Homework Assignment #2 Statistical Machine Translation Solution

    • Introduction

This assignment will give you experience in working with n-gram models, smoothing, and statistical ma-chine 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- 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.

    • Background

Canadian Hansard data

The main corpus for this assignment comes from the o cial 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 les (*.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 nth sentence in one le corresponds to the nth sentence in its corresponding le (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 ltered 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 le 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., Chretien becomes Chretien).

To test your code, you may like to use the samples provided at /u/cs401/A2 SMT/data/Toy/.


Add-  smoothing

Recall that the maximum likelihood estimate of the probability of the current word wt given the previous word wt 1 is
P (wt j wt  1) =
Count (wt  1; wt)
:
(1)

Count (wt  1)




Copyright c 2019 Mohamed Abdalla, Frank Rudzicz. All rights reserved.



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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-  smoothing generalizes Laplace smoothing by adding  to the count of each bigram, where 0 <

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
P (wt j wt  1; ; kVk) =

Count (wt
1; wt) +
:
(2)

Count (wt
1) +  kVk



    • 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- nal punctuation (sentences have already been determined for you), commas, colons and semicolons, parentheses, dashes between parentheses, mathematical operators (e.g., +, -, <, >, =), and quotation marks. Certain contractions are required in French, often to eliminate vowel clusters. When the input language is ‘french’, separate the following contractions:


Type
Modi cation
Example



Singular de nite 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.,
and apostrophe from
j’ai ) j’ ai
‘dropped’-e ce, je)



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.

A template of this function has been provided for you at /u/cs401/A2 SMT/code/preprocess.py.

Make your changes to a copy of this    le and submit your version.









    • Lidstone, 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.

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2. Compute n-gram counts [15 marks]

Next, implement a function to simply count all unigrams and bigrams in the preprocessed training data, namely:

LM = lm train(data dir, language, fn LM)


that returns a special language model structure (a dictionary), LM, de ned below. This function trains on all of the data les in data dir that end in either ‘e’ for English or ‘f’ for French (which is speci ed in the argument language) and saves the structure that it returns in the lename 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 eldnames (i.e. keys) to the ‘uni’ structure are words and the values of those elds 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 elds are the total counts of ‘wt 1wt’ in the training data.

E.g.,

    • 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 train.py. Note that this template calls preprocess.


Make your changes to a copy of the lm train.py 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-  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 -smoothed estimate of the sentence. In the case of smoothing, the arguments delta and vocabSize must also be speci ed (where 0< 1).

When computing your MLE estimate, if you encounter the situation where
Count(wtwt+1)
= 0=0, then

Count(wt)

assume that the probability P (wt+1 j wt) = 0 or, equivalently, log P (wt+1 j wt) =



. Negative in nity 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 prob.py. Make your changes to a copy of the log prob.py template and submit your version.


We also provide you with the function /u/cs401/A2 SMT/code/perplexity.py, which returns the per-plexity 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- versions. Try at least 3 to 5 di erent values of ac-cording to your judgment. Submit a report, Task3.txt, which summarizes your ndings. Your report can additionally include experiments on the log-probabilities of individual sentences.






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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 rst num sentences read in data les from train dir. The parameter max iter speci es 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 j bird) = 0:8

Here, we will use a simpli ed version of IBM-1 in which we ignore the NULL word and we ignore align-ments 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

lenF
Y
P (A; F j E) =    t(fj j eaj )
j=1

where aj is the index of the word in E which is aligned with the jth 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 ve 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. Do-ing 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 initial-
ize 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

AM[‘SENTEND’][‘SENTEND’] = 1.

A template of this function has been provided for you at /u/cs401/A2 SMT/code/align ibm1.py. 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 speci cations above. Make your changes to a copy of the align ibm1.py 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 le evalAlign.py (there is a very sparse template of this le at /u/cs401/A2 SMT/code/).

To decode, we are providing the function

english = decode(french, LM, AM),

at /u/cs401/A2 SMT/code/decode.py. 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




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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, speci cally:


    1. /u/cs401/A2 SMT/data/Hansard/Testing/Task5.e, from the Hansards.

    2. /u/cs401/A2 SMT/data/Hansard/Testing/Task5.google.e, Google’s translations of the French phrases2.


To evaluate each translation, use the BLEU score from lecture 6, i.e.,

BLEU = BPC   (p1p2 : : : pn)(1=n)
(3)

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 di erent references di er 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 , or other test data from other les in /u/cs401/A2 SMT/data/Hansard/Testing/.


Submit your evaluation procedure, evalAlign.py, along with a report, Task5.txt, which summarizes your ndings. If you make any changes to any other les, submit those les 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 align-ment 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 nd e^ = arg maxe P (e j 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 o ers 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.


    • See https://developers.google.com/api-client-library/python/apis/translate/v2, but be prepared to pay.

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Read the sequence-to-sequence tutorial at https://www.tensorflow.org/tutorials/seq2seq and apply it to these data. Is the performance signi cantly better (or di erent) than IBM-1 on these data?


The website https://www.allsides.com/unbiased-balanced-news curates news articles on par-ticular events or stories according to their perceived political bias, using the spectrum used in As-signment 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...

    • General speci cation

We will test your code on di erent training and testing documents in addition to those speci ed 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 speci cations and formatting requirements, including program arguments and le names.

If a program uses a le or helper script name that is speci ed 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 speci ed 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.


































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4.1    Submission requirements

This assignment is submitted electronically. Submit your assignment on MarkUs. Do not tar or compress your les, and do not place your les 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 preprocess.py, lm train.py, lm prob.py, align ibm1.py, and evalAlign.py, along with any other source les 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 le 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 les.

    5. Your ID  le 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    les.

    • 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.

    • Suggestions

This assignment uses a simpli ed 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


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