CUPED Variance Reduction

Problem

Apply CUPED variance reduction. With theta = cov(x, y) / var(x), adjust y_i to y_i - theta * (x_i - mean_x).

Return [adjusted_mean, variance_reduction] where variance_reduction = 1 - var(adjusted)/var(y). If var(x) or var(y) is 0, return [mean_y, 0.0].

Hint

A pre-experiment covariate correlated with the metric lets you explain away variance.

case 1

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

expected: [2.5,1]

case 2

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

expected: [2.5,0]

case 3

in: [[2,4,6,8],[1,3,5,7]]

expected: [5,1]

case 4

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

expected: [2.5,0]

Starter codePython

def cuped_variance_reduction(y, x):
    # Returns [adjusted_mean, variance_reduction]
    # Your code here
    pass

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