322 lines
12 KiB
Python
322 lines
12 KiB
Python
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# -*- coding: utf-8 -*-
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# Natural Language Toolkit: IBM Model 2
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#
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# Copyright (C) 2001-2013 NLTK Project
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# Authors: Chin Yee Lee, Hengfeng Li, Ruxin Hou, Calvin Tanujaya Lim
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# URL: <http://nltk.org/>
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# For license information, see LICENSE.TXT
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"""
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Lexical translation model that considers word order.
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IBM Model 2 improves on Model 1 by accounting for word order.
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An alignment probability is introduced, a(i | j,l,m), which predicts
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a source word position, given its aligned target word's position.
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The EM algorithm used in Model 2 is:
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E step - In the training data, collect counts, weighted by prior
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probabilities.
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(a) count how many times a source language word is translated
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into a target language word
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(b) count how many times a particular position in the source
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sentence is aligned to a particular position in the target
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sentence
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M step - Estimate new probabilities based on the counts from the E step
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Notations:
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i: Position in the source sentence
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Valid values are 0 (for NULL), 1, 2, ..., length of source sentence
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j: Position in the target sentence
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Valid values are 1, 2, ..., length of target sentence
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l: Number of words in the source sentence, excluding NULL
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m: Number of words in the target sentence
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s: A word in the source language
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t: A word in the target language
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References:
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Philipp Koehn. 2010. Statistical Machine Translation.
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Cambridge University Press, New York.
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Peter E Brown, Stephen A. Della Pietra, Vincent J. Della Pietra, and
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Robert L. Mercer. 1993. The Mathematics of Statistical Machine
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Translation: Parameter Estimation. Computational Linguistics, 19 (2),
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263-311.
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"""
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from __future__ import division
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import warnings
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from collections import defaultdict
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from nltk.translate import AlignedSent
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from nltk.translate import Alignment
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from nltk.translate import IBMModel
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from nltk.translate import IBMModel1
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from nltk.translate.ibm_model import Counts
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class IBMModel2(IBMModel):
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"""
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Lexical translation model that considers word order
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>>> bitext = []
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>>> bitext.append(AlignedSent(['klein', 'ist', 'das', 'haus'], ['the', 'house', 'is', 'small']))
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>>> bitext.append(AlignedSent(['das', 'haus', 'ist', 'ja', 'groß'], ['the', 'house', 'is', 'big']))
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>>> bitext.append(AlignedSent(['das', 'buch', 'ist', 'ja', 'klein'], ['the', 'book', 'is', 'small']))
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>>> bitext.append(AlignedSent(['das', 'haus'], ['the', 'house']))
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>>> bitext.append(AlignedSent(['das', 'buch'], ['the', 'book']))
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>>> bitext.append(AlignedSent(['ein', 'buch'], ['a', 'book']))
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>>> ibm2 = IBMModel2(bitext, 5)
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>>> print(round(ibm2.translation_table['buch']['book'], 3))
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1.0
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>>> print(round(ibm2.translation_table['das']['book'], 3))
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0.0
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>>> print(round(ibm2.translation_table['buch'][None], 3))
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0.0
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>>> print(round(ibm2.translation_table['ja'][None], 3))
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0.0
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>>> print(ibm2.alignment_table[1][1][2][2])
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0.938...
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>>> print(round(ibm2.alignment_table[1][2][2][2], 3))
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0.0
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>>> print(round(ibm2.alignment_table[2][2][4][5], 3))
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1.0
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>>> test_sentence = bitext[2]
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>>> test_sentence.words
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['das', 'buch', 'ist', 'ja', 'klein']
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>>> test_sentence.mots
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['the', 'book', 'is', 'small']
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>>> test_sentence.alignment
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Alignment([(0, 0), (1, 1), (2, 2), (3, 2), (4, 3)])
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"""
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def __init__(self, sentence_aligned_corpus, iterations, probability_tables=None):
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"""
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Train on ``sentence_aligned_corpus`` and create a lexical
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translation model and an alignment model.
