KL Calibration Divergence

Problem

Compute the KL divergence used to score calibration ranges: normalize p and q to distributions, floor q at eps, and return sum p_i * ln(p_i / q_i), skipping terms where p_i is zero. Lower divergence means the quantized distribution better matches the reference.

The signature is kl_calibration_divergence(p, q, eps=1e-9).

Hint

KL is asymmetric: it is zero only when the two normalized histograms match.

Test cases

case 1

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

expected: 0

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: 0.14384103622589042

case 4

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

expected: 20.72326583694641

Starter codePython

import math
def kl_calibration_divergence(p, q, eps=1e-9):
    # Your code here
    pass

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