robince / gcmi Goto Github PK

Hello Dr. Robin Ince,

I was using you gcmi code to measure information between two signals with 39 and 300 dimension. but i have enconterd an error in the cholsky decomposition. it says that matrix is no positive definite. I understood that its a problem of my input matrix because its eigen values include negative values. I have tried to modified the eigen values replacing negative values with zeros and then recomposing the original matrix. but still i get the same error. I just want to ask you did you ever encounter this type of problem?

my error

LinAlgError Traceback (most recent call last)
in
----> 1 chCxy = np.linalg.cholesky(Cxy)

~\Anaconda3\lib\site-packages\numpy\linalg\linalg.py in cholesky(a)
731 t, result_t = _commonType(a)
732 signature = 'D->D' if isComplexType(t) else 'd->d'
--> 733 r = gufunc(a, signature=signature, extobj=extobj)
734 return wrap(r.astype(result_t, copy=False))
735

~\Anaconda3\lib\site-packages\numpy\linalg\linalg.py in _raise_linalgerror_nonposdef(err, flag)
90
91 def _raise_linalgerror_nonposdef(err, flag):
---> 92 raise LinAlgError("Matrix is not positive definite")
93
94 def _raise_linalgerror_eigenvalues_nonconvergence(err, flag):

LinAlgError: Matrix is not positive definite

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

Thanks for making this method for mutual information estimation available. I have done a quick test in matlab (and python) on a donut-shaped bivariate distribution for which I would expect the mutual information to be non-zero. However the result that gcmi_cc gives is very close to zero.

Is this an expected result, or do I use the functions incorrectly?

Here is the matlab code for the test:

t=(1:1999)'/200.;
s1 = normrnd(1.,0.1,[2000,1]) * sin( 2*pi*t );
s2 = normrnd(1.,0.1,[2000,1]) * sin( 2*pi*t - 0.5*pi );
gcmi_cc( s1, s2 ) % gives as answer: -3.5968e-04

Hi !

Thank you a lot for this nice code. I think there's a mistake for the Python version of the gcmi_ccd. Pz should be the sum of idx (and not x.shape) :

Pz[zi] = idx.sum()  # or thsx.shape[-1]

Among the other mutual information estimators, your one looks promising. Are you willing to ship your python implementation to pypi? I'd like to use your package (that hopefully will be updated) instead of just copying the source code.
Thank you.

Dear Robin,

I find your mutual information estimator practically useful for continuos-continuos typical data. But it overestimates the mutual information if the data does not follow Gaussian distribution. Is your estimator supposed to work with Gaussian only distributed data?

I can describe in details my test but it makes sense if your estimator accepts non-gaussian.

Cheers,
Danylo.

Hi,

I am using Python 3.6.5 on a windows machine. I generate 2D data sets: linear and nonlinear distributions, following the Python code at https://minepy.readthedocs.io/en/latest/python.html

By the way, these distributions are shown in the paper "A statistical framework for neuroimaging data analysis based on mutual information estimated via a gaussian copula"

Then, I created my script to compute GCMI and got these results:
a) 7 linear distributions:
26.4952
0.7085
0.1584
0.0015
0.1033
0.7295
10.5505

I would expect that the first and last to have a GCMI of 1 - assuming 1 is the highest value meaning a perfect dependence

b) 7 nonlinear distributions:
-0.0004
-0.0001
-0.0003
-0.0003
0.0004
0.0022
-0.0003

What is the meaning of negative correlation values? why are these values so low?

I attached to this issue: my script and input data.

Many thanks,

Ivan

Python_GCMI_2D_Synthetic_Data.zip