发表机构
University of Oxford; Nanyang Technological University; KU Leuven（牛津大学; 南洋理工大学; 鲁汶大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出LazyHMC方法，通过惰性求值开发适用于无限维概率程序的梯度HMC变体及无回跳采样器，经高斯混合聚类等实验验证其有效性。
AI 中文摘要
哈密顿蒙特卡洛（HMC）是概率编程中一种成功的通用推断方法，但在常规形式下它需要梯度和有限维参数空间。在Haskell中，惰性求值使概率程序能在隐式无限维空间上表示随机过程及其他非参数贝叶斯模型。本文通过惰性求值为这种无限维场景开发了基于梯度的HMC的新形式。对于自动微分，我们基于“柱形解析划分下的分段解析（PACAP）”这一新概念开展分析，以证明即使程序是无限维且惰性定义的，似然函数的梯度也具有有限支撑。对于蒙特卡洛方法本身，我们开发了若干HMC变体及一个无回跳采样器，它们在无限维参数空间上运行，且因惰性求值仍具有高效性。实验涵盖高斯混合聚类、随机游走以及带泊松过程变点的分段常数回归。
英文摘要
Hamiltonian Monte Carlo (HMC) is a successful generic inference method in probabilistic programming, but in its ordinary formulation it needs gradients and finite-dimensional parameter spaces. In Haskell, lazy evaluation lets probabilistic programs express stochastic processes and other non-parametric Bayesian models over implicit infinite-dimensional spaces. This paper develops new formulations of gradient-based HMC for this infinite-dimensional setting, via lazy evaluation. For automatic differentiation, we provide an analysis based on a new notion of "piecewise analytic under cylindrical analytic partition" (PACAP), to show that even if a program is infinite-dimensional and defined lazily, the gradient of the likelihood function is finitely supported. For the Monte Carlo method itself, we develop several HMC variants and a No-U-Turn Sampler that operate over the infinite-dimensional parameter space but are still productive because of lazy evaluation. Experiments cover Gaussian mixture clustering, random walks, and piecewise-constant regression with Poisson-process changepoints.
Comments41 pages
Journal refProc. ACM Program. Lang. 10, ICFP, Article 298 (2026)
DOI：10.1145/3828696
