A simple estimator of the correlation kernel matrix of a determinantal point process
Christian Gouriéroux, Yang Lu
TL;DR
This work tackles the challenge of estimating the correlation kernel $K$ of a determinantal point process (DPP) on a finite state space. It introduces a closed-form estimator $K^*$ that, under mild identifiability assumptions, is consistent and asymptotically normal for the pseudo-true kernel within the identified set arising from $D$-similarity. The key innovation is that all model-identifying information can be recovered from low-order principal minors (orders 1–3), enabling a practical, fast estimator that can serve as a stand-alone method or as a reliable initializer for MLE-based learning, with rigorous large-deviation guarantees. The paper also discusses constrained DPP models, comparing with prior literature, and provides extensions to special irreducibility cases and a detailed large-deviation analysis, highlighting improved theoretical guarantees and computational efficiency for DPP kernel learning.
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.