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.

翻译：因果结构学习是通过贝叶斯网络（BN）编码变量间因果关系的重要技术。仅从现实观测数据恢复因果结构缺乏精确性，而大语言模型（LLM）的发展正为因果性开辟新前沿。LLM在利用定义研究变量的"文本"输入发现变量间因果关系方面展现出强大能力，这可能导致因果性的新层级和新阶梯产生。我们聚焦于基于LLM的因果结构学习这一新兴主题中的关键问题——处理来自LLM的错误先验因果陈述，这在当前专家主导先验资源的背景下鲜少被考虑。作为开创性尝试，我们提出一种无需人工干预即可抵御先验错误的BN学习策略。聚焦边级先验，我们将可能的先验错误分为三类：顺序一致型、顺序反转型和不相关型，并在数据充足假设下理论分析它们对结构汉明距离（SHD）的影响。令人关注的是，我们发现并证明仅顺序反转型错误会导致一种独特无环闭包结构（定义为"准环"）的增加。基于此洞察，我们采用事后策略通过评估"准环"增量来识别顺序反转型先验错误。通过在真实与合成数据集上的实证评估，我们证明了该策略对先验错误的鲁棒性。具体而言，我们突出展示了其在保留大部分正确先验知识的同时，抵御顺序反转型错误的显著能力。