  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.
