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

Christian Gouri\'eroux; Yang Lu

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

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arxiv 2505.14529 v1 pith:4OMCQ74R submitted 2025-05-20 stat.ML cs.LG

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

Christian Gouri\'eroux , Yang Lu This is my paper

classification stat.ML cs.LG

keywords estimatorkernelcorrelationdeterminantalmatrixpointprocessalgorithms

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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.

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Determinantal Point Process Approximation under Positive and Negative Dependence
math.ST 2026-07 accept novelty 7.0

For weakly positively associated targets the independent product is globally optimal among all DPP approximations, while disjoint negatively correlated pairs guarantee a strict improvement over independence.