Efficient Causal Structure Learning via Modular Subgraph Integration

TL;DR

Efficient Causal Structure Learning via Modular Subgraph Integration introduces VISTA, a scalable framework that tackles the combinatorial DAG search by decomposing the global graph into Markov Blanket–centered subgraphs and merging their edge evidence through a frequency-aware weighted voting rule with exponential decay controlled by $\lambda$. The method is model-agnostic, enabling plug-and-play with arbitrary MB estimators and local learners, and enforces global acyclicity via a Greedy Feedback Arc Set (FAS) post-processing step. The authors establish finite-sample error guarantees and asymptotic consistency for the aggregation and demonstrate, across extensive synthetic and real-data experiments, that VISTA consistently improves accuracy and computational efficiency relative to a wide range of baselines. Together, these contributions offer a robust, scalable approach to causal discovery that preserves base-learner flexibility while providing theoretical guarantees and practical performance gains across graph sizes up to at least several hundred nodes.

Abstract

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.

Figures (10)

• Figure 1: F1 score comparison as the number of nodes increases.
• Figure 2: Pseudocode of VISTA framework
• Figure 3: Overview of VISTA, a modular framework for causal discovery: (1) dividing via Markov Blankets identification, (2) parallel subgraph structure identification using a base learner, and (3) global aggregation through weighted voting. The framework then applies cycle resolution (GreedyFAS) and weight-based filtering to produce the final DAG.
• Figure 4: Precision–recall trade-off under varying $\lambda$, where threshold $t=0.5$.
• Figure 5: Performance of DAG-GNN on SF5 Graphs.

Theorems & Definitions (18)

• Proposition 3.1: Coverage of a DAG by Markov-Blanket Subgraphs
• proof
• Theorem 3.2: Sufficient Condition for Weighted Voting Accuracy
• Corollary 3.3: Lower bound on node in subgraphs
• Theorem 3.4: Practical choice of $\lambda$
• Theorem 3.5: Asymptotic Consistency
• proof
• proof
• Lemma E.1: Structure‑aware global error bound
• proof