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

2018/06/06 by Yi Wu, Wu, Yi, Siddharth Srivastava +7 · 1 citation
Computer Science · #AI-based Problem Solving and Planning #Artificial Intelligence (cs.AI) #Bayesian Modeling and Causal Inference #FOS: Computer and information sciences #Logic, Reasoning, and Knowledge #Machine Learning (cs.LG) #Machine Learning and Algorithms #Programming Languages (cs.PL)

paper · pdf · doi:10.48550/arxiv.1806.02027

openalex publication_date 2018/06/06 · openalex created_date 2019/07/30 · openalex updated_date 2026/07/28

Abstract

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

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