Score-Function Estimator

Problem

For a Gaussian distribution N(mu, sigma^2), the score function is (z - mu) / sigma^2, so the score-function (REINFORCE) estimator of d/dmu E[f(z)] is the sample average of f(z_i) * (z_i - mu) / sigma^2.

Given the function values f_values and the corresponding samples z_values, return that estimate.

Hint

The score-function estimator needs only function evaluations, not derivatives of f.

Test cases

case 1

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

expected: 0

case 2

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

expected: 1

case 3

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

expected: 0.6666666666666666

Starter codePython

def score_function_estimator(f_values, z_values, mu, sigma):
    # Your code here
    pass

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