Duality induced by an embedding structure of determinantal point process
<|reference_start|>Duality induced by an embedding structure of determinantal point process: 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.<|reference_end|>
@article{hino2024duality,
    title={Duality induced by an embedding structure of determinantal point process},
    author={Hideitsu Hino, Keisuke Yano},
    journal={arXiv preprint arXiv:2404.11024},
    year={2024},
    archivePrefix={arXiv},
    eprint={2404.11024},
    primaryClass={math.ST cs.IT math.IT stat.ML stat.TH}
}