Perfect Simulation of Determinantal Point Processes

TL;DR

This paper introduces a perfect simulation method for determinantal point processes using coupling from the past, providing a more efficient alternative to rejection sampling, with theoretical bounds on coalescence time.

Contribution

It develops a general framework for perfect simulation of DPPs via CFTP, including bounds on coalescence time and applications to stationary models.

Findings

Bound on coalescence time: $K|b1| log K|b1|$

Framework applicable to stationary DPP models

Improves simulation efficiency over rejection sampling

Abstract

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 $K|\Lambda|\log K|\Lambda|$. An application is given to the stationary models in DPP.