  Several researchers have proposed minimisation of maximum mean discrepancy
(MMD) as a method to quantise probability measures, i.e., to approximate a
target distribution by a representative point set. We consider sequential
algorithms that greedily minimise MMD over a discrete candidate set. We propose
a novel non-myopic algorithm and, in order to both improve statistical
efficiency and reduce computational cost, we investigate a variant that applies
this technique to a mini-batch of the candidate set at each iteration. When the
candidate points are sampled from the target, the consistency of these new
algorithm - and their mini-batch variants - is established. We demonstrate the
algorithms on a range of important computational problems, including
optimisation of nodes in Bayesian cubature and the thinning of Markov chain
output.
