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About this paper
Alessandro Barp, Francois-Xavier Briol, Anthony D. Kennedy, Mark Girolami
This paper offers a comprehensive review of Hamiltonian Monte Carlo (HMC), detailing its geometric and physical foundations, and explaining how these principles enable efficient high-dimensional sampling. The review clarifies the theoretical underpinnings of advanced HMC variants and current research directions, aiming to bridge the knowledge gap for applied scientists.
Key insights
- HMC's efficiency in high-dimensional sampling is attributed to its simulation of Hamiltonian dynamics, which generates proposals along contours of constant energy, efficiently exploring probability regions.
- Symplectic integrators are crucial for HMC, as they preserve the essential properties of Hamiltonian dynamics (e.g., volume preservation, time-reversibility) necessary for satisfying the detailed balance condition.
- Advanced methods like RMHMC leverage the target density's local geometry through position-dependent Riemannian metrics to adapt proposal generation, while SHMC improves acceptance rates by sampling from a distribution related to a shadow Hamiltonian.
Summary by alphaXiv.
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