Importance Sampling Estimate (Seeded)

Problem

Estimate E[X] for a discrete variable with the given values and target distribution using importance sampling from proposal. Draw n samples from the proposal with random.Random(seed) via inverse transform, weight sample i by target[i] / proposal[i], and return the average weight times value. Return 0.0 for n <= 0.

Hint

Use inverse transform sampling with cumsum of the proposal.

Test cases

case 1

in: [[1,2,3],[0.2,0.3,0.5],[0.3333333333333333,0.3333333333333333,0.3333333333333333],20000,42]

expected: 2.3056949999998686

case 2

in: [[1,2,3],[0.2,0.3,0.5],[0.3333333333333333,0.3333333333333333,0.3333333333333333],20000,7]

expected: 2.2922099999998724

case 3

in: [[1,2,3],[0.2,0.3,0.5],[0.5,0.3,0.2],10000,1]

expected: 2.3073200000001353

case 4

in: [[1,2,3],[0.2,0.3,0.5],[0.3333333333333333,0.3333333333333333,0.3333333333333333],0,5]

expected: 0

Starter codePython

import random


def importance_sampling_estimate(values, target, proposal, n, seed):
    # Your code here
    pass

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