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The interaction information (II) in 3D is defined as a generalization of the 2D mutual information (MI).
$$
\begin{eqnarray}
I(X:Y:Z)
&=& I(X:Y) - I(X:Y|Z) \\
&=& H(X) + H(Y)+H(Z) - H(XY) - H(XZ) - H(YZ) + H(XYZ)
\end{eqnarray}
$$
II can be negative, for example for $Z = \mathrm{XOR}(X, Y)$. It i...
In probability theory and information theory, the mutual information (MI) of two random variables is a measure of the mutual dependence between the two variables. More specifically, it quantifies the "amount of information" (in units such as shannons, commonly called bits) obtained about one random variable through observing the other random variable. The concept of mutual information is intimately linked to that of entropy of a random variable, a fundamental notion in information theory that quantifies the expected "amount of information" held in a random variable.
Not limited to real-valued...
