LazyHMC: Hamiltonian Monte Carlo Simulation for Lazy, Infinite Dimensional Probabilistic Programs

• URL: http://arxiv.org/abs/2608.08588v1
• Date: Sun, 09 Aug 2026 09:05:51 GMT
• Title: LazyHMC: Hamiltonian Monte Carlo Simulation for Lazy, Infinite Dimensional Probabilistic Programs
• Abstract summary: Hamiltonian Monte Carlo (HMC) is a successful generic inference method in probabilistic programming.<n>In Haskell, lazy evaluation lets programs express processes over implicit infinitedimensional spaces.<n>This paper develops new formulations of gradient-based HMC for this infinite-dimensional setting.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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