Annealed Importance Sampling (AIS) and its Sequential Monte Carlo (SMC) extensions are state-of-the-art methods for estimating normalizing constants of probability distributions. We propose here a novel Monte Carlo algorithm, Annealed Flow Transport (AFT), that builds upon AIS and SMC and combines them with normalizing flows (NF) for improved performance. This method transports a set of particles using not only importance sampling (IS), Markov chain Monte Carlo (MCMC) and resampling steps - as in SMC, but also relies on NF which are learned sequentially to push particles towards the successive annealed targets. We provide limit theorems for the resulting Monte Carlo estimates of the normalizing constant and expectations with respect to the target distribution. Additionally, we show that a continuous-time scaling limit of the population version of AFT is given by a Feynman--Kac measure which simplifies to the law of a controlled diffusion for expressive NF. We demonstrate experimentally the benefits and limitations of our methodology on a variety of applications.

本文提出了一种新的蒙特卡罗算法Annealed Flow Transport (AFT)，它 结合使用了Annealed Importance Sampling (AIS)、Sequential Monte Carlo (SMC)和normalizing flows (NFs)，可以更准确地估计概率分布的归一化常数和与目标分布有关的期望值。

退火流输运蒙特卡罗