On Accelerated Mixing of the No-U-turn Sampler
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866915396378951680 |
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| author | Oberdörster, Stefan |
| author_facet | Oberdörster, Stefan |
| contents | Recent progress on the theory of variational hypocoercivity established that Randomized Hamiltonian Monte Carlo -- at criticality -- can achieve pronounced acceleration in its convergence and hence sampling performance over diffusive dynamics. Manual critical tuning being unfeasible in practice has motivated automated algorithmic solutions, notably the No-U-turn Sampler. Beyond its empirical success, a rigorous study of this method's ability to achieve accelerated convergence has been missing. We initiate this investigation combining a concentration of measure approach to examine the automatic tuning mechanism with a coupling based mixing analysis for Hamiltonian Monte Carlo. In certain Gaussian target distributions, this yields a precise characterization of the sampler's behavior resulting, in particular, in rigorous mixing guarantees describing the algorithm's ability and limitations in achieving accelerated convergence. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_13259 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On Accelerated Mixing of the No-U-turn Sampler Oberdörster, Stefan Statistics Theory Probability Computation Machine Learning Recent progress on the theory of variational hypocoercivity established that Randomized Hamiltonian Monte Carlo -- at criticality -- can achieve pronounced acceleration in its convergence and hence sampling performance over diffusive dynamics. Manual critical tuning being unfeasible in practice has motivated automated algorithmic solutions, notably the No-U-turn Sampler. Beyond its empirical success, a rigorous study of this method's ability to achieve accelerated convergence has been missing. We initiate this investigation combining a concentration of measure approach to examine the automatic tuning mechanism with a coupling based mixing analysis for Hamiltonian Monte Carlo. In certain Gaussian target distributions, this yields a precise characterization of the sampler's behavior resulting, in particular, in rigorous mixing guarantees describing the algorithm's ability and limitations in achieving accelerated convergence. |
| title | On Accelerated Mixing of the No-U-turn Sampler |
| topic | Statistics Theory Probability Computation Machine Learning |
| url | https://arxiv.org/abs/2507.13259 |