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CS 6320.002: Natural Language Processing Fall 2019
Homework 1 – 90 points Issued 26 Aug. 2019
Deliverables: A tarball or zip file containing your code and your PDF writeup.
0 Getting Started
Make sure you have downloaded the data for this assignment:
• • •
shakespeare.txt, the complete plays of Shakespeare warpeace.txt, Tolstoy’s War and Peace sonnets.txt, Shakespeare’s sonnets
A Basic N-Gram Language Model – 27 points
We will start with a very basic n-gram language model. Open a new file and write a generator function get ngrams(n, text), where n is an int that tells you the size of the n-grams, and text is a list of words/strings (if you don’t know what a generator function is, look up the yield keyword). The function’s output should be n-gram tuples of the form (word, context), where word is a string and context is a tuple of the n-1 preceding words/strings. Make sure to pad text with enough start tokens ‘<s>’ to be able to make n-grams for the first n-1 words; also make sure to add stop token ‘</s>’ (we will need it in Part 4).
Next, define a class NGramLM. Write its initialization method init (self, n), which saves the int n and initializes three internal variables:
• self.ngram counts for n-grams seen in the training data,
• self.context counts for contexts seen in the training data,
• self.vocabulary for keeping track of words seen in the training data.
Writeup Question 1.1: What data types did you use for the two counters and the vocabulary, and did you initialize the vocabulary to be empty or already containing some token(s)? Explain why. You may want to wait to answer this question until after you complete the programming parts, in case you change your mind.
Add a method update(self, text) that updates the NGramLM’s internal counts and vocabulary for the n-grams in text, which is again a list of words/strings.
Now write a function create ngramlm(n, corpus path) that returns an NGramLM trained on the data in the file corpus path. This is not a word tokenization homework, so simply use split() to tokenize lines using whitespace.

Now that we can train a model, we need to be able to use it to predict word and sentence probabilities. Write a method word prob(self, word, context) that returns the prob- ability of the n-gram (word, context) using the model’s internal counters; the output should be a float. If context is previously unseen (ie. not in the training data), the probability should be 1/|V |, where V is the model’s vocabulary.
Writeup Question 1.2: Why do we have a special case for unseen contexts? Why do we set the probability to be 1/|V |?
To predict the probability of a sentence, we multiply together its n-gram probabilities. This can be a very small number, so to avoid underflow, we will report the sentence’s log probability instead. Import the math library and write a function text prob(model, text) that returns the log probability of text, which is again a list of words/strings, under model, which is a trained NGramLM. The choice of base for the log doesn’t matter as long as it’s consistent, so we will just use the library’s default base e. The output of this function should be a (negative) float.
We are now ready to predict the probability of a sentence. Train a trigram NGramLM on warpeace.txt and use it to predict the probabilities of the following sentences:
• God has given it to me, let him who touches it beware! • Where is the prince, my Dauphin?
Writeup Question 1.3: What are your model’s predicted probabilities for these two sentences? Did anything unusual happen when you ran the second sentence? Explain what happened and why. (If you’re not sure or can’t remember from what we talked about in class, try stepping through your code to see what’s going on.)
2 Out-of-Vocabulary Words and Smoothing – 30 points
First we will add support for out-of-vocabulary words. We need to add a special token ‘<unk>’ to our vocabulary and get counts for it by replacing some of the words in the training data with ‘<unk>’.
Write a function mask rare(corpus) that takes an entire training corpus (eg. all of warpeace.txt) and returns a copy of corpus with words that appear only once replaced by the ‘<unk>’ token.
Update create ngramlm() to use the masked version of the training corpus. You will also need to update NGramLM.word prob() to use the ‘<unk>’ token’s counts whenever a word or context contains an out-of-vocabulary word.
Writeup Question 2.1: Try predicting the log probability of that second sentence again. Have we fixed whatever was going on? Why or why not?
Now we will implement smoothing. Add a new argument delta=0 to the method

word prob () (if you aren’t familiar with this notation, look up argument default values) and update the method to return Laplace-smoothed probabilities. Be careful with this step! The formula for Laplace smoothing in the slides is specifically for bigrams only; it won’t work correctly for larger n-grams. You will need to modify the formula to apply to larger n-grams.
(Hint 1: You are modifying a probability distribution. What does it mean to be a probability distribution?)
(Hint 2: You may want to add another internal variable to NGramLM to make this modi- fication easier to implement.)
Writeup Question 2.2: How did you modify the Laplace smoothing formula? Explain why the modification was necessary.
Writeup Question 2.3: Try predicting the log probabilities of both sentences again using different values for delta. What do you get? How does the value of delta affect the predicted log probabilities? Based on these examples, do you think Laplace smoothing works well for n-gram language models? Why or why not?
Let’s try another type of smoothing: linear interpolation. Define a class NGramInterpolator and write the following methods:

