  Causality lies at the heart of scientific inquiry, serving as the fundamental
basis for understanding interactions among variables in physical systems.
Despite its central role, current methods for causal inference face significant
challenges due to nonlinear dependencies, stochastic interactions,
self-causation, collider effects, and influences from exogenous factors, among
others. While existing methods can effectively address some of these
challenges, no single approach has successfully integrated all these aspects.
Here, we address these challenges with SURD: Synergistic-Unique-Redundant
Decomposition of causality. SURD quantifies causality as the increments of
redundant, unique, and synergistic information gained about future events from
past observations. The formulation is non-intrusive and applicable to both
computational and experimental investigations, even when samples are scarce. We
benchmark SURD in scenarios that pose significant challenges for causal
inference and demonstrate that it offers a more reliable quantification of
causality compared to previous methods.
