Causal structure learning has long been the central task of inferring causal insights from data. Despite the abundance of real-world processes exhibiting higher-order mechanisms, however, an explicit treatment of interactions in causal discovery has received little attention. In this work, we focus on extending the causal additive model (CAM) to additive models with higher-order interactions. This second level of modularity we introduce to the structure learning problem is most easily represented by a directed acyclic hypergraph which extends the DAG. We introduce the necessary definitions and theoretical tools to handle the novel structure we introduce and then provide identifiability results for the hyper DAG, extending the typical Markov equivalence classes. We next provide insights into why learning the more complex hypergraph structure may actually lead to better empirical results. In particular, more restrictive assumptions like CAM correspond to easier-to-learn hyper DAGs and better finite sample complexity. We finally develop an extension of the greedy CAM algorithm which can handle the more complex hyper DAG search space and demonstrate its empirical usefulness in synthetic experiments.

翻译：因果结构学习长期以来是从数据中推断因果洞察的核心任务。然而，尽管现实世界过程普遍表现出高阶机制，但因果发现中对交互作用的显式处理却鲜受关注。在本研究中，我们致力于将因果加性模型（CAM）扩展至包含高阶交互作用的加性模型。我们为结构学习问题引入的第二层模块性，最易通过扩展有向无环图（DAG）的有向无环超图来表征。我们提出了处理这一新型结构所需的定义与理论工具，随后给出了超DAG的可识别性结果，扩展了典型的马尔可夫等价类。接着，我们深入阐释了学习更复杂的超图结构何以能带来更优的实证结果。具体而言，CAM等限制性更强的假设对应于更易学习的超DAG及更优的有限样本复杂度。最后，我们开发了贪婪CAM算法的扩展版本，该算法能够处理更复杂的超DAG搜索空间，并通过合成实验验证了其实际效用。