Description
Machine Translation
For this assignment you will develop models for machine translation. The goal is to implement
two translation models, IBM model 1 and IBM model 2, and apply these models to predict
English/Spanish word alignments.
Both models estimate the conditional probability of a foreign
sentence f1 . . . fm and an alignment a1 . . . am given a particular English sentence e1 . . . el and
length m. The simpler model, IBM model 1, defines the conditional probability with a single
set of parameters t as
P(f1 . . . fn, a1 . . . am|e1 . . . el
, m) = 1
(l + 1)m
Ym
i=1
t(fi
|eai)
The richer model, IBM model 2, defines the same conditional probability with two sets of
parameters t and q
P(f1 . . . fn, a1 . . . am|e1 . . . el
, m) = Ym
i=1
q(ai
|i, l, m)t(fi
|eai)
1 Preliminaries
1.1 Training Data
The main task of this assignment is to estimate these parameters from data. We estimate
the parameters from a parallel corpus of aligned sentences. Each entry in the corpus contains two versions of the same sentence, one in English and one in Spanish. The parallel
corpus we are using is a subset of the Europarl corpus [Koehn, 2005] accessed from http:
//www.statmt.org/europarl/ which contains aligned sentences from the proceedings of the
European Parliament.
The training corpus is split into two files, corpus.en and corpus.es, which contain English and
Spanish sentences respectively. The i-th sentence in the English file is a translation of the i-th
sentence in the Spanish file.
The files are in UTF-8, contain one sentence per line, and words
are separated by a space.
> head -n 3 corpus.en
resumption of the session
i declare resumed the session of the european parliament adjourned on …
Although , as you will have seen , the dreaded millennium bug failed …
> head -n 3 corpus.es
reanudacion del periodo de sesiones
declaro reanudado el perodo de sesiones del parlamento europeo …
como todos han podido comprobar , el gran ” efecto del ano 2000 ” no se …
1.2 IBM Model 1
The full algorithm for IBM model 1 is given on page 21 in the Collins notes http://www.cs.
columbia.edu/~mcollins/ibm12.pdf. We recommend closely reading those notes for a full
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description of the problem. The core portion of the algorithm is summarized here.
Recall that IBM model 1 only has word translation parameters t(f|e) which can be interpreted
as the conditional probability of generating a foreign word f from an English word e (or from
NULL).
We can estimate t(f|e) using the EM algorithm, which iterates through the parallel corpus
repeatedly. For the k-th sentence pair and each index i in the foreign sentence f
(k) and j in the
English sentence e
(k)
, we define
δ(k, i, j) =
t(f
(k)
i
|e
(k)
j
)
Plk
j=0 t(f
(k)
i
|e
(k)
j
)
where lk is the length of the English sentence. The delta function is used to update the expected
counts for the current iteration:
c(e
(k)
j
, f(k)
i
) ← c(e
(k)
j
, f(k)
i
) + δ(k, i, j)
c(e
(k)
j
) ← c(e
(k)
j
) + δ(k, i, j)
After each iteration through the parallel corpus, we revise our estimate for t parameters:
t(f|e) = c(e, f)
c(e)
for all possible foreign words f and English words e (and NULL).
1.3 IBM Model 2
The complete algorithm for estimating IBM model 2 parameters is given on page 13 of the
Collins notes http://www.cs.columbia.edu/~mcollins/ibm12.pdf. Be sure to understand
the details of this algorithm before beginning to code the assignment.
Note that IBM model 2 extends the implementation of the EM algorithm for IBM model 1. The
main additional step is adapting the delta function to include q(j|i, l, m)
δ(k, i, j) =
q(j|i, lk, mk)t(f
(k)
i
|e
(k)
j
)
Plk
j=0 q(j|i, lk, mk)t(f
(k)
i
|e
(k)
j
)
and computing expected counts c(j|i, l, m) and c(i, l, m)
After each iteration through the corpus we re-estimate the t(fi
, ej ) parameters as before and
add new updates for the q parameters:
q(j|i, l, m) = c(j|i, l, m)
c(i, l, m)
1.4 Evaluation
We provide aligned development and test data, dev.en / dev.es in order to evaluate alignment
accuracy. The format of these files is identical to the corpus training files, one sentence per line
with aligned sentences.
