Partial Information Rate Decomposition

Area of Science:

• Information theory
• Network science
• Time series analysis

Background:

• Partial information decomposition (PID) is used to study high-order interactions in networks.
• Existing PID methods struggle with dynamic networks and time series data, leading to incomplete analyses.
• There is a need for a method that accurately captures temporal statistical structures in dynamic systems.

Purpose of the Study:

• To introduce a novel framework, partial information rate decomposition (PIRD), for analyzing dynamic networks.
• To overcome limitations of traditional PID in depicting high-order effects in time series.
• To provide a principled method for quantifying dynamic information sharing in complex systems.

Main Methods:

• Formalized PIRD using lattice theory to decompose dynamically shared information between source and target processes.
• Implemented PIRD for Gaussian processes via spectral expansion of information rates.
• Validated the PIRD framework in simulated network systems.

Main Results:

• PIRD provides a more complete and less misleading depiction of high-order effects in dynamic networks compared to traditional PID.
• The spectral expansion method effectively implements PIRD for Gaussian processes.
• The framework successfully analyzed time series data from large-scale climate oscillations.

Conclusions:

• PIRD is a powerful new framework for understanding complex information flow in dynamic systems.
• The method accurately captures temporal statistical structures, improving analysis of multivariate time series.
• PIRD has practical applications in fields like climate science and network analysis.