Nonlinear MCMC for Bayesian Machine Learning

TL;DR

This paper applies a nonlinear MCMC method to Bayesian machine learning, providing convergence guarantees and demonstrating its effectiveness on complex sampling tasks like Bayesian neural networks on CIFAR10.

Contribution

It introduces a convergence-guaranteed nonlinear MCMC approach tailored for Bayesian machine learning applications.

Findings

Proven convergence in total variation for the nonlinear MCMC method.

Successful application to Bayesian neural networks on CIFAR10.

Enhanced sampling efficiency in high-dimensional Bayesian models.

Abstract

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.