mlsanityData to 7 Oct 2026

Rapid Mixing of Hamiltonian Monte Carlo on Strongly Log-Concave Distributions

arXiv 1708.07114 ↗First posted 23 Aug 2017math.PR stat.CO stat.MEcited by 12

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Abstract (arXiv)

We obtain several quantitative bounds on the mixing properties of the Hamiltonian Monte Carlo (HMC) algorithm for a strongly log-concave target distribution π on ℝd, showing that HMC mixes quickly in this setting. One of our main results is a dimension-free bound on the mixing of an "ideal" HMC chain, which is used to show that the usual leapfrog implementation of HMC can sample from π using only O(d^frac14) gradient evaluations. This dependence on dimension is sharp, and our results significantly extend and improve previous quantitative bounds on the mixing of HMC.

Key facts. Cited by 12 papers in the map (data through 7 Oct 2026). First posted on arXiv 23 Aug 2017.

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Citing papers per year: 2021: 6; 2022: 2; 2023: 1; 2024: 3.

12 papers.

  1. 2021Mixing Time Guarantees for Unadjusted Hamiltonian Monte Carlocited by 18
  2. 2021When is the Convergence Time of Langevin Algorithms Dimension Independent? A Composite Optimization Viewpointcited by 12
  3. 2023When does Metropolized Hamiltonian Monte Carlo provably outperform Metropolis-adjusted Langevin algorithm?cited by 12
  4. 2021Asymptotic bias of inexact Markov Chain Monte Carlo methods in high dimensioncited by 11
  5. 2024Accelerating Approximate Thompson Sampling with Underdamped Langevin Monte Carlocited by 10
  6. 2021An Introduction to Hamiltonian Monte Carlo Method for Samplingcited by 8
  7. 2022Transport Score Climbing: Variational Inference Using Forward KL and Adaptive Neural Transportcited by 8
  8. 2021Entropy-based adaptive Hamiltonian Monte Carlocited by 5
  9. 2024Faster Sampling via Stochastic Gradient Proximal Samplercited by 5
  10. 2024Ensemble-Based Annealed Importance Samplingcited by 4
  11. 2022Hamiltonian Adaptive Importance Samplingcited by 2
  12. 2021Hamiltonian Monte Carlo with Asymmetrical Momentum Distributionscited by 1