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Translation direction is from ``AlignedSent.mots`` to
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``AlignedSent.words``.
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:param sentence_aligned_corpus: Sentence-aligned parallel corpus
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:type sentence_aligned_corpus: list(AlignedSent)
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:param iterations: Number of iterations to run training algorithm
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:type iterations: int
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:param probability_tables: Optional. Use this to pass in custom
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probability values. If not specified, probabilities will be
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set to a uniform distribution, or some other sensible value.
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If specified, all the following entries must be present:
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``translation_table``, ``alignment_table``.
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See ``IBMModel`` for the type and purpose of these tables.
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:type probability_tables: dict[str]: object
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"""
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super(IBMModel2, self).__init__(sentence_aligned_corpus)
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if probability_tables is None:
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# Get translation probabilities from IBM Model 1
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# Run more iterations of training for Model 1, since it is
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# faster than Model 2
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ibm1 = IBMModel1(sentence_aligned_corpus, 2 * iterations)
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self.translation_table = ibm1.translation_table
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self.set_uniform_probabilities(sentence_aligned_corpus)
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else:
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# Set user-defined probabilities
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self.translation_table = probability_tables['translation_table']
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self.alignment_table = probability_tables['alignment_table']
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for n in range(0, iterations):
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self.train(sentence_aligned_corpus)
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self.align_all(sentence_aligned_corpus)
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def set_uniform_probabilities(self, sentence_aligned_corpus):
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# a(i | j,l,m) = 1 / (l+1) for all i, j, l, m
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l_m_combinations = set()
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for aligned_sentence in sentence_aligned_corpus:
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l = len(aligned_sentence.mots)
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m = len(aligned_sentence.words)
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if (l, m) not in l_m_combinations:
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l_m_combinations.add((l, m))
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initial_prob = 1 / (l + 1)
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if initial_prob < IBMModel.MIN_PROB:
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warnings.warn(
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"A source sentence is too long ("
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+ str(l)
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+ " words). Results may be less accurate."
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)
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for i in range(0, l + 1):
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for j in range(1, m + 1):
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self.alignment_table[i][j][l][m] = initial_prob
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def train(self, parallel_corpus):
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counts = Model2Counts()
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for aligned_sentence in parallel_corpus:
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src_sentence = [None] + aligned_sentence.mots
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trg_sentence = ['UNUSED'] + aligned_sentence.words # 1-indexed
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l = len(aligned_sentence.mots)
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m = len(aligned_sentence.words)
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# E step (a): Compute normalization factors to weigh counts
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total_count = self.prob_all_alignments(src_sentence, trg_sentence)
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# E step (b): Collect counts
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for j in range(1, m + 1):
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t = trg_sentence[j]
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for i in range(0, l + 1):
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s = src_sentence[i]
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count = self.prob_alignment_point(i, j, src_sentence, trg_sentence)
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normalized_count = count / total_count[t]
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counts.update_lexical_translation(normalized_count, s, t)
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counts.update_alignment(normalized_count, i, j, l, m)
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# M step: Update probabilities with maximum likelihood estimates
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self.maximize_lexical_translation_probabilities(counts)
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self.maximize_alignment_probabilities(counts)
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def maximize_alignment_probabilities(self, counts):
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MIN_PROB = IBMModel.MIN_PROB
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for i, j_s in counts.alignment.items():
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for j, src_sentence_lengths in j_s.items():
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for l, trg_sentence_lengths in src_sentence_lengths.items():
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for m in trg_sentence_lengths:
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estimate = (
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counts.alignment[i][j][l][m]
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/ counts.alignment_for_any_i[j][l][m]
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)
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self.alignment_table[i][j][l][m] = max(estimate, MIN_PROB)
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def prob_all_alignments(self, src_sentence, trg_sentence):
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"""
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Computes the probability of all possible word alignments,
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expressed as a marginal distribution over target words t
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Each entry in the return value represents the contribution to
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the total alignment probability by the target word t.
