We explore the application of a nonlinear MCMC technique first introduced in [1] to problems in Bayesian machine learning. We provide a convergence guarantee in total variation that uses novel results for long-time convergence and large-particle (``propagation of chaos'') convergence. We apply this nonlinear MCMC technique to sampling problems including a Bayesian neural network on CIFAR10.

We explore the application of a nonlinear MCMC technique first introduced in [1] to problems in Bayesian machine learning. We provide a convergence guarantee in total variation that uses novel results for long-time convergence and large-particle ( propagation of chaos'') convergence. We apply this nonlinear MCMC technique to sampling problems including a Bayesian neural network on CIFAR10.

In this paper, we study the long-time convergence and uniform strong propagation of chaos for a class of nonlinear Markov chains for Markov chain Monte Carlo (MCMC). Our technique is quite simple, making use of recent contraction estimates for linear Markov kernels and basic techniques from Markov theory and analysis. Moreover, the same proof strategy applies to both the long-time convergence and propagation of chaos. We also show, via some experiments, that these nonlinear MCMC techniques are viable for use in real-world high-dimensional inference such as Bayesian neural networks.