# Piecewise-Deterministic Markov Chain Monte Carlo

arXiv: https://arxiv.org/abs/1707.05296 · HTML: https://mlsanity.com/paper/1707.05296/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Jul 2017.

## Built on by (most cited first, 7 of 7)

- [Geometric Methods for Sampling, Optimisation, Inference and Adaptive Agents](https://mlsanity.com/paper/2203.10592/) (2022)
- [Log-density gradient covariance and automatic metric tensors for Riemann manifold Monte Carlo methods](https://mlsanity.com/paper/2211.01746/) (2022)
- [Stochastic Gradient Piecewise Deterministic Monte Carlo Samplers](https://mlsanity.com/paper/2406.19051/) (2024)
- [The Application of Zig-Zag Sampler in Sequential Markov Chain Monte Carlo](https://mlsanity.com/paper/2111.10210/) (2021)
- [Piecewise Deterministic Markov Processes for Bayesian Neural Networks](https://mlsanity.com/paper/2302.08724/) (2023)
- [Scalable Monte Carlo for Bayesian Learning](https://mlsanity.com/paper/2407.12751/) (2024)
- [Reflected Proximal Dynamics for Accelerated High-Accuracy Log-Concave Sampling](https://mlsanity.com/paper/2610.16248/) (2026)

## Abstract (arXiv)

A novel class of non-reversible Markov chain Monte Carlo schemes relying on continuous-time piecewise-deterministic Markov Processes has recently emerged. In these algorithms, the state of the Markov process evolves according to a deterministic dynamics which is modified using a Markov transition kernel at random event times. These methods enjoy remarkable features including the ability to update only a subset of the state components while other components implicitly keep evolving and the ability to use an unbiased estimate of the gradient of the log-target while preserving the target as invariant distribution. However, they also suffer from important limitations. The deterministic dynamics used so far do not exploit the structure of the target. Moreover, exact simulation of the event times is feasible for an important yet restricted class of problems and, even when it is, it is application specific. This limits the applicability of these techniques and prevents the development of a generic software implementation of them. We introduce novel MCMC methods addressing these shortcomings. In particular, we introduce novel continuous-time algorithms relying on exact Hamiltonian flows and novel non-reversible discrete-time algorithms which can exploit complex dynamics such as approximate Hamiltonian dynamics arising from symplectic integrators while preserving the attractive features of continuous-time algorithms. We demonstrate the performance of these schemes on a variety of applications.