The analysis of scientific data and complex multivariate systems requires information quantities that capture relationships among multiple random variables. Recently, new information-theoretic measures have been developed to overcome the shortcomings of classical ones, such as mutual information, that are restricted to considering pairwise interactions. Among them, the concept of information synergy and redundancy is crucial for understanding the high-order dependencies between variables. One of the most prominent and versatile measures based on this concept is O-information, which provides a clear and scalable way to quantify the synergy-redundancy balance in multivariate systems. However, its practical application is limited to simplified cases. In this work, we introduce S$\Omega$I, which allows for the first time to compute O-information without restrictive assumptions about the system. Our experiments validate our approach on synthetic data, and demonstrate the effectiveness of S$\Omega$I in the context of a real-world use case.

翻译：科学数据与复杂多变量系统的分析需要能够捕捉多个随机变量之间关系的信息量。近期，为克服经典信息度量（如仅能处理两两交互的互信息）的局限性，研究者开发了新的信息论测度。其中，基于信息协同与冗余的概念对于理解变量间的高阶依赖关系至关重要。作为该概念中最为突出且通用的测度之一，O信息提供了一种清晰且可扩展的方式来量化多变量系统中的协同-冗余平衡。然而，其实际应用仍局限于简化场景。本工作首次提出了S$Ω$I，使得无需对系统施加严格假设即可计算O信息。我们在合成数据上验证了该方法的有效性，并通过真实场景案例展示了S$Ω$I的实际应用价值。