将信息分解中的协同信息解释为广播信道的协作增益。
Broadcast Channel Cooperative Gain: An Operational Interpretation of Partial Information Decomposition
- 通过广播信道容量理论，给出部分信息分解的严格操作解释。
- 协同信息对应信道的协作增益或其下界，具有明确物理意义。
- 为生物信号与机器学习中的信息分解应用提供理论支撑。
部分信息分解近年来在生物信号处理和机器学习中得到应用。尽管影响广泛，但该分解最初基于非正式且启发式的方法提出，其确切操作意义尚不清晰。本文通过将部分信息分解与广播信道容量联系起来，填补了这一空白。广播信道是信息论中研究充分的模型。我们证明，分解中的协同信息可被严格解释为相应广播信道上的协作增益，或其下界。这一解释有助于从业者更准确地理解并拓展部分信息分解的应用。
原文摘要 · Abstract (English)
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.
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