# CMPSC442: Homework 4

\$35.00

## 1. Spam Filter [95 points]

In this section, you will implement a minimal system for spam filtering. You should unzip the
homework4_data.zip file in the same location as your skeleton file; this will create a
homework4_data/train folder and a homework4_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 homework4_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 = “homework4_data/train/ham/”
[‘of’, ‘my’, ‘outstanding’, ‘mail’]
[‘for’, ‘Preferences’, ‘-‘, “didn’t”]
>>> spam_dir = “homework4_data/train/spam/”
[‘You’, ‘are’, ‘receiving’, ‘this’]
[”, ”, ‘

‘, ‘
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
where w is a word in the vocabulary V, α is the smoothing constant (typically in the range 0 < α
≤ 1), and denotes a special word that will be substituted for unknown tokens at test
time.
>>> paths = [“homework4_data/train/ham/ham%d” % i
… for i in range(1, 11)]
>>> p = log_probs(paths, 1e-5)
>>> p[“the”]
-3.6080194731874062
>>> p[“line”]
-4.272995709320345
>>> paths = [“homework4_data/train/spam/spam%d” % i
… for i in range(1, 11)]
>>> p = log_probs(paths, 1e-5)
>>> p[“Credit”]
-5.837004641921745
>>> p[“”]
-20.34566288044584

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 “” in order to avoid zero probabilities.
Recall from the lecture slides that for a given class c ∈ {spam, ¬spam},
P(w) = , count(w) + α
(∑ count( )) + α(|V| + 1) w ∈V ′ w′
P(⟨UNK⟩) = α
(∑ count( )) + α(|V| + 1) w ∈V ′ w′
P(c ∣ document) ∼ P(c) ∏P(w ∣ c , count(w)

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.
>>> sf = SpamFilter(“homework4_data/train/spam”,
… “homework4_data/train/ham”, 1e-5)
>>> sf.is_spam(“homework4_data/train/spam/spam1”)
True
>>> sf.is_spam(“homework4_data/train/spam/spam2”)
True
>>> sf = SpamFilter(“homework4_data/train/spam”,
… “homework4_data/train/ham”, 1e-5)
>>> sf.is_spam(“homework4_data/train/ham/ham1”)
False
>>> sf.is_spam(“homework4_data/train/ham/ham2”)
False

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.
>>> sf = SpamFilter(“homework4_data/train/spam”,
P(c ∣ document) ∼ P(c) ∏P(w ∣ c ,
w∈V
)
count(w)
log( ). P(w ∣ spam)
P(w)
log( ). P(w ∣ ¬spam)
P(w)
… “homework4_data/train/ham”, 1e-5)
>>> sf.most_indicative_spam(5)
[‘<a’, ‘<input’, ”, ‘<meta’,”]>>> sf = SpamFilter(“homework4_data/train/spam”,… “homework4_data/train/ham”, 1e-5)>>> sf.most_indicative_ham(5)[‘Aug’, ‘ilug@linux.ie’, ‘install’,’spam.’, ‘Group:’]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 anysignificant stumbling blocks?3. [2 points] Which aspects of this assignment did you like? Is there anything you would havechanged?