  A fundamental problem in Bayesian inference and statistical machine learning
is to efficiently sample from multimodal distributions. Due to metastability,
multimodal distributions are difficult to sample using standard Markov chain
Monte Carlo methods. We propose a new sampling algorithm based on a birth-death
mechanism to accelerate the mixing of Langevin diffusion. Our algorithm is
motivated by its mean field partial differential equation (PDE), which is a
Fokker-Planck equation supplemented by a nonlocal birth-death term. This PDE
can be viewed as a gradient flow of the Kullback-Leibler divergence with
respect to the Wasserstein-Fisher-Rao metric. We prove that under some
assumptions the asymptotic convergence rate of the nonlocal PDE is independent
of the potential barrier, in contrast to the exponential dependence in the case
of the Langevin diffusion. We illustrate the efficiency of the birth-death
accelerated Langevin method through several analytical examples and numerical
experiments.
