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

arXiv: https://arxiv.org/abs/2404.15253 · HTML: https://mlsanity.com/paper/2404.15253/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 90 references that are in the map.
- First posted on arXiv 23 Apr 2024.

## Builds on (most cited first, 22 of 22)

- [A Conceptual Introduction to Hamiltonian Monte Carlo](https://mlsanity.com/paper/1701.02434/) (2017)
- [Composable Effects for Flexible and Accelerated Probabilistic Programming in NumPyro](https://mlsanity.com/paper/1912.11554/) (2019)
- [Structured Logconcave Sampling with a Restricted Gaussian Oracle](https://mlsanity.com/paper/2010.03106/) (2020)
- [The Randomized Midpoint Method for Log-Concave Sampling](https://mlsanity.com/paper/1909.05503/) (2019)
- [Improved analysis for a proximal algorithm for sampling](https://mlsanity.com/paper/2202.06386/) (2022)
- [Geometric integrators and the Hamiltonian Monte Carlo method](https://mlsanity.com/paper/1711.05337/) (2017)
- [On the Ergodicity, Bias and Asymptotic Normality of Randomized Midpoint Sampling Method](https://mlsanity.com/paper/2011.03176/) (2020)
- [A general perspective on the Metropolis-Hastings kernel](https://mlsanity.com/paper/2012.14881/) (2020)
- [Optimizing The Integrator Step Size for Hamiltonian Monte Carlo](https://mlsanity.com/paper/1411.6669/) (2014)
- [Connecting the Dots: Numerical Randomized Hamiltonian Monte Carlo with State-Dependent Event Rates](https://mlsanity.com/paper/2005.01285/) (2020)
- [Unadjusted Hamiltonian MCMC with Stratified Monte Carlo Time Integration](https://mlsanity.com/paper/2211.11003/) (2022)
- [Delayed rejection Hamiltonian Monte Carlo for sampling multiscale distributions](https://mlsanity.com/paper/2110.00610/) (2021)
- [Couplings for Multinomial Hamiltonian Monte Carlo](https://mlsanity.com/paper/2104.05134/) (2021)
- [The Apogee to Apogee Path Sampler](https://mlsanity.com/paper/2112.08187/) (2021)
- [Adaptive step size selection for Hessian-based manifold Langevin samplers](https://mlsanity.com/paper/1501.07454/) (2015)
- [Identifying the Optimal Integration Time in Hamiltonian Monte Carlo](https://mlsanity.com/paper/1601.00225/) (2016)
- [On the convergence of dynamic implementations of Hamiltonian Monte Carlo and No U-Turn Samplers](https://mlsanity.com/paper/2307.03460/) (2023)
- [Non-reversibly updating a uniform [0,1] value for Metropolis accept/reject decisions](https://mlsanity.com/paper/2001.11950/) (2020)
- [Randomized Time Riemannian Manifold Hamiltonian Monte Carlo](https://mlsanity.com/paper/2206.04554/) (2022)
- [On the accept-reject mechanism for Metropolis-Hastings algorithms](https://mlsanity.com/paper/2011.04493/) (2020)
- [Dimension-free path-integral molecular dynamics without preconditioning](https://mlsanity.com/paper/1911.00931/) (2019)
- [Randomized Runge-Kutta-Nystr"om Methods for Unadjusted Hamiltonian and Kinetic Langevin Monte Carlo](https://mlsanity.com/paper/2310.07399/) (2023)

## Built on by (most cited first, 9 of 9)

- [Mixing of the No-U-Turn Sampler and the Geometry of Gaussian Concentration](https://mlsanity.com/paper/2410.06978/) (2024)
- [AutoStep: Locally adaptive involutive MCMC](https://mlsanity.com/paper/2410.18929/) (2024)
- [A Langevin sampling algorithm inspired by the Adam optimizer](https://mlsanity.com/paper/2504.18911/) (2025)
- [The Within-Orbit Adaptive Leapfrog No-U-Turn Sampler](https://mlsanity.com/paper/2506.18746/) (2025)
- [On Accelerated Mixing of the No-U-turn Sampler](https://mlsanity.com/paper/2507.13259/) (2025)
- [Asymptotically exact variational flows via involutive MCMC kernels](https://mlsanity.com/paper/2506.02162/) (2025)
- [A Theoretical Comparison of No-U-Turn Sampler Variants: Necessary and Sufficient Convergence Conditions and Mixing Time Analysis under Gaussian Targets](https://mlsanity.com/paper/2603.18640/) (2026)
- [ATLAS: Adapting Trajectory Lengths and Step-Size for Hamiltonian Monte Carlo](https://mlsanity.com/paper/2410.21587/) (2024)
- [Ballistic Convergence in Hit-and-Run Monte Carlo and a Coordinate-free Randomized Kaczmarz Algorithm](https://mlsanity.com/paper/2412.07643/) (2024)

## 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.