Partial Information Decomposition and the Information Delta: A Geometric Unification Disentangling Non-Pairwise...

Area of Science:

• Information theory
• Computational neuroscience
• Genetics

Background:

• Information theory offers measures of interdependence but lacks detailed relationship characterization.
• Partial Information Decomposition (PID) decomposes mutual information but lacks a standard computation method.
• The Information Delta framework analyzes genetic dependencies with a geometric interpretation but needs generalization.

Purpose of the Study:

• To establish the equivalence between the Partial Information Decomposition (PID) and Information Delta frameworks.
• To enable the application of findings between these two frameworks.
• To provide a unified approach for characterizing multivariable information.

Main Methods:

• Equating key mathematical expressions of PID and Information Delta.
• Applying the Bertschinger et al. approach to address linkage disequilibrium within the Information Delta framework.
• Mapping PID solutions to the delta measure space.

Main Results:

• Demonstrated the substantial equivalence of the PID and Information Delta frameworks.
• Showcased how PID solutions can be visualized within the delta measure space.
• Identified constraints for optimization in the Information Delta framework using a specific PID solution.

Conclusions:

• The PID and Information Delta frameworks are largely equivalent, facilitating cross-disciplinary insights.
• The equivalence allows for solving open problems in one framework using methods from the other.
• A clear geometric understanding of information decomposition is achieved through this unification.