Gibbs Flow for Approximate Transport with Applications to Bayesian Computation
提出一种通过常微分方程和全条件分布构建近似传输映射的方法，将易采样分布映射到复杂目标分布，并作为序贯蒙特卡洛采样器的提议分布，在固定计算复杂度下显著提升性能。
Abstract Let π0 and π1 be two distributions on the Borel space (Rd,B(Rd)). Any measurable function T:Rd→Rd 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-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.