Self-Normalized Importance Sampling Estimate

Problem

Self-normalized importance sampling estimates E[f(X)] as the weighted average of sampled values using weights target[sample] / proposal[sample]. Return sum(weight * value) / sum(weight) over the given sample indices. Return 0.0 for empty or invalid arguments.

Hint

Normalizing by the total weight removes the need to know the target's normalizing constant.

Test cases

case 1

in: [[1,2,3],[0.2,0.3,0.5],[0.5,0.25,0.25],[0,1,2]]

expected: 2.4444444444444446

case 2

in: [[1,2],[0.5,0.5],[0.5,0.5],[0,0,1]]

expected: 1.3333333333333333

case 3

in: [[2,4],[0.25,0.75],[0.5,0.5],[1,1]]

expected: 4

case 4

in: [[1],[1],[1],[]]

expected: 0

case 5

in: [[1,2],[0.5,0.5],[0.5,0.5],[5]]

expected: 0

Starter codePython

def self_normalized_is_estimate(values, target, proposal, samples):
    # Your code here
    pass

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