LazyHMC brings Hamiltonian Monte Carlo to infinite-dimensional probabilistic programs
New Haskell-based LazyHMC enables gradient-based inference on infinite-dimensional stochastic processes with lazy evaluation and 3 benchmark experiments
Hamiltonian Monte Carlo just got lazy. LazyHMC brings gradient-based HMC to infinite-dimensional probabilistic programs in Haskell, using lazy evaluation to handle stochastic processes and non-parametric Bayesian models. The paper introduces PACAP, a new analysis showing the likelihood gradient stays finitely supported even in infinite-dimensional, lazily defined programs. It also presents several HMC variants and a No-U-Turn Sampler that remain productive over infinite-dimensional parameter spaces. Experiments cover Gaussian mixture clustering, random walks, and piecewise-constant regression with Poisson-process changepoints.
- LazyHMC enables Hamiltonian Monte Carlo on infinite-dimensional probabilistic programs via Haskell's lazy evaluation
- Introduces PACAP analysis proving gradients are finitely supported even when programs are lazy and infinite-dimensional
- Includes a No-U-Turn Sampler variant tested on Gaussian mixture clustering, random walks, and Poisson-process changepoint regression
Why It Matters
This brings efficient gradient-based inference to expressive infinite-dimensional Bayesian models, potentially unlocking new classes of non-parametric probabilistic programs in Haskell.