GCMI in Python gives unexpected results

[DominiqueMakowski]

Hi @robince, I just stumbled on your work and it's super interesting! I see we have somewhat related interests in complexity metrics ☺️

We recently implemented quite a lot of complexity algos in neurokit, and we also have a function to compute Mutual Info using different types of methods. I myself am not an expert at all of this, but I managed to adapt & implement some of these methods so that they are easy to use.

I think it'd be great to add GC MI, and I gave it a quick try by using your code, but unfortunately the results are somewhat unexpected. I computed the MI of two small series under different conditions of noise, using "traditional" approaches and GCMI (MI6 in the plot), but the pattern doesn't look like the others...

Am I missing something? Or misunderstanding how to use this function?

The code to reproduce the fig is in this PR neuropsychology/NeuroKit#677 (& here's the link to the adaptation (mostly streamlining) of your code: https://github.com/neuropsychology/NeuroKit/pull/677/files)

let me know what you think! cheers

[robince]

I think your signal is y=x**2 + noise. GCMI won't detect this sort of symmetric effect, it can detect only monotonic effects (it is like a rank correlation). You could try adding in abs(x) as a second dimension of x.

Also I apprecaite your interest but GCMI is licensed under the GPL so code can't be reused and released under MIT.

[DominiqueMakowski]

Thanks for your reply

You could try adding in abs(x) as a second dimension of x.

I am not sure what you mean here?

GCMI is licensed under the GPL

Ah sorry I missed that. Shame, I'll close the PR then!

[robince]

nk.mutual_information(np.abs(x), y + noise, method="gc")

would I think be sensitive to y=x**2 effect, but requires some sort of prior knowledge (and would lose linear effects). In general if you want to have sensitivity to a symmetric effect you can create a 2d variable np.stack([x, np.abs(x-np.median(x))]) and put that as a 2d input for GCMI. There is a cost in terms of sensitivity and sampling variance for going to 2d and it's not very elegant, but just a suggestion :)

nk.mutual_information(np.stack([x, np.abs(x-np.median(x))]), y + noise, method="gc")

Sorry about the incompatible license. I have always preferred the GPL for publically funded academic work, but perhaps that view is a bit out of date now!