# Randomized Time Riemannian Manifold Hamiltonian Monte Carlo

arXiv: https://arxiv.org/abs/2206.04554 · HTML: https://mlsanity.com/paper/2206.04554/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Jun 2022.

## Built on by (most cited first, 3 of 3)

- [GIST: Gibbs self-tuning for locally adaptive Hamiltonian Monte Carlo](https://mlsanity.com/paper/2404.15253/) (2024)
- [Tuning diagonal scale matrices for HMC](https://mlsanity.com/paper/2403.07495/) (2024)
- [The Within-Orbit Adaptive Leapfrog No-U-Turn Sampler](https://mlsanity.com/paper/2506.18746/) (2025)

## Abstract (arXiv)

Hamiltonian Monte Carlo (HMC) algorithms which combine numerical approximation of Hamiltonian dynamics on finite intervals with stochastic refreshment and Metropolis correction are popular sampling schemes, but it is known that they may suffer from slow convergence in the continuous time limit. A recent paper of Bou-Rabee and Sanz-Serna (Ann. Appl. Prob., 27:2159-2194, 2017) demonstrated that this issue can be addressed by simply randomizing the duration parameter of the Hamiltonian paths. In this article, we use the same idea to enhance the sampling efficiency of a constrained version of HMC, with potential benefits in a variety of application settings. We demonstrate both the conservation of the stationary distribution and the ergodicity of the method. We also compare the performance of various schemes in numerical studies of model problems, including an application to high-dimensional covariance estimation.