Gradients of O-information highlight synergy and redundancy in physiological applications

Abstract

The study of high order dependencies in complex systems has recently led to the introduction of statistical synergy, a novel quantity corresponding to a form of emergence in which patterns at large scales are not traceable from lower scales. As a consequence, several works in the last years dealt with the synergy and its counterpart, the redundancy. In particular, the O-information is a signed metric that measures the balance between redundant and synergistic statistical dependencies. In spite of its growing use, this metric does not provide insight about the role played by low-order scales in the formation of high order effects. To fill this gap, the framework for the computation of the O-information has been recently expanded introducing the so-called gradients of this metric, which measure the irreducible contribution of a variable (or a group of variables) to the high order informational circuits of a system. Here, we review the theory behind the O-information and its gradients and present the potential of these concepts in the field of network physiology, showing two new applications relevant to brain functional connectivity probed via functional resonance imaging and physiological interactions among the variability of heart rate, arterial pressure, respiration and cerebral blood flow.

Time-varying synergy/redundancy dominance in the human cerebral cortex

“…We note that this approach refers to temporal localization, and is not to be confused with spatial localization, which examines lower-order contributions to the higher-order O-information [43], a technique which has already been fruitfully applied to BOLD fMRI data [36]. The time-localized O-information, on the other hand, can be used to conduct an analysis of the time-varying structure of higher order redundant and synergistic interactions, and has not yet been applied to BOLD fMRI data.…”

“…The O-information, a heuristic measure of redundancy/synergy dominance [1,35], has been instrumental in revealing the presence of higher order interactions in the cortex as measured with blood oxygen-level dependent functional magnetic resonance imaging (BOLD fMRI) [10,17,36], in particular because it scales to handle interactions of many components, unlike other statistical approaches, such as the partial information decomposition [9]. Like many other information theoretic metrics, the O-information can be written as an expected value over all of a system's realized states.…”