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Causal structure learning, a prominent technique for encoding cause andeffect relationships among variables, through Bayesian Networks (BNs). Merelyrecovering causal structures from real-world observed data lacks precision,while the development of Large Language Models (LLM) is opening a new frontierof causality. LLM presents strong capability in discovering causalrelationships between variables with the "text" inputs defining theinvestigated variables, leading to a potential new hierarchy and new ladder ofcausality. We aim an critical issue in the emerging topic of LLM based causalstructure learning, to tackle erroneous prior causal statements from LLM, whichis seldom considered in the current context of expert dominating priorresources. As a pioneer attempt, we propose a BN learning strategy resilient toprior errors without need of human intervention. Focusing on the edge-levelprior, we classify the possible prior errors into three types:order-consistent, order-reversed, and irrelevant, and provide their theoreticalimpact on the Structural Hamming Distance (SHD) under the presumption ofsufficient data. Intriguingly, we discover and prove that only theorder-reversed error contributes to an increase in a unique acyclic closedstructure, defined as a "quasi-circle". Leveraging this insight, a post-hocstrategy is employed to identify the order-reversed prior error by its impacton the increment of "quasi-circles". Through empirical evaluation on both realand synthetic datasets, we demonstrate our strategy's robustness against priorerrors. Specifically, we highlight its substantial ability to resistorder-reversed errors while maintaining the majority of correct priorknowledge.

Mitigating Prior Errors in Causal Structure Learning: Towards LLM driven Prior Knowledge