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Partial mutual information

Partial mutual information

The partial mutual information between random variables $X$ , $Y$ , and $Z$ is defined by

$I(X, Y ; Z) = H(X, Z) + H(Z, Y) - H(Z) - H(X, Z, Y)$

where $H$ denotes the Shannon differential entropy. It measures the amount of information shared by $X$ and $Y$ while discounting the possibility that $Z$ drives both $X$ and $Y$ . If $Z$ is independent of both $X$ and $Y$ , then partial mutual information degenerates to mutual information.

References

Partial Mutual Information for Coupling Analysis of Multivariate Time Series,
Stefan Frenzel and Bernd Pompe,
Physical Review Letters, 2007.

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