Orbital MCMC

10/15/2020

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by   Kirill Neklyudov, et al.

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Markov Chain Monte Carlo (MCMC) is a computational approach to fundamental problems such as inference, integration, optimization, and simulation. Recently, the framework (Involutive MCMC) was proposed describing a large body of MCMC algorithms via two components: a stochastic acceptance test and an involutive deterministic function. This paper demonstrates that this framework is a special case of a larger family of algorithms operating on orbits of continuous deterministic bijections. We describe this family by deriving a novel MCMC kernel, which we call orbital MCMC (oMCMC). We provide a theoretical analysis and illustrate its utility using simple examples.