# Towards practical PDMP sampling: Metropolis adjustments, locally adaptive step-sizes, and NUTS-based time lengths

arXiv: https://arxiv.org/abs/2503.11479 · HTML: https://mlsanity.com/paper/2503.11479/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Mar 2025.

## Built on by (most cited first, 2 of 2)

- [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)

## Abstract (arXiv)

Piecewise-Deterministic Markov Processes (PDMPs) hold significant promise for sampling from complex probability distributions. However, their practical implementation is hindered by the need to compute model-specific bounds. Conversely, while Hamiltonian Monte Carlo (HMC) offers a generally efficient approach to sampling, its inability to adaptively tune step sizes impedes its performance when sampling complex distributions like funnels. To address these limitations, we introduce three innovative concepts: (a) a Metropolis-adjusted approximation for PDMP simulation that eliminates the need for explicit bounds without compromising the invariant measure, (b) an adaptive step size mechanism compatible with the Metropolis correction, and (c) a No U-Turn Sampler (NUTS)-inspired scheme for dynamically selecting path lengths in PDMPs. These three ideas can be seamlessly integrated into a single, `doubly-adaptive' PDMP sampler with favourable robustness and efficiency properties.