KG-SoftMAP: Soft Knowledge-Graph Priors for Bayesian Network Structure Learning from Sparse Discrete Data
Learning Bayesian network (BN) structure from sparse discrete data is hard: when each instance records only a few variables, most variable pairs lack the joint observations needed for reliable scoring, and data-only methods recover little structure. Imperfect domain knowledge, expressible as a weighted directed knowledge graph (KG), is often available. KG-SoftMAP encodes such a KG as a finite-strength, confidence-weighted edge prior and maximizes a MAP objective that adds this logit-form prior to the BDeu score. With an informative but imperfect KG, KG-SoftMAP recovers partial directed structure even at observation rate rho=0.05, with directed F1 (DF1) of 0.19-0.32 across benchmarks. At higher observation rates within this sparse grid, DF1 reaches 0.44-0.66 at rho=0.20 and 0.46-0.64 at rho=0.40. Across the same three rates, KG-SoftMAP without the KG prior averages DF1 0.00, 0.19, and 0.21. Stress tests that corrupt, remove, or blur the KG signal, together with checks on LLM-extracted graphs beyond canonical benchmarks, show that recovery rises and falls with KG quality. On three real sparse educational datasets without ground-truth DAGs, we evaluate prediction, calibration, and KG-consistency. On Short Answer Feedback (SAF), KG-SoftMAP+VE reaches Fail-class F1 0.75 versus 0.78 for logistic regression while also providing an inspectable concept graph, calibrated Fail probabilities, and posterior queries from partially observed concept evidence. The remaining datasets sharpen the operating picture: weak heuristic KG signal leaves prediction unchanged, while an independent expert ontology moves the learned graph toward expert relatedness.