mlsanityData to 7 Oct 2026

GIST: Gibbs self-tuning for locally adaptive Hamiltonian Monte Carlo

arXiv 2404.15253 ↗First posted 23 Apr 2024stat.CO math.ST stat.MLcited by 9

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Abstract (arXiv)

We introduce a novel and flexible framework for constructing locally adaptive Hamiltonian Monte Carlo (HMC) samplers by Gibbs sampling the algorithm's tuning parameters conditionally based on the position and momentum at each step. For adaptively sampling path lengths, our Gibbs self-tuning (GIST) approach encompasses randomized HMC, multinomial HMC, the No-U-Turn Sampler (NUTS), and the Apogee-to-Apogee Path Sampler as special cases. We exemplify the GIST framework with a novel alternative to NUTS for locally adapting path lengths, evaluated with an exact Hamiltonian for a high-dimensional, ill-conditioned Gaussian measure and with the leapfrog integrator for a suite of diverse models.

Key facts. Cited by 9 papers in the map (data through 7 Oct 2026). Builds on 22 of its 90 references that are in the map. First posted on arXiv 23 Apr 2024.

Builds on

22 of 90 references.

References · 22

  1. 2017A Conceptual Introduction to Hamiltonian Monte Carlocited by 207
  2. 2019Composable Effects for Flexible and Accelerated Probabilistic Programming in NumPyrocited by 187
  3. 2020Structured Logconcave Sampling with a Restricted Gaussian Oraclecited by 85
  4. 2019The Randomized Midpoint Method for Log-Concave Samplingcited by 77
  5. 2022Improved analysis for a proximal algorithm for samplingcited by 72
  6. 2017Geometric integrators and the Hamiltonian Monte Carlo methodcited by 25
  7. 2020On the Ergodicity, Bias and Asymptotic Normality of Randomized Midpoint Sampling Methodcited by 23
  8. 2020A general perspective on the Metropolis-Hastings kernelcited by 9
  9. 2014Optimizing The Integrator Step Size for Hamiltonian Monte Carlocited by 8
  10. 2020Connecting the Dots: Numerical Randomized Hamiltonian Monte Carlo with State-Dependent Event Ratescited by 8
  11. 2022Unadjusted Hamiltonian MCMC with Stratified Monte Carlo Time Integrationcited by 8
  12. 2021Delayed rejection Hamiltonian Monte Carlo for sampling multiscale distributionscited by 7
10 more
  1. 2021Couplings for Multinomial Hamiltonian Monte Carlocited by 5
  2. 2021The Apogee to Apogee Path Samplercited by 5
  3. 2015Adaptive step size selection for Hessian-based manifold Langevin samplerscited by 4
  4. 2016Identifying the Optimal Integration Time in Hamiltonian Monte Carlocited by 4
  5. 2023On the convergence of dynamic implementations of Hamiltonian Monte Carlo and No U-Turn Samplerscited by 4
  6. 2020Non-reversibly updating a uniform [0,1] value for Metropolis accept/reject decisionscited by 3
  7. 2022Randomized Time Riemannian Manifold Hamiltonian Monte Carlocited by 3
  8. 2020On the accept-reject mechanism for Metropolis-Hastings algorithmscited by 2
  9. 2019Dimension-free path-integral molecular dynamics without preconditioningcited by 1
  10. 2023Randomized Runge-Kutta-Nystr"om Methods for Unadjusted Hamiltonian and Kinetic Langevin Monte Carlocited by 1

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 4; 2025: 4; 2026: 1.

9 papers.

  1. 2024AutoStep: Locally adaptive involutive MCMCcited by 4
  2. 2024Mixing of the No-U-Turn Sampler and the Geometry of Gaussian Concentrationcited by 3
  3. 2025A Langevin sampling algorithm inspired by the Adam optimizercited by 3
  4. 2025The Within-Orbit Adaptive Leapfrog No-U-Turn Samplercited by 2
  5. 2025Asymptotically exact variational flows via involutive MCMC kernelscited by 1
  6. 2025On Accelerated Mixing of the No-U-turn Samplercited by 1
  7. 2024ATLAS: Adapting Trajectory Lengths and Step-Size for Hamiltonian Monte Carlocited by 0
  8. 2024Ballistic Convergence in Hit-and-Run Monte Carlo and a Coordinate-free Randomized Kaczmarz Algorithmcited by 0
  9. 2026A Theoretical Comparison of No-U-Turn Sampler Variants: Necessary and Sufficient Convergence Conditions and Mixing Time Analysis under Gaussian Targetscited by 0