Distance correlation versus mutual information

I’ve worked with the mutual information for some time. But I found a very recent measure in the “correlation world” that can also be used to measure distribution independence, the so called “distance correlation” ( also termed Brownian correlation): http://en.wikipedia.org/wiki/Brownian_covariance. I checked the papers where this measure is introduced, but without finding any allusion to the mutual information.

So, my questions are:

  • Do they solve exactly the same problem? If not, how the problems are different?
  • And if the previous question can be answered on the positive, what are the advantages of using one or the other?

Answer

Information / mutual information does not depend on the possible values, it depends only on the probabilities therefore it is less sensitive. Distance correlation is more powerful and simpler to compute. For a comparision see

http://www-stat.stanford.edu/~tibs/reshef/comment.pdf

Attribution
Source : Link , Question Author : dsign , Answer Author : gabor J Szekely

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