Joint Entropy from Counts

Problem

Compute the joint entropy H(X, Y) in bits from a 2D table of counts. Normalize by the grand total and skip zero entries in the sum. Return 0.0 for an empty or all-zero table.

Hint

Convert every cell to a probability and add -p log2 p.

Test cases

case 1

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

expected: 2

case 2

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

expected: 1

case 3

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

expected: 1.8464393446710154

case 4

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

expected: 0

case 5

in: [[[3]]]

expected: 0

Starter codePython

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

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