This repository provides an implementation of the method in:

• Tobias Mages and Christian Rohner. Quantifying Redundancies and Synergies with Measures of Inequality https://doi.org/10.48550/arXiv.2407.04415 (preprint)

• demo.py: provides a simple usage example
• attribute_decomposition.py: implements the presented method

Requirements: pandas

attribute_decomposition.py: computeInequaltyDecomposition(.) take the followign arguments:

• f: the generator function for an f-divergence
• p: the parameter 0<=p<=1
• modelCSV: the CSV-file containing the system model
• delimiter: the used deliminator in the CSV-file
• indicatorColumnName: the column name in the CSV-file for the indicator variable.
• individualCountColumnName: the column name in the CSV-file for the number of individuals with this indicator and attributes. Therefore and like used in the puplication examples, the total indicator value contributed by each entry/row is the given indicator value times the number of individuals. To represent a subgroup as model entry/row, use the group-size in individualCountColumnName and use the average indicator value of the subgroup in indicatorColumnName.
• AttributeColumnNameList: the list of column name in the CSV-file for the attributes of the decomposition.
• return value: a list of tuples. Each tuple contains the atom name, cumultive and partial result.

from attribute_decomposition import computeInequaltyDecomposition, printDecompositition

# define the generator function of an f-divergence
f = lambda x: (x-1)**2

# compute the decomposition
result = computeInequaltyDecomposition(f, 0.4, 'model.csv', ',', 'Indicator value','Number of individuals', ['Attribute 1', 'Attribute 2'])

# print the result on the union-lattice representation
printDecompositition(result)
#               Atom               , cumulative, partial
# [['Attribute 1', 'Attribute 2']] ,   0.589246, 0.000000
#        [['Attribute 2']]         ,   0.299376, 0.117162 <- Unique A1
#        [['Attribute 1']]         ,   0.360000, 0.056538 <- Unique A2
#[['Attribute 1'], ['Attribute 2']],   0.416538, 0.172708 <- Synergetic
#               [[]]               ,   0.000000, 0.242838 <- Redundant