Hierarchical causal structure discovery from layered topological orderings
TL;DR
HiTOC is proposed, a Hierarchical Topological Ordering framework for Causal discovery that constructs the global causal structure via layer-wise integration of local orderings over induced subsets by Markov Blanket and achieves state-of-the-art performance in both accuracy and scalability, particularly in high-dimensional and structurally complex settings.
Abstract
Causal discovery aims to recover the underlying directed acyclic graph (DAG) from observational data. Ordering-based methods offer a scalable perspective to global DAG search by estimating a topological order and assigning edges accordingly. However, existing approaches depend on repeated full-graph score evaluations and assume that local score minima correspond to causal sinks, an assumption that breaks down under statistical noise, model misspecification, or dense local dependencies. To overcome these limitations, we propose HiTOC, a Hierarchical Topological Ordering framework for Causal discovery that constructs the global causal structure via layer-wise integration of local orderings over induced subsets by Markov Blanket. At each iteration, nodes identified as sinks through local score-based rankings are peeled off to form hierarchical layers, avoiding global permutation search. HiTOC provides a clearer hierarchical structure via recursive modular inference and sink extraction, enabling interpretable layer-wise inference and localizing potential errors to small subgraphs. To ensure robustness under local inconsistencies, we further introduce a calibration mechanism with theoretical guarantees. Empirical results demonstrate that HiTOC achieves state-of-the-art performance in both accuracy and scalability, particularly in high-dimensional and structurally complex settings.