Bagging Variance Reduction

Problem

Averaging B bagged predictors whose pairwise correlation is correlation and whose individual variance is sigma_squared gives variance correlation * sigma_squared + (1 - correlation) * sigma_squared / B. Return that variance, or 0.0 for invalid inputs.

Hint

The correlated part of the variance never averages away; only the idiosyncratic part shrinks.

Test cases

case 1

in: [1,0.5,10]

expected: 0.55

case 2

in: [1,0,100]

expected: 0.01

case 3

in: [4,0.25,3]

expected: 2

case 4

in: [1,1,5]

expected: 1

case 5

in: [1,0.2,-2]

expected: 0

Starter codePython

def bagging_variance_reduction(sigma_squared, correlation, n_estimators):
    # Your code here
    pass

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