# Numerical Generalized Randomized Hamiltonian Monte Carlo for piecewise smooth target densities

arXiv: https://arxiv.org/abs/2504.18210 · HTML: https://mlsanity.com/paper/2504.18210/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 52 references that are in the map.
- First posted on arXiv 25 Apr 2025.

## Builds on (most cited first, 11 of 11)

- [Hands-on Bayesian Neural Networks -- a Tutorial for Deep Learning Users](https://mlsanity.com/paper/2007.06823/) (2020)
- [The Bouncy Particle Sampler: A Non-Reversible Rejection-Free Markov Chain Monte Carlo Method](https://mlsanity.com/paper/1510.02451/) (2015)
- [Geometric integrators and the Hamiltonian Monte Carlo method](https://mlsanity.com/paper/1711.05337/) (2017)
- [Piecewise Deterministic Markov Processes for Continuous-Time Monte Carlo](https://mlsanity.com/paper/1611.07873/) (2016)
- [When does Metropolized Hamiltonian Monte Carlo provably outperform Metropolis-adjusted Langevin algorithm?](https://mlsanity.com/paper/2304.04724/) (2023)
- [Connecting the Dots: Numerical Randomized Hamiltonian Monte Carlo with State-Dependent Event Rates](https://mlsanity.com/paper/2005.01285/) (2020)
- [PDMP Monte Carlo methods for piecewise-smooth densities](https://mlsanity.com/paper/2111.05859/) (2021)
- [Piecewise Deterministic Markov Processes for Scalable Monte Carlo on Restricted Domains](https://mlsanity.com/paper/1701.04244/) (2017)
- [Tuning diagonal scale matrices for HMC](https://mlsanity.com/paper/2403.07495/) (2024)
- [Log-density gradient covariance and automatic metric tensors for Riemann manifold Monte Carlo methods](https://mlsanity.com/paper/2211.01746/) (2022)
- [Hamiltonian Monte Carlo on ReLU Neural Networks is Inefficient](https://mlsanity.com/paper/2410.22065/) (2024)

## Abstract (arXiv)

Traditional gradient-based sampling methods, like standard Hamiltonian Monte Carlo, require that the desired target distribution is continuous and differentiable. This limits the types of models one can define, although the presented models capture the reality in the observations better. In this project, Generalized Randomized Hamiltonian Monte Carlo (GRHMC) processes for sampling continuous densities with discontinuous gradient and piecewise smooth targets are proposed. The methods combine the advantages of Hamiltonian Monte Carlo methods with the nature of continuous time processes in the form of piecewise deterministic Markov processes to sample from such distributions. It is argued that the techniques lead to GRHMC processes that admit the desired target distribution as the invariant distribution in both scenarios. Simulation experiments verifying this fact and several relevant real-life models are presented, including a new parameterization of the spike and slab prior for regularized linear regression that returns sparse coefficient estimates and a regime switching volatility model.