Gaussian Mixture Likelihood

Problem

Return the likelihood of x under a one-dimensional Gaussian mixture with component weights weights, means means and standard deviations sigmas: sum over components of weights[k] * N(x; means[k], sigmas[k]^2). Return 0.0 for empty or mismatched inputs or a nonpositive standard deviation.

Hint

Evaluate each component density and take the weighted sum.

Test cases

case 1

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

expected: 0.320456502460288

case 2

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

expected: 0.15747636067966145

case 3

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

expected: 0.19947114020071635

case 4

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

expected: 0.29920671030107454

Starter codePython

import math


def gaussian_mixture_likelihood(weights, means, sigmas, x):
    # Your code here
    pass

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