# Natural Language Toolkit: IBM Model 1 # # Copyright (C) 2001-2013 NLTK Project # Author: Chin Yee Lee # Hengfeng Li # Ruxin Hou # Calvin Tanujaya Lim # Based on earlier version by: # Will Zhang # Guan Gui # URL: # For license information, see LICENSE.TXT """ Lexical translation model that ignores word order. In IBM Model 1, word order is ignored for simplicity. As long as the word alignments are equivalent, it doesn't matter where the word occurs in the source or target sentence. Thus, the following three alignments are equally likely:: Source: je mange du jambon Target: i eat some ham Alignment: (0,0) (1,1) (2,2) (3,3) Source: je mange du jambon Target: some ham eat i Alignment: (0,2) (1,3) (2,1) (3,1) Source: du jambon je mange Target: eat i some ham Alignment: (0,3) (1,2) (2,0) (3,1) Note that an alignment is represented here as (word_index_in_target, word_index_in_source). The EM algorithm used in Model 1 is: :E step: In the training data, count how many times a source language word is translated into a target language word, weighted by the prior probability of the translation. :M step: Estimate the new probability of translation based on the counts from the Expectation step. Notations --------- :i: Position in the source sentence Valid values are 0 (for NULL), 1, 2, ..., length of source sentence :j: Position in the target sentence Valid values are 1, 2, ..., length of target sentence :s: A word in the source language :t: A word in the target language References ---------- Philipp Koehn. 2010. Statistical Machine Translation. Cambridge University Press, New York. Peter E Brown, Stephen A. Della Pietra, Vincent J. Della Pietra, and Robert L. Mercer. 1993. The Mathematics of Statistical Machine Translation: Parameter Estimation. Computational Linguistics, 19 (2), 263-311. """ import warnings from collections import defaultdict from nltk.translate import AlignedSent, Alignment, IBMModel from nltk.translate.ibm_model import Counts class IBMModel1(IBMModel): """ Lexical translation model that ignores word order >>> bitext = [] >>> bitext.append(AlignedSent(['klein', 'ist', 'das', 'haus'], ['the', 'house', 'is', 'small'])) >>> bitext.append(AlignedSent(['das', 'haus', 'ist', 'ja', 'groß'], ['the', 'house', 'is', 'big'])) >>> bitext.append(AlignedSent(['das', 'buch', 'ist', 'ja', 'klein'], ['the', 'book', 'is', 'small'])) >>> bitext.append(AlignedSent(['das', 'haus'], ['the', 'house'])) >>> bitext.append(AlignedSent(['das', 'buch'], ['the', 'book'])) >>> bitext.append(AlignedSent(['ein', 'buch'], ['a', 'book'])) >>> ibm1 = IBMModel1(bitext, 5) >>> print(round(ibm1.translation_table['buch']['book'], 3)) 0.889 >>> print(round(ibm1.translation_table['das']['book'], 3)) 0.062 >>> print(round(ibm1.translation_table['buch'][None], 3)) 0.113 >>> print(round(ibm1.translation_table['ja'][None], 3)) 0.073 >>> test_sentence = bitext[2] >>> test_sentence.words ['das', 'buch', 'ist', 'ja', 'klein'] >>> test_sentence.mots ['the', 'book', 'is', 'small'] >>> test_sentence.alignment Alignment([(0, 0), (1, 1), (2, 2), (3, 2), (4, 3)]) """ def __init__(self, sentence_aligned_corpus, iterations, probability_tables=None): """ Train on ``sentence_aligned_corpus`` and create a lexical translation model. Translation direction is from ``AlignedSent.mots`` to ``AlignedSent.words``. :param sentence_aligned_corpus: Sentence-aligned parallel corpus :type sentence_aligned_corpus: list(AlignedSent) :param iterations: Number of iterations to run training algorithm :type iterations: int :param probability_tables: Optional. Use this to pass in custom probability values. If not specified, probabilities will be set to a uniform distribution, or some other sensible value. If specified, the following entry must be present: ``translation_table``. See ``IBMModel`` for the type and purpose of this table. :type probability_tables: dict[str]: object """ super().