mlsanityData to 7 Oct 2026

An Introduction to Hamiltonian Monte Carlo Method for Sampling

arXiv 2108.12107 ↗First posted 27 Aug 2021cs.DS cs.LG math.PRcited by 8

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Abstract (arXiv)

The goal of this article is to introduce the Hamiltonian Monte Carlo (HMC) method -- a Hamiltonian dynamics-inspired algorithm for sampling from a Gibbs density π(x) propto e-f(x). We focus on the "idealized" case, where one can compute continuous trajectories exactly. We show that idealized HMC preserves π and we establish its convergence when f is strongly convex and smooth.

Key facts. Cited by 8 papers in the map (data through 7 Oct 2026). Builds on 19 of its 58 references that are in the map. First posted on arXiv 27 Aug 2021.

Builds on

19 of 58 references.

References · 19

  1. 2014Stochastic Gradient Hamiltonian Monte Carlocited by 341
  2. 2014Identifying and attacking the saddle point problem in high-dimensional non-convex optimizationcited by 286
  3. 2017Non-convex learning via Stochastic Gradient Langevin Dynamics: a nonasymptotic analysiscited by 242
  4. 2014Theoretical guarantees for approximate sampling from smooth and log-concave densitiescited by 206
  5. 2015Non-asymptotic convergence analysis for the Unadjusted Langevin Algorithmcited by 195
  6. 2016High-dimensional Bayesian inference via the Unadjusted Langevin Algorithmcited by 144
  7. 2017Underdamped Langevin MCMC: A non-asymptotic analysiscited by 131
  8. 2018Log-concave sampling: Metropolis-Hastings algorithms are fastcited by 117
  9. 2020Structured Logconcave Sampling with a Restricted Gaussian Oraclecited by 85
  10. 2019Fast mixing of Metropolized Hamiltonian Monte Carlo: Benefits of multi-step gradientscited by 51
  11. 2013Hamiltonian Monte Carlo for Hierarchical Modelscited by 50
  12. 2018Coupling and Convergence for Hamiltonian Monte Carlocited by 36
7 more
  1. 2017Convergence Rate of Riemannian Hamiltonian Monte Carlo and Faster Polytope Volume Computationcited by 32
  2. 2019Optimal Convergence Rate of Hamiltonian Monte Carlo for Strongly Logconcave Distributionscited by 28
  3. 2016On the Geometric Ergodicity of Hamiltonian Monte Carlocited by 19
  4. 2016Geodesic Walks in Polytopescited by 13
  5. 2017Rapid Mixing of Hamiltonian Monte Carlo on Strongly Log-Concave Distributionscited by 12
  6. 2014Optimizing The Integrator Step Size for Hamiltonian Monte Carlocited by 8
  7. 2016Rapid Mixing of Geodesic Walks on Manifolds with Positive Curvaturecited by 7

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Cited by year

Citing papers per year: 2021: 1; 2022: 5; 2023: 1; 2024: 0; 2025: 1.

8 papers.

  1. 2023Improved Discretization Analysis for Underdamped Langevin Monte Carlocited by 26
  2. 2025Langevin Soft Actor-Critic: Efficient Exploration through Uncertainty-Driven Critic Learningcited by 17
  3. 2021Sampling from Log-Concave Distributions with Infinity-Distance Guaranteescited by 8
  4. 2022Hamiltonian Monte Carlo for efficient Gaussian sampling: long and random stepscited by 8
  5. 2022Accelerating Hamiltonian Monte Carlo via Chebyshev Integration Timecited by 7
  6. 2022A blob method for inhomogeneous diffusion with applications to multi-agent control and samplingcited by 6
  7. 2022Bayesian Inference with Latent Hamiltonian Neural Networkscited by 2
  8. 2022On the Dissipation of Ideal Hamiltonian Monte Carlo Samplercited by 1