We introduce a mean-field ODE and corresponding interacting particle systems (IPS) for sampling, based on kernel approximations of Fisher–Rao gradient flow. Simulating these IPS requires no gradients of the target density; we only need the ability to sample from a chosen reference distribution and to compute the unnormalized target-to-reference density ratio. The mean-field ODE is obtained by kernelizing the solution of a weighted Poisson equation for a velocity potential that realizes a tractable path between the reference and target densities---for instance, the geometric mixture of the reference and target, which is the path of a particular Fisher–Rao gradient flow. This system can then be discretized over finite samples.
We demonstrate that the resulting IPS can produce high-quality samples from varied target distributions, and highlight progress in several open design questions underlying these methods: selecting effective kernels and random feature approximations; localization in high-dimensional problems; and choosing a “good” path and schedule along this path.
Copyright. All Rights Reserved.