Nonparametric Hamiltonian Monte Carlo

TL;DR

This paper introduces Nonparametric Hamiltonian Monte Carlo (NP-HMC), an extension of HMC for nonparametric probabilistic models expressed in universal PPLs, enabling more effective inference on complex, infinite-dimensional models.

Contribution

It proposes NP-HMC, a novel algorithm that generalizes HMC to nonparametric models using tree representable functions, with correctness proof and empirical performance improvements.

Findings

NP-HMC outperforms existing methods on nonparametric examples

Provides a correctness proof for the NP-HMC algorithm

Enables inference on models with infinite-dimensional parameter spaces

Abstract

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.