🤖 AI Summary
Conventional pairwise causal models fail to capture synergistic, higher-order causal interactions among variables in complex systems.
Method: We propose a higher-order causal definition based on optimal conditional transfer entropy, formally characterizing pure synergistic multivariate causality (e.g., XOR-like logic) for the first time. Causal influence is attributed to variable *sets* rather than individual variables, and confounding and mediation effects are rigorously controlled within an information-theoretic framework.
Contribution: Our approach overcomes fundamental limitations of Granger causality and standard transfer entropy, enabling a principled transition from causal *networks* to causal *hypernetworks*. It successfully identifies synergistic causal structures—undetectable by existing methods—in both theoretical benchmarks and biologically realistic neuronal dynamics simulations. These results demonstrate its effectiveness and broad applicability to real-world complex systems.
📝 Abstract
The description of the dynamics of complex systems, in particular the capture of the interaction structure and causal relationships between elements of the system, is one of the central questions of interdisciplinary research. While the characterization of pairwise causal interactions is a relatively ripe field with established theoretical concepts and the current focus is on technical issues of their efficient estimation, it turns out that the standard concepts such as Granger causality or transfer entropy may not faithfully reflect possible synergies or interactions of higher orders, phenomena highly relevant for many real-world complex systems. In this paper, we propose a generalization and refinement of the information-theoretic approach to causal inference, enabling the description of truly multivariate, rather than multiple pairwise, causal interactions, and moving thus from causal networks to causal hypernetworks. In particular, while keeping the ability to control for mediating variables or common causes, in case of purely synergistic interactions such as the exclusive disjunction, it ascribes the causal role to the multivariate causal set but not to individual inputs, distinguishing it thus from the case of, e.g., two additive univariate causes. We demonstrate this concept by application to illustrative theoretical examples as well as a biophysically realistic simulation of biological neuronal dynamics recently reported to employ synergistic computations.
Published by the American Physical Society
2025