  Hamiltonian Monte Carlo (HMC) improves the computational efficiency of the
Metropolis algorithm by reducing its random walk behavior. Riemannian Manifold
HMC (RMHMC) further improves HMC's performance by exploiting the geometric
properties of the parameter space. However, the geometric integrator used for
RMHMC involves implicit equations that require costly numerical analysis (e.g.,
fixed-point iteration). In some cases, the computational overhead for solving
implicit equations undermines RMHMC's benefits. To avoid this problem, we
propose an explicit geometric integrator that replaces the momentum variable in
RMHMC by velocity. We show that the resulting transformation is equivalent to
transforming Riemannian Hamilton dynamics to Lagrangian dynamics. Experimental
results show that our method improves RMHMC's overall computational efficiency.
All computer programs and data sets are available online
(http://www.ics.uci.edu/~babaks/Site/Codes.html) in order to allow replications
of the results reported in this paper.
