# Stochastic Gradient Piecewise Deterministic Monte Carlo Samplers

arXiv: https://arxiv.org/abs/2406.19051 · HTML: https://mlsanity.com/paper/2406.19051/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 37 references that are in the map.
- First posted on arXiv 27 Jun 2024.

## Builds on (most cited first, 21 of 21)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [A Survey of Uncertainty in Deep Neural Networks](https://mlsanity.com/paper/2107.03342/) (2021)
- [Stochastic Gradient Hamiltonian Monte Carlo](https://mlsanity.com/paper/1402.4102/) (2014)
- [A Complete Recipe for Stochastic Gradient MCMC](https://mlsanity.com/paper/1506.04696/) (2015)
- [Measuring Sample Quality with Kernels](https://mlsanity.com/paper/1703.01717/) (2017)
- [Stochastic gradient Markov chain Monte Carlo](https://mlsanity.com/paper/1907.06986/) (2019)
- [Posterior Concentration for Sparse Deep Learning](https://mlsanity.com/paper/1803.09138/) (2018)
- [The Bouncy Particle Sampler: A Non-Reversible Rejection-Free Markov Chain Monte Carlo Method](https://mlsanity.com/paper/1510.02451/) (2015)
- [The Barker proposal: combining robustness and efficiency in gradient-based MCMC](https://mlsanity.com/paper/1908.11812/) (2019)
- [Piecewise Deterministic Markov Processes for Continuous-Time Monte Carlo](https://mlsanity.com/paper/1611.07873/) (2016)
- [The Boomerang Sampler](https://mlsanity.com/paper/2006.13777/) (2020)
- [Quantifying the accuracy of approximate diffusions and Markov chains](https://mlsanity.com/paper/1605.06420/) (2016)
- [Piecewise-Deterministic Markov Chain Monte Carlo](https://mlsanity.com/paper/1707.05296/) (2017)
- [Relativistic Monte Carlo](https://mlsanity.com/paper/1609.04388/) (2016)
- [PDMP Monte Carlo methods for piecewise-smooth densities](https://mlsanity.com/paper/2111.05859/) (2021)
- [Stochastic Bouncy Particle Sampler](https://mlsanity.com/paper/1609.00770/) (2016)
- [Large-Scale Stochastic Sampling from the Probability Simplex](https://mlsanity.com/paper/1806.07137/) (2018)
- [Reversible Jump PDMP Samplers for Variable Selection](https://mlsanity.com/paper/2010.11771/) (2020)
- [Approximations of Piecewise Deterministic Markov Processes and their convergence properties](https://mlsanity.com/paper/2109.11827/) (2021)
- [Robust Approximate Sampling via Stochastic Gradient Barker Dynamics](https://mlsanity.com/paper/2405.08999/) (2024)

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

- [Bouncy particle sampler with infinite exchanging parallel tempering](https://mlsanity.com/paper/2509.02003/) (2025)
- [Some aspects of robustness in modern Markov Chain Monte Carlo](https://mlsanity.com/paper/2511.21563/) (2025)

## Abstract (arXiv)

Recent work has suggested using Monte Carlo methods based on piecewise deterministic Markov processes (PDMPs) to sample from target distributions of interest. PDMPs are non-reversible continuous-time processes endowed with momentum, and hence can mix better than standard reversible MCMC samplers. Furthermore, they can incorporate exact sub-sampling schemes which only require access to a single (randomly selected) data point at each iteration, yet without introducing bias to the algorithm's stationary distribution. However, the range of models for which PDMPs can be used, particularly with sub-sampling, is limited. We propose approximate simulation of PDMPs with sub-sampling for scalable sampling from posterior distributions. The approximation takes the form of an Euler approximation to the true PDMP dynamics, and involves using an estimate of the gradient of the log-posterior based on a data sub-sample. We thus call this class of algorithms stochastic-gradient PDMPs. Importantly, the trajectories of stochastic-gradient PDMPs are continuous and can leverage recent ideas for sampling from measures with continuous and atomic components. We show these methods are easy to implement, present results on their approximation error and demonstrate numerically that this class of algorithms has similar efficiency to, but is more robust than, stochastic gradient Langevin dynamics.