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On Extractable Shared Information

Max Planck Institute for Mathematics in the Sciences, 04103 Leipzig, Germany
Frankfurt Institute for Advanced Studies, 60438 Frankfurt, Germany
Author to whom correspondence should be addressed.
Entropy 2017, 19(7), 328;
Received: 31 May 2017 / Accepted: 22 June 2017 / Published: 3 July 2017
We consider the problem of quantifying the information shared by a pair of random variables X 1 , X 2 about another variable S. We propose a new measure of shared information, called extractable shared information, that is left monotonic; that is, the information shared about S is bounded from below by the information shared about f ( S ) for any function f. We show that our measure leads to a new nonnegative decomposition of the mutual information I ( S ; X 1 X 2 ) into shared, complementary and unique components. We study properties of this decomposition and show that a left monotonic shared information is not compatible with a Blackwell interpretation of unique information. We also discuss whether it is possible to have a decomposition in which both shared and unique information are left monotonic. View Full-Text
Keywords: information decomposition; multivariate mutual information; left monotonicity; Blackwell order information decomposition; multivariate mutual information; left monotonicity; Blackwell order
MDPI and ACS Style

Rauh, J.; Banerjee, P.K.; Olbrich, E.; Jost, J.; Bertschinger, N. On Extractable Shared Information. Entropy 2017, 19, 328.

AMA Style

Rauh J, Banerjee PK, Olbrich E, Jost J, Bertschinger N. On Extractable Shared Information. Entropy. 2017; 19(7):328.

Chicago/Turabian Style

Rauh, Johannes, Pradeep K. Banerjee, Eckehard Olbrich, Jürgen Jost, and Nils Bertschinger. 2017. "On Extractable Shared Information" Entropy 19, no. 7: 328.

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