Expanding the transfer entropy to identify information circuits in complex systems

Area of Science:

• Neuroscience
• Information Theory
• Complexity Science

Background:

• Understanding complex systems requires identifying causal relationships between variables.
• Transfer entropy quantifies information flow but can be computationally intensive and difficult to interpret for complex interactions.
• Existing methods struggle to isolate irreducible sets of variables that predict future states.

Purpose of the Study:

• To develop a formal expansion of transfer entropy to identify irreducible sets of variables.
• To associate these sets with informational circuits and their characteristics within a system.
• To apply this novel methodology to real-world complex data, such as electroencephalography (EEG).

Main Methods:

• Formal expansion of transfer entropy to highlight variable contributions.
• Assumption of Gaussianity for computational tractability.
• Utilizing exact formulas for conditional mutual information under Gaussianity.
• Application to electroencephalography (EEG) datasets.

Main Results:

• Identification of multiplets representing informational circuits.
• Association of multiplet contributions with the directionality of information flow.
• Successful application and validation on two distinct EEG datasets.
• Demonstration of the method's ability to uncover complex information pathways.

Conclusions:

• The proposed transfer entropy expansion effectively identifies critical variable sets and informational circuits.
• The method provides insights into the structure and dynamics of complex systems.
• Gaussian assumption offers a computationally feasible approach for analyzing complex data like EEG.
• This framework advances the analysis of information flow in neuroscience and other complex systems.