Reproduce “An operational information decomposition via synergistic disclosure” on OpenResearch

About this paper

Fernando Rosas, Pedro Mediano, Borzoo Rassouli, Adam Barrett

Researchers at Imperial College London and University of Cambridge introduce an operational information decomposition framework, defining synergy as the maximal information about a target that can be disclosed from sources while preserving privacy about individual subsystems. This approach yields a computationally tractable measure for synergy and a coarse-grained decomposition that scales linearly, offering a practical tool for analyzing high-order interactions in complex systems.

Key insights

• Grounding synergy in an operational definition related to "disclosing information under privacy constraints" offers a transparent and computationally tractable alternative to purely axiomatic approaches.
• The "backbone decomposition" provides a non-negative, linearly scalable method to summarize high-order interactions, effectively capturing the order of interactions in systems like Gibbs distributions.
• The concept of "self-synergy" (S_alpha(X)) can quantify a system's "synergistic capacity," representing the intrinsic potential for a set of variables to exhibit synergistic behavior about any target.

Summary by alphaXiv.