• •
init (self, n, lambdas), where n is the size of the largest n-gram considered by the model and lambda is a list of length n containing the interpolation factors (floats) in descending order of n-gram size. This method should save n and lambdas and initialize n internal NGramLMs, one for each n-gram size.
update(self, text) should update all of the internal NGramLMs.
word prob(self, word, context, delta=0) should return the linearly interpo-
lated probability using lambdas and the probabilities given by the internal NGramLMs.
Writeup Question 2.4: Train a trigram NGramInterpolator with lambdas = [0.33, 0.33, 0.33] and use it to predict the log probabilities of the two example sentences. What do you get? How does its compare with the base NGramLM, both with and without smoothing?
3 Perplexity – 15 points
Write a function perplexity(model, corpus path) that returns the perplexity of a trained model on the test data in the file corpus path. You will need to load the test data from file, just like you loaded the training data (you don’t need to mask rare words, though), and you will need to count N, the total number of tokens in the test data.

Writeup Question 3.1: Train two trigram NGramLMs on shakespeare.txt, one with smoothing (use delta = 0.5) and one without. (As you have probably noticed, the NGramInterpolator is slower because it builds multiple models, so we will be using plain NGramLMs for the rest of the homework.) Evaluate the two models’ perplexities using sonnets.txt as the test data. What do you get? Does anything unusual happen? Explain what and why.
Writeup Question 3.2: Evaluate the perplexities of a smoothed (delta = 0.5) tri- gram NGramLM trained on shakespeare.txt and one trained on warpeace.txt. Use sonnets.txt as the test data for both. What do you get? Which one performs better, and why do you think that’s the case?
Writeup Question 3.3: Authorship identification is an important task in NLP. Can you think of a way to use language models to determine who wrote an unknown piece of text? Explain your idea and how it would work (you don’t need to implement it).
4 Generation – 15 points
Let’s generate some text. Import the random library and set random.seed(1) (this will keep your random number generator consistent across different runs of your code). Add a method random word(self, context, delta=0) to NGramLM that returns a word sampled from the model’s probability distribution for context. Your method should perform the following steps:
1. Sort self.vocabulary according to Python’s default ordering (basically alphabet- ically order).
2. Generate a random number r ∈ [0.0, 1.0) using random.random(). This value r is how you know which word to return.
3. Iterate through the words in the sorted vocabulary and compute their probabilities given context. These probabilities all sum to 1.0, so if we imagine a number line from 0.0 to 1.0, the space on that number line can be divided up into zones corre- sponding to the words. For example, if the first words are “apple” and “banana,” with probabilities 0.09 and 0.57, respectively, then [0.0, 0.9) belongs to “apple” and [0.9, 0.66) belongs to “banana,” and so on. Return the word whose zone contains r.
Once we can generate words, we can generate sentences. Write a function random text(model, max length, delta=0) that generates up to max length words, using the previously gen- erated words as context for each new word. The initial context should consist of start tokens ‘<s>’, and the function should return the generated string immediately if the
stop token ‘</s>’ is generated.

Writeup Question 4.1: Train a trigram model on shakespeare.txt and generate 5 sentences with max length = 10. What did you generate? Are they good (Elizabethan) English sentences? What are some problems you see with the generated sentences?
Let’s try a different way of sampling. Write a method likeliest word(self, context, delta=0 that returns the n-gram with the highest probability for context. You will also need a function likeliest text(model, max length, delta=0), which will be almost identical to random text().
Writeup Question 4.2: Train four models – one bigram, one trigram, one 4-gram, and one 5-gram – on shakespeare.txt and generate the likeliest sentence for each one using max length = 10. What did you generate? Do you notice anything about these sentences? How do they compare to each other? How do they compare to the randomly- generated sentences?
5 Meta Questions – 3 points
Writeup Question 5.1: How long did this homework take you to complete (not counting
extra credit)?
Writeup Question 5.2: Did you discuss this homework with anyone?
6 Extra Credit – 10 points
Choose one of the following to implement. (You are welcome to do more than one if you want, but only one will be graded, and you must indicate which one you want me to grade. There is no extra-extra credit for doing more than one.)
• Katz backoff
• Kneser-Ney smoothing • Beam search
You can use as many new variables, functions, and methods to do this as you like. Thoroughly comment your code! If I can’t figure out what it’s doing, I won’t give credit.
Writeup Question 6.1a: For Katz backoff and Kneser-Ney, evaluate the perplexity of a trigram model trained on shakespeare.txt on sonnets.txt, using beta = 0.75, and report the result in your writeup. How does it compare with the unsmoothed and Laplace-smoothed perplexities from Question 3.1? (Keep in mind that the formulae for Katz backoff and Kneser-Ney in the slides are specifically for bigrams; you will need to generalize them to handle arbitrary n-grams.)
Writeup Question 6.1b: For beam search, generate 5 sentences with a trigram model trained on shakespeare.txt and max length = 10, using k = 3, and put the gener- ated sentences in your writeup. How do they compare to the generated sentences from Questions 4.1 and 4.2?

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