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. We propose KG-SoftMAP, which encodes such a KG as a soft, confidence-weighted, data-overridable edge prior and maximizes a MAP objective combining the BDeu score with a logit-form prior; the KG may be expert-curated or LLM-extracted. On controlled synthetic benchmarks, the only setting with ground-truth DAGs, KG-SoftMAP recovers partial directed structure at $ρ=0.05$ (DF1 $0.14$ to $0.29$, versus near-zero baselines) and substantially more once $ρ\geq0.2$ (DF1 $0.46$ to $0.96$), when paired with an informative but imperfect KG; recovery degrades gracefully as KG quality drops. On real sparse educational data, which has no ground-truth DAG, we evaluate deployment-facing measures only: prediction, calibration, and KG-consistency. The learned BN is best read as a diagnostic model: on SAF it trails logistic regression by $0.03$ F1_FAIL while providing KG-consistent edges, calibrated joint probabilities, and inference from arbitrary observed concept subsets; when no meaningful KG exists, discriminative logistic regression is preferable.