Duality induced by an embedding structure of determinantal point process
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866916210109579264 |
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| author | Hino, Hideitsu Yano, Keisuke |
| author_facet | Hino, Hideitsu Yano, Keisuke |
| contents | This paper investigates the information geometrical structure of a determinantal point process (DPP). It demonstrates that a DPP is embedded in the exponential family of log-linear models. The extent of deviation from an exponential family is analyzed using the $\mathrm{e}$-embedding curvature tensor, which identifies partially flat parameters of a DPP. On the basis of this embedding structure, the duality related to a marginal kernel and an $L$-ensemble kernel is discovered. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_11024 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Duality induced by an embedding structure of determinantal point process Hino, Hideitsu Yano, Keisuke Statistics Theory Information Theory Machine Learning This paper investigates the information geometrical structure of a determinantal point process (DPP). It demonstrates that a DPP is embedded in the exponential family of log-linear models. The extent of deviation from an exponential family is analyzed using the $\mathrm{e}$-embedding curvature tensor, which identifies partially flat parameters of a DPP. On the basis of this embedding structure, the duality related to a marginal kernel and an $L$-ensemble kernel is discovered. |
| title | Duality induced by an embedding structure of determinantal point process |
| topic | Statistics Theory Information Theory Machine Learning |
| url | https://arxiv.org/abs/2404.11024 |