Sebastiano Stramaglia, Luca Faes, Jesus M. Cortes, and Daniele Marinazzo. Disentangling high-order effects in the transfer entropy. Phys Rev Res 6, L032007 (2024). [pdf]
Abstract
Transfer entropy (TE), the primary method for determining directed information flow within a network system,
can exhibit bias—either in deficiency or excess—during both pairwise and conditioned calculations, owing to
high-order dependencies among the dynamic processes under consideration and the remaining processes in the
system used for conditioning. Here, we propose a novel approach. Instead of conditioning TE on all network
processes except the driver and the target, as in its fully conditioned version, or not conditioning at all, as
in the pairwise approach, our method searches for both the multiplets of variables that maximize information
flow and those that minimize it. This provides a decomposition of TE into unique, redundant, and synergistic
atoms. Our approach enables the quantification of the relative importance of high-order effects compared to
pure two-body effects in information transfer between two processes, while also highlighting the processes
that contribute to building these high-order effects alongside the driver. We demonstrate the application of our
approach in climatology by analyzing data from El Niño and the Southern Oscillation.
