A Path-Based Partial Information Decomposition

Area of Science:

• Information Theory
• Statistical Modeling
• Network Analysis

Background:

• Traditional mutual information measures lack nuanced decomposition.
• Probabilistic graphical models offer a framework for complex systems.
• Partial information decomposition aims to quantify unique, redundant, and synergistic information.

Purpose of the Study:

• Propose a novel mutual information measure based on path analysis in graphical models.
• Develop a method for partial information decomposition into non-negative, additive components.
• Validate the measure against established axioms and theoretical properties.

Main Methods:

• Representing random variables as probabilistic graphical models.
• Modeling graph edges as discrete memoryless communication channels.
• Utilizing multilinear stochastic maps (tensors) to process probability mass functions along paths.

Main Results:

• Introduced 'path-based mutual information', a novel information measure.
• Derived intuitive, non-negative, and additive components: redundant, unique, and synergistic information.
• Demonstrated that path-based redundancy satisfies key axioms (Williams & Beer, Harder, Bertschinger) and data processing inequality.

Conclusions:

• Path-based mutual information provides a rigorous framework for partial information decomposition.
• The measure aligns with established theoretical requirements for information components.
• This approach highlights information theory's capacity for detailed system analysis.