Discrete-Continuous Mixtures in Probabilistic Programming: Generalized\n Semantics and Inference Algorithms

Abstract

Despite the recent successes of probabilistic programming languages (PPLs) in\nAI applications, PPLs offer only limited support for random variables whose\ndistributions combine discrete and continuous elements. We develop the notion\nof measure-theoretic Bayesian networks (MTBNs) and use it to provide more\ngeneral semantics for PPLs with arbitrarily many random variables defined over\narbitrary measure spaces. We develop two new general sampling algorithms that\nare provably correct under the MTBN framework: the lexicographic likelihood\nweighting (LLW) for general MTBNs and the lexicographic particle filter (LPF),\na specialized algorithm for state-space models. We further integrate MTBNs into\na widely used PPL system, BLOG, and verify the effectiveness of the new\ninference algorithms through representative examples.\n