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，为克服经典信息测度（如仅能处理两两相互作用的互信息）的局限性，人们开发了新的信息论测度。其中，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。基于该概念最突出且通用的测度之一是O-信息，它能清晰且可扩展地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情形。在本工作中，我们提出SΩI，首次实现了无需对系统施加限制性假设即可计算O-信息。实验在合成数据上验证了该方法，并展示了SΩI在真实应用场景中的有效性。