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CMPSC442: Homework 5
CMPSC442: Homework 5 [100 points]
TO PREPARE AND SUBMIT HOMEWORK
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Instructions
In this assignment, you will implement a basic spam filter using naive Bayes classification.
A skeleton file homework5_cmpsc442.py containing empty definitions for each question has been
provided. A zip file called homework5_data.zip has also been provided that contains the input train
and test data. Since portions of this assignment will be graded automatically, none of the names or
function signatures in the skeleton template file should be modified. However, you are free to
introduce additional variables or functions if needed.
You may import definitions from any standard Python library, and are encouraged to do so in case you
find yourself reinventing the wheel. If you are unsure where to start, consider taking a look at the data
structures and functions defined in the collections, email, math, and os modules.
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]
8/19/22, 6:19 PM Homework 5
file:///Users/kxk302/Downloads/homework1-7html/homework5-cmpsc442.html 2/4
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/"
>>> load_tokens(ham_dir+"ham1")[200:204]
['of', 'my', 'outstanding', 'mail']
>>> load_tokens(ham_dir+"ham2")[110:114]
['for', 'Preferences', '-', "didn't"]
>>> spam_dir = "homework5_data/train/spam/"
>>> load_tokens(spam_dir+"spam1")[1:5]
['You', 'are', 'receiving', 'this']
>>> load_tokens(spam_dir+"spam2")[:4]
['<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
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.
>>> paths = ["homework5_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 = ["homework5_data/train/spam/spam%d" % i
... for i in range(1, 11)]
>>> p = log_probs(paths, 1e-5)
>>> p["Credit"]
-5.837004641921745
P(w) = ,
count(w) + α
(∑ count( )) + α(|V| + 1) w ∈V
′ w′
P(⟨UNK⟩) =
α
(∑ count( )) + α(|V| + 1) w ∈V
′ w′
8/19/22, 6:19 PM Homework 5
file:///Users/kxk302/Downloads/homework1-7html/homework5-cmpsc442.html 3/4
>>> p["<UNK>"]
-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 "<UNK>" in order to avoid zero probabilities.
Recall from the lecture slides that for a given class c ∈ {spam, ¬spam},
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("homework5_data/train/spam",
... "homework5_data/train/ham", 1e-5)
>>> sf.is_spam("homework5_data/train/spam/spam1")
True
>>> sf.is_spam("homework5_data/train/spam/spam2")
True
>>> sf = SpamFilter("homework5_data/train/spam",
... "homework5_data/train/ham", 1e-5)
>>> sf.is_spam("homework5_data/train/ham/ham1")
False
>>> sf.is_spam("homework5_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
P(c ∣ document) ∼ P(c) ∏P(w ∣ c ,
w∈V
)
count(w)
log( )
.
P(w ∣ spam)
P(w)
log( )
.
P(w ∣ ¬spam)
P(w)
8/19/22, 6:19 PM Homework 5
file:///Users/kxk302/Downloads/homework1-7html/homework5-cmpsc442.html 4/4
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("homework5_data/train/spam",
... "homework5_data/train/ham", 1e-5)
>>> sf.most_indicative_spam(5)
['<a', '<input', '<html>', '<meta',
'</head>']
>>> sf = SpamFilter("homework5_data/train/spam",
... "homework5_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 any
significant stumbling blocks?
3. [2 points] Which aspects of this assignment did you like? Is there anything you would have
changed?
