  Causal structure learning, a prominent technique for encoding cause and
effect relationships among variables, through Bayesian Networks (BNs). Merely
recovering causal structures from real-world observed data lacks precision,
while the development of Large Language Models (LLM) is opening a new frontier
of causality. LLM presents strong capability in discovering causal
relationships between variables with the "text" inputs defining the
investigated variables, leading to a potential new hierarchy and new ladder of
causality. We aim an critical issue in the emerging topic of LLM based causal
structure learning, to tackle erroneous prior causal statements from LLM, which
is seldom considered in the current context of expert dominating prior
resources. As a pioneer attempt, we propose a BN learning strategy resilient to
prior errors without need of human intervention. Focusing on the edge-level
prior, we classify the possible prior errors into three types:
order-consistent, order-reversed, and irrelevant, and provide their theoretical
impact on the Structural Hamming Distance (SHD) under the presumption of
sufficient data. Intriguingly, we discover and prove that only the
order-reversed error contributes to an increase in a unique acyclic closed
structure, defined as a "quasi-circle". Leveraging this insight, a post-hoc
strategy is employed to identify the order-reversed prior error 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
knowledge.
