Download the module info.py into your project directory, and do:
from info import compute as compute_mutual_information
X = [1, 2, 3, 4, 5]
Y = [4, 1, 3, 4, 2]
X_range = (1, 5)
Y_range = (1, 5) # 5 did not occur in the sample Y yet
[mi_XY, mi_XY_normalized, everything] = compute_mutual_information(X, Y, [X_range, Y_range])
# `everything` is a nested dictionary that contains other normalized variants
# of mutual information, as well as some commonly used information theoretic
# metrics such as entropy, conditional entropy, self-information (also known as
# information content or surprisal). known as information content or
# surprisal), relative entropy (also known as KL-divergence or information
# gain). Joint and marginal probability mass functions and contingency tables
# are also included for convenience. Note the example output is computed using
# 1000 samples.
everything = {
'N': 1000,
'entropy': {'X': 2.3168095633619847,
'Y': 2.3199539124456714,
'XY': 4.625700518983682,
'X-given-Y': 2.3088909556216985,
'Y-given-X': 2.305746606538012},
'mutual-information': {
'standard': 0.01106295682397285,
# normalize by entropy (asymmetric), ranges from [0, 1]
'normalized-by-HX': 0.0047750825095521,
'normalized-by-HY': 0.0047750825095521,
# other normalization variants (symmetric)
'symmetric': 0.004771844361565519,
'redundancy': 0.0023859221807827594,
'generalized-pearson-correlation': 0.004771845458771204,
'generalized-total-correlation': 0.0047750825095521,
'information-quality-ratio': 0.0023916284200784154,
'adjusted-mutual-information': 'TODO'},
'self-information': {'X': array([2.35845397, 2.41119543, 2.23786383, 2.48196851, 2.14560532]),
'Y': array([2.29335894, 2.42662547, 2.32192809, 2.20423305, 2.37332725]),
'XY': array([[4.83650127, 4.50635267, 4.57346686, 4.68038207, 4.50635267],
[4.53951953, 5.01158797, 4.83650127, 4.87832144, 4.53951953],
[4.57346686, 4.96578428, 4.60823228, 5.15842936, 4.13289427],
[4.64385619, 4.44222233, 4.21089678, 4.79585928, 4.60823228],
[4.83650127, 4.83650127, 4.64385619, 4.57346686, 4.60823228]])}
'count': {'X': array([[195, 188, 212, 179, 226],
[195, 188, 212, 179, 226],
[195, 188, 212, 179, 226],
[195, 188, 212, 179, 226],
[195, 188, 212, 179, 226]]),
'Y': array([[204, 204, 204, 204, 204],
[186, 186, 186, 186, 186],
[200, 200, 200, 200, 200],
[217, 217, 217, 217, 217],
[193, 193, 193, 193, 193]])},
'XY': array([[35, 44, 42, 39, 44],
[43, 31, 35, 34, 43],
[42, 32, 41, 28, 57],
[40, 46, 54, 36, 41],
[35, 35, 40, 42, 41]]),
'p': {'X': array([[0.195, 0.188, 0.212, 0.179, 0.226],
[0.195, 0.188, 0.212, 0.179, 0.226],
[0.195, 0.188, 0.212, 0.179, 0.226],
[0.195, 0.188, 0.212, 0.179, 0.226],
[0.195, 0.188, 0.212, 0.179, 0.226]]),
'Y': array([[0.204, 0.204, 0.204, 0.204, 0.204],
[0.186, 0.186, 0.186, 0.186, 0.186],
[0.2 , 0.2 , 0.2 , 0.2 , 0.2 ],
[0.217, 0.217, 0.217, 0.217, 0.217],
[0.193, 0.193, 0.193, 0.193, 0.193]])}
'XY': array([[0.035, 0.044, 0.042, 0.039, 0.044],
[0.043, 0.031, 0.035, 0.034, 0.043],
[0.042, 0.032, 0.041, 0.028, 0.057],
[0.04 , 0.046, 0.054, 0.036, 0.041],
[0.035, 0.035, 0.04 , 0.042, 0.041]]),
}