Nonparametric Hamiltonian Monte Carlo

Conference item

Probabilistic programming uses programs to express generative models whose posterior probability is then computed by built-in inference engines. A challenging goal is to develop general purpose inference algorithms that work out-of-the-box 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 infinite-dimensional 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 (NP-HMC) algorithm which generalises HMC to nonparametric models. Inputs to NP-HMC are a new class of measurable functions called “tree representable”, which serve as a language-independent representation of the density functions of probabilistic programs in a universal PPL. We provide a correctness proof of NP-HMC, and empirically demonstrate significant performance improvements over existing approaches on several nonparametric examples.

Authors: Mak, C; Zaiser, F; Ong, L

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: Journal of Machine Learning Research
• Pages: 7336-7347
• Series: Proceedings of Machine Learning Research
• Series number: 139
• Publication date: 2021-07-01
• Acceptance date: 2021-05-08
• Event title: Thirty-eighth International Conference on Machine Learning (ICML 2021)
• Event location: Virtual event
• Event website: https://icml.cc/Conferences/2021
• Event start date: 2021-07-18
• Event end date: 2021-07-24
• ISSN: 2640-3498
• Language: English
• Keywords: FFR