This test is purely non-parametric, it is based on the characteristic
function evaluated at the data (OK basically their Fourier transform),
following a characterization of independence by A. Renyi, though its actual
implementation depends on pairwise distances and that is something I must
understand better first.
I made a proof of concept creating a X~N(0,1) and Y=X^2. An ideal
non-linear correlation should yield 1, since this is a purely functional
relationship. It is well-known that Pearson's correlation is 0 for this
case. Rizzo and coauthors' coefficient yields 0.49 in my test.
Also, according to their paper "Brownian Distance Covariance", their
p-value is always less than that of the correlation (see the examples
there).
2012/9/3 Gael Varoquaux <[email protected]>
> On Mon, Sep 03, 2012 at 01:54:58AM +0200, Analytic Bastard wrote:
> > It would be useful to test whether any classification or regression
> > problem can be tractable. After all, if two variables are
> independent, it
> > won't be possible to try to classify or do regression with them.
>
> In my experience, such tests are not very powerfull, as they are weakly
> parametric, and thus do not give a good answer to that question.
>
> Do you have an example of the use of these tools on real world problem?
>
> Gael
>
>
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