Causality is a central topic in scientific inquiry, yet for complex systems, the identification and analysis of synergistic causation remain a challenging and fundamental problem. In the context of causal relations among multivariate variables, a decomposition framework grounded in interventionist causation is still lacking. To address this gap, this paper proposes Partial Effective Information Decomposition (PEID), a framework that decomposes the influence of multiple source variables on a target variable under maximum-entropy interventions into unique and synergistic information, thereby providing a unified and computable characterization of synergistic causal relations. Theoretically, in the three-variable case, the proposed framework is compatible with the major axioms of Partial Information Decomposition (PID). Empirically, under maximum-entropy interventions, correlations among input variables are removed, causing redundancy to vanish and thereby enabling PEID to compute synergistic relations. Furthermore, based on this framework, it is possible to define causal graphs containing hyperedges as well as downward causation, thus offering a unified toolkit for analyzing cross-scale and multivariate causal mechanisms in complex systems. Finally, applying the framework to a machine-learning-based air quality forecasting task on KnowAir-V2, we demonstrate that PEID can extract interpretable inter-station causal structures from a learned dynamical model. These results suggest that PEID provides a general interventionist information-theoretic tool for analyzing multivariate and synergistic causal mechanisms in complex systems.
Causal discovery from observational data is a fundamental yet challenging task in scientific research. While existing approaches are primarily based on conditional independence tests, structure scores, or restrictive functional assumptions, we propose Decoupled Causal Discovery (DCD), a novel decoupling-based perspective that does not rely on these methodologies. DCD directly identifies the Markov boundary (MB) by decoupling non-target variables via weighting functions, such that only variables within the MB preserve dependence with the target under the decoupled distribution. Building on this, DCD iteratively constructs the Completed Partially Directed Acyclic Graph (CPDAG) by exploiting structural asymmetries within the MBs. We establish the theoretical identifiability, soundness, and completeness of DCD. Empirical evaluations demonstrate that DCD achieves strong performance, particularly excelling in challenging noise regimes.
Learning causal models from high-dimensional data is a significant challenge, particularly in real-world settings where violations of core assumptions lead to causal identifiability issues. Although massive amounts of prior knowledge are available, and contain valuable causal information, effectively integrating this knowledge into the causal discovery process remains an open problem. We introduce CausalSTeward (CAST), a novel human-in-the-loop framework for interactively assembling large causal models. CausalSteward is a multi-agent collaborative system that tackles high-dimensional causality through a divide-and-conquer approach where large clusters of variables are iteratively partitioned and then separately analyzed. Our framework fuses prior knowledge with a data-driven approach by using tailored tools such as retrieval augmented generation and conditional independence tests. Finally, we use this work to examine the capabilities and limitations of causal reasoning in multi-agent frameworks, and how the human-in-the-loop can contribute to accurate and trustworthy results.
Nicholas Tagliapietra, Gian Lorenzo Marchioni, Moritz Willig +3
Constraint-based causal discovery is widely used for learning causal structures, but heavy reliance on conditional independence (CI) testing makes it computationally expensive in high-dimensional settings. To mitigate this limitation, many divide-and-conquer frameworks have been proposed, but most assume causal sufficiency, i.e., no latent variables. In this paper, we show that divide-and-conquer strategies can be theoretically generalized beyond causal sufficiency to settings with latent variables. Specifically, we propose a recursive decomposition framework, termed DiCoLa, that enables divide-and-conquer causal discovery in the presence of latent variables. It recursively decomposes the global learning task into smaller subproblems and integrates their solutions through a principled reconstruction step to recover the global structure. We theoretically establish the soundness and completeness of the proposed framework. Extensive experiments on synthetic data demonstrate that our approach significantly improves computational efficiency across a range of causal discovery algorithms, while experiments on a real-world dataset further illustrate its practical effectiveness.