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

TL;DR

This paper establishes a rigorous operational interpretation of partial information decomposition by linking it to the capacity of broadcast channels, clarifying its meaning and expanding its applications.

Contribution

It connects partial information decomposition to broadcast channel capacity, providing a formal operational interpretation that was previously heuristic.

Findings

Synergistic information corresponds to cooperative gain in broadcast channels.

Provides a lower bound for cooperative gain using partial information measures.

Enhances understanding of partial information decomposition in practical contexts.

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.