Name
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 x 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). |
Year | DOI | Venue |
|---|---|---|
2019 | 10.1007/978-3-030-26980-7_18 | GEOMETRIC SCIENCE OF INFORMATION |
Keywords | Field | DocType |
Hamiltonian Monte Carlo, MCMC, Irreversible diffusions, Lie Groups, Geometric mechanics, Langevin dynamics, Sampling | Lie group,Mathematical physics,Dissipation,Symplectic geometry,Hamiltonian system,Symplectic integrator,Ornstein–Uhlenbeck process,Momentum,Statistics,Lie algebra,Mathematics | Conference |
Volume | ISSN | Citations |
11712 | 0302-9743 | 0 |
PageRank | References | Authors |
0.34 | 0 | 3 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Alexis Arnaudon | 1 | 9 | 2.55 |
| Alessandro Barp | 2 | 2 | 2.44 |
| So Takao | 3 | 0 | 0.34 |