Decomposing Multivariate Information Rates in Networks of Random Processes

The Partial Information Decomposition (PID) framework has emerged as a powerful tool for analyzing high-order interdependencies in complex network systems. However, its application to dynamic processes remains challenging due to the implicit assumption of memorylessness, which often falls in real-world scenarios. In this work, we introduce the framework of Partial Information Rate Decomposition (PIRD) that extends PID to random processes with temporal correlations. By leveraging mutual information rate (MIR) instead of mutual information (MI), our approach decomposes the dynamic information shared by multivariate random processes into unique, redundant, and synergistic contributions obtained aggregating information rate atoms in a principled manner. To solve PIRD, we define a pointwise redundancy rate function based on the minimum MI principle applied locally in the frequency-domain representation of the processes. The framework is validated in benchmark simulations of Gaussian systems, demonstrating its advantages over traditional PID in capturing temporal correlations and showing how the spectral representation may reveal scale-specific higher-order interaction that are obscured in the time domain. Furthermore, we apply PIRD to a physiological network comprising cerebrovascular and cardiovascular variables, revealing frequency-dependent redundant information exchange during a protocol of postural stress. Our results highlight the necessity of accounting for the full temporal statistical structure and spectral content of vector random processes to meaningfully perform information decomposition in network systems with dynamic behavior such as those typically encountered in neuroscience and physiology.