Efficient Causal Structure Learning via Modular Subgraph Integration

Learning causal structures from observational data remains a fundamental yet computationally intensive task, particularly in high-dimensional settings where existing methods face challenges such as the super-exponential growth of the search space and increasing computational demands. To address this, we introduce VISTA (Voting-based Integration of Subgraph Topologies for Acyclicity), a modular framework that decomposes the global causal structure learning problem into local subgraphs based on Markov Blankets. The global integration is achieved through a weighted voting mechanism that penalizes low-support edges via exponential decay, filters unreliable ones with an adaptive threshold, and ensures acyclicity using a Feedback Arc Set (FAS) algorithm. The framework is model-agnostic, imposing no assumptions on the inductive biases of base learners, is compatible with arbitrary data settings without requiring specific structural forms, and fully supports parallelization. We also theoretically establish finite-sample error bounds for VISTA, and prove its asymptotic consistency under mild conditions. Extensive experiments on both synthetic and real datasets consistently demonstrate the effectiveness of VISTA, yielding notable improvements in both accuracy and efficiency over a wide range of base learners.

💡 Research Summary

The paper tackles the notoriously difficult problem of learning causal directed acyclic graphs (DAGs) from purely observational data, especially in high‑dimensional regimes where the search space grows super‑exponentially and existing algorithms become computationally prohibitive. To overcome these challenges, the authors propose VISTA (Voting‑based Integration of Subgraph Topologies for Acyclicity), a modular, model‑agnostic framework that decomposes the global learning task into many small, tractable subproblems and then recombines the results in a principled way.

Key components

1. Divide via Markov blankets – For each variable (v) the algorithm first estimates its Markov blanket (parents, children, and co‑parents). The subgraph induced by ({v}\cup MB(v)) is guaranteed to contain all true edges incident to (v). This property (Proposition 3.1) ensures that no causal edge is lost during decomposition.
2. Local learning – Any off‑the‑shelf causal learner (NOTEARS, DAG‑GNN, GES, etc.) can be run independently on each subgraph. Because each subgraph is small, the local learning step is fast and can be fully parallelized across cores or machines.
3. Weighted voting aggregation – After local learning, each ordered pair ((X,Y)) receives a count (A) of votes for (X\rightarrow Y) and (B) for the opposite direction. The total number of votes is (m=A+B). A confidence‑adjusted score is computed as
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