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Accelerated Information Gradient Flow

Authors :
Yifei Wang
Wuchen Li
Source :
Journal of Scientific Computing. 90
Publication Year :
2021
Publisher :
Springer Science and Business Media LLC, 2021.

Abstract

We present a framework for Nesterov's accelerated gradient flows in probability space to design efficient mean-field Markov chain Monte Carlo (MCMC) algorithms for Bayesian inverse problems. Here four examples of information metrics are considered, including Fisher-Rao metric, Wasserstein-2 metric, Kalman-Wasserstein metric and Stein metric. For both Fisher-Rao and Wasserstein-2 metrics, we prove convergence properties of accelerated gradient flows. In implementations, we propose a sampling-efficient discrete-time algorithm for Wasserstein-2, Kalman-Wasserstein and Stein accelerated gradient flows with a restart technique. We also formulate a kernel bandwidth selection method, which learns the gradient of logarithm of density from Brownian-motion samples. Numerical experiments, including Bayesian logistic regression and Bayesian neural network, show the strength of the proposed methods compared with state-of-the-art algorithms.

Details

ISSN :
15737691 and 08857474
Volume :
90
Database :
OpenAIRE
Journal :
Journal of Scientific Computing
Accession number :
edsair.doi.dedup.....d382de8b3b06dee66fff8b33219541af