# Optimal Quantisation of Probability Measures Using Maximum Mean Discrepancy

Teymur, Onur, Gorham, Jackson, Riabiz, Marina, Oates, Chris J. (2021) Optimal Quantisation of Probability Measures Using Maximum Mean Discrepancy. Proceedings of Machine Learning Research, 130 . pp. 1027-1035. ISSN 2640-3498. (KAR id:90453)

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## Abstract

Several researchers have proposed minimisation of maximum mean discrepancy (MMD) as a method to quantise probability measures, i.e., to approximate a 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 algorithms—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.

Item Type: Article maximum mean discrepancy, probability Q Science > QA Mathematics (inc Computing science) > QA273 Probabilities Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science Onur Teymur 29 Sep 2021 09:16 UTC 11 Oct 2021 16:15 UTC https://kar.kent.ac.uk/id/eprint/90453 (The current URI for this page, for reference purposes)