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arXiv · 2010.07064

Optimal quantisation of probability measures using maximum mean discrepancy

Onur Teymur·Jackson Gorham·Marina Riabiz·Chris. J. Oates
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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 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.

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Onur Teymur, Jackson Gorham, Marina Riabiz, Chris. J. Oates. 2021-02-12. Optimal quantisation of probability measures using maximum mean discrepancy. https://arxiv.org/abs/2010.07064

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