Total Variation Distance

Problem

Compute the total variation distance between two probability distributions:

TV = 0.5 * sum(|p_i - q_i|)

The result always lies between 0 and 1.

Hint

TV is half the L1 distance because probability mass shifted from one outcome must land somewhere else.

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: 0.25

case 4

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

expected: 0.09999999999999999

Starter codePython

def total_variation(p, q):
    # Your code here
    pass

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