hi everybody,(adsbygoogle = window.adsbygoogle || []).push({});

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.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Mutual information. concave/convex

Can you offer guidance or do you also need help?

Draft saved
Draft deleted

**Physics Forums | Science Articles, Homework Help, Discussion**