Accelerate Sampling Using Birth-Death Dynamics

In this talk, I will discuss the birth-death dynamics for sampling multimodal probability distributions, which is the spherical Hellinger gradient flow of relative entropy. The advantage of the birth-death dynamics is that, unlike any local dynamics such as Langevin dynamics, it allows global movement of mass directly from one mode to another, without the difficulty of going through low probability regions. We prove that the birth death dynamics converges to the unique invariant measure with a uniform rate under some mild conditions, showing its potential of overcoming metastability. We will also show that on torus, the kernelized dynamics, which is used for numerical simulation, Gamma-converges to the idealized dynamics as the kernel bandwidth shrinks to zero. Joint work with Yulong Lu (UMass Amherst) and Dejan Slepcev (CMU).