New Insights into Causal Structure Learning Limitations

This research investigates the fundamental challenges in causal structure learning, specifically focusing on algorithms designed to identify Directed Acyclic Graphs (DAGs) from data. It highlights that current methods, such as NOTEARS and DAGMA, encounter significant difficulties when the underlying graph structure approaches the boundary of being a valid DAG, meaning it's close to containing cycles. The paper demonstrates that at these critical junctures, the algorithms exhibit a lack of clear ranking for potential structural changes. The study introduces new theoretical insights into the "selection time" for identifying specific causal structures, particularly isolated cycles, and how score margins influence this. It also proposes a method for certifying parts of the causal graph, like skeleton and unshielded collider labels, with high confidence, even when the true generating graph is unknown. This certification process provides a robust way to validate certain structural elements, showing that while these certified labels are consistent with optimal scores, they may still differ from the true underlying graph in some cases.