Sampling from high-dimensional, multimodal distributions using automatically tuned, tempered Hamiltonian Monte Carlo
自动调参的回火哈密顿蒙特卡洛：高维多峰分布采样AI 解读 ↓
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自动调参的回火哈密顿蒙特卡洛：高维多峰分布采样
- 研究问题
- 如何缓解哈密顿蒙特卡洛在高维强多峰分布中难以跨峰的问题，并降低回火方法的参数调节负担？
- 方法与思路
- 作者模拟温度先升后降的时变哈密顿动力学，通过使哈密顿量近似平稳的时间尺度变换设计自动调参策略。
- 材料陈述的贡献
- 摘要称提出自动调参 THMC，并在数值实验中显示其维度扩展表现优于两种比较方法，另用于多峰后验采样。
- 阅读关注点
- 应核对采样算法如何保持目标分布、调参所用信息与计算成本，以及跨峰混合和维度扩展比较的指标与设定。
- 阅读边界
- 仅据 Crossref 在线优先版本摘要；算法有效性条件和实验数值未展开，所述比较不能推广到全部高维多峰目标。
原文摘要
Abstract Hamiltonian Monte Carlo (HMC) is widely used for sampling from high-dimensional target distributions with densities known up to proportionality. While HMC exhibits favourable scaling properties in high dimensions, it struggles with strongly multimodal distributions. Tempering methods are commonly used to address multimodality, but they can be difficult to tune, especially in high-dimensional settings. In this study, we propose a method that combines tempering with HMC to enable efficient sampling from high-dimensional, strongly multimodal distributions. Our approach simulates the dynamics of a time-varying Hamiltonian in which the temperature increases and then decreases over time. In the first phase, the simulated trajectory gradually explores low-density regions farther from the mode; the second phase guides it back towards a local mode. We develop efficient tuning strategies based on a time-scale transformation under which the Hamiltonian becomes approximately stationary. This leads to a tempered Hamiltonian Monte Carlo (THMC) algorithm with automatic tuning. We demonstrate numerically that our method scales more effectively with dimension than adaptive parallel tempering and tempered sequential Monte Carlo. Finally, we apply our THMC to sample from strongly multimodal posterior distributions arising in Bayesian inference.