title: Bivariate measure of redundant information.
abstract: We define a measure of redundant information based on projections in the space of probability distributions. Redundant information between random variables is information that is shared between those variables. But, in contrast to mutual information, redundant information denotes information that is shared about the outcome of a third variable. Formalizing this concept, and being able to measure it, is required for the non-negative decomposition of mutual information into redundant and synergistic information. Previous attempts to formalize redundant or synergistic information struggle to capture some desired properties. We introduce a new formalism for redundant information and prove that it satisfies all the properties necessary outlined in earlier work, as well as an additional criterion that we propose to be necessary to capture redundancy. We also demonstrate the behavior of this new measure for several examples, compare it to previous measures, and apply it to the decomposition of transfer entropy.
authors: Adaptive Systems Research Group University of Hertfordshire, University of Hertfordshire, AL10 9AB Hatfield, United Kingdom. m.harder@herts.ac.uk
authors: Malte
authors: M
authors: Harder
authors: Christoph
authors: C
authors: Salge
authors: Daniel
authors: D
authors: Polani
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D016247:Information Storage and Retrieval / Q000379:methods*; D015233:Models, Statistical