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Mutual information. concave/convex

by PetitPrince
Tags: concave or convex, information, mutual
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Nov20-11, 09:17 AM
P: 1
hi everybody,

while looking on the mutual information of two variables, one find that it is concave of p(x) given p(x|y) and convex of p(x|y) given p(x).

the first statement is okey, but when it comes to proving the second, i get stuck, even when i find proofs already done i didn't get how they can conclude the convexity of I(x,y) as a function of p(x|y) from the convexity of the relative entropy D(p||q).

here is a piece of the proof i didnt understand

if you have any idea, i'd very much appreciate it.

thank you in advance.
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