Conditional mutual information

In probability theory, particularly information theory, the conditional mutual information is, in its most basic form, the expected value of the mutual information of two random variables given the value of a third. == Definition == For random variables X {\displaystyle X} , Y {\displaystyle Y} , and Z {\displaystyle Z} with support sets X {\displaystyle {\mathcal {X}}} , Y {\displaystyle {\mathcal {Y}}} and Z {\displaystyle {\mathcal {Z}}} , we define the conditional mutual information as I ( X ; Y | Z ) = ∫ Z D K L ( P ( X , Y ) | Z ‖ P X | Z ⊗ P Y | Z ) d P Z {\displaystyle I(X;Y|Z)=\int _{\mathcal {Z}}D_{\mathrm {KL} }(P_{(X,Y)|Z}\|P_{X|Z}\otimes P_{Y|Z})dP_{Z}} .

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Conditional mutual information

In probability theory, particularly information theory, the conditional mutual information is, in its most basic form, the expected value of the mutual information of two random variables given the value of a third. == Definition == For random variables X {\displaystyle X} , Y {\displaystyle Y} , and Z {\displaystyle Z} with support sets X {\displaystyle {\mathcal {X}}} , Y {\displaystyle {\mathcal {Y}}} and Z {\displaystyle {\mathcal {Z}}} , we define the conditional mutual information as I ( X ; Y | Z ) = ∫ Z D K L ( P ( X , Y ) | Z ‖ P X | Z ⊗ P Y | Z ) d P Z {\displaystyle I(X;Y|Z)=\int _{\mathcal {Z}}D_{\mathrm {KL} }(P_{(X,Y)|Z}\|P_{X|Z}\otimes P_{Y|Z})dP_{Z}} .

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Source: Wikipedia "Conditional mutual information" · CC BY-SA 4.0

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