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Mutual information. concave/convex

  1. Nov 20, 2011 #1
    hi everybody, :smile:

    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.
  2. jcsd
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