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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

http://ocw.usu.edu/Electrical_and_Computer_Engineering/Information_Theory/lecture3.pdf

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

thank you in advance.

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# Mutual information. concave/convex

Can you offer guidance or do you also need help?

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