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 \(\textrm{e}\) $\text{e}$ -embedding curvature tensor, which identifies partially flat parameters of a DPP. On the basis of this embedding structure, an information-geometrical relationship between a marginal kernel and an L-ensemble kernel is discovered.