Broadcast Channel Cooperative Gain: An Operational Interpretation of Partial Information Decomposition
This provides a rigorous foundation for practitioners in biological signal processing and machine learning to better explain and expand applications of partial information decomposition.
The paper tackles the unclear operational meaning of partial information decomposition by connecting it to the capacity of broadcast channels, showing that synergistic information can be interpreted as cooperative gain or a lower bound on this gain.
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.