Nonparametric estimation of continuous determinantal point processes with kernel methods
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.