mlsanityData to 14 Oct 2026

The Geometric Foundations of Hamiltonian Monte Carlo

arXiv 1410.5110 ↗First posted 19 Oct 2014stat.MEcited by 19

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Abstract (arXiv)

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.

Key facts. Cited by 19 papers in the map (data through 14 Oct 2026). First posted on arXiv 19 Oct 2014.

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2021: 4; 2022: 5; 2023: 3; 2024: 5; 2025: 1; 2026: 1.

19 papers.

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  1. 2021MCMC Variational Inference via Uncorrected Hamiltonian Annealingcited by 39
  2. 2023Conditional Optimal Transport on Function Spacescited by 26
  3. 2021A Survey of Monte Carlo Methods for Parameter Estimationcited by 23
  4. 2024Energy based diffusion generator for efficient sampling of Boltzmann distributionscited by 7
  5. 2022Second Order Ensemble Langevin Method for Sampling and Inverse Problemscited by 6
  6. 2022Geometric Methods for Sampling, Optimisation, Inference and Adaptive Agentscited by 5
  7. 2023On the convergence of dynamic implementations of Hamiltonian Monte Carlo and No U-Turn Samplerscited by 4
  8. 2024Diffeomorphic Measure Matching with Kernels for Generative Modelingcited by 4
  9. 2022Variational Representations of Annealing Paths: Bregman Information under Monotonic Embeddingcited by 3
  10. 2022History-Based, Bayesian, Closure for Stochastic Parameterization: Application to Lorenz '96cited by 3
  11. 2025Uncertainty quantification of neural network models of evolving processes via Langevin samplingcited by 2
  12. 2021Hamiltonian Monte Carlo with Asymmetrical Momentum Distributionscited by 1
7 more
  1. 2022Staying the course: Locating equilibria of dynamical systems on Riemannian manifolds defined by point-cloudscited by 1
  2. 2024Hamiltonian Monte Carlo on ReLU Neural Networks is Inefficientcited by 1
  3. 2026Counterdiabatic Hamiltonian Monte Carlocited by 1
  4. 2021The Application of Zig-Zag Sampler in Sequential Markov Chain Monte Carlocited by 0
  5. 2023Geometric Ergodicity in Modified Variations of Riemannian Manifold and Lagrangian Monte Carlocited by 0
  6. 2024Repelling-Attracting Hamiltonian Monte Carlocited by 0
  7. 2024Multi-fidelity Hamiltonian Monte Carlocited by 0