Recycling intermediate steps to improve Hamiltonian Monte Carlo
arXiv:1511.06925 · doi:10.1214/19-BA1171
Abstract
Hamiltonian Monte Carlo (HMC) and related algorithms have become routinely used in Bayesian computation. In this article, we present a simple and provably accurate method to improve the efficiency of HMC and related algorithms with essentially no extra computational cost. This is achieved by {recycling the intermediate states along simulated trajectories of Hamiltonian dynamics. Standard algorithms use only the end points of trajectories, wastefully discarding all the intermediate states. Compared to the alternative methods for utilizing the intermediate states, our algorithm is simpler to apply in practice and requires little programming effort beyond the usual implementations of HMC and related algorithms. Our algorithm applies straightforwardly to the no-U-turn sampler, arguably the most popular variant of HMC. Through a variety of experiments, we demonstrate that our recycling algorithm yields substantial computational efficiency gains.
22 pages, 16 figures (+ Supplement 6 pages, 4 figures)
References in corpus (6)
- On the Geometric Ergodicity of Hamiltonian Monte Carlo
- Rapid Mixing of Hamiltonian Monte Carlo on Strongly Log-Concave Distributions
- Compressible Generalized Hybrid Monte Carlo
- Adaptive Hamiltonian and Riemann Manifold Monte Carlo Samplers
- Towards Unifying Hamiltonian Monte Carlo and Slice Sampling
- Recycling intermediate steps to improve Hamiltonian Monte Carlo