# Approximating Probabilistic Inference in Statistical EL with Knowledge Graph Embeddings

arXiv: https://arxiv.org/abs/2407.11821 · HTML: https://mlsanity.com/paper/2407.11821/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 47 references that are in the map.
- First posted on arXiv 16 Jul 2024.

## Builds on (most cited first, 14 of 14)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Embedding Entities and Relations for Learning and Inference in Knowledge Bases](https://mlsanity.com/paper/1412.6575/) (2014)
- [BoxE: A Box Embedding Model for Knowledge Base Completion](https://mlsanity.com/paper/2007.06267/) (2020)
- [Analogical Inference for Multi-Relational Embeddings](https://mlsanity.com/paper/1705.02426/) (2017)
- [EL Embeddings: Geometric construction of models for the Description Logic EL ++](https://mlsanity.com/paper/1902.10499/) (2019)
- [Improving Local Identifiability in Probabilistic Box Embeddings](https://mlsanity.com/paper/2010.04831/) (2020)
- [Faithiful Embeddings for EL++ Knowledge Bases](https://mlsanity.com/paper/2201.09919/) (2022)
- [Probabilistic Box Embeddings for Uncertain Knowledge Graph Reasoning](https://mlsanity.com/paper/2104.04597/) (2021)
- [Dual Box Embeddings for the Description Logic EL++](https://mlsanity.com/paper/2301.11118/) (2023)
- [Description Logic EL++ Embeddings with Intersectional Closure](https://mlsanity.com/paper/2202.14018/) (2022)
- [Towards Statistical Reasoning in Description Logics over Finite Domains (Full Version)](https://mlsanity.com/paper/1706.03207/) (2017)
- [Mining EL Bases with Adaptable Role Depth](https://mlsanity.com/paper/2102.10689/) (2021)
- [Statistical EL is ExpTime-complete](https://mlsanity.com/paper/1911.00696/) (2019)
- [Probabilistic Reasoning in the Description Logic ALCP with the Principle of Maximum Entropy (Full Version)](https://mlsanity.com/paper/1606.09521/) (2016)

## Built on by (most cited first, 5 of 5)

- [ArgRAG: Explainable Retrieval Augmented Generation using Quantitative Bipolar Argumentation](https://mlsanity.com/paper/2508.20131/) (2025)
- [DAGE: DAG Query Answering via Relational Combinator with Logical Constraints](https://mlsanity.com/paper/2410.22105/) (2024)
- [Scalable Uncertainty Reasoning in Knowledge Graphs](https://mlsanity.com/paper/2605.16568/) (2026)
- [ProbSPARQL: Querying Knowledge Graphs with Multi-dimensional, Uncertain Numeric Data](https://mlsanity.com/paper/2607.18262/) (2026)
- [Uncertainty in Representation Learning on Knowledge Graphs](https://mlsanity.com/paper/2610.06974/) (2026)

## Abstract (arXiv)

Statistical information is ubiquitous but drawing valid conclusions from it is prohibitively hard. We explain how knowledge graph embeddings can be used to approximate probabilistic inference efficiently using the example of Statistical EL (SEL), a statistical extension of the lightweight Description Logic EL. We provide proofs for runtime and soundness guarantees, and empirically evaluate the runtime and approximation quality of our approach.