Irreversible Langevin MCMC on Lie Groups

Abstract

It is well-known that irreversible MCMC algorithms converge faster to their stationary distributions than reversible ones. Using the special geometric structure of Lie groups G and dissipation fields compatible with the symplectic structure, we construct an irreversible HMC-like MCMC algorithm on G, where we first update the momentum by solving an OU process on the corresponding Lie algebra g, and then approximate the Hamiltonian system on G × g with a reversible symplectic integrator followed by a Metropolis-Hastings correction step. In particular, when the OU process is simulated over sufficiently long times, we recover HMC as a special case. We illustrate this algorithm numerically using the example G = SO(3).