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An Information-Theoretic Perspective on Coarse-Graining, Including the Transition from Micro to Macro

Information Decomposition and Synergy

Max Planck Institute for Mathematics in the Sciences, Inselstraße 22, 04103 Leipzig, Germany
Frankfurt Institute for Advanced Studies, Ruth-Moufang-Straße 1, 60438 Frankfurt am Main, Germany
Institute of Algebraic Geometry, Leibniz Universität Hannover, Welfengarten 1, 30167 Hannover, Germany
Author to whom correspondence should be addressed.
Academic Editor: Rick Quax
Entropy 2015, 17(5), 3501-3517;
Received: 26 March 2015 / Revised: 12 May 2015 / Accepted: 19 May 2015 / Published: 22 May 2015
(This article belongs to the Special Issue Information Processing in Complex Systems)
Recently, a series of papers addressed the problem of decomposing the information of two random variables into shared information, unique information and synergistic information. Several measures were proposed, although still no consensus has been reached. Here, we compare these proposals with an older approach to define synergistic information based on the projections on exponential families containing only up to k-th order interactions. We show that these measures are not compatible with a decomposition into unique, shared and synergistic information if one requires that all terms are always non-negative (local positivity). We illustrate the difference between the two measures for multivariate Gaussians. View Full-Text
Keywords: Shannon information; mutual information; information decomposition; shared information; synergy Shannon information; mutual information; information decomposition; shared information; synergy
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MDPI and ACS Style

Olbrich, E.; Bertschinger, N.; Rauh, J. Information Decomposition and Synergy. Entropy 2015, 17, 3501-3517.

AMA Style

Olbrich E, Bertschinger N, Rauh J. Information Decomposition and Synergy. Entropy. 2015; 17(5):3501-3517.

Chicago/Turabian Style

Olbrich, Eckehard, Nils Bertschinger, and Johannes Rauh. 2015. "Information Decomposition and Synergy" Entropy 17, no. 5: 3501-3517.

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