Continual Repeated Annealed Flow Transport Monte Carlo
This work addresses the problem of efficient and accurate sampling for researchers in computational statistics and machine learning, though it appears incremental as it builds directly on prior methods.
The authors tackled the problem of improving sampling methods in machine learning by proposing CRAFT, which combines sequential Monte Carlo with variational inference using normalizing flows, and demonstrated that it outperforms existing methods like Annealed Flow Transport Monte Carlo and Stochastic Normalizing Flows on challenging examples, achieving impressively accurate results in a lattice field theory case.
We propose Continual Repeated Annealed Flow Transport Monte Carlo (CRAFT), a method that combines a sequential Monte Carlo (SMC) sampler (itself a generalization of Annealed Importance Sampling) with variational inference using normalizing flows. The normalizing flows are directly trained to transport between annealing temperatures using a KL divergence for each transition. This optimization objective is itself estimated using the normalizing flow/SMC approximation. We show conceptually and using multiple empirical examples that CRAFT improves on Annealed Flow Transport Monte Carlo (Arbel et al., 2021), on which it builds and also on Markov chain Monte Carlo (MCMC) based Stochastic Normalizing Flows (Wu et al., 2020). By incorporating CRAFT within particle MCMC, we show that such learnt samplers can achieve impressively accurate results on a challenging lattice field theory example.