Diagnosing Suboptimal Cotangent Disintegrations in Hamiltonian Monte Carlo
Michael [ Department of Statistics, University of Warwick, Coventry CV4 7AL, UK .
Abstract
When properly tuned, Hamiltonian Monte Carlo scales to some of the most challenging high-dimensional problems at the frontiers of applied statistics, but when that tuning is suboptimal the performance leaves much to be desired. In this paper I show how suboptimal choices of one critical degree of freedom, the cotangent disintegration, manifest in readily observed diagnostics that facilitate the robust application of the algorithm.
中文速览
哈密顿蒙特卡洛（Hamiltonian Monte Carlo, HMC）是目前最强大的高维贝叶斯推断算法之一，但它的表现对一个关键参数——余切分解（cotangent disintegration，即动量分布的选取方式）——极为敏感，选得不好会导致采样效率低下甚至结果有偏。本文从"能量层级随机游走"的视角重新审视HMC的工作机制，指出动量重采样在能量空间的探索效率是衡量余切分解优劣的核心，并据此推导出几个可直接从采样历史中估算的实用诊断指标，包括贝叶斯缺失信息分数（Bayesian Fraction of Missing Information, BFMI）、能量的有效样本量以及能量变化直方图对比。通过多个实际例子，作者展示了这些诊断工具如何准确捕捉到余切分解次优时的异常信号。这项工作为HMC用户提供了一套无需修改模型即可检验算法调参质量的实操方法，有助于在复杂统计推断中更可靠地使用HMC。
原文 arXiv:1604.00695;中英对照 + 大白话阅读 https://aha.fim.ai/paper/1604.00695v1