Conditional Entropy from Counts

Problem

Compute the conditional entropy H(Y|X) in bits from a 2D table of counts, where rows index the values of X and columns the values of Y. Each row contributes its probability mass times the entropy of its conditional distribution. Return 0.0 for an empty or all-zero table.

Hint

Use H(Y|X) = sum_x p(x) H(Y | X = x), skipping empty rows.

Test cases

case 1

in: [[[1,1],[1,1]]]

expected: 1

case 2

in: [[[2,0],[0,2]]]

expected: 0

case 3

in: [[[1,2],[3,4]]]

expected: 0.965148445440323

case 4

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

expected: 0

case 5

in: [[[3,1],[1,3]]]

expected: 0.8112781244591329

Starter codePython

import math
def conditional_entropy_counts(counts):
    # Your code here
    pass

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