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 $\mathcal G$ and dissipation fields compatible with the symplectic structure, we construct an irreversible HMC-like MCMC algorithm on $\mathcal G$, where we first update the momentum by solving an OU process on the corresponding Lie algebra $\mathfrak g$, and then approximate the Hamiltonian system on $\mathcal G \times \mathfrak g$ 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 $\mathcal G = SO(3)$.
- Publication:
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arXiv e-prints
- Pub Date:
- March 2019
- DOI:
- 10.48550/arXiv.1903.08939
- arXiv:
- arXiv:1903.08939
- Bibcode:
- 2019arXiv190308939A
- Keywords:
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- Mathematics - Statistics Theory;
- Mathematics - Differential Geometry