Article ID: 2025EDP7178
Causal discovery aims to infer cause-and-effect relationships from observational data, a crucial step beyond statistical correlation. A prominent method for this is the Linear Non-Gaussian Acyclic Model (LiNGAM), which can uniquely identify the causal structure by assuming linear relationships and non-Gaussian noise. LiNGAM-based algorithms typically depend on two key components: a search algorithm to determine the causal ordering of variables, and an independence measure to guide the search. Recent work, LiNGAM-MMI, proposed that replacing the simple greedy search with a global, shortest-path search led to superior performance, particularly when unmeasured common causes (confounders) are present. However, the claim was based on experiments that also modified the independence measure from the original baseline, making it difficult to isolate the source of the improvement.
To address this, we perform extensive experiments to test whether the search algorithm was truly the driver of performance, hypothesizing that the choice of independence measure is the dominant factor. In particular, we introduce a unified beam search framework that serves as both an analytical tool to disentangle these components and a practical algorithm with a scalable performance-complexity trade-off. Our simulations comparing the kNN-based Copula Entropy (CopEnt) with the Pairwise Likelihood Ratio (PLR) establish that the independence measure is the dominant factor, to the extent that a simple greedy search with a more effective measure, PLR, outperforms a global search with a less effective one, CopEnt, on general graphs. Furthermore, we find no evidence that the benefit of a more complex search algorithm is specific to handling unmeasured confounders, suggesting it instead serves to overcome general estimation errors arising from finite data. Finally, we demonstrate that the strong performance with CopEnt reported in the previous work was an artifact of a simplistic experimental setup, as its performance advantage is reversed on more realistic and complex structures, including Erdős-Rényi (ER) and Scale-Free (SF) networks.
