Despite of the recent successes of probabilistic programming languages (PPLs) in AI applications, PPLs offer only limited support for discrete-continuous mixture random variables. 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 which are provably correct under the MTBN framework: lexicographic likelihood weighting (LLW) for general MTBNs and lexicographic particle filter (LPF), a specialized algorithm for state space models. We further integrate MTBN into a widely used PPL system, BLOG, and verify the effectiveness of our new inference algorithms through representative examples.

本篇研究开发了概率编程语言（PPLs）的度量叙事贝叶斯网络（MTBNs）的概念，并使用它来提供更多的语义，包括有限的支持组合离散和连续元素的随机变量。最终将MTBNs集成到广泛使用的概率编程语言系统BLOG中，并通过代表性的算例验证了新的推理算法的有效性。

概率编程中的离散连续混合: 广义语义和推断算法