发表机构
Universität Heidelberg; University of Tübingen; ELLIS Institute Tübingen（海德堡大学; 图宾根大学; 图宾根ELLIS研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究从热力学角度分析微正则哈密顿蒙特卡洛算法，证明其满足亥姆霍兹定理，提出扩展至低维推断的新算法，并论证正则MCMC更自然。
AI 中文摘要
最近提出的微正则哈密顿蒙特卡洛算法尚未从热力学角度进行详细研究；本研究旨在填补这一空白。我们展示了如何推导热力学状态变量和势函数，从而证明该算法的构造在形式上代表了一个微正则热力学系综。特别地，我们（解析地和数值地）证明了该算法满足亥姆霍兹定理，即热力学第一定律的另一种表述。此外，我们构建了一种新的采样算法，将原始算法扩展到低维推断问题。最后，我们认为从热力学和信息论的角度来看，正则马尔可夫链蒙特卡洛算法比微正则哈密顿蒙特卡洛算法更为自然。
英文摘要
The recently proposed Microcanonical Hamiltonian Monte Carlo algorithm has not yet been studied in detail from a thermodynamic point of view; this work aims to fill that gap. We demonstrate how thermodynamical state variables and potentials can be derived and thereby demonstrate that the construction of the algorithm formally represents a microcanonical thermodynamic ensemble. In particular, we demonstrate (analytically and numerically) that the algorithm fulfils the Helmholtz theorem, an alternative formulation of the first law of thermodynamics. Furthermore, we construct a new sampling algorithm that extends the original to lower-dimensional inference problems. Finally, we argue that canonical Markov Chain Monte Carlo algorithms are more natural than Microcanonical Hamiltonian Monte Carlo from the thermodynamic and information-theoretic point of view.
