Super-Samples from Kernel Herding

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 rateO(1/T) which is much faster than the usual O(1 / √ T) for iid random samples. We illustrate kernel herding by approximating Bayesian predictive distributions. 1

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