Convergence of Kinetic Langevin Monte Carlo on Lie groups

arXiv:2403.12012v1 Announce Type: cross
Abstract: Explicit, momentum-based dynamics for optimizing functions defined on Lie groups was recently constructed, based on techniques such as variational optimization and left trivialization. We appropriately add tractable noise to the optimization dynamics to turn it into a sampling dynamics, leveraging the advantageous feature that the momentum variable is Euclidean despite that the potential function lives on a manifold. We then propose a Lie-group MCMC sampler, by delicately discretizing the resulting kinetic-Langevin-type sampling dynamics. The Lie …

abstract arxiv convergence cs.lg cs.na dynamics feature functions math.na math.pr math.st noise optimization sampling stat.ml stat.th tractable type