Computer Science 401 Homework Assignment #2 Statistical Machine Translation solved


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1 Introduction
This assignment will give you experience in working with n-gram models, smoothing, and statistical machine translation through word alignment. Knowledge of French is not required.
Your tasks are to build bigram and unigram models of English and French, to smooth their probabilities
using add-δ discounting, to build a world-alignment model between English and French using the IBM-1
model, and to use these models to translate French sentences into English with a decoder that we provide.
The programming language for this assignment is Python3.
2 Background
Canadian Hansard data
The main corpus for this assignment comes from the official records (Hansards) of the 36th Canadian
Parliament, including debates from both the House of Representatives and the Senate. This corpus is
available at /u/cs401/A2 SMT/data/Hansard/ and has been split into Training/ and Testing/ directories.
This data set consists of pairs of corresponding files (*.e is the English equivalent of the French *.f)
in which every line is a sentence. Here, sentence alignment has already been performed for you. That is,
the n
th sentence in one file corresponds to the n
th sentence in its corresponding file (e.g., line n in fubar.e
is aligned with line n in fubar.f). Note that this data only consists of sentence pairs; many-to-one,
many-to-many, and one-to-many alignments are not included.
Furthermore, for the purposes of this assignment we have filtered this corpus down to sentences with
between approximately 4 and 15 tokens to simplify the computational requirements of alignment and
decoding. We have also converted the file encodings from ISO-8859-1 to ASCII so as to further simplify
the problem. This involved transliterating the original text to remove diacritics, i.e., accented characters
(e.g., Chr´etien becomes Chretien).
To test your code, you may like to use the samples provided at /u/cs401/A2 SMT/data/Toy/.
Add-δ smoothing
Recall that the maximum likelihood estimate of the probability of the current word wt given the previous
word wt−1 is
| wt−1) = Count(wt−1, wt)
. (1)
c 2019 Mohamed Abdalla, Frank Rudzicz. All rights reserved.
Count(wt−1, wt) refers to the number of times the word sequence wt−1wt appears in a training corpus, and
Count(wt−1) refers to the number of times the word wt−1 appears in that corpus.
Laplace’s method of add-1 smoothing for n-grams simulates observing otherwise unseen events by
providing probability mass to those unseen events by discounting events we have seen. Although the
simplest of all smoothing methods, in practice this approach does not work well because too much of the
n-gram probability mass is assigned to unseen events, thereby increasing the overall entropy unacceptably.
Add-δ smoothing generalizes Laplace smoothing by adding δ to the count of each bigram, where 0 <
δ ≤ 1, and normalizing accordingly. This method is generally attributed to G.J. Lidstone1
. Given a known
vocabulary V of size kVk, the probability of the current word wt given the previous word wt−1 in this
model is
| wt−1; δ, kVk) = Count(wt−1, wt) + δ
Count(wt−1) + δkVk. (2)
3 Your tasks
1. Preprocess input text [5 marks]
First, implement the following Python function:
preprocess(in sentence, language)
that returns a version of the input sentence in sentence that is more amenable to training. For both
languages, separate sentence-final punctuation (sentences have already been determined for you), commas,
colons and semicolons, parentheses, dashes between parentheses, mathematical operators (e.g., +, -, <, >,
=), and quotation marks. Add SENTSTART to the beginning of the sentence, and SENTEND to the end of the
sentence. Certain contractions are required in French, often to eliminate vowel clusters. When the input
language is ‘french’, separate the following contractions:
Type Modification Example
Singular definite article Separate leading l’ from l’election ⇒ l’ election
(le, la) concatenated word
Single-consonant words Separate leading consonant je t’aime ⇒ je t’ aime,
ending in e-‘muet’ (e.g.,
‘dropped’-e ce, je, te)
and apostrophe from j’ai ⇒ j’ ai
concatenated word
que Separate leading qu’ from qu’on ⇒ qu’ on,
concatenated word qu’il ⇒ qu’ il
Conjunctions Separate following on or il puisqu’on ⇒ puisqu’ on,
puisque and lorsque lorsqu’il ⇒ lorsqu’ il
Any words containing apostrophes not encapsulated by the above rules can be left as-is. Additionally, the following French words should not be separated: d’abord, d’accord, d’ailleurs, d’habitude. The
preprocess function must return a preprocessed sentence with SENTSTART preceding the sentence, and
SENTEND appended to the sentence;
e.g., preprocess(“je t’aime.”, “f”) should return “SENTSTART je t’ aime . SENTEND”.
