mlsanityData to 7 Oct 2026

On the Geometric Ergodicity of Hamiltonian Monte Carlo

arXiv 1601.08057 ↗First posted 29 Jan 2016stat.CO stat.ME stat.MLcited by 19

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Abstract (arXiv)

We establish general conditions under which Markov chains produced by the Hamiltonian Monte Carlo method will and will not be geometrically ergodic. We consider implementations with both position-independent and position-dependent integration times. In the former case we find that the conditions for geometric ergodicity are essentially a gradient of the log-density which asymptotically points towards the centre of the space and grows no faster than linearly. In an idealised scenario in which the integration time is allowed to change in different regions of the space, we show that geometric ergodicity can be recovered for a much broader class of tail behaviours, leading to some guidelines for the choice of this free parameter in practice.

Key facts. Cited by 19 papers in the map (data through 7 Oct 2026). First posted on arXiv 29 Jan 2016.

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Citing papers per year: 2021: 6; 2022: 2; 2023: 5; 2024: 4; 2025: 0; 2026: 2.

19 papers.

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  1. 2021An Introduction to Hamiltonian Monte Carlo Method for Samplingcited by 8
  2. 2022Second Order Ensemble Langevin Method for Sampling and Inverse Problemscited by 6
  3. 2021Entropy-based adaptive Hamiltonian Monte Carlocited by 5
  4. 2022Geometric Methods for Sampling, Optimisation, Inference and Adaptive Agentscited by 5
  5. 2024Listening to the Noise: Blind Denoising with Gibbs Diffusioncited by 5
  6. 2021A Unifying and Canonical Description of Measure-Preserving Diffusionscited by 4
  7. 2023On the convergence of dynamic implementations of Hamiltonian Monte Carlo and No U-Turn Samplerscited by 4
  8. 2024Ensemble-Based Annealed Importance Samplingcited by 4
  9. 2023Reflection coupling for unadjusted generalized Hamiltonian Monte Carlo in the nonconvex stochastic gradient casecited by 3
  10. 2021On Lq Convergence of the Hamiltonian Monte Carlocited by 1
  11. 2021Hamiltonian Monte Carlo with Asymmetrical Momentum Distributionscited by 1
  12. 2024Non-asymptotic bounds for forward processes in denoising diffusions: Ornstein-Uhlenbeck is hard to beatcited by 1
7 more
  1. 2021An MCMC Method to Sample from Lattice Distributionscited by 0
  2. 2023Geometric Ergodicity in Modified Variations of Riemannian Manifold and Lagrangian Monte Carlocited by 0
  3. 2023Differentially Private Statistical Inference through β-Divergence One Posterior Samplingcited by 0
  4. 2023Learning variational autoencoders via MCMC speed measurescited by 0
  5. 2024Repelling-Attracting Hamiltonian Monte Carlocited by 0
  6. 2026A Theoretical Comparison of No-U-Turn Sampler Variants: Necessary and Sufficient Convergence Conditions and Mixing Time Analysis under Gaussian Targetscited by 0
  7. 2026LazyHMC: Hamiltonian Monte Carlo Simulation for Lazy, Infinite Dimensional Probabilistic Programscited by 0