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

arXiv: https://arxiv.org/abs/1806.02027 · HTML: https://mlsanity.com/paper/1806.02027/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Jun 2018.

## Built on by (most cited first, 4 of 4)

- [Declarative Probabilistic Logic Programming in Discrete-Continuous Domains](https://mlsanity.com/paper/2302.10674/) (2023)
- [Measure Theoretic Weighted Model Integration](https://mlsanity.com/paper/2103.13901/) (2021)
- [First-Order Context-Specific Likelihood Weighting in Hybrid Probabilistic Logic Programs](https://mlsanity.com/paper/2201.11165/) (2022)
- [String Diagrams with Factorized Densities](https://mlsanity.com/paper/2305.02506/) (2023)

## Abstract (arXiv)

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.