mlsanityData to 7 Oct 2026

Coupling and Convergence for Hamiltonian Monte Carlo

arXiv 1805.00452 ↗First posted 1 May 2018math.PR stat.CO stat.MLcited by 36

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Abstract (arXiv)

Based on a new coupling approach, we prove that the transition step of the Hamiltonian Monte Carlo algorithm is contractive w.r.t. a carefully designed Kantorovich (L1 Wasserstein) distance. The lower bound for the contraction rate is explicit. Global convexity of the potential is not required, and thus multimodal target distributions are included. Explicit quantitative bounds for the number of steps required to approximate the stationary distribution up to a given error are a direct consequence of contractivity. These bounds show that HMC can overcome diffusive behaviour if the duration of the Hamiltonian dynamics is adjusted appropriately.

Key facts. Cited by 36 papers in the map (data through 7 Oct 2026). First posted on arXiv 1 May 2018.

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 9; 2022: 2; 2023: 10; 2024: 7; 2025: 5; 2026: 3.

36 papers.

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  1. 2024Optimal score estimation via empirical Bayes smoothingcited by 60
  2. 2025Accelerated Diffusion Models via Speculative Samplingcited by 30
  3. 2021Mixing Time Guarantees for Unadjusted Hamiltonian Monte Carlocited by 18
  4. 2021When is the Convergence Time of Langevin Algorithms Dimension Independent? A Composite Optimization Viewpointcited by 12
  5. 2023When does Metropolized Hamiltonian Monte Carlo provably outperform Metropolis-adjusted Langevin algorithm?cited by 12
  6. 2024Entropy contraction of the Gibbs sampler under log-concavitycited by 12
  7. 2021Asymptotic bias of inexact Markov Chain Monte Carlo methods in high dimensioncited by 11
  8. 2023Fast sampling from constrained spaces using the Metropolis-adjusted Mirror Langevin algorithmcited by 11
  9. 2025Diffusion Models are Secretly Exchangeable: Parallelizing DDPMs via Autospeculationcited by 11
  10. 2023Convergence Rates for Non-Log-Concave Sampling and Log-Partition Estimationcited by 10
  11. 2025Improving the evaluation of samplers on multi-modal targetscited by 9
  12. 2021An Introduction to Hamiltonian Monte Carlo Method for Samplingcited by 8
24 more
  1. 2022Unadjusted Hamiltonian MCMC with Stratified Monte Carlo Time Integrationcited by 8
  2. 2021Convergence Analysis of Schr"odinger-F"ollmer Sampler without Convexitycited by 7
  3. 2025Predictability Enables Parallelization of Nonlinear State Space Modelscited by 7
  4. 2024Efficient Sampling on Riemannian Manifolds via Langevin MCMCcited by 6
  5. 2021Bounding Wasserstein distance with couplingscited by 5
  6. 2024Faster Sampling via Stochastic Gradient Proximal Samplercited by 5
  7. 2021Decentralized Bayesian Learning with Metropolis-Adjusted Hamiltonian Monte Carlocited by 4
  8. 2023Mean-Square Analysis of Discretized Ito Diffusions for Heavy-tailed Samplingcited by 4
  9. 2023Non-Log-Concave and Nonsmooth Sampling via Langevin Monte Carlo Algorithmscited by 4
  10. 2023On the convergence of dynamic implementations of Hamiltonian Monte Carlo and No U-Turn Samplerscited by 4
  11. 2022Unbiased Estimation using Underdamped Langevin Dynamicscited by 3
  12. 2023Reflection coupling for unadjusted generalized Hamiltonian Monte Carlo in the nonconvex stochastic gradient casecited by 3
  13. 2024Mixing of the No-U-Turn Sampler and the Geometry of Gaussian Concentrationcited by 3
  14. 2024Linear-cost unbiased posterior estimates for crossed effects and matrix factorization models via couplingscited by 2
  15. 2026Accelerating Speculative Diffusions via Block Verificationcited by 2
  16. 2021Hamiltonian Monte Carlo with Asymmetrical Momentum Distributionscited by 1
  17. 2023Geometric ergodicity of SGLD via reflection couplingcited by 1
  18. 2023Subsampling Error in Stochastic Gradient Langevin Diffusionscited by 1
  19. 2023Randomized Runge-Kutta-Nystr"om Methods for Unadjusted Hamiltonian and Kinetic Langevin Monte Carlocited by 1
  20. 2025FREE: Uncertainty-Aware Autoregression for Parallel Diffusion Transformerscited by 1
  21. 2026Speculative Sampling For Faster Molecular Dynamicscited by 1
  22. 2021Antithetic Riemannian Manifold And Quantum-Inspired Hamiltonian Monte Carlocited by 0
  23. 2024On Convergence of the Alternating Directions SGHMC Algorithmcited by 0
  24. 2026A Theoretical Comparison of No-U-Turn Sampler Variants: Necessary and Sufficient Convergence Conditions and Mixing Time Analysis under Gaussian Targetscited by 0