Bernoulli Naive Bayes Log-Posterior

Problem

For a Bernoulli naive Bayes model, the unnormalized log posterior of a class is log(prior) plus the sum over features of x[i] * log(theta[i]) + (1 - x[i]) * log(1 - theta[i]). Given a binary feature vector, the class prior, and per-feature success probabilities, return that score. Return 0.0 for invalid probabilities or mismatched lengths.

Hint

Take logarithms of the prior and the per-feature Bernoulli probabilities, then add.

Test cases

case 1

in: [[1,0],0.6,[0.9,0.3]]

expected: -0.9728610833625495

case 2

in: [[0,0],0.5,[0.2,0.4]]

expected: -1.4271163556401456

case 3

in: [[1,1],0.7,[0.95,0.8]]

expected: -0.6311117896404927

case 4

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

expected: -0.6931471805599453

case 5

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

expected: 0

Starter codePython

import math


def bernoulli_naive_bayes_log_posterior(x, prior, feature_probs):
    # Your code here
    pass

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