2021/06/18 by Carol Mak, Mak, Carol, Fabian Zaiser +3
Computer Science · #Bayesian Modeling and Causal Inference #Computation (stat.CO) #Explainable Artificial Intelligence (XAI) #FOS: Computer and information sciences #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Machine Learning and Algorithms #Programming Languages (cs.PL)
paper · pdf · doi:10.48550/arxiv.2106.10238
openalex publication_date 2021/06/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.