Integrating expert knowledge, e.g. from large language models, into causal discovery algorithms can be challenging when the knowledge is not guaranteed to be correct. Expert recommendations may contradict data-driven results, and their reliability can vary significantly depending on the domain or specific query. Existing methods based on soft constraints or inconsistencies in predicted causal relationships fail to account for these variations in expertise. To remedy this, we propose L2D-CD, a method for gauging the correctness of expert recommendations and optimally combining them with data-driven causal discovery results. By adapting learning-to-defer (L2D) algorithms for pairwise causal discovery (CD), we learn a deferral function that selects whether to rely on classical causal discovery methods using numerical data or expert recommendations based on textual meta-data. We evaluate L2D-CD on the canonical T\"ubingen pairs dataset and demonstrate its superior performance compared to both the causal discovery method and the expert used in isolation. Moreover, our approach identifies domains where the expert's performance is strong or weak. Finally, we outline a strategy for generalizing this approach to causal discovery on graphs with more than two variables, paving the way for further research in this area.

本研究解决了将不完全可靠的专家知识整合进因果发现算法的问题。我们提出了一种称为L2D-CD的新方法，通过学习延迟算法来优化专家建议与数据驱动因果发现结果的结合。研究表明，该方法在因果发现中表现优于传统方法，并能识别专家表现的强弱领域，为未来研究奠定基础。

学习延迟以进行带有不完美专家的因果发现