# 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?
• Try to write down explicitly 'distance correlation' and 'mutual information' for a simple example. In the second case you will get logarithms, while in the first - not. – Piotr Migdal Jan 10 '12 at 11:52
• @PiotrMigdal Yes, I'm aware of that difference. Could you please explain why is it important? Please, take into account that I'm not a statistician... – dsign Jan 10 '12 at 11:56
• For ma a standard tool measuring mutual dependence of probability distributions is the mutual information. It has a lot of nice properties and its interpretation is straightforward. However, there may be specific problems where distance correlation is preferred (but I have never used it in my life). So what is the problem you are trying to solve? – Piotr Migdal Jan 10 '12 at 14:53
• This comment is a few years late but Columbia University's Statistics Dept made the academic year 2013-2014 a year of focus on measures of dependence. In April-May 2014, a workshop was held that brought together the top academics doing work in this field including the Reshef Brothers (MIC), Gabor Szekely (distance correlations), Subhadeep Mukhopadhay to name a few. Here's a link to the program that includes many pdfs from the presentations. dependence2013.wikischolars.columbia.edu/… – Mike Hunter Oct 15 '15 at 11:24