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| """Smoothing algorithms for language modeling.
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| According to Chen & Goodman 1995 these should work with both Backoff and
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| Interpolation.
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| """
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| from operator import methodcaller
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| from nltk.lm.api import Smoothing
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| from nltk.probability import ConditionalFreqDist
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| def _count_values_gt_zero(distribution):
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| """Count values that are greater than zero in a distribution.
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| Assumes distribution is either a mapping with counts as values or
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| an instance of `nltk.ConditionalFreqDist`.
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| """
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| as_count = (
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| methodcaller("N")
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| if isinstance(distribution, ConditionalFreqDist)
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| else lambda count: count
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| )
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| return sum(
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| 1 for dist_or_count in distribution.values() if as_count(dist_or_count) > 0
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| )
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| class WittenBell(Smoothing):
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| """Witten-Bell smoothing."""
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| def __init__(self, vocabulary, counter, **kwargs):
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| super().__init__(vocabulary, counter, **kwargs)
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| def alpha_gamma(self, word, context):
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| alpha = self.counts[context].freq(word)
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| gamma = self._gamma(context)
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| return (1.0 - gamma) * alpha, gamma
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| def _gamma(self, context):
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| n_plus = _count_values_gt_zero(self.counts[context])
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| return n_plus / (n_plus + self.counts[context].N())
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| def unigram_score(self, word):
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| return self.counts.unigrams.freq(word)
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| class AbsoluteDiscounting(Smoothing):
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| """Smoothing with absolute discount."""
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| def __init__(self, vocabulary, counter, discount=0.75, **kwargs):
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| super().__init__(vocabulary, counter, **kwargs)
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| self.discount = discount
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| def alpha_gamma(self, word, context):
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| alpha = (
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| max(self.counts[context][word] - self.discount, 0)
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| / self.counts[context].N()
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| )
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| gamma = self._gamma(context)
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| return alpha, gamma
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| def _gamma(self, context):
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| n_plus = _count_values_gt_zero(self.counts[context])
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| return (self.discount * n_plus) / self.counts[context].N()
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| def unigram_score(self, word):
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| return self.counts.unigrams.freq(word)
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| class KneserNey(Smoothing):
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| """Kneser-Ney Smoothing.
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| This is an extension of smoothing with a discount.
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| Resources:
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| - https://pages.ucsd.edu/~rlevy/lign256/winter2008/kneser_ney_mini_example.pdf
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| - https://www.youtube.com/watch?v=ody1ysUTD7o
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| - https://medium.com/@dennyc/a-simple-numerical-example-for-kneser-ney-smoothing-nlp-4600addf38b8
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| - https://www.cl.uni-heidelberg.de/courses/ss15/smt/scribe6.pdf
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| - https://www-i6.informatik.rwth-aachen.de/publications/download/951/Kneser-ICASSP-1995.pdf
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| """
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| def __init__(self, vocabulary, counter, order, discount=0.1, **kwargs):
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| super().__init__(vocabulary, counter, **kwargs)
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| self.discount = discount
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| self._order = order
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| def unigram_score(self, word):
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| word_continuation_count, total_count = self._continuation_counts(word)
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| return word_continuation_count / total_count
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| def alpha_gamma(self, word, context):
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| prefix_counts = self.counts[context]
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| word_continuation_count, total_count = (
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| (prefix_counts[word], prefix_counts.N())
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| if len(context) + 1 == self._order
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| else self._continuation_counts(word, context)
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| )
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| alpha = max(word_continuation_count - self.discount, 0.0) / total_count
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| gamma = self.discount * _count_values_gt_zero(prefix_counts) / total_count
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| return alpha, gamma
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| def _continuation_counts(self, word, context=tuple()):
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| """Count continuations that end with context and word.
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| Continuations track unique ngram "types", regardless of how many
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| instances were observed for each "type".
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| This is different than raw ngram counts which track number of instances.
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| """
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| higher_order_ngrams_with_context = (
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| counts
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| for prefix_ngram, counts in self.counts[len(context) + 2].items()
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| if prefix_ngram[1:] == context
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| )
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| higher_order_ngrams_with_word_count, total = 0, 0
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| for counts in higher_order_ngrams_with_context:
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| higher_order_ngrams_with_word_count += int(counts[word] > 0)
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| total += _count_values_gt_zero(counts)
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| return higher_order_ngrams_with_word_count, total
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|