A template of this function has been provided for you at /u/cs401/A2 SMT/code/
Make your changes to a copy of this file and submit your version.
1Lidstone, G. J. (1920) Note on the general case of the Bayes-Laplace formula for inductive or a priori probabilities.
Transactions of the Faculty of Actuaries 8:182–192.
2. Compute n-gram counts [15 marks]
Next, implement a function to simply count all unigrams and bigrams in the preprocessed training data,
LM = lm train(data dir, language, fn LM)
that returns a special language model structure (a dictionary), LM, defined below. This function trains on
all of the data files in data dir that end in either ‘e’ for English or ‘f’ for French (which is specified in the
argument language) and saves the structure that it returns in the filename fn LM.
The structure returned by this function should be called ‘LM’ and must have two keys: ‘uni’ and ‘bi’,
each of which holds structures (additional dictionaries) which incorporate unigram and bigram counts,
respectively. The fieldnames (i.e. keys) to the ‘uni’ structure are words and the values of those fields are
the total counts of those words in the training data. The keys to the ‘bi’ structure are words (wt−1) and
their values are dictionaries. The keys of those sub-dictionaries are also words (wt) and the values of those
fields are the total counts of ‘wt−1wt
’ in the training data.
>> LM[‘uni’][‘word’] = 5 % the word ‘word’ appears 5 times in training
>> LM[‘bi’][‘word’][‘bird’] = 2 % the bigram ‘word bird’ appears twice in training
A template of this function has been provided for you at /u/cs401/A2 SMT/code/lm Note
that this template calls preprocess.
Make your changes to a copy of the lm template and submit your version. Train two language
models, one for English and one for French, on the data at /u/cs401/A2 SMT/data/Hansard/Training/.
You will use these models for subsequent tasks.
3. Compute log-likelihoods and add-δ log-likelihoods [20 marks]
Now implement a function to compute the log-likelihoods of test sentences, namely:
logProb = lm prob(sentence, LM, smoothing, delta, vocabSize) .
This function takes sentence (a previously preprocessed string) and a language model LM (as produced
by lm train). If the argument smoothing is (‘False’), this function returns the maximum-likelihood
estimate of the sentence. If the argument type is ‘True’, this function returns a δ-smoothed estimate of
the sentence. In the case of smoothing, the arguments delta and vocabSize must also be specified (where
0 < δ ≤ 1). When computing your MLE estimate, if you encounter the situation where Count(wtwt+1) Count(wt) = 0/0, then assume that the probability P(wt+1 | wt) = 0 or, equivalently, log P(wt+1 | wt) = −∞. Negative infinity in Python is represented by float(‘-inf’). Use log base 2 (i.e. log2()). A template of this function has been provided for you at /u/cs401/A2 SMT/code/log Make your changes to a copy of the log template and submit your version. We also provide you with the function /u/cs401/A2 SMT/code/, which returns the perplexity of a test corpus given a language model. You do not need to modify this function. Using the language models learned in Task 2, compute the perplexity of the data at /u/cs401/A2 SMT/data/Hansard/Testing/ for each language and for both the MLE and add-δ versions. Try at least 3 to 5 different values of δ according to your judgment. Submit a report, Task3.txt, which summarizes your findings. Your report can additionally include experiments on the log-probabilities of individual sentences. 3 4. Implement IBM-1 [25 marks] Now implement the IBM-1 algorithm to learn word alignments between English and French words, namely: AM = align ibm1(train dir, num sentences, max iter, fn AM). This function trains on the first num sentences read in data files from train dir. The parameter max iter specifies the maximum number of times the EM algorithm iterates before being terminated. This function returns a specialized alignment model structure, AM, in which AM[‘eng word’][‘fre word’] holds the probability (not log probability) of the word eng word aligning to fre word. In this sense, AM is essentially the t distribution from class, e.g., >> AM[‘bird’][‘oiseau’] = 0.8 % t(oiseau | bird) = 0.8
Here, we will use a simplified version of IBM-1 in which we ignore the NULL word and we ignore alignments where an English word would align with no French word, as discussed in class. So, the probability
of an alignment A of a French sentence F, given a known English sentence E is
P(A, F | E) =
t(fj | eaj
where aj is the index of the word in E which is aligned with the j
th word in F and lenF is the number of
tokens in the French sentence. Since we are only using IBM-1, we employ the simplifying assumption that
every alignment is equally likely.