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To obtain probability(alignment | src_sentence, trg_sentence),
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simply sum the entries in the return value.
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:return: Probability of t for all s in ``src_sentence``
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:rtype: dict(str): float
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"""
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alignment_prob_for_t = defaultdict(lambda: 0.0)
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for j in range(1, len(trg_sentence)):
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t = trg_sentence[j]
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for i in range(0, len(src_sentence)):
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alignment_prob_for_t[t] += self.prob_alignment_point(
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i, j, src_sentence, trg_sentence
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)
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return alignment_prob_for_t
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def prob_alignment_point(self, i, j, src_sentence, trg_sentence):
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"""
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Probability that position j in ``trg_sentence`` is aligned to
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position i in the ``src_sentence``
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"""
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l = len(src_sentence) - 1
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m = len(trg_sentence) - 1
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s = src_sentence[i]
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t = trg_sentence[j]
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return self.translation_table[t][s] * self.alignment_table[i][j][l][m]
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def prob_t_a_given_s(self, alignment_info):
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"""
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Probability of target sentence and an alignment given the
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source sentence
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"""
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prob = 1.0
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l = len(alignment_info.src_sentence) - 1
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m = len(alignment_info.trg_sentence) - 1
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for j, i in enumerate(alignment_info.alignment):
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if j == 0:
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continue # skip the dummy zeroeth element
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trg_word = alignment_info.trg_sentence[j]
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src_word = alignment_info.src_sentence[i]
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prob *= (
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self.translation_table[trg_word][src_word]
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* self.alignment_table[i][j][l][m]
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)
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return max(prob, IBMModel.MIN_PROB)
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def align_all(self, parallel_corpus):
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for sentence_pair in parallel_corpus:
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self.align(sentence_pair)
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def align(self, sentence_pair):
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"""
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Determines the best word alignment for one sentence pair from
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the corpus that the model was trained on.
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The best alignment will be set in ``sentence_pair`` when the
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method returns. In contrast with the internal implementation of
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IBM models, the word indices in the ``Alignment`` are zero-
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indexed, not one-indexed.
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:param sentence_pair: A sentence in the source language and its
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counterpart sentence in the target language
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:type sentence_pair: AlignedSent
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"""
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best_alignment = []
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l = len(sentence_pair.mots)
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m = len(sentence_pair.words)
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for j, trg_word in enumerate(sentence_pair.words):
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# Initialize trg_word to align with the NULL token
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best_prob = (
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self.translation_table[trg_word][None]
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* self.alignment_table[0][j + 1][l][m]
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)
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best_prob = max(best_prob, IBMModel.MIN_PROB)
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best_alignment_point = None
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for i, src_word in enumerate(sentence_pair.mots):
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align_prob = (
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self.translation_table[trg_word][src_word]
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* self.alignment_table[i + 1][j + 1][l][m]
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)
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if align_prob >= best_prob:
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best_prob = align_prob
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best_alignment_point = i
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best_alignment.append((j, best_alignment_point))
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sentence_pair.alignment = Alignment(best_alignment)
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class Model2Counts(Counts):
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"""
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Data object to store counts of various parameters during training.
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Includes counts for alignment.
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"""
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def __init__(self):
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super(Model2Counts, self).__init__()
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self.alignment = defaultdict(
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lambda: defaultdict(lambda: defaultdict(lambda: defaultdict(lambda: 0.0)))
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)
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self.alignment_for_any_i = defaultdict(
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lambda: defaultdict(lambda: defaultdict(lambda: 0.0))
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)
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def update_lexical_translation(self, count, s, t):
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self.t_given_s[t][s] += count
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self.any_t_given_s[s] += count
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def update_alignment(self, count, i, j, l, m):
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self.alignment[i][j][l][m] += count
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self.alignment_for_any_i[j][l][m] += count
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