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.