An embedding structure of determinantal point process

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 $$\textrm{e}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mtext>e</mml:mtext> </mml:math> -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.