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Measure Transport with Kernel Stein Discrepancy

Lookup NU author(s): Matthew Fisher, Dr Matt Graham, Dr Dennis Prangle, Professor Chris Oates

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Abstract

Copyright © 2021 by the author(s). Measure transport underpins several recent algorithms for posterior approximation in the Bayesian context, wherein a transport map is sought to minimise the Kullback-Leibler divergence (KLD) from the posterior to the approximation. The KLD is a strong mode of convergence, requiring absolute continuity of measures and placing restrictions on which transport maps can be permitted. Here we propose to minimise a kernel Stein discrepancy (KSD) instead, requiring only that the set of transport maps is dense in an L2 sense and demonstrating how this condition can be validated. The consistency of the associated posterior approximation is established and empirical results suggest that KSD is a competitive and more flexible alternative to KLD for measure transport.


Publication metadata

Author(s): Fisher MA, Nolan TH, Graham MM, Prangle D, Oates CJ

Publication type: Conference Proceedings (inc. Abstract)

Publication status: Published

Conference Name: 24th International Conference on Artificial Intelligence and Statistics

Year of Conference: 2021

Pages: 1054-1062

Online publication date: 18/03/2021

Acceptance date: 02/04/2021

ISSN: 2640-3498

Publisher: ML Research Press

URL: https://proceedings.mlr.press/v130/fisher21a.html

Series Title: Proceedings of Machine Learning Research


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