KG-SoftMAP: Soft Knowledge-Graph Priors for Bayesian Network Structure Learning from Sparse Discrete Data

A new method called KG-SoftMAP aims to improve Bayesian network structure learning from sparse discrete data by incorporating soft, weighted knowledge-graph priors, according to a paper posted to arXiv [1]. The approach is designed for settings where data alone is insufficient to recover reliable variable relationships [1]. Learning the structure of a Bayesian network (BN) from sparse discrete data is a difficult problem because most variable pairs lack the joint observations needed for reliable scoring, and data-only methods recover little structure [1]. The authors propose KG-SoftMAP, which encodes imperfect domain knowledge as a weighted directed knowledge graph (KG) and uses it as a soft, confidence-weighted, data-overridable edge prior [1]. The method maximizes a maximum a posteriori (MAP) objective that combines the Bayesian Dirichlet equivalent uniform (BDeu) score with a logit-form prior [1]. The KG can be curated by experts or extracted using a large language model (LLM) [1]. On controlled synthetic benchmarks, the only setting with ground-truth directed acyclic graphs (DAGs), KG-SoftMAP recovered partial directed structure at a density threshold of 0.05, achieving a directed F1 (DF1) score between 0.14 and 0.29, compared to near-zero scores for baseline methods [1]. When the density threshold reached 0.2 or higher, the DF1 score rose to between 0.46 and 0.96 when paired with an informative but imperfect KG [1]. The paper notes that recovery performance degrades gracefully as the quality of the knowledge graph decreases [1]. On real sparse educational data from the SAF dataset, which lacks a ground-truth DAG, the evaluation focused on deployment-facing measures: prediction, calibration, and consistency with the knowledge graph [1]. The learned BN is best interpreted as a diagnostic model, trailing logistic regression by 0.03 in the F1 score for failure prediction while providing KG-consistent edges, calibrated joint probabilities, and the ability to perform inference from arbitrary subsets of observed concepts [1]. The authors state that when no meaningful knowledge graph exists, discriminative logistic regression is the preferable approach [1].