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arXiv · 1701.07805

On extractable shared information

Johannes Rauh·Pradeep Kr. Banerjee·Eckehard Olbrich·Jürgen Jost·Nils Bertschinger
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Abstract

We consider the problem of quantifying the information shared by a pair of random variables $X_{1},X_{2}$ about another variable $S$. We propose a new measure of shared information, called extractable shared information, that is left monotonic; that is, the information shared about $S$ is bounded from below by the information shared about $f(S)$ for any function $f$. We show that our measure leads to a new nonnegative decomposition of the mutual information $I(S;X_1X_2)$ into shared, complementary and unique components. We study properties of this decomposition and show that a left monotonic shared information is not compatible with a Blackwell interpretation of unique information. We also discuss whether it is possible to have a decomposition in which both shared and unique information are left monotonic.

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Johannes Rauh, Pradeep Kr. Banerjee, Eckehard Olbrich, Jürgen Jost, Nils Bertschinger. 2017-11-10. On extractable shared information. https://doi.org/10.3390/e19070328

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