320 lines
12 KiB
Python
320 lines
12 KiB
Python
# -*- coding: utf-8 -*-
|
|
# Natural Language Toolkit: IBM Model 2
|
|
#
|
|
# Copyright (C) 2001-2013 NLTK Project
|
|
# Authors: Chin Yee Lee, Hengfeng Li, Ruxin Hou, Calvin Tanujaya Lim
|
|
# URL: <http://nltk.org/>
|
|
# For license information, see LICENSE.TXT
|
|
|
|
"""
|
|
Lexical translation model that considers word order.
|
|
|
|
IBM Model 2 improves on Model 1 by accounting for word order.
|
|
An alignment probability is introduced, a(i | j,l,m), which predicts
|
|
a source word position, given its aligned target word's position.
|
|
|
|
The EM algorithm used in Model 2 is:
|
|
E step - In the training data, collect counts, weighted by prior
|
|
probabilities.
|
|
(a) count how many times a source language word is translated
|
|
into a target language word
|
|
(b) count how many times a particular position in the source
|
|
sentence is aligned to a particular position in the target
|
|
sentence
|
|
|
|
M step - Estimate new probabilities based on the counts from the E 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
|
|
l: Number of words in the source sentence, excluding NULL
|
|
m: Number of words in the 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
|
|
from nltk.translate import Alignment
|
|
from nltk.translate import IBMModel
|
|
from nltk.translate import IBMModel1
|
|
from nltk.translate.ibm_model import Counts
|
|
|
|
|
|
class IBMModel2(IBMModel):
|
|
"""
|
|
Lexical translation model that considers 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']))
|
|
|
|
>>> ibm2 = IBMModel2(bitext, 5)
|
|
|
|
>>> print(round(ibm2.translation_table['buch']['book'], 3))
|
|
1.0
|
|
>>> print(round(ibm2.translation_table['das']['book'], 3))
|
|
0.0
|
|
>>> print(round(ibm2.translation_table['buch'][None], 3))
|
|
0.0
|
|
>>> print(round(ibm2.translation_table['ja'][None], 3))
|
|
0.0
|
|
|
|
>>> print(ibm2.alignment_table[1][1][2][2])
|
|
0.938...
|
|
>>> print(round(ibm2.alignment_table[1][2][2][2], 3))
|
|
0.0
|
|
>>> print(round(ibm2.alignment_table[2][2][4][5], 3))
|
|
1.0
|
|
|
|
>>> 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 and an alignment 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, all the following entries must be present:
|
|
``translation_table``, ``alignment_table``.
|
|
See ``IBMModel`` for the type and purpose of these tables.
|
|
:type probability_tables: dict[str]: object
|
|
"""
|
|
super(IBMModel2, self).__init__(sentence_aligned_corpus)
|
|
|
|
if probability_tables is None:
|
|
# Get translation probabilities from IBM Model 1
|
|
# Run more iterations of training for Model 1, since it is
|
|
# faster than Model 2
|
|
ibm1 = IBMModel1(sentence_aligned_corpus, 2 * iterations)
|
|
self.translation_table = ibm1.translation_table
|
|
self.set_uniform_probabilities(sentence_aligned_corpus)
|
|
else:
|
|
# Set user-defined probabilities
|
|
self.translation_table = probability_tables["translation_table"]
|
|
self.alignment_table = probability_tables["alignment_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):
|
|
# a(i | j,l,m) = 1 / (l+1) for all i, j, l, m
|
|
l_m_combinations = set()
|
|
for aligned_sentence in sentence_aligned_corpus:
|
|
l = len(aligned_sentence.mots)
|
|
m = len(aligned_sentence.words)
|
|
if (l, m) not in l_m_combinations:
|
|
l_m_combinations.add((l, m))
|
|
initial_prob = 1 / (l + 1)
|
|
if initial_prob < IBMModel.MIN_PROB:
|
|
warnings.warn(
|
|
"A source sentence is too long ("
|
|
+ str(l)
|
|
+ " words). Results may be less accurate."
