Introducing an Explicit Symplectic Integration Scheme for Riemannian Manifold Hamiltonian Monte Carlo
This work addresses efficiency issues for practitioners using RMHMC in Bayesian inference, though it is incremental as it provides an alternative to existing integrators.
The paper tackles the computational burden of Riemannian manifold Hamiltonian Monte Carlo (RMHMC) by introducing an explicit symplectic integration scheme that reduces the number of higher-order derivative calculations per leapfrog step, demonstrating efficacy in reducing computational costs.
We introduce a recent symplectic integration scheme derived for solving physically motivated systems with non-separable Hamiltonians. We show its relevance to Riemannian manifold Hamiltonian Monte Carlo (RMHMC) and provide an alternative to the currently used generalised leapfrog symplectic integrator, which relies on solving multiple fixed point iterations to convergence. Via this approach, we are able to reduce the number of higher-order derivative calculations per leapfrog step. We explore the implications of this integrator and demonstrate its efficacy in reducing the computational burden of RMHMC. Our code is provided in a new open-source Python package, hamiltorch.