Monte Carlo with kernel-based Gibbs measures: Guarantees for probabilistic herding

arXiv:2402.11736v1 Announce Type: new
Abstract: Kernel herding belongs to a family of deterministic quadratures that seek to minimize the worst-case integration error over a reproducing kernel Hilbert space (RKHS). In spite of strong experimental support, it has revealed difficult to prove that this worst-case error decreases at a faster rate than the standard square root of the number of quadrature nodes, at least in the usual case where the RKHS is infinite-dimensional. In this theoretical paper, we study a joint …

abstract arxiv case cs.lg error experimental family faster gibbs herding integration kernel math.pr prove rate space stat.ml support type