Bertschinger, NilsNilsBertschingerRauh, JohannesJohannesRauhOlbrich, EckehardEckehardOlbrichJost, JürgenJürgenJostAy, NihatNihatAy2022-11-152022-11-152014-04-15Entropy 16 (4): 2161-2183 (2014)http://hdl.handle.net/11420/14055We propose new measures of shared information, unique information and synergistic information that can be used to decompose the multi-information of a pair of random variables (Y,Z) with a third random variable X. Our measures are motivated by an operational idea of unique information which suggests that shared information and unique information should depend only on the pair marginal distributions of (X,Y) and (X,Z). Although this invariance property has not been studied before, it is satisfied by other proposed measures of shared information. The invariance property does not uniquely determine our new measures, but it implies that the functions that we define are bounds to any other measures satisfying the same invariance property. We study properties of our measures and compare them to other candidate measures.en1099-43002014421612183MDPIInformation decompositionMutual informationShannon informationShared informationSynergyComputer Science - Information TheoryComputer Science - Information TheoryMathematics - Information Theory94A15, 94A17InformatikMathematikJournal Article10.3390/e160421611311.2852v2Other