Partial Information Rate Decomposition

Partial information decomposition (PID) is a principled and flexible method to unveil complex high-order interactions in multiunit network systems. Though being defined exclusively for random variables, PID is ubiquitously applied to multivariate time series taken as realizations of random processes with temporal statistical structure. Here, to overcome the incomplete and sometimes misleading depiction of high-order effects by PID schemes applied to dynamic networks, we introduce the framework of "partial information rate decomposition (PIRD)." PIRD is first formalized applying lattice theory to decompose the information shared dynamically between a target random process and a set of source processes, and then implemented for Gaussian processes through a spectral expansion of information rates. The PIRD framework is validated in simulated network systems and demonstrated in the practical analysis of time series from large-scale climate oscillations.