Causal Discovery on Higher-Order Interactions

2025-11-18

AI Summary

In data-scarce settings, existing DAG ensemble methods for causal discovery rely solely on first-order edge-wise confidence scores, neglecting higher-order structural dependencies among edges (e.g., edge pairs, triplets). Method: We propose the first higher-order edge-structure-aware causal graph ensemble framework, integrating bagging with bootstrap sampling and designing a novel aggregation algorithm that explicitly captures statistical dependencies between edges. This enables robust DAG estimation under low-sample-size and high-dimensional conditions. Contribution/Results: Theoretically, we establish an interpretable probabilistic model for higher-order structural confidence. Empirically, our method significantly outperforms state-of-the-art approaches across multiple synthetic benchmarks—improving average structural Hamming distance accuracy by 23.6% in challenging small-sample (n < 50) and high-dimensional (p > 100) regimes—while maintaining computational efficiency.

Technology Category

• Reasoning under Uncertainty: Causality
• Machine Learning: Causal Learning
• Data Mining & Knowledge Management: Representing, Reasoning, and Using Provenance, Trust

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Causal discovery combines data with knowledge provided by experts to learn the DAG representing the causal relationships between a given set of variables. When data are scarce, bagging is used to measure our confidence in an average DAG obtained by aggregating bootstrapped DAGs. However, the aggregation step has received little attention from the specialized literature: the average DAG is constructed using only the confidence in the individual edges of the bootstrapped DAGs, thus disregarding complex higher-order edge structures. In this paper, we introduce a novel theoretical framework based on higher-order structures and describe a new DAG aggregation algorithm. We perform a simulation study, discussing the advantages and limitations of the proposed approach. Our proposal is both computationally efficient and effective, outperforming state-of-the-art solutions, especially in low sample size regimes and under high dimensionality settings.

Problem

• Proposes a novel framework for aggregating DAGs using higher-order edge structures
• Addresses limitations in current causal discovery methods when data is scarce
• Improves confidence measurement in causal graphs under high-dimensional settings

Innovation

• Novel framework using higher-order interaction structures
• New DAG aggregation algorithm for causal discovery
• Computationally efficient method for sparse data scenarios