Necessary symmetries in non-reversible sampling by Event-Chain Monte Carlo and generalization to non-translational flows

Michel Manon, CNRS, Université Clermont-Auvergne

First developed for particle and spin systems [1], Event-Chain Monte Carlo (ECMC) methods generate continuous-time and non-reversible Markov processes which often display significant accelerations compared to their reversible counterparts [2, 3, 4]. Thanks to the addition of an extra variable v, the generated non-reversible processes consist of ballistic phases, set by v, over the state space up to some event; at an event, the parameter v defining the ballistic trajectory is resampled by some Markov kernel. The scheme then is rejection-free and relies on a control by the events of the ballistic exploration to ensure the correct invariant distribution. Such processes are now analytically described as Piecewise Deterministic Markov Processes (PDMP) and are used well beyond statistical physics as for general Bayesian inference tasks [5, 6]. Their analytical understanding, especially regarding convergence properties, is under a growing interest. In this talk, I will discuss how the control of the ballistic flow at the events has first been under much focus (e.g. generalization of pairwise to n-body or any interactions [7, 8]), while the development of alternative ballistic flows beyond standard translational updates has received smaller attention [9]. Such flows are, however, necessary for irreducibility in the case of anisotropic particles. I will then distinctly define the essential symmetries that such ECMC algorithms must adhere to, differentiating between necessary and sufficient conditions. This analysis [10] leads to the establishment of the necessary rotational invariance of the probability flows and of the minimum event rate. This rate identifies with the corresponding infinitesimal Metropolis rejection rate. It leads to the definition of two classes of interest of general flows: the ideal and uniform-ideal flows, that respectively suppresses or reduces the minimum event rate. Finally, I will present a comprehensive non-reversible sampling of a systems of hard dimers by introducing rotational flows, which are uniform-ideal. This implementation results in a speed-up of up to ∼ 3 compared to the state-of-the-art ECMC/Metropolis hybrid scheme.

Area: CS35 - Monte Carlo methods and Applications I (Francesca R Crucinio, Alessandra Iacobucci, Andrea Bertazzi)

Keywords: Event-Chain Monte Carlo; Piecewise Deterministic Markov Processes; Statistical Physics; Particle Systems; Anisotropic Particles; Dimers

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