Continual Repeated Annealed Flow Transport Monte Carlo
Alex Matthews, Michael Arbel, Danilo Jimenez Rezende, Arnaud Doucet
Abstract
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.
BibTeX
@InProceedings{pmlr-v162-matthews22a,
title = {Continual Repeated Annealed Flow Transport {M}onte {C}arlo},
author = {Matthews, Alex and Arbel, Michael and Rezende, Danilo Jimenez and Doucet, Arnaud},
booktitle = {Proceedings of the 39th International Conference on Machine Learning},
pages = {15196--15219},
year = {2022},
editor = {Chaudhuri, Kamalika and Jegelka, Stefanie and Song, Le and Szepesvari, Csaba and Niu, Gang and Sabato, Sivan},
volume = {162},
series = {Proceedings of Machine Learning Research},
month = {17--23 Jul},
publisher = {PMLR},
pdf = {https://proceedings.mlr.press/v162/matthews22a/matthews22a.pdf},
url = {https://proceedings.mlr.press/v162/matthews22a.html},
abstract = {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.}
}