A scalable estimator of higher-order information in complex dynamical systems
This work addresses the challenge of analyzing large complex systems, such as neuroscience data, by providing a scalable estimator for higher-order information, which is incremental as it builds on existing information theory frameworks.
The paper tackles the problem of characterizing higher-order information integration in complex dynamical systems, which is hindered by poor scalability of existing techniques, and introduces M-information, a novel measure that scales gracefully with system size and is shown to be resilient to noise, index critical behavior in neuronal populations, and reflect states of consciousness and task performance in neuroimaging data.
Our understanding of complex systems rests on our ability to characterise how they perform distributed computation and integrate information. Advances in information theory have introduced several quantities to describe complex information structures, where collective patterns of coordination emerge from higher-order (i.e. beyond-pairwise) interdependencies. Unfortunately, the use of these approaches to study large complex systems is severely hindered by the poor scalability of existing techniques. Moreover, there are relatively few measures specifically designed for multivariate time series data. Here we introduce a novel measure of information about macroscopic structures, termed M-information, which quantifies the higher-order integration of information in complex dynamical systems. We show that M-information can be calculated via a convex optimisation problem, and we derive a robust and efficient algorithm that scales gracefully with system size. Our analyses show that M-information is resilient to noise, indexes critical behaviour in artificial neuronal populations, and reflects states of consciousness and task performance in real-world macaque and mouse neuroimaging data. Furthermore, M-information can be incorporated into existing information decomposition frameworks to reveal a comprehensive taxonomy of information dynamics. Taken together, these results help us unravel collective computation in large complex systems.