Mitigating Prior Errors in Causal Structure Learning: A Resilient Approach via Bayesian Networks

Causal structure learning (CSL), a prominent technique for encoding cause-and-effect relationships among variables, through Bayesian Networks (BNs). Although recovering causal structure solely from data is a challenge, the integration of prior knowledge, revealing partial structural truth, can markedly enhance learning quality. However, current methods based on prior knowledge exhibit limited resilience to errors in the prior, with hard constraint methods disregarding priors entirely, and soft constraints accepting priors based on a predetermined confidence level, which may require expert intervention. To address this issue, we propose a strategy resilient to edge-level prior errors for CSL, thereby minimizing human intervention. We classify prior errors into different types and provide their theoretical impact on the Structural Hamming Distance (SHD) under the presumption of sufficient data. Intriguingly, we discover and prove that the strong hazard of prior errors is associated with a unique acyclic closed structure, defined as ``quasi-circle''. Leveraging this insight, a post-hoc strategy is employed to identify the prior errors by its impact on the increment of ``quasi-circles''. Through empirical evaluation on both real and synthetic datasets, we demonstrate our strategy's robustness against prior errors. Specifically, we highlight its substantial ability to resist order-reversed errors while maintaining the majority of correct prior.