Optimal Ensemble Weight

Problem

Compute the minimum-variance ensemble weight for model A: w = (var_b - cov) / (var_a + var_b - 2 * cov) using population statistics, clamped to [0, 1]. Return 0.5 when there are fewer than two paired errors, lengths differ, or the denominator is 0.

Hint

The variance-minimizing weight leans on the more stable model and on whichever error is less correlated.

Test cases

case 1

in: [[0,0,0,0],[1,2,3,4]]

expected: 1

case 2

in: [[1,2,3,4],[2,3,4,5]]

expected: 0.5

case 3

in: [[3,1,4,1,5,9],[2,7,1,8,2,8]]

expected: 0.5520661157024793

case 4

in: [[1],[2]]

expected: 0.5

case 5

in: [[],[]]

expected: 0.5

Starter codePython

def optimal_ensemble_weight(errors_a, errors_b):
    # Your code here
    pass

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