Dual Total Correlation

Problem

Compute the dual total correlation in bits of a 3D joint distribution joint[x][y][z]:

DTC = H(X,Y) + H(X,Z) + H(Y,Z) - 2 * H(X,Y,Z)

Equivalently, H(X,Y,Z) minus the sum of H(X|YZ) + H(Y|XZ) + H(Z|XY).

Hint

Dual total correlation equals total correlation for three variables only in special cases.

case 1

in: [[[[0.125,0.125],[0.125,0.125]],[[0.125,0.125],[0.125,0.125]]]]

expected: 0

case 2

in: [[[[0.5,0],[0,0]],[[0,0],[0,0.5]]]]

expected: 1

case 3

in: [[[[0.25,0.25],[0,0]],[[0,0],[0.25,0.25]]]]

expected: 1

case 4

in: [[[[0.2,0.1],[0.05,0.05]],[[0.05,0.05],[0.1,0.2]]]]

expected: 0.43365938015714

Starter codePython

import math
def dual_total_correlation(joint):
    # Your code here
    pass

4 test cases · run your code against them in the editor