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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2302.07471 |
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| _version_ | 1866911849271787520 |
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| author | Kobayashi, Shimpei Ohno, Yu |
| author_facet | Kobayashi, Shimpei Ohno, Yu |
| contents | We study a statistical manifold $(\mathcal{N}, g^F, \nabla^{A}, \nabla^{A*})$ of multivariate normal distributions, where $g^F$ is the Fisher metric and $\nabla^{A}$ is the Amari-Chentsov connection and $\nabla^{A*}$ is its conjugate connection. We will show that it admits a solvable Lie group structure and moreover the Amari-Chentsov connection $\nabla^{A}$ on $(\mathcal{N}, g^F)$ will be characterized by the conjugate symmetry, i.e., a curvatures identity $R=R^*$ of a connection $\nabla$ and its conjugate connection $\nabla^*$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_07471 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A characterization of the alpha-connections on the statistical manifold of multivariate normal distributions Kobayashi, Shimpei Ohno, Yu Differential Geometry We study a statistical manifold $(\mathcal{N}, g^F, \nabla^{A}, \nabla^{A*})$ of multivariate normal distributions, where $g^F$ is the Fisher metric and $\nabla^{A}$ is the Amari-Chentsov connection and $\nabla^{A*}$ is its conjugate connection. We will show that it admits a solvable Lie group structure and moreover the Amari-Chentsov connection $\nabla^{A}$ on $(\mathcal{N}, g^F)$ will be characterized by the conjugate symmetry, i.e., a curvatures identity $R=R^*$ of a connection $\nabla$ and its conjugate connection $\nabla^*$. |
| title | A characterization of the alpha-connections on the statistical manifold of multivariate normal distributions |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2302.07471 |