DeepAI AI Chat
Log In Sign Up

Nonreversible MCMC from conditional invertible transforms: a complete recipe with convergence guarantees

by   Achille Thin, et al.

Markov Chain Monte Carlo (MCMC) is a class of algorithms to sample complex and high-dimensional probability distributions. The Metropolis-Hastings (MH) algorithm, the workhorse of MCMC, provides a simple recipe to construct reversible Markov kernels. Reversibility is a tractable property that implies a less tractable but essential property here, invariance. Reversibility is however not necessarily desirable when considering performance. This has prompted recent interest in designing kernels breaking this property. At the same time, an active stream of research has focused on the design of novel versions of the MH kernel, some nonreversible, relying on the use of complex invertible deterministic transforms. While standard implementations of the MH kernel are well understood, the aforementioned developments have not received the same systematic treatment to ensure their validity. This paper fills the gap by developing general tools to ensure that a class of nonreversible Markov kernels, possibly relying on complex transforms, has the desired invariance property and leads to convergent algorithms. This leads to a set of simple and practically verifiable conditions.


page 1

page 2

page 3

page 4


Long-Time Convergence and Propagation of Chaos for Nonlinear MCMC

In this paper, we study the long-time convergence and uniform strong pro...

Multiple projection MCMC algorithms on submanifolds

We propose new Markov Chain Monte Carlo algorithms to sample probability...

Peskun-Tierney ordering for Markov chain and process Monte Carlo: beyond the reversible scenario

Historically time-reversibility of the transitions or processes underpin...

Variational MCMC

We propose a new class of learning algorithms that combines variational ...

Fourier transform MCMC, heavy tailed distributions and geometric ergodicity

Markov Chain Monte Carlo methods become increasingly popular in applied ...

Automating Involutive MCMC using Probabilistic and Differentiable Programming

Involutive MCMC is a unifying mathematical construction for MCMC kernels...