Directed networks and resting-state effective brain connectivity with state-space reconstruction using reservoir computing causality

Abstract Causality theory is a complex field involving philosophy, mathematics, and computer science. It relies on the temporal precedence of cause over a consequence or unidirectional propagation of changes. Despite these simple principles, normative modeling of causal relationships is conceptually and computationally challenging. Model-free approaches provide insights into large, complex, and chaotic networks, but suffer from false positive and false negative inferences caused by meaningless statistical and temporal correlations. Machine learning advancements have extended these data-driven methods to nonlinear systems, yet inherited similar drawbacks as linear approaches. Interestingly, newer proposals within this model-free paradigm reverse the temporal precedence using the internal structure of the driven variable to recover information from the driving one. Efficient machine learning models combined with these state space reconstruction methods automate part of the process, potentially reducing inductive biases during training and inference. However, their translation into neuroscience, especially neuroimaging, is limited due to complex interpretations and a lack of systematic analyses of the results. Here, we exploited these methods combining them with normative analyses to reconstruct chaotic relationships and networks emerging from neuroimaging data. We validated the proposed scores with a chaotic yet solved system and rebuilt brain networks both in synthetic and real scenarios. We compared our method and heuristics with well-established alternatives providing a comprehensive and transparent benchmark. We obtained higher accuracies and reduced false inferences compared to Granger causality in tasks with known ground truth. When tested to unravel directed influences in brain networks meaningful predictions were found to exist between nodes from the default mode network. The presented framework explores reservoir computing for causality detection, offering a conceptual detour from traditional premises and has the potential to provide theoretical guidance opening perspectives for studying cognition and neuropathologies. Author summary In sciences, reliable methods to distinguish causes from consequences are crucial. Despite some progress, researchers are often unsatisfied with the current understanding of causality modeling and its predictions. In neuroscience, causality detection requires imposing world models or assessing statistical utility to predict future values. These approaches, known as model-based and model-free, have advantages and drawbacks. A recent model-free approach augmented with artificial networks tries to autonomously explore the internal structure of the system, (i.e, the state space), to identify directed predictions from consequences to causes but not the other way around. This has not been extensively studied in large networks nor in the human brain, and systematic attempts to reveal its capabilities and inferences are lacking. Here, the proposal is expanded to large systems and further validated in chaotic systems, challenging neuronal simulations, and networks derived from real brain activity. Although the manuscript does not claim true causality, it presents new ideas in the context of current trends in data-driven causality theory. Directed networks encoding causality are hypothesized to contain more information than correlation-based relationships. Hence, despite its evident difficulties, causality detection methods can hold the key to new and more precise discoveries in brain health and disease.