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The geometric foundations of Hamiltonian Monte Carlo
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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.
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Inferring kinetic parameters of oscillatory gene regulation from single cell time-series data
Burton, J., Manning, C. S., Rattray, M., Papalopulu, N., & Kursawe, J. (2021) · Journal of The Royal Society Interface · doi:10.1098/rsif.2021.0393 · Cited by 9
Zhou, S., & Li, Q. (2025) · Scientific Reports · doi:10.1038/s41598-025-31685-9
“…adjust computational budgets: computed via adaptive Runge-Kutta methods with tolerance ϵ tol that balances gradient accuracy and computation cost 45 ( ) , while stability is ensured through spectral norm regularization that constrains the maximum eigenvalue of the Jacobian ∂f ∂h to remain below…”
Metadata
- Authors
- Betancourt, M., Byrne, S., Livingstone, S., & Girolami, M.
- Venue
- Bernoulli
- Published
- 2017-11-01
- Volume
- 23
- Issue
- 4A
- Pages
- 2257-2298
- ISSN
- 1350-7265 (ISSN-L)
- OpenAlex
- W2962703949
- Cited by
- 452
- References
- 53
- FWCI
- 22.24
- Type
- journal article
- Language
- en
- Open access
- green
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