A Conceptual Introduction to Hamiltonian Monte Carlo
@article{Betancourt2017ACI, title={A Conceptual Introduction to Hamiltonian Monte Carlo}, author={Michael Betancourt}, journal={arXiv: Methodology}, year={2017} }
Hamiltonian Monte Carlo has proven a remarkable empirical success, but only recently have we begun to develop a rigorous understanding of why it performs so well on difficult problems and how it is best applied in practice. Unfortunately, that understanding is confined within the mathematics of differential geometry which has limited its dissemination, especially to the applied communities for which it is particularly important. In this review I provide a comprehensive conceptual account of…
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678 Citations
Geometry and Dynamics for Markov Chain Monte Carlo
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The aim of this review is to provide a comprehensive introduction to the geometric tools used in Hamiltonian Monte Carlo at a level accessible to statisticians, machine learners, and other users of the methodology with only a basic understanding of Monte Carlo methods.
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The aim of this review is to provide a comprehensive introduction to the geometric tools used in Hamiltonian Monte Carlo at a level accessible to statisticians, machine learners and other users of the methodology with only a basic understanding of Monte Carlo methods.
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Probabilistic Path HMC (PPHMC) is developed as a first step to sampling distributions on spaces with intricate combinatorial structure, and a surrogate function to ease the transition across a boundary on which the log-posterior has discontinuous derivatives can greatly improve efficiency.
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A theoretical basis for the use of non-canonical Hamiltonian dynamics in MCMC is established, and a symplectic, leapfrog-like integrator is constructed allowing for the implementation of magnetic HMC.
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- 2020
The aim is to develop a framework making establishing correctness of complex Markov chain Monte Carlo kernels a purely mechanical or algebraic exercise, while making communication of ideas simpler and unambiguous by allowing a stronger focus on essential features of the kernels.
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Hamiltonian Dynamics Monte Carlo is a popular method used in simulating complicated distribution. The performance of HMC highly depends on geometry of the momentum-state dual space; we investigate…
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A General Metric for Riemannian Hamiltonian Monte Carlo Michael Betancourt University College London August 30th, 2013 I’m going to talk about probability and geometry, but not information geometry!…