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

Determinantal Point Process (DPP) is a flexible family of distributions for random sets defined on the finite state space { 1, ...,d }, or equivalently for multivariate binary variables. This family is parameterized by either the L-ensemble kernel Σ, which is symmetric positive definite (SPD), or the correlation kernel matrix K, which is SPD, with eigenvalues lying strictly between 0 and 1. The literature has considered the maximum likelihood estimation (MLE) of Σ and K or its algorithmic analogues (Affandi et al., 2014; Brunel et al., 2017a,b), but it has since been shown that i) the likelihood function has at least 2