Super-Samples from Kernel Herding

Abstract

We extend the herding algorithm to continuous spaces by using the kernel trick. The resulting "kernel herding" algorithm is an infinite memory deterministic process that learns to approximate a PDF with a collection of samples. We show that kernel herding decreases the error of expectations of functions in the Hilbert space at a rate O(1/T) which is much faster than the usual O(1/pT) for iid random samples. We illustrate kernel herding by approximating Bayesian predictive distributions.