A simple estimator of the correlation kernel matrix of a determinantal point process

TL;DR

This paper introduces a simple, closed-form estimator for the correlation kernel matrix of a determinantal point process, facilitating easier implementation and initialization for learning algorithms.

Contribution

It provides a novel, easy-to-compute estimator for the DPP kernel, with proven consistency, asymptotic normality, and large deviation properties.

Findings

Estimator is consistent and asymptotically normal.

Can be used as a starting point for maximum likelihood learning.

Simplifies the implementation of DPP models.

Abstract

The Determinantal Point Process (DPP) is a parameterized model for multivariate binary variables, characterized by a correlation kernel matrix. This paper proposes a closed form estimator of this kernel, which is particularly easy to implement and can also be used as a starting value of learning algorithms for maximum likelihood estimation. We prove the consistency and asymptotic normality of our estimator, as well as its large deviation properties.