Annealed Flow Transport Monte Carlo
This work addresses the challenge of accurate normalizing constant estimation for researchers in computational statistics and machine learning, representing an incremental advancement over existing methods.
The authors tackled the problem of estimating normalizing constants of probability distributions by proposing Annealed Flow Transport (AFT), a Monte Carlo algorithm that combines Annealed Importance Sampling, Sequential Monte Carlo, and normalizing flows, resulting in improved performance demonstrated experimentally on various applications.
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 (NFs) 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 NFs 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 NFs. We demonstrate experimentally the benefits and limitations of our methodology on a variety of applications.