Perfect Simulation of Determinantal Point Processes

Laurent Decreusefond (1, 2) , Ian Flint (1, 2) , Kah Choon Low (1, 2)

1 LTCI - Laboratoire Traitement et Communication de l'Information
2 Télécom ParisTech

Determinantal point processes (DPP) serve as a practicable modeling for many applications of repulsive point processes. A known approach for simulation was proposed in \cite{Hough(2006)}, which generate the desired distribution point wise through rejection sampling. Unfortunately, the size of rejection could be very large. In this paper, we investigate the application of perfect simulation via coupling from the past (CFTP) on DPP. We give a general framework for perfect simulation on DPP model. It is shown that the limiting sequence of the time-to-coalescence of the coupling is bounded by $$O\left(\int_{E}{J(x,x) d\nu(x)}\log{\int_{E}{J(x,x) d\nu(x)}}\right).$$ An application is given to the stationary models in DPP.

Mots clés: Determinantal point processes; coupling from the past

Domaines: Probabilités [math.PR]; Statistiques [math.ST]; Théorie [stat.TH]; Modélisation et simulation

Laurent Decreusefond, Ian Flint, Kah Choon Low. Perfect Simulation of Determinantal Point Processes. [Research Report] Telecom ParisTech. 2013. ⟨hal-00879101⟩