CRPS from Quantile Losses

Problem

Approximate the continuous ranked probability score from quantile forecasts as CRPS = 2 * sum over k of QS_k / (K * n), where QS_k is the total pinball loss at quantile q_k, K the number of quantiles, and n the number of observations.

Return 0.0 when inputs are empty or when the counts of forecast lists and quantiles differ.

Hint

The quantile-score representation lets a finite set of quantiles approximate CRPS.

Test cases

case 1

in: [[10,12,14],[[9,11,13],[13,14,15]],[0.25,0.75]]

expected: 0.75

case 2

in: [[5],[[4],[6]],[0.1,0.9]]

expected: 0.19999999999999998

case 3

in: [[1,2,3],[[1,2,3]],[0.5]]

expected: 0

case 4

in: [[1,2],[],[]]

expected: 0

Starter codePython

def crps_from_quantile_losses(actual, forecasts, quantiles):
    # Your code here
    pass

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