XBIC: Shapley-Weighted BIC for Score-Based Causal Discovery in Discrete Bayesian Networks

ICLR 2026 Conference Submission19086 Authors

Keywords: XAI, Explainability, practical implementation, Bayesian network structure learning

TL;DR: Empirical plug-in method XBIC, a Shapley-weighted BIC that uses per-edge attributions to guide score-based DAG search for discrete Bayesian networks.

Abstract: Score-based causal discovery for purely discrete data remains dominated by hill-climbing with the Bayesian Information Criterion (BIC), yet BIC often struggles to orient edges within Markov-equivalence classes. We introduce XBIC, a principled enhancement that soft-weights BIC's complexity penalty with edge-specific Shapley evidence: when a candidate parent contributes strongly to its child's likelihood, XBIC reduces the penalty proportionally, while defaulting to standard BIC when support is weak. Across ten benchmark discrete Bayesian networks (6--76 nodes) and seven sample-size regimes (700 runs), XBIC yields consistent gains, improving oriented-edge \(F_{1}\) by 5.6\% over hill-climbing BIC, 9.6\% over a generalized-score GES variant, and 20.9\% over PC. XBIC remains a drop-in upgrade within the familiar BIC framework. To facilitate adoption and reproducibility, we release code, data splits, and scripts at https://anonymous.4open.science/r/causal_discovery_shap-6900/README.md

Primary Area: probabilistic methods (Bayesian methods, variational inference, sampling, UQ, etc.)

Submission Number: 19086