  The rate of convergence of weighted kernel herding (WKH) and sequential
Bayesian quadrature (SBQ), two kernel-based sampling algorithms for estimating
integrals with respect to some target probability measure, is investigated.
Under verifiable conditions on the chosen kernel and target measure, we
establish a near-geometric rate of convergence for target measures that are
nearly atomic. Furthermore, we show these algorithms perform comparably to the
theoretical best possible sampling algorithm under the maximum mean
discrepancy. An analysis is also conducted in a distributed setting. Our
theoretical developments are supported by empirical observations on simulated
data as well as a real world application.
