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Conditional entropy

Information theory · Formula · Not yet linked from a lesson

H(Y∣X)=H(X,Y)−H(X)H(Y \mid X) = H(X, Y) - H(X)

How much uncertainty is left in Y once you already know X. It reaches zero when X determines Y outright, and stays at the full entropy of Y when X tells you nothing about it.

Symbols

H(X,Y)H(X, Y)
The joint entropy of both variables.
H(X)H(X)
The entropy of X alone.
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