标题： 关于NUTS采样的加速混合 显示英文标题

标题： On Accelerated Mixing of the No-U-turn Sampler

摘要： 最近在变分次 coercivity 理论上的进展表明，临界情况下随机哈密顿蒙特卡洛可以显著加速其收敛性，从而提高采样性能。由于手动临界调整在实践中不可行，这促使了自动算法解决方案的发展，特别是无-U-turn 采样器。除了其经验成功之外，对该方法能否实现加速收敛的严格研究一直缺失。我们通过结合测度集中方法来研究自动调整机制，并利用基于耦合的哈密顿蒙特卡洛混合分析来启动这项研究。在某些高斯目标分布中，这给出了对采样器行为的精确描述，特别是得出了描述算法在实现加速收敛方面的能力和局限性的严格混合保证。 显示英文摘要

摘要： 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.