Mutual Information of Adjacent Letters

Problem

Given a 2D matrix of adjacent-letter counts, normalize it into a joint distribution and return the mutual information in bits:

I = sum p(i, j) * log2(p(i, j) / (p(i) * p(j)))

Skip cells with zero count.

Hint

Perfectly correlated letters carry one bit; independent letters carry none.

case 1

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

expected: 0

case 2

in: [[[4,0],[0,4]]]

expected: 1

case 3

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

expected: 0.005802149014345649

case 4

in: [[[1,0],[0,1]]]

expected: 1

Starter codePython

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

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