The Geometric Foundations of Hamiltonian Monte Carlo
arXiv:1410.5110
Abstract
Although Hamiltonian Monte Carlo has proven an empirical success, the lack of a rigorous theoretical understanding of the algorithm has in many ways impeded both principled developments of the method and use of the algorithm in practice. In this paper we develop the formal foundations of the algorithm through the construction of measures on smooth manifolds, and demonstrate how the theory naturally identifies efficient implementations and motivates promising generalizations.
arXiv comment45 pages, 13 figures
References in corpus (4)
- Hamiltonian Monte Carlo Without Detailed Balance
- Driving Markov chain Monte Carlo with a dependent random stream
- Curvature and Concentration of Hamiltonian Monte Carlo in High Dimensions
- How to view an MCMC simulation as a permutation, with applications to parallel simulation and improved importance sampling
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