Gibbs flow for approximate transport with applications to Bayesian computation

Abstract

Letandbe two distributions on the Borel space. Any measurable functionsuch thatifis called a transport map fromto. For anyand, if one could obtain an analytical expression for a transport map fromto, then this could be straightforwardly applied to sample from any distribution. One would map draws from an easy-to-sample distributionto the target distributionusing 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 fromusing 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-discretised 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.