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Entropy 2014, 16(4), 1985-2000;

Intersection Information Based on Common Randomness

Computation and Neural Systems, Caltech, Pasadena, CA 91125, USA
Dept. of Electrical & Computer Engineering, Colorado State University, Fort Collins, CO 80523, USA
Department of Computer Science, University of Colorado, Boulder, CO 80309, USA
Center for Complexity and Collective Computation, Wisconsin Institute for Discovery, University of Wisconsin-Madison, Madison, WI 53715, USA
Complexity Sciences Center and Physics Dept, University of California Davis, Davis, CA 95616, USA
Santa Fe Institute, 1399 Hyde Park Rd, Santa Fe, NM 87501, USA
Author to whom correspondence should be addressed.
Received: 25 October 2013 / Revised: 27 March 2014 / Accepted: 28 March 2014 / Published: 4 April 2014
(This article belongs to the Special Issue Entropy Methods in Guided Self-Organization)
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The introduction of the partial information decomposition generated a flurry of proposals for defining an intersection information that quantifies how much of “the same information” two or more random variables specify about a target random variable. As of yet, none is wholly satisfactory. A palatable measure of intersection information would provide a principled way to quantify slippery concepts, such as synergy. Here, we introduce an intersection information measure based on the Gács-Körner common random variable that is the first to satisfy the coveted target monotonicity property. Our measure is imperfect, too, and we suggest directions for improvement. View Full-Text
Keywords: intersection information; partial information decomposition; lattice; Gács–Körner; synergy; redundant information intersection information; partial information decomposition; lattice; Gács–Körner; synergy; redundant information
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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Griffith, V.; Chong, E.K.P.; James, R.G.; Ellison, C.J.; Crutchfield, J.P. Intersection Information Based on Common Randomness. Entropy 2014, 16, 1985-2000.

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