Belhadji, Ayoub (1994-....)

We study approximation problems in reproducing kernel Hilbert spaces (RKHS) using random nodes. More precisely, we focus on kernel quadrature and kernel interpolation for smooth functions living in an RKHS using nodes that follow the distribution of a determinantal point process (DPP) tailored to the RKHS. We prove fast convergence rates that depend on the eigenvalues of the RKHS kernel. This unified analysis gives new insights on the rates of the quadratures and interpolations based on DPPs, especially for high dimensional numerical integration problems.