__init__(sentence_aligned_corpus) if probability_tables is None: self.set_uniform_probabilities(sentence_aligned_corpus) else: # Set user-defined probabilities self.translation_table = probability_tables["translation_table"] for n in range(0, iterations): self.train(sentence_aligned_corpus) self.align_all(sentence_aligned_corpus) def set_uniform_probabilities(self, sentence_aligned_corpus): initial_prob = 1 / len(self.trg_vocab) if initial_prob < IBMModel.MIN_PROB: warnings.warn( "Target language vocabulary is too large (" + str(len(self.trg_vocab)) + " words). " "Results may be less accurate." ) for t in self.trg_vocab: self.translation_table[t] = defaultdict(lambda: initial_prob) def train(self, parallel_corpus): counts = Counts() for aligned_sentence in parallel_corpus: trg_sentence = aligned_sentence.words src_sentence = [None] + aligned_sentence.mots # E step (a): Compute normalization factors to weigh counts total_count = self.prob_all_alignments(src_sentence, trg_sentence) # E step (b): Collect counts for t in trg_sentence: for s in src_sentence: count = self.prob_alignment_point(s, t) normalized_count = count / total_count[t] counts.t_given_s[t][s] += normalized_count counts.any_t_given_s[s] += normalized_count # M step: Update probabilities with maximum likelihood estimate self.maximize_lexical_translation_probabilities(counts) def prob_all_alignments(self, src_sentence, trg_sentence): """ Computes the probability of all possible word alignments, expressed as a marginal distribution over target words t Each entry in the return value represents the contribution to the total alignment probability by the target word t. To obtain probability(alignment | src_sentence, trg_sentence), simply sum the entries in the return value. :return: Probability of t for all s in ``src_sentence`` :rtype: dict(str): float """ alignment_prob_for_t = defaultdict(lambda: 0.0) for t in trg_sentence: for s in src_sentence: alignment_prob_for_t[t] += self.prob_alignment_point(s, t) return alignment_prob_for_t def prob_alignment_point(self, s, t): """ Probability that word ``t`` in the target sentence is aligned to word ``s`` in the source sentence """ return self.translation_table[t][s] def prob_t_a_given_s(self, alignment_info): """ Probability of target sentence and an alignment given the source sentence """ prob = 1.0 for j, i in enumerate(alignment_info.alignment): if j == 0: continue # skip the dummy zeroeth element trg_word = alignment_info.trg_sentence[j] src_word = alignment_info.src_sentence[i] prob *= self.translation_table[trg_word][src_word] return max(prob, IBMModel.MIN_PROB) def align_all(self, parallel_corpus): for sentence_pair in parallel_corpus: self.align(sentence_pair) def align(self, sentence_pair): """ Determines the best word alignment for one sentence pair from the corpus that the model was trained on. The best alignment will be set in ``sentence_pair`` when the method returns. In contrast with the internal implementation of IBM models, the word indices in the ``Alignment`` are zero- indexed, not one-indexed. :param sentence_pair: A sentence in the source language and its counterpart sentence in the target language :type sentence_pair: AlignedSent """ best_alignment = [] for j, trg_word in enumerate(sentence_pair.words): # Initialize trg_word to align with the NULL token best_prob = max(self.translation_table[trg_word][None], IBMModel.MIN_PROB) best_alignment_point = None for i, src_word in enumerate(sentence_pair.mots): align_prob = self.translation_table[trg_word][src_word] if align_prob >= best_prob: # prefer newer word in case of tie best_prob = align_prob best_alignment_point = i best_alignment.append((j, best_alignment_point)) sentence_pair.alignment = Alignment(best_alignment)