CS 534: Homework #3 SOLUTION

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CS 534: Homework #3
Submission Instructions: The homework is due on Oct 19th at 11:59 PM ET on Gradescope. A
part of your homework will be automatically graded by a Python autograder. The autograder
will support Python 3.10. Additional packages and their versions can be found in the
requirements.txt. Please be aware that the use of other packages and/or versions outside of
those in the file may cause your homework to fail some test cases due to incompatible method calls
or the inability to import the module. We have split the homework into 2 parts on Gradescope, the
autograded portion, and the written answer portion. If either of the two parts is late, then your
homework is late.
1. Upload PDF to HW3-Written Assignment: Create a single high-quality PDF with your
solutions to the non-coding problems. The solutions must be typed (e.g., Word, Google Docs,
or LaTeX) and each problem appropriately tagged on Gradescope. If we must search through
your entire PDF for each problem, you may lose points! Note that you must submit the code
used to generate your results in the Code part of the assignment, otherwise you may not get
any points for the results.
2. Submit code to the HW3-Code Assignment: Your submitted code must contain the
following files: ‘’, ‘’, ‘README.txt’. You must submit ALL files you used
to generate the results but the autograder will only copy these files when running the test
cases so make sure they are self-contained (i.e., capable of running standalone). Make sure
you always upload ALL of these files when you (re)submit.
1. (2+3+2+2+2+6=17pts) Preprocessing Data for Loan Default Prediction
We will consider a simplified subset of the Lending Club Loan Data that was
previously available on Kaggle (
lending-club) for the next few problems. The goal is to determine whether or not an
individual applicant will default on the loan (i.e., unable to make the required payments to
pay back the borrowed money). Using ideas from a Kaggle Kernel by Kacper Wozniak1
, we
have preprocessed the dataset the following steps:
• Removed any column that has more than 50% of the observations missing
• Remove any row with at least one missing value
• Removed any loans that are not Fully Paid or Charged Off (defaulted)
• Only used individual applicants (i.e., join types are ignored)
1The kernel is available at
• Removed columns referring to “Active” loan accounts, joint applicants, or with too
many unique values that preprocessing may take longer than necessary (i.e., policy code,
employee title)
• Convert the loan status to a binary variable (class) as Fully Paid (0) vs Charged Off
• Subsample the data for a smaller dataset
The resulting dataset (loan default.csv) contains 2850 loans with 26 features. The goal of
this problem is to prepare the data for the next problem. The functions specified should be
in the file ‘’.
(a) (Written) Why would you potentially be interested in optimizing for F2 score compared
to F1 score in the context of finding individuals that are likely to default?
(b) (Written) How will you partition the loan data to assess the model performance and
choose hyperparameter? Justify your choice and write code to partition the data
(c) (Code) Write a function compute correlation(x, corrtype) that takes in a numpy
2D array, x, the string of the correlation type (i.e., ‘pearson’, ‘kendall’, and ‘spearman’)
to calculate and returns a numpy 2D matrix of the correlation between the features of
(d) (Code) Write a function rank correlation(x, y) that takes in a numpy 2d array, x, a
numpy 1d array, y, and returns the rank of the features in x based on correlation criteria
presented in the class. The function should output a numpy array in descending order
of the most correlated feature column (i.e., [3, 1, 0, 2] would suggest the 4th feature has
the highest rank correlation followed by 2nd, then 1st feature.)
(e) (Code) Write a function rank mutual(x, y) that that takes in a numpy 2d array, x,
a numpy 1d array, y, and returns the rank of the features in x based on the mutual
information presented in the class. The function output format is the same as 1d which is
the descending order of the most correlated feature column based on mutual information.
(f) (Written) Using 1c, 1d, 1e, perform feature selection using the three different methods
independently. For each one, justify your selection (e.g., what you are using as thresholds
for discarding highly correlated variables and the metric or what you’ll choose as the
top k ranked features).
2. (4+6+3+3+6+2=24 pts) Decision Tree to Predict Loan Defaults
Use the sklearn decision tree package to predict the loan status. The functions specified
should be in the file ‘’
(a) (Code) Write a function tune dt(x, y, dparams, lsparams) that takes in the data
where x is a numpy 2d array and y is a numpy 1d array (assume test as already been
set aside for this purpose), a list of max depth values for the decision tree, and a list of
a minimum number of samples that each leaf must contain and determines the optimal
parameters based on grid search and the AUC metric. Your function should return a
dictionary with the keys “best-depth”, “best-leaf-samples” and the optimal value from
the two lists (i.e., a single value for each setting). Your dictionary can have other keys
but must have these 2 keys.
(b) (Written) What is the best choice of the two parameters based on 2a? Plot the
“validation” AUC (based on 1b) on a single plot (either do a 3D plot or use the size of
the point to encode the AUC) as a function of the two parameters.
(c) (Written) Re-train a decision tree on the entire training data using the optimal max
depth and the minimum number of samples from 2b. What are the AUC, F1, and F2
score on the test set?
(d) (Written) Create a visualization of the top 3 levels of your decision tree from 2c.
