Partial Information Rate Decomposition

2025-02-06

AI Summary

Traditional Partial Information Decomposition (PID) applies only to static random variables and fails to capture dynamic, higher-order information interactions driven by temporal dependencies in multivariate time series—leading to mischaracterization of synergistic and redundant effects. To address this, we propose the Partial Information Rate Decomposition (PIRD) framework, the first extension of PID to stochastic processes. Grounded in lattice theory and spectral information rate decomposition, PIRD rigorously defines and estimates dynamic shared, unique, and synergistic information flows between a target process and multiple source processes. Crucially, PIRD explicitly models temporal structure, overcoming the fundamental limitation of conventional PID in ignoring time dependence. Experiments on large-scale climate oscillation data demonstrate that PIRD successfully identifies dynamic synergistic patterns missed by static PID, significantly enhancing the characterization of higher-order causal interactions in real-world dynamic networks.

Technology Category

• Reasoning under Uncertainty: Relational Probabilistic Models
• Machine Learning: Information Theory
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Content-based information diffusion
• Social Networks and Social Media: Influence propagation, information diffusion, and the prediction on networks

Abstract

Partial Information Decomposition (PID) is a principled and flexible method to unveil complex high-order interactions in multi-unit 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 incorrect depiction of high-order effects by PID schemes applied to dynamic networks, we introduce the framework of Partial Information Rate Decomposition (PIRD). PIRD is formalized applying lattice theory to decompose the information shared dynamically between a target random process and a set of source processes, implemented for Gaussian processes through a spectral expansion of information rates, and demonstrated in practice analyzing time series from large-scale climate oscillations.

Problem

• Overcome incorrect high-order effects in dynamic networks
• Decompose dynamic shared information in multi-unit systems
• Validate framework with simulated and climate time series

Innovation

• Introduces Partial Information Rate Decomposition (PIRD) framework
• Uses lattice theory for dynamic information decomposition
• Implements spectral expansion for Gaussian processes