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Optimal Quantisation of Probability Measures Using Maximum Mean Discrepancy

Lookup NU author(s): Dr Onur Teymur, Professor Chris OatesORCiD

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Abstract

Copyright © 2021 by the author(s)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.

Publication metadata

Author(s): Teymur O, Gorham J, Riabiz M, Oates CJ

Publication type: Conference Proceedings (inc. Abstract)

Publication status: Published

Conference Name: International Conference on Artificial Intelligence and Statistics (AISTATS)

Year of Conference: 2021

Pages: 1027-1035

Acceptance date: 02/04/2021

Publisher: ML Research Press

URL: http://proceedings.mlr.press/v130/teymur21a.html

Series Title: Proceedings of Machine Learning Research

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