Jensen-Shannon Distance

Problem

Compute the Jensen-Shannon distance between two distributions, the square root of the Jensen-Shannon divergence in bits. The divergence is 0.5*KL(p||m) + 0.5*KL(q||m) with the mixture m = (p + q)/2, and zero entries are skipped.

Hint

Build the average distribution first, then measure both KL terms relative to it.

Test cases

case 1

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

expected: 1

case 2

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

expected: 0

case 3

in: [[0.5,0.5],[0.25,0.75]]

expected: 0.22089576884901735

case 4

in: [[0.9,0.1],[0.1,0.9]]

expected: 0.7287004915675019

Starter codePython

import math
def js_distance(p, q):
    # Your code here
    pass

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