  Determinantal Point Process (DPPs) are statistical models for repulsive point
patterns. Both sampling and inference are tractable for DPPs, a rare feature
among models with negative dependence that explains their popularity in machine
learning and spatial statistics. Parametric and nonparametric inference methods
have been proposed in the finite case, i.e. when the point patterns live in a
finite ground set. In the continuous case, only parametric methods have been
investigated, while nonparametric maximum likelihood for DPPs -- an
optimization problem over trace-class operators -- has remained an open
question. In this paper, 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 an RKHS. This leads to a finite-dimensional
problem, with strong statistical ties to the original MLE. Moreover, we
propose, analyze, and demonstrate a fixed point algorithm to solve this
finite-dimensional problem. Finally, we also provide a controlled estimate of
the correlation kernel of the DPP, thus providing more interpretability.
