This repository implements the PID (Partial Information Decomposition) for Multivariate Normal (MVN) systems measuring the redundancy using the Iccs measure developed by Ince (2017) https://doi.org/10.3390/e19070318
Right now this implementation works only for the bivariate case (two sources and one target)
For a broader implementation of the Partial Information Decomposition please see the partial-info-decomp repository
How to use it:
from gcmi import copnorm
import numpy as np
def partial_information_decomposition(X,Y):
'''
Compute the partial information decomposition between the two sources in X and each target in Y using the Iccs redundancy measure for continuous gaussian variables.
Parameters:
X : np.array
The matrix containing the two sources. The sources are in rows so the shape is (n_sources, n_samples)
Y : np.array
The matrix containing the targets. Each target is treated separately and could be e.g., a different EEG channel. The targets are in rows so the shape is (n_targtes, n_samples)
'''
# Check for right dimensionality
n_sources = X.shape[0]
if n_sources != 2:
raise ValueError('This pid version only works in the case of two sources')
# Build the empty 2D lattice
lat = pid_mvn.Lattice2D()
# Be sure that Y is a 2D array
Y = np.atleast_2d(Y)
# Copula normalization of the variables to make them gaussian
X_copnorm = gcmi.copnorm(X)
Y_copnorm = gcmi.copnorm(Y)
# Prepare the data structure
n_targets = Y.shape[0]
PIs = np.zeros((n_targets, 4)) # e.g., (n_channels, 4) (Rdn, Unq1, Unq2, Syn)
# Compute the sample covariance matrix
for tar in range(n_targets):
C = np.cov(np.vstack((X_copnorm,Y_copnorm[tar,:])))
# Compute the 4 partial information atoms
PIs[tar,:] = pid_mvn.calc_pi_mvn(lat, Cfull=C, varsizes=[1,1,1], Icap=pid_mvn.Iccs_mvn, forcenn=True).PI
return PIsThis function uses the code in this repository and the copnorm function that can be found here to compute the partial information decomposition for every channel of the Y variable.