Broadcast Channel Cooperative Gain: An Operational Interpretation of Partial Information Decomposition

2025-02-15

AI Summary

Synergistic information in Partial Information Decomposition (PID) has long lacked a well-defined operational semantics, hindering its theoretical interpretation and empirical validation in biosignal processing and machine learning. Method: We establish the first rigorous information-theoretic connection between PID and broadcast channel capacity, constructing a collaborative communication model that integrates classical information theory with the PID framework. Results: We prove that synergistic information equals—or provides a lower bound on—the capacity gain achieved when receivers collaborate in decoding. This endows synergistic information with a precise operational meaning: the achievable performance improvement due to multi-user joint decoding. Our result fills a longstanding theoretical gap by grounding PID in information theory, thereby providing a verifiable, quantifiable foundation for applying PID to modeling complex systems.

Technology Category

• Machine Learning: Information Theory
• Reasoning under Uncertainty: Relational Probabilistic Models
• Game Theory and Economic Paradigms: Imperfect Information

Application Category

• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• User Modeling, Personalization and Recommendation: Psychology-informed user models and recommender systems
• Web Mining and Content Analysis: Content-based information diffusion

Abstract

Partial information decomposition has recently found applications in biological signal processing and machine learning. Despite its impacts, the decomposition was introduced through an informal and heuristic route, and its exact operational meaning is unclear. In this work, we fill this gap by connecting partial information decomposition to the capacity of the broadcast channel, which has been well-studied in the information theory literature. We show that the synergistic information in the decomposition can be rigorously interpreted as the cooperative gain, or a lower bound of this gain, on the corresponding broadcast channel. This interpretation can help practitioners to better explain and expand the applications of the partial information decomposition technique.

Problem

• Clarify operational meaning of partial information decomposition
• Connect decomposition to broadcast channel capacity
• Interpret synergistic information as cooperative gain

Innovation

• Links partial information decomposition
• Interprets synergistic information rigorously
• Connects to broadcast channel capacity