Control Variates Estimate

Problem

Control-variate estimator of E[X] using samples_x, samples_y and the known mean of Y. Estimate beta = Cov(X, Y) / Var(Y) with n - 1 denominators, then return mean(X) - beta * (mean(Y) - known_mean_y).

Return mean(X) when the sample is degenerate or Y has zero variance.

Hint

Subtract the control's observed error scaled by the regression coefficient.

Test cases

case 1

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

expected: 2.5

case 2

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

expected: 4

case 3

in: [[1,1,1,1],[1,2,3,4],2.5]

expected: 1

case 4

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

expected: 2

Starter codePython

def control_variates_estimate(samples_x, samples_y, known_mean_y):
    # Your code here
    pass

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