Approximating Probabilistic Inference in Statistical $\mathcalEL$ with Knowledge Graph Embeddings

Yuqicheng Zhu, Nico Potyka, Bo Xiong, Trung-Kien Tran, Mojtaba Nayyeri, Evgeny Kharlamov, Steffen Staab
Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence, PMLR 337:8312-8329, 2026.

Abstract

In domains where statistical data is collected across hierarchically organized categories, drawing valid conclusions requires reasoning jointly about proportions and the structure of the domain. Statistical $\mathcal{EL}$ ($\mathcal{SEL}$) formalizes this kind of reasoning, but exact inference is \textsc{ExpTime}-hard and no implementation exists. We show how knowledge graph embeddings can approximate $\mathcal{SEL}$ inference efficiently. We prove analytical runtime and soundness guarantees, and empirically evaluate the runtime and approximation quality of our approach.

Cite this Paper

BibTeX
@InProceedings{pmlr-v337-zhu26a, title = {Approximating Probabilistic Inference in Statistical $\mathcal{EL}$ with Knowledge Graph Embeddings}, author = {Zhu, Yuqicheng and Potyka, Nico and Xiong, Bo and Tran, Trung-Kien and Nayyeri, Mojtaba and Kharlamov, Evgeny and Staab, Steffen}, booktitle = {Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence}, pages = {8312--8329}, year = {2026}, editor = {Perković, Emilija and Malinsky, Daniel}, volume = {337}, series = {Proceedings of Machine Learning Research}, month = {17--21 Aug}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v337/main/assets/zhu26a/zhu26a.pdf}, url = {https://proceedings.mlr.press/v337/zhu26a.html}, abstract = {In domains where statistical data is collected across hierarchically organized categories, drawing valid conclusions requires reasoning jointly about proportions and the structure of the domain. Statistical $\mathcal{EL}$ ($\mathcal{SEL}$) formalizes this kind of reasoning, but exact inference is \textsc{ExpTime}-hard and no implementation exists. We show how knowledge graph embeddings can approximate $\mathcal{SEL}$ inference efficiently. We prove analytical runtime and soundness guarantees, and empirically evaluate the runtime and approximation quality of our approach.} }
Endnote
%0 Conference Paper %T Approximating Probabilistic Inference in Statistical $\mathcalEL$ with Knowledge Graph Embeddings %A Yuqicheng Zhu %A Nico Potyka %A Bo Xiong %A Trung-Kien Tran %A Mojtaba Nayyeri %A Evgeny Kharlamov %A Steffen Staab %B Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2026 %E Emilija Perković %E Daniel Malinsky %F pmlr-v337-zhu26a %I PMLR %P 8312--8329 %U https://proceedings.mlr.press/v337/zhu26a.html %V 337 %X In domains where statistical data is collected across hierarchically organized categories, drawing valid conclusions requires reasoning jointly about proportions and the structure of the domain. Statistical $\mathcal{EL}$ ($\mathcal{SEL}$) formalizes this kind of reasoning, but exact inference is \textsc{ExpTime}-hard and no implementation exists. We show how knowledge graph embeddings can approximate $\mathcal{SEL}$ inference efficiently. We prove analytical runtime and soundness guarantees, and empirically evaluate the runtime and approximation quality of our approach.
APA
Zhu, Y., Potyka, N., Xiong, B., Tran, T., Nayyeri, M., Kharlamov, E. & Staab, S.. (2026). Approximating Probabilistic Inference in Statistical $\mathcalEL$ with Knowledge Graph Embeddings. Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research 337:8312-8329 Available from https://proceedings.mlr.press/v337/zhu26a.html.

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