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CMPSC442: Homework 4 [100 points] Solution
TO PREPARE AND SUBMIT HOMEWORK
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Instructions
In this assignment, you will implement a basic spam filter using naive Bayes classification.
Do not modify any names or function signatures in the provided template file, or the autograder cannot test your functions. However, you are free to introduce additional variables or functions if needed.
You will find that in addition to a problem specification, most programming questions also include one or two examples from the Python interpreter. These are meant to illustrate typical use cases to clarify the assignment, and are not comprehensive test suites. In addition to performing your own testing, you are strongly encouraged to verify that your code gives the expected output for these examples before submitting.
It is highly recommended that you follow the Python style guidelines set forth in PEP 8, which was written in part by the creator of Python. However, your code will not be graded for style.
1. Spam Filter [95 points]
In this section, you will implement a minimal system for spam filtering. You should unzip the homework5_data.zip file in the same location as your skeleton file; this will create a
homework5_data/train folder and a homework5_data/dev folder. You will begin by processing the
raw training data. Next, you will proceed by estimating the conditional probability distributions of the words in the vocabulary determined by each document class. Lastly, you will use a naive Bayes model to make predictions on the publicly available test set, located in homework5_data/dev.
1. [5 points] Making use of the email module, write a function load_tokens(email_path) that
reads the email at the specified path, extracts the tokens from its message, and returns them as a list.
Specifically, you should use the email.message_from_file(file_obj) function to create a
message object from the contents of the file, and the email.iterators.body_line_iterator(message) function to iterate over the lines in the
message. Here, tokens are considered to be contiguous substrings of non-whitespace characters.
>>> ham_dir = "homework5_data/train/ham/" >>> spam_dir = "homework5_data/train/spam/
>>> load_tokens(ham_dir+"ham1")[200:204] >>> load_tokens(spam_dir+"spam1")[1:5]
['of', 'my', 'outstanding', 'mail'] ['You', 'are', 'receiving', 'this']
>>> load_tokens(ham_dir+"ham2")[110:114] >>> load_tokens(spam_dir+"spam2")[:4]
['for', 'Preferences', '-', "didn't"] ['<html>', '<body>', '<center>', '<h3>'] 2. [30 points] Write a function log_probs(email_paths, smoothing) that returns a dictionary from the words contained in the given emails to their Laplace-smoothed log-probabilities. Specifically, if the set V denotes the vocabulary of words in the emails, then the probabilities should be computed by taking the logarithms of
( count(w′ ))+ α ⟨UNK⟩) = ( ′ α′ )
P(w) =, P( ∑ w′∈V count(w ) + α(|V| + 1) ∑ w ∈V count(w ) + α(|V| + 1)
where w is a word in the vocabulary V, α is the smoothing constant (typically in the range 0 < α ≤ 1), and <UNK> denotes a special word that will be substituted for unknown tokens at test time.
3. [10 points] Write an initialization method
__init__(self, spam_dir, ham_dir, smoothing) in the SpamFilter class that creates two log-probability dictionaries corresponding to the emails in the provided spam and ham directories, then stores them internally for future use. Also compute the class probabilities P(spam) and P(¬spam) based on the number of files in the input directories.
4. [25 points] Write a method is_spam(self, email_path) in the SpamFilter class that returns a Boolean value indicating whether the email at the given file path is predicted to be spam. Tokens which were not encountered during the training process should be converted into the special word "<UNK>" in order to avoid zero probabilities.
P(c ∣ document) ∼ P(c) ∏ P(w ∣ c)count(w),
w∈V
where the normalization constant 1 / P(document) is the same for both classes and can therefore be ignored. Here, the count of a word is computed over the input document to be classified.
These computations should be computed in log-space to avoid underflow.
5. [25 points] Suppose we define the spam indication value of a word w to be the quantity
.
Similarly, define the ham indication value of a word w to be
.
Write a pair of methods most_indicative_spam(self, n) and most_indicative_ham(self, n) in the SpamFilter class which return the n most indicative
words for each category, sorted in descending order based on their indication values. You should restrict the set of words considered for each method to those which appear in at least one spam email and one ham email. Hint: The probabilities computed within the
__init__(self, spam_dir, ham_dir, smoothing) method are sufficient to calculate these quantities.
2. Feedback [5 points]
1. [1 point] Approximately how long did you spend on this assignment?
2. [2 points] Which aspects of this assignment did you find most challenging? Were there any significant stumbling blocks?
3. [2 points] Which aspects of this assignment did you like? Is there anything you would have changed?
