[Feature] Gaussian-Copula Mutual Information

[DominiqueMakowski]

• Try re-implementing GCMI for signal processing.

There is an open-source Python implementation in https://github.com/robince/gcmi, but it gives unexpected results, below is a comparison of GCMI ("MI6") vs. other methods. It doesn't follow the same pattern at all...

import numpy as np
import pandas as pd

x = np.random.normal(size=400)
y = x**2

data = pd.DataFrame()
for level in np.linspace(0.01, 3, 200):
    noise = np.random.normal(scale=level, size=400)
    rez = pd.DataFrame({"Noise": [level]})
    rez["MI1"] = nk.mutual_information(x, y + noise, method="varoquaux", sigma=1)
    rez["MI2"] = nk.mutual_information(x, y + noise, method="varoquaux", sigma=0)
    rez["MI3"] = nk.mutual_information(x, y + noise, method="nolitsa")
    rez["MI4"] = nk.mutual_information(x, y + noise, method="knn")
    rez["MI5"] = nk.mutual_information(x, y + noise, method="max")
    rez["MI6"] = nk.mutual_information(x, y + noise, method="gc")
    data = pd.concat([data, rez], axis=0)

# Rescale on the same range for visualization purposes
data["MI1"] = nk.rescale(data["MI1"])
data["MI2"] = nk.rescale(data["MI2"])
data["MI3"] = nk.rescale(data["MI3"])
data["MI4"] = nk.rescale(data["MI4"])
data["MI5"] = nk.rescale(data["MI5"])
data["MI6"] = nk.rescale(data["MI6"])

data.plot(x="Noise", y=["MI1", "MI2", "MI3", "MI4", "MI5", "MI6"], kind="line")

[codecov-commenter]

Codecov Report

Merging #677 (6e254ba) into dev (9e7775c) will decrease coverage by 0.15%.
The diff coverage is 5.88%.

@@            Coverage Diff             @@
##              dev     #677      +/-   ##
==========================================
- Coverage   52.95%   52.79%   -0.16%     
==========================================
  Files         271      271              
  Lines       12249    12282      +33     
==========================================
- Hits         6486     6484       -2     
- Misses       5763     5798      +35     

Impacted Files	Coverage Δ
neurokit2/complexity/information_mutual.py	12.84% <5.88%> (-3.16%)	⬇️
neurokit2/rsp/rsp_simulate.py	93.75% <0.00%> (-4.47%)	⬇️
neurokit2/signal/signal_fixpeaks.py	73.50% <0.00%> (+0.64%)	⬆️

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[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 a lot for your input @robince!