Optimal transport between determinantal point processes and application to fast simulation

TL;DR

This paper studies optimal transportation between determinantal point processes (DPPs), providing methods to estimate distribution distances and applying these to improve the speed and scale of DPP simulation.

Contribution

It introduces new techniques for estimating distances between DPP distributions and demonstrates a fast simulation algorithm capable of handling over ten thousand points.

Findings

Effective distance estimation between DPPs

Fast simulation algorithm for large-scale DPPs

Simulation of over ten thousand points in reasonable time

Abstract

We analyze several optimal transportation problems between de-terminantal point processes. We show how to estimate some of the distances between distributions of DPP they induce. We then apply these results to evaluate the accuracy of a new and fast DPP simulation algorithm. We can now simulate in a reasonable amount of time more than ten thousands points.