Quantifying Unique Information

Entropy

Nils Bertschinger¹  Johannes Rauh¹  Eckehard Olbrich¹  Jürgen Jost¹ 

[1] Max Planck Institute for Mathematics in the Sciences, Inselstraße 23, 04109 Leipzig, Germany

关键词: Shannon information;    mutual information;    information decomposition;    shared information;    synergy;   

DOI  :  10.3390/e16042161

来源: mdpi

【 摘 要 】

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.

MSC Classification: 94A15, 94A17

【 授权许可】

CC BY   
© 2014 by the authors; licensee MDPI, Basel, Switzerland