Nonparametric estimation of continuous determinantal point processes with kernel methods

Nom de l'orateur
Michael Fanuel
Etablissement de l'orateur
Université de Lille
Date et heure de l'exposé
Lieu de l'exposé

Determinantal Point Processes (DPPs) elegantly model repulsive point patterns. A natural problem is the estimation of a DPP given a few samples. Parametric and nonparametric inference methods have been studied in the finite case, i.e. when the point patterns are sampled in a finite ground set. In the continuous case, several parametric methods have been proposed but nonparametric methods have received little attention. In this talk, we discuss a nonparametric approach for continuous DPP estimation leveraging recent advances in kernel methods. We show that a restricted version of this maximum likelihood (MLE) problem falls within the scope of a recent representer theorem for nonnegative functions in a Reproducing Kernel Hilbert Space. This leads to a finite-dimensional problem, with strong statistical ties to the original MLE.