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Gibbs flow for approximate transport with applications to Bayesian computation

Heng, J; Doucet, A; Pokern, Y; (2021) Gibbs flow for approximate transport with applications to Bayesian computation. ournal of the Royal Statistical Society Series B (Statistical Methodology) , 83 (1) pp. 156-187. 10.1111/rssb.12404. Green open access

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Abstract

Let π0 and π1 be two distributions on the Borel space (R d , B(R d )). Any measurable function T : R d → R d such that Y = T(X) ∼ π1 if X ∼ π0 is called a transport map from π0 to π1. For any π0 and π1, if one could obtain an analytical expression for a transport map from π0 to π1, then this could be straightforwardly applied to sample from any distribution. One would map draws from an easy-to-sample distribution π0 to the target distribution π1 using this transport map. Although it is usually impossible to obtain an explicit transport map for complex target distributions, we show here how to build a tractable approximation of a novel transport map. This is achieved by moving samples from π0 using an ordinary differential equation with a velocity field that depends on the full conditional distributions of the target. Even when this ordinary differential equation is time-discretized and the full conditional distributions are numerically approximated, the resulting distribution of mapped samples can be efficiently evaluated and used as a proposal within sequential Monte Carlo samplers. We demonstrate significant gains over state-of-the-art sequential Monte Carlo samplers at a fixed computational complexity on a variety of applications.

Type: Article
Title: Gibbs flow for approximate transport with applications to Bayesian computation
Open access status: An open access version is available from UCL Discovery
DOI: 10.1111/rssb.12404
Publisher version: https://doi.org/10.1111/rssb.12404
Language: English
Additional information: This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions.
Keywords: Mass transport; Markov chain Monte Carlo; Normalizing constants; Path Sampling; Sequential Monte Carlo
UCL classification: UCL
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Statistical Science
URI: https://discovery.ucl.ac.uk/id/eprint/10123803
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