GMM Responsibility

Problem

Compute the responsibility of each 1D Gaussian component for point x: prior_k * N(x | mean_k, var_k), normalized to sum to 1.

If a variance is <= 0, the component density is 1.0 at its mean and 0.0 elsewhere. Return 0.0 for every component when the total weight is 0; empty components return [].

Hint

Responsibility is the posterior probability of the component given the point.

Test cases

case 1

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

expected: [0.7310585786300048,0.2689414213699951]

case 2

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

expected: [0.6224593312018546,0.37754066879814546]

case 3

in: [2,[0,2],[1,1],[0.3,0.7]]

expected: [0.054821162438825934,0.945178837561174]

case 4

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

expected: []

Starter codePython

import math
def gmm_responsibility(x, means, variances, priors):
    # Your code here
    pass

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