Approximating Probabilistic Inference in Statistical EL with Knowledge Graph Embeddings

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.