2019

Accelerated Information Gradient flow

Wang, Yifei, Li, Wuchen

Understand

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.

Built on

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