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Synergy, Redundancy and Common Information
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We consider the problem of decomposing the total mutual information conveyed by a pair of predictor random variables about a target random variable into redundant, unique and synergistic contributions. We focus on the relationship between "redundant information" and the more familiar information-theoretic notions of "common information". Our main contribution is an impossibility result. We show that for independent predictor random variables, any common information based measure of redundancy cannot induce a nonnegative decomposition of the total mutual information. Interestingly, this entails that any reasonable measure of redundant information cannot be derived by optimization over a single random variable.
Forward citations
Cited by 2 Pith papers
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The mathematical landscape of partial information decomposition: A comprehensive review of properties and measures
A comprehensive survey plus new theorems systematically comparing PID redundancy measures and their axioms, with a Z3-checked map of property implications and incompatibilities.
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Dissipation alters modes of information encoding in small quantum reservoirs near criticality
In a two-oscillator quantum reservoir, near the critical coupling J=|Δ|, information encoding switches from redundant to synergistic, with synergy aiding short-term and dissipation aiding longer-term memory.
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