Note: The na¨ıve approach to initializing AM is to have a uniform distribution over all possible English (e)
and French (f) words, i.e., AM[‘e’][‘f’] = 1/kVF k, where kVF k is the size of the French vocabulary. Doing so, however, will consume too much memory and computation time. Instead, you can initialize AM[‘e’]
uniformly over only those French words that occur in corresponding French sentences. For example,
given only the training sentence pairs
the house la maison
house of commons chambre des communes
Andromeda galaxy galaxie d’Andromede
, you would initialize the structure AM[‘house’][‘la’] = 0.2, AM[‘house’][‘maison’] = 0.2, AM[‘house’][‘chambre’]
= 0.2, AM[‘house’][‘des’] = 0.2, AM[‘house’][‘communes’] = 0.2. There would be no probability
of generating galaxie from house. Note that you can force AM[‘SENTSTART’][‘SENTSTART’] = 1 and
A template of this function has been provided for you at /u/cs401/A2 SMT/code/align You
will notice that we have suggested a general structure of empty helper functions here, but you are free to
implement this function as you wish, as long as it meets with the specifications above. Make your changes
to a copy of the align template and submit your version.
5. Translate and evaluate the test data [10 marks]
You will now produce your own translations, obtain reference translations from Google and the Hansards,
and use the latter to evaluate the former, with a BLEU score. This will all be done in the file
(there is a very sparse template of this file at /u/cs401/A2 SMT/code/) and in BLEU
To decode, we are providing the function
english = decode(french, LM, AM),
at /u/cs401/A2 SMT/code/ Here, french is a preprocessed French sentence, LM and AM are
your English language model from Task 2 and your alignment model trained from Task 4, respectively, and
lmtype, delta, and vocabSize parameterize smoothing, as before in Task 3. You do not need to change
the decode function, but you may (see the Bonus section, below).
For evaluation, translate the 25 French sentences in /u/cs401/A2 SMT/data/Hansard/Testing/Task5.f
with the decode function and evaluate them using corresponding reference sentences, specifically:
1. /u/cs401/A2 SMT/data/Hansard/Testing/Task5.e, from the Hansards.
2. /u/cs401/A2 SMT/data/Hansard/Testing/, Google’s translations of the French phrases2
To evaluate each translation, implement the BLEU score in BLEU Use the BLEU score from
lecture 6, i.e.,
BLEU = BPC × (p1p2 . . . pn)
Repeat this task with at least four alignment models (trained on 1K, 10K, 15K, and 30K sentences,
respectively) and with three values of n in the BLEU score (i.e., n = 1, 2, 3). You should therefore have
25×4×3 BLEU scores in your evaluation. Write a short subjective analysis of how the different references
differ from each other, and whether using more than 2 of them might be better (or worse).
In all cases, you can use the MLE language model (i.e., specify lmtype = ‘’). Optionally, you can try
additional alignment models, smoothed language model with varying δ, or other test data from other files
in /u/cs401/A2 SMT/data/Hansard/Testing/.
Submit your evaluation procedure,, along with a report, Task5.txt, which summarizes
your findings. If you make any changes to any other files, submit those files as well.
Bonus [up to 15 marks]
We will give bonus marks for innovative work going substantially beyond the minimal requirements. Your
overall mark for this assignment cannot exceed 100%.
You may decide to pursue any number of tasks of your own design related to this assignment, although
you should consult with the instructor or the TA before embarking on such exploration. Certainly, the
rest of the assignment takes higher priority. Some ideas:
• Try additional smoothing methods (e.g., Good-Turing, Knesser-Ney) and re-run the experiments in
Task 3, above. Submit your code and an associated discussion.
• Implement the IBM-2 model of word-alignment, otherwise replicating Task 4 above. Ideally, translate
the test data using this model and compute the error, as you did for Task 5. How does this model
compare to IBM-1? Submit your code and an associated discussion.