(e) (Written) Analyze the effects of three different filtering methods, 1c, 1d, 1e,
independently on the decision tree by determining the optimal parameters using 2a
and then re-training the data on the entire training data in 2c and report the AUC, F1,
and F2 score in a table.
(f) (Written) Comment on the effect of feature selection for decision trees based on your
results from 2c and 2e.
3. (3 + 5 + 2 + 4 + 8 + 4 + 5 + 8 + 2 + 4 + 5 + 5 + 4 = 59 pts) Spam Detection
via Perceptron
We have provided a new e-mail spam dataset, which is a
subset of the SpamAssassin Public Corpus (see
publiccorpus/). Here is a sample email that contains a URL, an email address (at the end),
numbers and dollar amounts.
> Anyone knows how much it costs to host a web portal ?
> Well, it depends on how many visitors youre expecting. This can be anywhere
from less than 10 bucks a month to a couple of $100. You should checkout or perhaps Amazon EC2 if youre running something big…
To unsubscribe yourself from this mailing list,
send an email to:
We have already implemented the following email preprocessing steps: lower-casing; removal
of HTML tags; normalization of URLs, e-mail addresses, and numbers. In addition,
words have been reduced to their stemmed form. For example, “discount”, “discounts”,
“discounted” and “discounting” are all replaced with “discount”. Finally, we removed all
non-words and punctuation. The result of these preprocessing steps on the same email is
shown below:
anyon know how much it cost to host a web portal well it depend on how mani visitor
your expect thi can be anywher from less than number buck a month to a coupl of
dollarnumb you should checkout httpaddr or perhap amazon ecnumb if your run someth
big to unsubscrib yourself from thi mail list send an email to emailaddr
For this problem, you will implement the Perceptron algorithm and apply it to the problem
of e-mail spam classification. You’ll be comparing two different variants of the algorithm as
well as the number of epochs through the data.
(a) (Written) What is your model assessment strategy? Justify your validation methodology.
(You may want to read the rest of this problem before you proceed to understand what
your tasks will be).
(b) (Code) Implement a Python function build vocab(train, test, minn) that does the
following steps. (1) builds a vocabulary list by finding all the words that occur across
the training set and ignores all words that appear in fewer than minn emails and (2)
transforms both the train and test emails into a feature vector x where the ith entry, xi
is 1 if the ith word in the vocabulary occurs in the email, and 0 otherwise. The function
output should be (1) the transformed training dataset which is a numpy 2D array of
size n × p where p is the number of words that occur at least in minn emails and n is
the number of emails in the training data, (2) the transformed test dataset which is a
numpy 2D array of size m × p where m is the number of emails in the test data and
p is determined from training, and (3) a dictionary that maps the word to the column
feature to the word (e.g., {know:0, cost:1, …, emailaddr: 100}).
(c) (Code) Implement the function get weights that returns the learned perceptron
weights, w.
(d) (Code) Implement the function sample update that given a single sample and the data
label returns the new weight w in the same format as 3c and whether or not there was a
mistake for the sample (1 for mistake, 0 for no mistake). For the corner case of w·x = 0,
predict the +1 class.
(e) (Code) Implement the train function of the perceptron algorithm that uses the
examples provided to the function. This function should assume the bias term will
be automatically folded into w by adding a constant feature (i.e., a column with all 1)
such that the input is n × (p + 1) if it was to be run after 3b. The function should
output a dictionary for each epoch (pass through the data) with the number of mistakes
associated with each epoch (epochs are expected to start at 1). The algorithm will
terminate either when all the points are correctly classified or the max number of epochs
have been reached.
(f) (Code) Implement the predict function of the perceptron algorithm where given new
data points, predicts the label. The output should be a numpy 1D array of size m.
(g) (Written) Train a perceptron using your training set specified in 3a. Plot the training
and estimated generalization error as a function of the maximum number of epochs.
What is the optimal algorithm and parameter? How many mistakes are made before
the algorithm terminates if you want to classify all the training points properly?
(h) (Code) Implement the train function of the averaged perceptron algorithm. Note that
the AvgPerceptron class inherits from the Perceptron class so it can re-use methods that
exist (if it makes sense). Rather than the current implementation in 3e, this one keeps
track of the average of all the weight vectors considered during the algorithm, including
examples where no mistake was made. The average weight vector is the “learned”
coefficient in the end as averaging reduces the variance between the different weight
vectors, and is a powerful means of preventing the learning algorithm from overfitting
(serving as a type of regularization). Note that only the learned coefficient reflects the
averaged weights, but internal updates still use the same weight updates w in 3e.
(i) (Code) Implement the get weights function of the averaged perceptron algorithm. It
should return the average weight vector.
(j) (Code) Implement the predict function of the averaged perceptron algorithm. The
prediction function should use the updated average weights.
(k) (Written) Plot the training and estimated generalization error as a function of the
maximum number of epochs for the averaged perceptron.
(l) (Written) What is your final or “optimal” algorithm? In other words, train the model
with as much data as you can possibly with the optimal algorithm + hyperparameter
(maximum number of epochs) values. What is the expected predictive performance of
this model?
(m) (Written) Using the vocabulary list together with the parameters learned in the previous
question, output the 15 words with the most positive weights. What are they? Which
15 words have the most negative weights?


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