In observational studies, the true causal model is typically unknown and needs to be estimated from available observational and limited experimental data. In such cases, the learned causal model is commonly represented as a partially directed acyclic graph (PDAG), which contains both directed and undirected edges indicating uncertainty of causal relations between random variables. The main focus of this paper is on the maximal orientation task, which, for a given PDAG, aims to orient the undirected edges maximally such that the resulting graph represents the same Markov equivalent DAGs as the input PDAG. This task is a subroutine used frequently in causal discovery, e. g., as the final step of the celebrated PC algorithm. Utilizing connections to the problem of finding a consistent DAG extension of a PDAG, we derive faster algorithms for computing the maximal orientation by proposing two novel approaches for extending PDAGs, both constructed with an emphasis on simplicity and practical effectiveness.

翻译：在观察性研究中，真实因果模型通常未知，需要从可获得的观察数据和有限的实验数据中估计。此时，学习到的因果模型常被表示为部分有向无环图（PDAG），其中同时包含有向边和无向边，以指示随机变量间因果关系的不确定性。本文主要关注极大定向任务：对于给定PDAG，该任务旨在极大化地定向无向边，使得最终图表示与输入PDAG相同的马尔可夫等价DAG。该任务是因果发现中频繁使用的子例程，例如著名PC算法的最后步骤。通过利用与寻找PDAG的一致DAG扩展问题之间的联系，我们推导出计算极大定向的更快算法：提出两种扩展PDAG的新方法，两者均以简洁性和实际有效性为设计重点。