mlsanityData to 7 Oct 2026

Geometric integrators and the Hamiltonian Monte Carlo method

arXiv 1711.05337 ↗First posted 14 Nov 2017math.PR cs.NA math.NAcited by 25

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Abstract (arXiv)

This paper surveys in detail the relations between numerical integration and the Hamiltonian (or hybrid) Monte Carlo method (HMC). Since the computational cost of HMC mainly lies in the numerical integrations, these should be performed as efficiently as possible. However, HMC requires methods that have the geometric properties of being volume-preserving and reversible, and this limits the number of integrators that may be used. On the other hand, these geometric properties have important quantitative implications on the integration error, which in turn have an impact on the acceptance rate of the proposal. While at present the velocity Verlet algorithm is the method of choice for good reasons, we argue that Verlet can be improved upon. We also discuss in detail the behavior of HMC as the dimensionality of the target distribution increases.

Key facts. Cited by 25 papers in the map (data through 7 Oct 2026). First posted on arXiv 14 Nov 2017.

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 9; 2022: 4; 2023: 3; 2024: 3; 2025: 3; 2026: 3.

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  1. 2021Mixing Time Guarantees for Unadjusted Hamiltonian Monte Carlocited by 18
  2. 2021Asymptotic bias of inexact Markov Chain Monte Carlo methods in high dimensioncited by 11
  3. 2021Efficient Learning of the Parameters of Non-Linear Models using Differentiable Resampling in Particle Filterscited by 9
  4. 2024GIST: Gibbs self-tuning for locally adaptive Hamiltonian Monte Carlocited by 9
  5. 2021Wasserstein distance estimates for the distributions of numerical approximations to ergodic stochastic differential equationscited by 8
  6. 2022Unadjusted Hamiltonian MCMC with Stratified Monte Carlo Time Integrationcited by 8
  7. 2022Second Order Ensemble Langevin Method for Sampling and Inverse Problemscited by 6
  8. 2024Hamiltonian Score Matching and Generative Flowscited by 6
  9. 2021Entropy-based adaptive Hamiltonian Monte Carlocited by 5
  10. 2022Geometric Methods for Sampling, Optimisation, Inference and Adaptive Agentscited by 5
  11. 2021A Unifying and Canonical Description of Measure-Preserving Diffusionscited by 4
  12. 2021Nonparametric Hamiltonian Monte Carlocited by 4
13 more
  1. 2021Better Training using Weight-Constrained Stochastic Dynamicscited by 4
  2. 2023On the convergence of dynamic implementations of Hamiltonian Monte Carlo and No U-Turn Samplerscited by 4
  3. 2024Tuning diagonal scale matrices for HMCcited by 4
  4. 2022Log-density gradient covariance and automatic metric tensors for Riemann manifold Monte Carlo methodscited by 3
  5. 2025Randomised Splitting Methods and Stochastic Gradient Descentcited by 3
  6. 2025The Within-Orbit Adaptive Leapfrog No-U-Turn Samplercited by 2
  7. 2023Randomized Runge-Kutta-Nystr"om Methods for Unadjusted Hamiltonian and Kinetic Langevin Monte Carlocited by 1
  8. 2021Truncated Log-concave Sampling with Reflective Hamiltonian Monte Carlocited by 0
  9. 2023Learning variational autoencoders via MCMC speed measurescited by 0
  10. 2025Numerical Generalized Randomized Hamiltonian Monte Carlo for piecewise smooth target densitiescited by 0
  11. 2026A Theoretical Comparison of No-U-Turn Sampler Variants: Necessary and Sufficient Convergence Conditions and Mixing Time Analysis under Gaussian Targetscited by 0
  12. 2026Accelerated sampling using SamAdams variable timesteps and position-adaptive Langevin dynamicscited by 0
  13. 2026Optimal scaling of MCMC algorithms: the Hamiltonian approachcited by 0