Conditional Entropy H(X|Y)

Problem

Given a 2D joint distribution joint[x][y], compute the conditional entropy H(X|Y) in bits using

H(X|Y) = H(X, Y) - H(Y)

where H(Y) is the entropy of the column marginals. Skip zero terms.

Hint

H(X|Y) = H(X, Y) - H(Y) because entropy is additive over the chain rule.

case 1

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

expected: 1

case 2

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

expected: 0

case 3

in: [[[0.1,0.2],[0.3,0.4]]]

expected: 0.8754887502163469

case 4

in: [[[0.5,0.25],[0,0.25]]]

expected: 0.5

Starter codePython

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

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