Hellinger Distance

Problem

Compute the Hellinger distance between two distributions:

H = sqrt(1 - sum(sqrt(p_i * q_i)))

Clamp the expression inside the square root at 0 to avoid tiny negative values from floating point.

Hint

sum(sqrt(p_i * q_i)) is the Bhattacharyya coefficient.

case 1

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

expected: 0

case 2

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

expected: 1

case 3

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

expected: 0.18459191128251476

case 4

in: [[0.1,0.2,0.7],[0.2,0.2,0.6]]

expected: 0.10249182368318223

Starter codePython

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

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