A Python demonstration of using ''infotheory'' to estimate mutual information under various conditions

mi_demo.py

###############################################################################
# Mutual Information demo for Python package - infotheory
# https://github.com/madvn/infotheory
# 
# Madhavun Candadai
# Dec, 2018
#
# Mutual information should be high for identical variables, slightly lower for
# noisy identical variables and low for random variables
###############################################################################

## Setup
dims = 4  # total dimensionality of all variables = 2+2 = 4
nreps = 1 # number of shifted binnings over which data is binned and averaged
nbins = [10]*dims # number of bins along each dimension of the data
mins = [0]*dims # min value or left edge of binning for each dimension
maxs = [1]*dims # max value or right edge of binning for each dimension

## Creating object
it = infotheory.InfoTools(dims, nreps)

## Specify binning
it.set_equal_interval_binning(nbins, mins, maxs)

## Adding data - concatenate data from all vars
for _ in range(10000):
    it.add_data_point(np.random.rand(dims))

## Invoke infotheory tools
varIDs = [0,0,1,1] # to identify the different vars
mi = it.mutual_info(varIDs) # mutual information between two random vars
mi /= np.log2(np.min(nbins)) # normalizing
print('Mutual information between the two random 2D data = {}'.format(mi))

varIDs = [0,-1,1,-1] # dimensions marked anything other than 0 or 1 are ignored for mutual information
mi = it.mutual_info(varIDs) # mutual information between first dimension two 2D random vars
mi /= np.log2(np.min(nbins)) # normalizing
print('Mutual information between first dimension of two random 2D data = {}'.format(mi))