mlsanityData to 7 Oct 2026

Unadjusted Hamiltonian MCMC with Stratified Monte Carlo Time Integration

arXiv 2211.11003 ↗First posted 20 Nov 2022math.PR cs.NA math.NAcited by 8

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Abstract (arXiv)

A randomized time integrator is suggested for unadjusted Hamiltonian Monte Carlo (uHMC) which involves a very minor modification to the usual Verlet time integrator, and hence, is easy to implement. For target distributions of the form μ(dx) propto e-U(x) dx where U: ℝd → ℝ≥ 0 is K-strongly convex but only L-gradient Lipschitz, and initial distributions nu with finite second moment, coupling proofs reveal that an varepsilon-accurate approximation of the target distribution in L2-Wasserstein distance boldsymbolW2 can be achieved by the uHMC algorithm with randomized time integration using Oleft((d/K)1/3 (L/K)5/3 varepsilon-2/3 log( boldsymbolW2(μ, nu) / varepsilon)^+right) gradient evaluations; whereas for such rough target densities the corresponding complexity of the uHMC algorithm with Verlet time integration is in general Oleft((d/K)1/2 (L/K)2 varepsilon-1 log( boldsymbolW2(μ, nu) / varepsilon)^+ right). Metropolis-adjustable randomized time integrators are also provided.

Key facts. Cited by 8 papers in the map (data through 7 Oct 2026). Builds on 15 of its 49 references that are in the map. First posted on arXiv 20 Nov 2022.

Builds on

15 of 49 references.

References · 15

  1. 2016High-dimensional Bayesian inference via the Unadjusted Langevin Algorithmcited by 144
  2. 2017Underdamped Langevin MCMC: A non-asymptotic analysiscited by 131
  3. 2019The Randomized Midpoint Method for Log-Concave Samplingcited by 77
  4. 2018Sharp convergence rates for Langevin dynamics in the nonconvex settingcited by 67
  5. 2018On sampling from a log-concave density using kinetic Langevin diffusionscited by 61
  6. 2019Fast mixing of Metropolized Hamiltonian Monte Carlo: Benefits of multi-step gradientscited by 51
  7. 2018Coupling and Convergence for Hamiltonian Monte Carlocited by 36
  8. 2019Optimal Convergence Rate of Hamiltonian Monte Carlo for Strongly Logconcave Distributionscited by 28
  9. 2017Geometric integrators and the Hamiltonian Monte Carlo methodcited by 25
  10. 2020On the Ergodicity, Bias and Asymptotic Normality of Randomized Midpoint Sampling Methodcited by 23
  11. 2021Mixing Time Guarantees for Unadjusted Hamiltonian Monte Carlocited by 18
  12. 2021Asymptotic bias of inexact Markov Chain Monte Carlo methods in high dimensioncited by 11
3 more
  1. 2020Connecting the Dots: Numerical Randomized Hamiltonian Monte Carlo with State-Dependent Event Ratescited by 8
  2. 2018Algorithmic Theory of ODEs and Sampling from Well-conditioned Logconcave Densitiescited by 7
  3. 2020Couplings for Andersen Dynamicscited by 2

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 5; 2024: 2; 2025: 0; 2026: 1.

8 papers.

  1. 2023Faster high-accuracy log-concave sampling via algorithmic warm startscited by 44
  2. 2023Improved Discretization Analysis for Underdamped Langevin Monte Carlocited by 26
  3. 2023When does Metropolized Hamiltonian Monte Carlo provably outperform Metropolis-adjusted Langevin algorithm?cited by 12
  4. 2024GIST: Gibbs self-tuning for locally adaptive Hamiltonian Monte Carlocited by 9
  5. 2023Reflection coupling for unadjusted generalized Hamiltonian Monte Carlo in the nonconvex stochastic gradient casecited by 3
  6. 2023Randomized Runge-Kutta-Nystr"om Methods for Unadjusted Hamiltonian and Kinetic Langevin Monte Carlocited by 1
  7. 2026A Non-asymptotic Analysis for Learning and Applying a Preconditioner in MCMCcited by 1
  8. 2024On Convergence of the Alternating Directions SGHMC Algorithmcited by 0