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