Stat-n-Ball: Enhancing Probabilistic Knowledge Graph Embeddings with Geometric and Confidence-Aware Models

Region-based Knowledge Graph Embedding (R-KGE) models, which represent entities as convex shapes (e.g., balls) and relations as geometric transformations in vector space, offer a promising approach for explainable and accurate reasoning over ontologies. However, existing R-KGE models assume perfect reliability of Knowledge Graphs (KGs), which is often unrealistic as real-world KGs are noisy and incomplete. To address this, Probabilistic Knowledge Graphs (P-KGs) associate axioms with confidence scores, capturing the uncertainty of their truthfulness. We propose Stat-n-Ball, a novel R-KGE framework that incorporates confidence scores by representing axioms' certainty as overlapping volumes between entities in vector space. Our approach enhances the geometric representation of KGs, enabling accurate link prediction and confidence estimation in probabilistic settings. Experimental evaluations on standard P-KG datasets demonstrate that Stat-n-Ball achieves atleast a 2× improvement in entity association detection and a minimum 5% reduction in confidence prediction error compared to state-of-the-art models. These results underscore its effectiveness in handling noisy and uncertain KGs while preserving logical and semantic integrity.