The No-Underrun Sampler: A Locally-Adaptive, Gradient-Free MCMC Method
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , , |
|---|---|
| Format: | Preprint |
| Publié: |
2025
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866909511537655808 |
|---|---|
| author | Bou-Rabee, Nawaf Carpenter, Bob Liu, Sifan Oberdörster, Stefan |
| author_facet | Bou-Rabee, Nawaf Carpenter, Bob Liu, Sifan Oberdörster, Stefan |
| contents | In this work, we introduce the No-Underrun Sampler (NURS), a locally-adaptive, gradient-free Markov chain Monte Carlo method that blends ideas from Hit-and-Run and the No-U-Turn Sampler. NURS dynamically adapts to the local scale of the target distribution without requiring gradient evaluations, making it especially suitable for applications where gradients are unavailable or costly. We establish key theoretical properties, including reversibility, formal connections to Hit-and-Run and Random Walk Metropolis, Wasserstein contraction comparable to Hit-and-Run in Gaussian targets, and bounds on the total variation distance between the transition kernels of Hit-and-Run and NURS. Empirical experiments, supported by theoretical insights, illustrate the ability of NURS to sample from Neal's funnel, a challenging multi-scale distribution from Bayesian hierarchical inference. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_18548 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The No-Underrun Sampler: A Locally-Adaptive, Gradient-Free MCMC Method Bou-Rabee, Nawaf Carpenter, Bob Liu, Sifan Oberdörster, Stefan Statistics Theory Probability Methodology 60J05, 65C05 In this work, we introduce the No-Underrun Sampler (NURS), a locally-adaptive, gradient-free Markov chain Monte Carlo method that blends ideas from Hit-and-Run and the No-U-Turn Sampler. NURS dynamically adapts to the local scale of the target distribution without requiring gradient evaluations, making it especially suitable for applications where gradients are unavailable or costly. We establish key theoretical properties, including reversibility, formal connections to Hit-and-Run and Random Walk Metropolis, Wasserstein contraction comparable to Hit-and-Run in Gaussian targets, and bounds on the total variation distance between the transition kernels of Hit-and-Run and NURS. Empirical experiments, supported by theoretical insights, illustrate the ability of NURS to sample from Neal's funnel, a challenging multi-scale distribution from Bayesian hierarchical inference. |
| title | The No-Underrun Sampler: A Locally-Adaptive, Gradient-Free MCMC Method |
| topic | Statistics Theory Probability Methodology 60J05, 65C05 |
| url | https://arxiv.org/abs/2501.18548 |