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Quantifying Unique Information

Max Planck Institute for Mathematics in the Sciences, Inselstraße 23, 04109 Leipzig, Germany
Santa Fe Institute, 1399 Hyde Park Rd, Santa Fe, NM 87501, USA
Author to whom correspondence should be addressed.
Entropy 2014, 16(4), 2161-2183;
Received: 15 January 2014 / Revised: 24 March 2014 / Accepted: 4 April 2014 / Published: 15 April 2014
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. 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

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

AMA Style

Bertschinger N, Rauh J, Olbrich E, Jost J, Ay N. Quantifying Unique Information. Entropy. 2014; 16(4):2161-2183.

Chicago/Turabian Style

Bertschinger, Nils, Johannes Rauh, Eckehard Olbrich, Jürgen Jost, and Nihat Ay. 2014. "Quantifying Unique Information" Entropy 16, no. 4: 2161-2183.

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