CSE Community Seminar

We examine determinantal point processes (DPPs), which are probabilistic models of repulsive particles, through the lens of approximation theory. Our study begins by analyzing the convergence of DPP-based quadrature rules tailored for a particular reproducing kernel Hilbert space (RKHS). We then explore the approximation of square-integrable functions from a finite number of evaluations using various finite-dimensional constructions. For both problems, we establish fast convergence rates that depend on the smoothness of the function. Moreover, we demonstrate how DPPs generalize i.i.d. sampling from the Christoffel function, which is standard in the literature. In particular, we explore the connections between DPPs and established frameworks in approximation theory, such as Quasi Monte Carlo methods and Gaussian quadrature. This work offers a unified framework for the approximation of integrals and functions across arbitrary domains.