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Example of calculating the probability of a word, from character probabilities
# A python example of calculating the probability of the word 'hine'
# See https://discourse.mozilla.org/t/quick-heads-up-on-some-metadata-confidence-estimate-work-were-doing/40618/2
# The probability that a word is incorrect before the nth letter:
def p_not_word(n, probabilities):
if n == 0:
return 0
else:
return probabilities[n - 1] * p_not_word(n - 1, probabilities) + \
(1 - probabilities[n - 1])
# The probability of a word being correctly emitted, given the character
# probabilities:
def p_word(probabilities):
return 1 - p_not_word(len(probabilities), probabilities)
# Character probabilities for the word 'hine' (including the following space):
# h i n e blank
hine = [0.994121, 0.998789, 0.999938, 0.998212, 0.841081]
# The probability of the word 'hine', assuming independent draws with those
# probabilities, following the probability tree:
p_hine = 1 - (
(1 - 0.994121) + # not h
0.994121 * (1 - 0.998789) + # h * not i
0.994121 * 0.998789 * (1 - 0.999938) + # h * i * not n
0.994121 * 0.998789 * 0.999938 * (1 - 0.998212) + # h * i * n * not e
0.994121 * 0.998789 * 0.999938 * 0.998212 * (1 - 0.841081) # h * i * n * e * not space
)
# Check the manual and the recursive calculation are the same
assert round(p_hine, 5) == round(p_word(hine), 5), \
'Error in the calculation of word probabilities'
# And here is the probability of the word 'hine' (0.83357883745)
print(p_word(hine))
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