We also provide a file, dev.key, which contains the manually annotated gold alignments for the
development sentences. The file contains lines of the form
2
…
6 7 3
6 7 4
6 8 5
…
Each line specifies a word alignment of the form SentenceIndex EnglishIndex ForeignIndex.
The first line of the example specifies that in the 6th pair of sentences the 7th English word
is aligned to the 3rd Spanish word. Note that the gold alignments do not include NULL word
alignments, all three indices start from 1, and there are no blank lines between sentences.
As an example, suppose the 6th sentence pair is:
• e = Do we want to make it happen ?
• f = ¿ Deseamos hacerla realidad ?
The gold word alignment, 6 7 3, indicates that the English word “happen” is aligned with the
Spanish word “hacerla”. The full alignment of the sentence pair is
For all of the questions in this assignment you should output predicted alignments in this
format. We have included a script eval alignment.py to evaluate the accuracy of these
alignments. Assuming that you have written alignments to a file dev.out, running python
eval alignment.py dev.key dev.out will give the F-Score of the predicted alignments compared to the gold alignments.
Note: The alignments given in the key file often map single foreign words to multiple English
words, whereas our models do not. For this reason it is impossible to get perfect recall or F-Score
on this dataset. For parts 1 and 2 we ignore this issue. Part 3 discusses a method to fix this
problem.
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2 Part 1 – IBM Model 1 (40%)
The first problem is to estimate the parameters of IBM model 1 using corpus.en and corpus.es
as input. Before implementing please read the following notes carefully
• Your implementation should only store t parameters for possible pairs of foreign and
English words, i.e. words that occur together in some parallel translation, and the special
English word NULL. We recommend implementing t as a collection of sparse maps for
each English word e where the keys of the map are the words f that are occur with e and
the values are the corresponding parameters t(f|e).
Using a non-sparse implementation will likely result in memory issues.
• In the initialization step, set t(f|e) to be the uniform distribution over all foreign words
that could be aligned to e in the corpus. More specifically
t(f|e) = 1
n(e)
where n(e) is the number of different words that occur in any translation of a sentence
containing e. Note that the special English word NULL can be aligned to any foreign word
in the corpus.
• Starting from the initial t(f|e) parameters, run 5 iterations of the EM algorithm for IBM
model 1 (this may take a while). When your model is completed, save your t parameters
to a file, as you will need them for the next problem.
• Finally, use your model to find alignments for the development sentence pairs dev.en /
dev.es. For each sentence, align each foreign word fi to the English word with the highest
t(f|e) score,
ai = arg max
j∈0…l
t(fi
|ej )
Write your alignments to a file in the format of dev.key described above. Check the
accuracy with eval alignments.py.
• Your report should include a brief summary of your IBM Model 1 implementation and
any specific challenges or issues that came up. If you could not get your implementation
working, describe where you got stuck.
• The expected F1-Score is 0.42.
3 Part 2 – IBM Model 2 (45%)
We now extend the alignment model to IBM model 2 by adding alignment parameters q(j|i, l, m)
• Initialize the q parameters to the uniform distribution over all j for each i, l, and m.
q(j|i, l, m) = 1
l + 1
You only need to store parameters for pairs of sentence lengths l and m that occur in the
corpus.
• To initialize the t(f|e) parameters, use the last set of parameters (after 5 iterations) produced by your implementation of IBM model 1.
• Run 5 iterations of EM for IBM model 2.
• As before, use the model to compute alignments for the development sentence pairs in the
corpus.
For each foreign word fi
, the best alignment is
ai = arg max
j∈0…l
q(j|i, l, m)t(fi
|ej )
Write your alignments to a file in the format of dev.key described above. Check the
accuracy with eval alignments.py .
