A heuristic independent particle approximation to determinantal point processes

TL;DR

This paper introduces a heuristic approximation method for determinantal point processes inspired by fermion physics, enabling fast sampling with minimal computational cost, useful for machine learning applications.

Contribution

It proposes a novel independent particle approximation for determinantal point processes based on physical intuition, simplifying sampling procedures.

Findings

Sampling cost is significantly reduced.

Numerical experiments demonstrate effective approximation.

Method is easy to implement with standard linear algebra routines.

Abstract

A determinantal point process is a stochastic point process that is commonly used to capture negative correlations. It has become increasingly popular in machine learning in recent years. Sampling a determinantal point process however remains a computationally intensive task. This note introduces a heuristic independent particle approximation to determinantal point processes. The approximation is based on the physical intuition of fermions and is implemented using standard numerical linear algebra routines. Sampling from this independent particle approximation can be performed at a negligible cost. Numerical results are provided to demonstrate the performance of the proposed algorithm.