Duality induced by an embedding structure of determinantal point process

Hideitsu Hino; Keisuke Yano

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arXiv · 2404.11024

Duality induced by an embedding structure of determinantal point process

Hideitsu Hino·Keisuke Yano

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Abstract

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.

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Hideitsu Hino, Keisuke Yano. 2024-04-17. Duality induced by an embedding structure of determinantal point process. https://arxiv.org/abs/2404.11024

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