Fisher, Matthew A;
Nolan, Tui;
Graham, Matthew M;
Prangle, Dennis;
Oates, Chris J;
(2021)
Measure Transport with Kernel Stein Discrepancy.
In:
Proceedings of the 24th International Conference on Artificial Intelligence and Statistics.
(pp. pp. 1054-1062).
PMLR
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Abstract
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 $L^2$ 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 competitive and more flexible alternative to KLD for measure transport.
| Type: | Proceedings paper |
|---|---|
| Title: | Measure Transport with Kernel Stein Discrepancy |
| Event: | Artificial Intelligence and Statistics |
| Open access status: | An open access version is available from UCL Discovery |
| Publisher version: | https://proceedings.mlr.press/v130/fisher21a.html |
| Language: | English |
| Additional information: | This version is the version of record. For information on re-use, please refer to the publisher's terms and conditions. |
| UCL classification: | UCL |
| URI: | https://discovery-pp.ucl.ac.uk/id/eprint/10166611 |
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