Laplace Smoothed Log Probability

Problem

Add-k smoothing estimates a categorical probability as (count + k) / (total + k * vocab_size). Given the token count, the total token count, the vocabulary size, and the smoothing constant k, return the natural log of that estimate. Return 0.0 when the inputs are invalid.

Hint

Smoothing adds k to every count and k times the vocabulary size to the denominator.

Test cases

case 1

in: [3,10,4,1]

expected: -1.252762968495368

case 2

in: [0,10,5,1]

expected: -2.70805020110221

case 3

in: [10,10,2,1]

expected: -0.08701137698962981

case 4

in: [0,0,3,2]

expected: -1.0986122886681098

case 5

in: [-1,10,4,1]

expected: 0

Starter codePython

import math


def laplace_smoothed_log_probability(count, total, vocab_size, k):
    # Your code here
    pass

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