# First-Order Context-Specific Likelihood Weighting in Hybrid Probabilistic Logic Programs

arXiv: https://arxiv.org/abs/2201.11165 · HTML: https://mlsanity.com/paper/2201.11165/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 74 references that are in the map.
- First posted on arXiv 26 Jan 2022.

## Builds on (most cited first, 11 of 11)

- [Context-Specific Independence in Bayesian Networks](https://mlsanity.com/paper/1302.3562/) (2013)
- [Lifted Variable Elimination: Decoupling the Operators from the Constraint Language](https://mlsanity.com/paper/1402.0565/) (2014)
- [Bayes-Ball: The Rational Pastime (for Determining Irrelevance and Requisite Information in Belief Networks and Influence Diagrams)](https://mlsanity.com/paper/1301.7412/) (2013)
- [New Liftable Classes for First-Order Probabilistic Inference](https://mlsanity.com/paper/1610.08445/) (2016)
- [Efficient Search-Based Weighted Model Integration](https://mlsanity.com/paper/1903.05334/) (2019)
- [Approximate Knowledge Compilation by Online Collapsed Importance Sampling](https://mlsanity.com/paper/1805.12565/) (2018)
- [On the Complexity and Approximation of Binary Evidence in Lifted Inference](https://mlsanity.com/paper/1311.6591/) (2013)
- [Discrete-Continuous Mixtures in Probabilistic Programming: Generalized Semantics and Inference Algorithms](https://mlsanity.com/paper/1806.02027/) (2018)
- [Lifted Hybrid Variational Inference](https://mlsanity.com/paper/2001.02773/) (2020)
- [Learning Distributional Programs for Relational Autocompletion](https://mlsanity.com/paper/2001.08603/) (2020)
- [Context-Specific Likelihood Weighting](https://mlsanity.com/paper/2101.09791/) (2021)

## Abstract (arXiv)

Statistical relational AI and probabilistic logic programming have so far mostly focused on discrete probabilistic models. The reasons for this is that one needs to provide constructs to succinctly model the independencies in such models, and also provide efficient inference. Three types of independencies are important to represent and exploit for scalable inference in hybrid models: conditional independencies elegantly modeled in Bayesian networks, context-specific independencies naturally represented by logical rules, and independencies amongst attributes of related objects in relational models succinctly expressed by combining rules. This paper introduces a hybrid probabilistic logic programming language, DC#, which integrates distributional clauses' syntax and semantics principles of Bayesian logic programs. It represents the three types of independencies qualitatively. More importantly, we also introduce the scalable inference algorithm FO-CS-LW for DC#. FO-CS-LW is a first-order extension of the context-specific likelihood weighting algorithm (CS-LW), a novel sampling method that exploits conditional independencies and context-specific independencies in ground models. The FO-CS-LW algorithm upgrades CS-LW with unification and combining rules to the first-order case.