发表机构
XOR Labs; Barcelona Collaboratorium for Modelling and Predictive Biology; Universal Biology Institute, University of Tokyo（XOR实验室; 巴塞罗那建模与预测生物学协作中心; 东京大学生物学研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文基于 Blackwell 序为多元高斯系统提出一种部分信息分解方法，证明高斯信道最优，给出高效算法，并验证其可扩展性及在最优控制中的应用。
AI 中文摘要
部分信息分解（PID）的目标是量化多个信源关于一个目标所提供的冗余信息和协同信息。PID 在机器学习、神经科学及其他领域有许多应用，但为高维连续系统定义并计算 PID 仍具挑战性。在此，我们基于 Blackwell 序为多元高斯系统定义了一种 PID，该序形式化了当一个信道比另一个信道信息量更大时的关系。我们证明了高斯信道在提取冗余信息和并集信息方面是最优的，从而为 PID 提供了直观的几何解释和高效的数值算法。我们的并集信息和协同信息与著名的 BROJA 度量一致，并且我们针对两个信源的情况推导出了两者的闭式表达式。我们还论证了 Blackwell 冗余（与 BROJA 不同）是唯一满足一组自然期望性质的现有冗余度量。我们展示了我们的方法在多达一千维或一千个信源的系统上的可扩展性。我们的方法在一个最优控制问题上进行了说明，在该问题中，它识别了传感器与记忆之间的冗余和协同交互。
英文摘要
The goal of the partial information decomposition (PID) is to quantify the redundant and synergistic information that multiple sources provide about a target. PID has many applications in machine learning, neuroscience, and other fields, but defining and computing it for high-dimensional continuous systems remains challenging. Here, we define a PID for multivariate Gaussian systems based on the Blackwell order, which formalizes when one channel is more informative than another. We prove that Gaussian channels are optimal for extracting both redundant and union information, yielding an intuitive geometric interpretation and an efficient numerical algorithm for the PID. Our union information and synergy coincide with the well-known BROJA measures, and we derive closed-form expressions for both in the case of two sources. We also argue that Blackwell redundancy (which differs from BROJA) is the only existing redundancy measure that satisfies a set of natural desiderata. We demonstrate the scalability of our method on systems with up to a thousand dimensions or sources. Our approach is illustrated on an optimal control problem, where it identifies redundant and synergistic interactions between sensor and memory.
