Towards practical PDMP sampling: Metropolis adjustments, locally adaptive step-sizes, and NUTS-based time lengths
Fuente:
arXiv
Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866909537571700736 |
|---|---|
| author | Chevallier, Augustin Power, Sam Sutton, Matthew |
| author_facet | Chevallier, Augustin Power, Sam Sutton, Matthew |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_11479 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Towards practical PDMP sampling: Metropolis adjustments, locally adaptive step-sizes, and NUTS-based time lengths Chevallier, Augustin Power, Sam Sutton, Matthew Computation Probability Statistics Theory Methodology 62-08 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. |
| title | Towards practical PDMP sampling: Metropolis adjustments, locally adaptive step-sizes, and NUTS-based time lengths |
| topic | Computation Probability Statistics Theory Methodology 62-08 |
| url | https://arxiv.org/abs/2503.11479 |