Let π0 and π1 be two probability measures on R d , equipped with the Borel σ-algebra is called a transport map from π0 to π1. If for any π0 and π1, 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 whose drift is a function of the full conditional distributions of the target. Even when this ordinary differential equation is time-discretized and the full conditional distributions are approximated numerically, the resulting distribution of the mapped samples can be evaluated and used as a proposal within Markov chain Monte Carlo and sequential Monte Carlo schemes. We show experimentally that it can improve significantly performance of state-of-the-art sequential Monte Carlo methods for a fixed computational complexity.
In particular, REF defines an approximation of the KR rearrangement between an input and a target measure via the solution of an ODE whose drift term depends only on the full conditionals of the target distribution.
Gibbs flow for approximate transport with applications to Bayesian computation
arXiv: Computation
Mathematics