|
|
)
|
|
|
|
for i in range(0, l + 1):
|
|
for j in range(1, m + 1):
|
|
self.alignment_table[i][j][l][m] = initial_prob
|
|
|
|
def train(self, parallel_corpus):
|
|
counts = Model2Counts()
|
|
for aligned_sentence in parallel_corpus:
|
|
src_sentence = [None] + aligned_sentence.mots
|
|
trg_sentence = ["UNUSED"] + aligned_sentence.words # 1-indexed
|
|
l = len(aligned_sentence.mots)
|
|
m = len(aligned_sentence.words)
|
|
|
|
# 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 j in range(1, m + 1):
|
|
t = trg_sentence[j]
|
|
for i in range(0, l + 1):
|
|
s = src_sentence[i]
|
|
count = self.prob_alignment_point(i, j, src_sentence, trg_sentence)
|
|
normalized_count = count / total_count[t]
|
|
|
|
counts.update_lexical_translation(normalized_count, s, t)
|
|
counts.update_alignment(normalized_count, i, j, l, m)
|
|
|
|
# M step: Update probabilities with maximum likelihood estimates
|
|
self.maximize_lexical_translation_probabilities(counts)
|
|
self.maximize_alignment_probabilities(counts)
|
|
|
|
def maximize_alignment_probabilities(self, counts):
|
|
MIN_PROB = IBMModel.MIN_PROB
|
|
for i, j_s in counts.alignment.items():
|
|
for j, src_sentence_lengths in j_s.items():
|
|
for l, trg_sentence_lengths in src_sentence_lengths.items():
|
|
for m in trg_sentence_lengths:
|
|
estimate = (
|
|
counts.alignment[i][j][l][m]
|
|
/ counts.alignment_for_any_i[j][l][m]
|
|
)
|
|
self.alignment_table[i][j][l][m] = max(estimate, MIN_PROB)
|
|
|
|
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 j in range(1, len(trg_sentence)):
|
|
t = trg_sentence[j]
|
|
for i in range(0, len(src_sentence)):
|
|
alignment_prob_for_t[t] += self.prob_alignment_point(
|
|
i, j, src_sentence, trg_sentence
|
|
)
|
|
return alignment_prob_for_t
|
|
|
|
def prob_alignment_point(self, i, j, src_sentence, trg_sentence):
|
|
"""
|
|
Probability that position j in ``trg_sentence`` is aligned to
|
|
position i in the ``src_sentence``
|
|
"""
|
|
l = len(src_sentence) - 1
|
|
m = len(trg_sentence) - 1
|
|
s = src_sentence[i]
|
|
t = trg_sentence[j]
|
|
return self.translation_table[t][s] * self.alignment_table[i][j][l][m]
|
|
|
|
def prob_t_a_given_s(self, alignment_info):
|
|
"""
|
|
Probability of target sentence and an alignment given the
|
|
source sentence
|
|
"""
|
|
prob = 1.0
|
|
l = len(alignment_info.src_sentence) - 1
|
|
m = len(alignment_info.trg_sentence) - 1
|
|
|
|
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]
|
|
* self.alignment_table[i][j][l][m]
|
|
)
|
|
|
|
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 = []
|
|
|
|
l = len(sentence_pair.mots)
|
|
m = len(sentence_pair.words)
|
|
|
|
for j, trg_word in enumerate(sentence_pair.words):
|
|
# Initialize trg_word to align with the NULL token
|
|
best_prob = (
|
|
self.translation_table[trg_word][None]
|
|
* self.alignment_table[0][j + 1][l][m]
|
|
)
|
|
best_prob = max(best_prob, 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]
|
|
* self.alignment_table[i + 1][j + 1][l][m]
|
|
)
|
|
if align_prob >= best_prob:
|
|
best_prob = align_prob
|
|
best_alignment_point = i
|
|
|
|
best_alignment.append((j, best_alignment_point))
|
|
|
|
sentence_pair.alignment = Alignment(best_alignment)
|
|
|
|
|
|
class Model2Counts(Counts):
|
|
"""
|
|
Data object to store counts of various parameters during training.
|
|
Includes counts for alignment.
|
|
"""
|
|
|
|
def __init__(self):
|
|
super(Model2Counts, self).__init__()
|
|
self.alignment = defaultdict(
|
|
lambda: defaultdict(lambda: defaultdict(lambda: defaultdict(lambda: 0.0)))
|
|
)
|
|
self.alignment_for_any_i = defaultdict(
|
|
lambda: defaultdict(lambda: defaultdict(lambda: 0.0))
|
|
)
|
|
|
|
def update_lexical_translation(self, count, s, t):
|
|
self.t_given_s[t][s] += count
|
|
self.any_t_given_s[s] += count
|
|
|
|
def update_alignment(self, count, i, j, l, m):
|
|
self.alignment[i][j][l][m] += count
|
|
self.alignment_for_any_i[j][l][m] += count
|