Constraint-based (CB) methods Eire widely used for discovering causal relationships in observational data. The PC-stable algorithm is a prominent example of CB methods. A critical component of the PC-stable algorithm is to find d-separators and perform conditional independence (CI) tests to eliminate spurious causal relationships. While the pairwise CI tests are necessary for identifying causal relationships, the error rate, where true causal relationships are erroneously removed, increases with the number of tests performed. Efficiently searching for the true d-separator set is thus a critical component to increase the accuracy of the causal graph. To this end, we propose a novel recursive algorithm for constructing causal graphs, based on a two-phase divide and conquer strategy. In phase one, we recursively partition the undirected graph using community detection, and subsequently construct partial skeletons from each partition. Phase two uses a bottom-up approach to merge the subgraph skeletons, ultimately yielding the full causal graph. Simulations on several real-world data sets show that our approach effectively finds the d-separators, leading to a significant improvement in the quality of causal graphs.
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