Difference between Cross Entropy and Joint Entropy
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Even they are using same notation, but have different meaning.
Cross Entropy:
x ~ p, y ~ q
H(p,q) = - Sum( p(x)*log(q(y)) )
Joint Entropy:
x ~ p, y ~ q, (x,y) ~ f
H(p,q) = - sum( f(x,y) * log( f(x,y)) )
Cross Entropy:
x ~ p, y ~ q
H(p,q) = - Sum( p(x)*log(q(y)) )
Joint Entropy:
x ~ p, y ~ q, (x,y) ~ f
H(p,q) = - sum( f(x,y) * log( f(x,y)) )
There a picture can help understanding:
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