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 ).
CITATION STYLE
Arnaudon, A., Barp, A., & Takao, S. (2019). Irreversible Langevin MCMC on Lie Groups. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 11712 LNCS, pp. 171–179). Springer. https://doi.org/10.1007/978-3-030-26980-7_18
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