Accelerated Information Gradient Flow

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