• We have not considered the null word when performing alignments. Re-implement the IBM-1 alignment model to include null words and the possibility that no English word aligns with a French word
(or vice versa). Submit your code and an associated discussion.
• Perform substantial data analysis of the error trends observed in each method you implement. This
must go well beyond the basic discussion already included in the assignment. Submit a report.
• The decoder we use here is extremely simple and incomplete. You can write your own decoder that
attempts to find ˆe = arg maxe P(e | f) using a heuristic A∗
search, for example. Alternatively, what
happens if you weight the contributions of the alignment and the language model to the overall
probability? Section 25.8 of the Jurafsky & Martin textbook offers some ideas on how to improve
the decoder. Submit your code and an associated discussion, comparing the decoded results to those
performed with the default decoder.
2See, but be prepared to pay.
• Read the sequence-to-sequence tutorial at and
apply it to these data. Is the performance significantly better (or different) than IBM-1 on these
• The website curates news articles on particular events or stories according to their perceived political bias, using the spectrum used in Assignment 1 (less ‘alternative’ news). We sampled a considerable amount of these data; they are
available at /s/course/csc401/A2/allSides (1.6GB) for you to examine. Unfortunately, since a
right-leaning report on a story is not strictly a translation of a right-leaning report (or vice versa),
the normal approach to sentence alignment (or SMT generally) does not apply; in our experiments,
performance was unacceptably random. You, however, may be more fortunate…
4 General specification
We will test your code on different training and testing documents in addition to those specified above.
Where possible, do not hardwire directory names into your code. As part of grading your assignment,
the grader will run your programs using test scripts. It is therefore important that each of your programs
precisely meets all the specifications and formatting requirements, including program arguments and file
If a program uses a file or helper script name that is specified within the program, it must read it
either from the directory in which the program is being executed, or it must read it from a subdirectory
of /u/cs401/ whose path is completely specified in the program. Do not hardwire the absolute address
of your home directory within the program; the grader does not have access to this directory.
All your programs must contain adequate internal documentation to be clear to the graders. External
documentation is not required.
4.1 Submission requirements
This assignment is submitted electronically. Submit your assignment on MarkUs. Do not tar or compress
your files, and do not place your files in subdirectories. Do not format your discussion as a PDF or Word
document — use plain text only. You should submit:
1. All your code for, lm, lm, align, BLEU, and, along with any other source files to which you made changes or which are necessary
to run your code in Python3 on teach.cs.
2. Your alignment model trained on 1k sentences from /u/cs401/A2 SMT/data/Hansard/Training/,
dumped in file am.pickle.
3. Your reports Task3.txt and Task5.txt.
4. Any material submitted towards a bonus mark. This should ideally be limited to code, results, and
reports as text files.
5. Your ID file as described in Assignment 1. A template of ID is available on the course web page.
You do not need to hand in your language models or other temporary files.
5 Using your own computer
If you want to do some or all of this assignment on your laptop or other computer, you will have to do
the extra work of downloading and installing the requisite software and data. You take on the risk that
your computer might not be adequate for the task. You are strongly advised to upload regular backups
of your work to teach.cs, so that if your machine fails or proves to be inadequate, you can immediately
continue working on the assignment at teach.cs. When you have completed the assignment, you should
try your programs out on teach.cs to make sure that they run correctly there. A submission that does
not work on teach.cs will get zero marks.
6 Suggestions
This assignment uses a simplified version of an alignment model which itself makes several major simplifying
assumptions and, as such, the results of the decoder will not be representative of the state-of-the-art in
statistical machine translation. You will generally be marked on how well you understand the underlying
concepts and algorithms. This approach was chosen for this assignment in order to give you a relative
reprieve in the mid-term workload. However, if you have the time you are highly encouraged to pursue
bonus work as indicated above. Exploring more complex models is not only interesting, but will give you
a fuller perspective on the techniques used in machine translation.
The following dates are suggestions as to how to spread out the work for this assignment. These dates
may not be applicable to you personally and they are not required deadlines. However, it’s a good idea to
try to spread things out so you don’t have to rush at the end.
Task 1 18 February
Task 2 25 February
Task 3 1 March
Task 4 4 March
Task 5 8 March