Mixture Average Log-Likelihood

Problem

Compute the average log density of a data set under a one-dimensional Gaussian mixture. For each point evaluate the log of the sum over components of weights[k] * N(x; means[k], sigmas[k]^2) stably with log-sum-exp, then average over the points. Return 0.0 when the inputs are empty, mismatched, or any standard deviation is nonpositive.

Hint

Evaluate every component log density, take a log-sum-exp, then average over the points.

Test cases

case 1

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

expected: -0.9189385332046728

case 2

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

expected: -1.252271866538006

case 3

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

expected: -1.9440342334791008

case 4

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

expected: -1.612085713764618

case 5

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

expected: 0

Starter codePython

import math


def mixture_average_log_likelihood(weights, means, sigmas, data):
    # Your code here
    pass

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