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Entropy 2014, 16(4), 1985-2000; doi:10.3390/e16041985
Article

Intersection Information Based on Common Randomness

1,* , 2
,
3
,
4
 and
5,6
1 Computation and Neural Systems, Caltech, Pasadena, CA 91125, USA 2 Dept. of Electrical & Computer Engineering, Colorado State University, Fort Collins, CO 80523, USA 3 Department of Computer Science, University of Colorado, Boulder, CO 80309, USA 4 Center for Complexity and Collective Computation, Wisconsin Institute for Discovery, University of Wisconsin-Madison, Madison, WI 53715, USA 5 Complexity Sciences Center and Physics Dept, University of California Davis, Davis, CA 95616, USA 6 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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Abstract

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.
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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