Causal Discovery on Higher-Order Interactions
Alessio Zanga, Marco Scutari, Fabio Stella
TL;DR
The paper tackles causal discovery from limited data by improving bagging-based DAG aggregation. It introduces higher-order structures via an incident-cover framework and a Generalized Model Averaging (GMA) algorithm to aggregate DAGs beyond edge-wise confidences. In simulations, the PMA variant often achieves the best in-sample and out-of-sample BIC and robust structural performance, especially in low-sample and high-dimensional settings. The work points to the value of accounting for higher-order interactions in causal graph learning and outlines directions for using topological orderings and weighting schemes in future research.
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.