Nonparametric Hamiltonian Monte Carlo
Abstract
Probabilistic programming uses programs to express generative models whose posterior probability is then computed by builtin inference engines. A challenging goal is to develop general purpose inference algorithms that work outofthebox for arbitrary programs in a universal probabilistic programming language (PPL). The densities defined by such programs, which may use stochastic branching and recursion, are (in general) nonparametric, in the sense that they correspond to models on an infinitedimensional parameter space. However standard inference algorithms, such as the Hamiltonian Monte Carlo (HMC) algorithm, target distributions with a fixed number of parameters. This paper introduces the Nonparametric Hamiltonian Monte Carlo (NPHMC) algorithm which generalises HMC to nonparametric models. Inputs to NPHMC are a new class of measurable functions called "tree representable", which serve as a languageindependent representation of the density functions of probabilistic programs in a universal PPL. We provide a correctness proof of NPHMC, and empirically demonstrate significant performance improvements over existing approaches on several nonparametric examples.
 Publication:

arXiv eprints
 Pub Date:
 June 2021
 DOI:
 10.48550/arXiv.2106.10238
 arXiv:
 arXiv:2106.10238
 Bibcode:
 2021arXiv210610238M
 Keywords:

 Computer Science  Machine Learning;
 Computer Science  Programming Languages;
 Statistics  Computation;
 Statistics  Machine Learning
 EPrint:
 Updated plots (after fixing minor bugs in the implementation) compared to the published version in Proceedings of the 38th International Conference on Machine Learning, PMLR 139, 2021. The conclusions of the version published at ICML 2021 are not affected