Incorporating Local Step-Size Adaptivity into the No-U-Turn Sampler using Gibbs Self Tuning
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866915466937630720 |
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| author | Bou-Rabee, Nawaf Carpenter, Bob Kleppe, Tore Selland Marsden, Milo |
| author_facet | Bou-Rabee, Nawaf Carpenter, Bob Kleppe, Tore Selland Marsden, Milo |
| contents | Adapting the step size locally in the no-U-turn sampler (NUTS) is challenging because the step-size and path-length tuning parameters are interdependent. The determination of an optimal path length requires a predefined step size, while the ideal step size must account for errors along the selected path. Ensuring reversibility further complicates this tuning problem. In this paper, we present a method for locally adapting the step size in NUTS that is an instance of the Gibbs self-tuning (GIST) framework. Our approach guarantees reversibility with an acceptance probability that depends exclusively on the conditional distribution of the step size. We validate our step-size-adaptive NUTS method on Neal's funnel density and a high-dimensional normal distribution, demonstrating its effectiveness in challenging scenarios. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_08259 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Incorporating Local Step-Size Adaptivity into the No-U-Turn Sampler using Gibbs Self Tuning Bou-Rabee, Nawaf Carpenter, Bob Kleppe, Tore Selland Marsden, Milo Methodology Probability Computation Adapting the step size locally in the no-U-turn sampler (NUTS) is challenging because the step-size and path-length tuning parameters are interdependent. The determination of an optimal path length requires a predefined step size, while the ideal step size must account for errors along the selected path. Ensuring reversibility further complicates this tuning problem. In this paper, we present a method for locally adapting the step size in NUTS that is an instance of the Gibbs self-tuning (GIST) framework. Our approach guarantees reversibility with an acceptance probability that depends exclusively on the conditional distribution of the step size. We validate our step-size-adaptive NUTS method on Neal's funnel density and a high-dimensional normal distribution, demonstrating its effectiveness in challenging scenarios. |
| title | Incorporating Local Step-Size Adaptivity into the No-U-Turn Sampler using Gibbs Self Tuning |
| topic | Methodology Probability Computation |
| url | https://arxiv.org/abs/2408.08259 |