• Your report should include a brief summary of your IBM Model 2 implementation and
any specific challenges or issues that came up. If you could not get your implementation
working, describe where you got stuck.
• The expected F1-Score is 0.45.
4 Part 3 – Growing Alignments (15%)
As we noted above, the gold alignments allow English words to be aligned with multiple Spanish
words. This section explores a method to get around this issue and generate more complete
alignments. This process is a crucial first step in order to extract a lexicon for phrase-based
translation. The recipe below was described in class when we discussed phrase-based translation.
It consists of the following steps
1. Estimate IBM model 2 for p(f|e) (exactly as in question 2).
2. Estimate IBM model 2 for p(e|f) (as in question 2 except with English as the foreign
language).
3. Calculate the best alignments with p(f|e) and p(e|f).
4. Calculate the intersection and union of these alignments.
5. Starting from the intersection, apply a heuristic to grow the alignment.
A good example heuristic was sketched out in class and is as follows:
1. Only explore alignment in the union of the p(f|e) and p(e|f) alignments
2. Add one alignment point at a time.
3. Only add alignment points which align a word that currently has no alignment.
4. At first, restrict ourselves to alignment points that are “neighbors” (adjacent or diagonal)
of current alignment points. Later, consider other alignment points.
For this problem, you should estimate both p(f|e) and p(e|f) and use these models to generate
new alignments. We recommend starting with the heuristic from the lecture and begin with the
intersection alignment while growing towards the union alignment. However, feel free to try out
different alignment heuristics to improve the score of the model.
Your report should include a brief summary of your approach for growing alignments. Discuss
improvements in performance, if any.
(** If you would like to get some ideas on growing heuristics, see Section 4.5 of this paper:
https://www.aclweb.org/anthology/N03-1017.pdf )
5 Report Guideline
5.1 IBM Model 1
a. Description of IBM Model 1 – What are IBM Models used for? What are the limitations?
b. Description of EM Algorithm
– What are the strengths and weaknesses?
c. Method Overview
– Provide a high-level description of your implementation
d. Results
– Report your F1 score. It should match the expected result. If not, partial credits will be
given if you discuss some challenges and issues in your implementation.
e. Discussion – Show how F1 score changes after each iteration; comment on the findings.
5.2 IBM Model 2
a. Description of IBM Model 2
– Why is it better than IBM Model 1? What are the limitations?
b. Method Overview
– Provide a high-level description of your implementation
c. Results
– Report your F1 score. It should match the expected result. If not, partial credits will be
given if you discuss some challenges and issues in your implementation.
d. Discussions
– Show how F1 score changes after each iteration; comment on the findings; compare with
the results from IBM Model 1.
– Use the type of table/graph as in the slides or in the instructions, show two correctly
aligned examples + two misaligned examples. Discuss the examples.
5.3 Growing Alignments
Note: You can implement the heuristics mentioned in class, and write your report based on
that. You are also welcome to try other methods.
(** If you would like to get some ideas on growing heuristics, see Section 4.5 of this paper:
https://www.aclweb.org/anthology/N03-1017.pdf )
a. Method Overview
– Provide a high-level description of your method
b. Results
– Report your F1 score.
6 Submission Instructions
Submit your work on Gradescope.
• Code: You will submit your code together with a neatly written README file to instruct
how to run your code with different settings. We assume that you always follow good
practice of coding (commenting, structuring), and these factors are not central to your
grade.
• Report: Submit your report, it should be four pages long, or less, in pdf (reasonable
font sizes).
7 Acknowledgments
Adapted with minor changes from a similar assignment by Michael Collins.
8 References
Philipp Koehn. Europarl: A parallel corpus for statistical machine translation. In MT
summit, volume 5, 2005.
Patrik Lambert, Adria De Gispert, Rafael Banchs, and Jose B Marino. Guidelines for
word alignment evaluation and manual alignment. Language Resources and Evaluation,
39(4):267285, 2005.
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