Collective Proposal Distributions for Nonlinear MCMC samplers: Mean-Field Theory and Fast Implementation

Over the last decades, various "non-linear" MCMC methods have arised. While appealing for their convergence speed and efficiency, their practical implementation and theoretical study remain challenging. In this paper, we introduce a large class of non-linear samplers that can be studied and simulated as the mean-field limit of a system of interacting particles. The practical implementation we propose leverages the computational power of modern hardware (GPU).