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Entropy 2014, 16(4), 2161-2183; doi:10.3390/e16042161

Quantifying Unique Information

1, 1,* , 1, 1,2 and 1,2
1 Max Planck Institute for Mathematics in the Sciences, Inselstraße 23, 04109 Leipzig, Germany 2 Santa Fe Institute, 1399 Hyde Park Rd, Santa Fe, NM 87501, USA
* Author to whom correspondence should be addressed.
Received: 15 January 2014 / Revised: 24 March 2014 / Accepted: 4 April 2014 / Published: 15 April 2014
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We propose new measures of shared information, unique information and synergistic information that can be used to decompose the mutual information of a pair of random variables (Y, Z) with a third random variable X. Our measures are motivated by an operational idea of unique information, which suggests that shared information and unique information should depend only on the marginal distributions of the pairs (X, Y) and (X,Z). Although this invariance property has not been studied before, it is satisfied by other proposed measures of shared information. The invariance property does not uniquely determine our new measures, but it implies that the functions that we define are bounds to any other measures satisfying the same invariance property. We study properties of our measures and compare them to other candidate measures.
Keywords: Shannon information; mutual information; information decomposition; shared information; synergy Shannon information; mutual information; information decomposition; shared information; synergy
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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Bertschinger, N.; Rauh, J.; Olbrich, E.; Jost, J.; Ay, N. Quantifying Unique Information. Entropy 2014, 16, 2161-2183.

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