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Article

On Extractable Shared Information

1
Max Planck Institute for Mathematics in the Sciences, 04103 Leipzig, Germany
2
Frankfurt Institute for Advanced Studies, 60438 Frankfurt, Germany
*
Author to whom correspondence should be addressed.
Entropy 2017, 19(7), 328; https://doi.org/10.3390/e19070328
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. https://doi.org/10.3390/e19070328

AMA Style

Rauh J, Banerjee PK, Olbrich E, Jost J, Bertschinger N. On Extractable Shared Information. Entropy. 2017; 19(7):328. https://doi.org/10.3390/e19070328

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. https://doi.org/10.3390/e19070328

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