title: Markov Chain Monte Carlo from Lagrangian Dynamics.
abstract: Hamiltonian Monte Carlo (HMC) improves the computational e ciency of the Metropolis-Hastings algorithm by reducing its random walk behavior. Riemannian HMC (RHMC) further improves the performance of HMC by exploiting the geometric properties of the parameter space. However, the geometric integrator used for RHMC involves implicit equations that require fixed-point iterations. In some cases, the computational overhead for solving implicit equations undermines RHMC's benefits. In an attempt to circumvent this problem, we propose an explicit integrator that replaces the momentum variable in RHMC by velocity. We show that the resulting transformation is equivalent to transforming Riemannian Hamiltonian dynamics to Lagrangian dynamics. Experimental results suggests that our method improves RHMC's overall computational e ciency in the cases considered. All computer programs and data sets are available online (http://www.ics.uci.edu/~babaks/Site/Codes.html) in order to allow replication of the results reported in this paper.
authors.affiliation: Department of Statistics, University of California, Irvine, Irvine, CA 92697, USA.
authors.forename: Shiwei
authors.initials: S
authors.lastname: Lan
authors.affiliation: Department of Statistical Science, University College London, London, WC1E 6BT, UK.
authors.forename: Vasileios
authors.initials: V
authors.lastname: Stathopoulos
authors.affiliation: Department of Statistics, University of California, Irvine, Irvine, CA 92697, USA.
authors.forename: Babak
authors.initials: B
authors.lastname: Shahbaba
authors.affiliation: Department of Statistical Science, University College London, London, WC1E 6BT, UK.
authors.forename: Mark
authors.initials: M
authors.lastname: Girolami
keywords: Explicit Integrator; Hamiltonian Monte Carlo; Lagrangian Dynamics; Riemannian Manifold