 2020-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-042ae0fc4d184c32919a3fb88adc8b9a2023-11-20T15:31:34ZengMDPI AGEntropy1099-43002020-09-012210110010.3390/e22101100An Elementary Introduction to Information GeometryFrank Nielsen0Sony Computer Science Laboratories, Tokyo 141-0022, JapanIn this survey, we describe the fundamental differential-geometric structures of information manifolds, state the fundamental theorem of information geometry, and illustrate some use cases of these information manifolds in information sciences. The exposition is self-contained by concisely introducing the necessary concepts of differential geometry. Proofs are omitted for brevity.https://www.mdpi.com/1099-4300/22/10/1100differential geometrymetric tensoraffine connectionmetric compatibilityconjugate connectionsdual metric-compatible parallel transport |
| spellingShingle | Frank Nielsen An Elementary Introduction to Information Geometry Entropy differential geometry metric tensor affine connection metric compatibility conjugate connections dual metric-compatible parallel transport |
| title | An Elementary Introduction to Information Geometry |
| title_full | An Elementary Introduction to Information Geometry |
| title_fullStr | An Elementary Introduction to Information Geometry |
| title_full_unstemmed | An Elementary Introduction to Information Geometry |
| title_short | An Elementary Introduction to Information Geometry |
| title_sort | elementary introduction to information geometry |
| topic | differential geometry metric tensor affine connection metric compatibility conjugate connections dual metric-compatible parallel transport |
| url | https://www.mdpi.com/1099-4300/22/10/1100 |
| work_keys_str_mv | AT franknielsen anelementaryintroductiontoinformationgeometry AT franknielsen elementaryintroductiontoinformationgeometry |