Gaussian Naive Bayes Log-Likelihood

Problem

For each class, compute the log-likelihood of a point under independent Gaussians: the sum over features of -0.5 * log(2 * pi * variance) - (x - mean)^2 / (2 * variance). means[c] and variances[c] hold the per-feature parameters of class c. Return the list of per-class log-likelihoods, or an empty list for mismatched shapes or a nonpositive variance.

Hint

The Gaussian log density is a normalization term minus the squared z-score over two.

Test cases

case 1

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

expected: [-1.8378770664093453,-2.8378770664093453]

case 2

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

expected: [-2.8378770664093453,-1.8378770664093453]

case 3

in: [[2],[[0]],[[4]]]

expected: [-2.112085713764618]

case 4

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

expected: []

case 5

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

expected: []

Starter codePython

import math


def gaussian_naive_bayes_log_likelihood(x, means, variances):
    # Your code here
    pass

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