Despite several advances in recent years, learning causal structures represented by directed acyclic graphs (DAGs) remains a challenging task in high dimensional settings when the graphs to be learned are not sparse. In this paper, we propose to exploit a low rank assumption regarding the (weighted) adjacency matrix of a DAG causal model to help address this problem. We utilize existing low rank techniques to adapt causal structure learning methods to take advantage of this assumption and establish several useful results relating interpretable graphical conditions to the low rank assumption. Specifically, we show that the maximum rank is highly related to hubs, suggesting that scale-free networks, which are frequently encountered in practice, tend to be low rank. Our experiments demonstrate the utility of the low rank adaptations for a variety of data models, especially with relatively large and dense graphs. Moreover, with a validation procedure, the adaptations maintain a superior or comparable performance even when graphs are not restricted to be low rank.

翻译：尽管近年来取得诸多进展，但在高维场景中，当待学习的图结构非稀疏时，以有向无环图（DAG）表征的因果结构学习仍是一项挑战性任务。本文提出利用DAG因果模型（加权）邻接矩阵的低秩假设来应对该问题。我们借助现有低秩技术，使因果结构学习方法能适配这一假设，并建立了若干关于可解释图属性与低秩假设关联性的实用结论。具体而言，我们证明最大秩与枢纽节点高度相关，这表明实践常见的无标度网络往往具有低秩特性。实验验证了低秩适配方法在多种数据模型（特别是较大规模稠密图）中的有效性。此外，通过验证流程，即便在非低秩图场景下，该方法仍能保持优越或相当的性能表现。