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mutual information

How many bits learning one variable's value tells you about another — the shared information between them.

$I(X;Y) := H(X) - H(X\mid Y) = H(X)+H(Y)-H(X,Y)$ , symmetric in $X$ and $Y$ .

Examples

Independent X and Y have $I(X;Y)=0$ ; a perfectly predictable pair has $I(X;Y)=H(X)$ .