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

arXiv: https://arxiv.org/abs/2606.10358 · HTML: https://mlsanity.com/paper/2606.10358/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 31 of its 61 references that are in the map.
- First posted on arXiv 9 Jun 2026.

## Builds on (most cited first, 30 of 31)

- [DAGs with NO TEARS: Continuous Optimization for Structure Learning](https://mlsanity.com/paper/1803.01422/) (2018)
- [Deep Knowledge Tracing](https://mlsanity.com/paper/1506.05908/) (2015)
- [On the Role of Sparsity and DAG Constraints for Learning Linear DAGs](https://mlsanity.com/paper/2006.10201/) (2020)
- [Learning Bayesian Networks: The Combination of Knowledge and Statistical Data](https://mlsanity.com/paper/1302.6815/) (2013)
- [Context-Aware Attentive Knowledge Tracing](https://mlsanity.com/paper/2007.12324/) (2020)
- [A Self-Attentive model for Knowledge Tracing](https://mlsanity.com/paper/1907.06837/) (2019)
- [Causal Inference and Causal Explanation with Background Knowledge](https://mlsanity.com/paper/1302.4972/) (2013)
- [DAGMA: Learning DAGs via M-matrices and a Log-Determinant Acyclicity Characterization](https://mlsanity.com/paper/2209.08037/) (2022)
- [DiBS: Differentiable Bayesian Structure Learning](https://mlsanity.com/paper/2105.11839/) (2021)
- [Towards an Appropriate Query, Key, and Value Computation for Knowledge Tracing](https://mlsanity.com/paper/2002.07033/) (2020)
- [Instructions and Guide for Diagnostic Questions: The NeurIPS 2020 Education Challenge](https://mlsanity.com/paper/2007.12061/) (2020)
- [Greedy Relaxations of the Sparsest Permutation Algorithm](https://mlsanity.com/paper/2206.05421/) (2022)
- [DAGs with No Curl: An Efficient DAG Structure Learning Approach](https://mlsanity.com/paper/2106.07197/) (2021)
- [pyKT: A Python Library to Benchmark Deep Learning based Knowledge Tracing Models](https://mlsanity.com/paper/2206.11460/) (2022)
- [simpleKT: A Simple But Tough-to-Beat Baseline for Knowledge Tracing](https://mlsanity.com/paper/2302.06881/) (2023)
- [Fast Scalable and Accurate Discovery of DAGs Using the Best Order Score Search and Grow-Shrink Trees](https://mlsanity.com/paper/2310.17679/) (2023)
- [Causal Inference with Large Language Model: A Survey](https://mlsanity.com/paper/2409.09822/) (2024)
- [Stable Differentiable Causal Discovery](https://mlsanity.com/paper/2311.10263/) (2023)
- [The Bayesian Structural EM Algorithm](https://mlsanity.com/paper/1301.7373/) (2013)
- [Large Language Models for Causal Discovery: Current Landscape and Future Directions](https://mlsanity.com/paper/2402.11068/) (2024)
- [Large Language Models are Effective Priors for Causal Graph Discovery](https://mlsanity.com/paper/2405.13551/) (2024)
- [Learning Bayesian Network Structure from Massive Datasets: The "Sparse Candidate" Algorithm](https://mlsanity.com/paper/1301.6696/) (2013)
- [Self-Compatibility: Evaluating Causal Discovery without Ground Truth](https://mlsanity.com/paper/2307.09552/) (2023)
- [Causal Structure Learning Supervised by Large Language Model](https://mlsanity.com/paper/2311.11689/) (2023)
- [Bayesian Network Constraint-Based Structure Learning Algorithms: Parallel and Optimised Implementations in the bnlearn R Package](https://mlsanity.com/paper/1406.7648/) (2014)
- [Greedy structure learning from data that contain systematic missing values](https://mlsanity.com/paper/2107.04184/) (2021)
- [A Construction of Bayesian Networks from Databases Based on an MDL Principle](https://mlsanity.com/paper/1303.1486/) (2013)
- [Learning Bayesian Networks with Incomplete Data by Augmentation](https://mlsanity.com/paper/1608.07734/) (2016)
- [Bayesian Network Structure Discovery Using Large Language Models](https://mlsanity.com/paper/2511.00574/) (2025)
- [Realizing LLMs' Causal Potential Requires Science-Grounded, Novel Benchmarks](https://mlsanity.com/paper/2510.16530/) (2025)

## Built on by (most cited first, 1 of 1)

- [Coupling Noisy Pairwise Knowledge to the DAG Posterior for Causal Discovery](https://mlsanity.com/paper/2610.04559/) (2026)

## Abstract (arXiv)

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.