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。近年来，新信息论测度被提出以克服经典测度（如仅考虑成对交互的互信息）的局限性。其中，信息协同与冗余的概念对于理解变量间高阶依赖关系至关重要。基于该概念的最重要且通用的测度之一是O-信息，它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，其实际应用仅限于简化案例。在本工作中，我们提出S$Ω$I，该方法首次实现了无需对系统施加限制性假设即可计算O-信息。我们的实验在合成数据上验证了该方法的有效性，并在真实场景中展示了S$Ω$I的实际应用效果。