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CSC311  Final Project
Final Project

Submission: You need to submit the following files through MarkUs1
:
• Your answers to Part A and B, as a PDF file titled final_report.pdf. You can produce the
file however you like (e.g. LATEX, Microsoft Word, scanner), as long as it is readable.
• The Python codes you used for both Part A and B, as a zip file code.zip. You may exclude
the folder /data from the starter code.
Late Submission: 10% of the marks will be deducted for each day late, up to a maximum of 3
days. After that, no submissions will be accepted.
Computing: To install Python and required libraries, see the instructions on the course web page.
Collaboration: You should form teams of 2-3 students. Your final report should list the
contributions of each team member.
1 Introduction
One of CSC311’s main objectives is to prepare you to apply machine learning algorithms to realworld tasks. The final project aims to help you get started in this direction. You will be performing
the following tasks:
• Try out existing algorithms to real-world tasks.
• Modify an existing algorithm to improve performance.
• Write a short report analyzing the result.
The final project is not intended to be a stressful experience. It is a good chance for you to
experiment, think, play, and hopefully have fun. These tasks are what you will be doing daily as a
data analyst/scientist or machine learning engineer.
2 Background & Task
Online education services, such as Khan Academy and Coursera, provide a broader audience with
access to high-quality education. On these platforms, students can learn new materials by watching
a lecture, reading course material, and talking to instructors in a forum. However, one disadvantage
of the online platform is that it is challenging to measure students’ understanding of the course
material. To deal with this issue, many online education platforms include an assessment component
to ensure that students understand the core topics. The assessment component is often composed
of diagnostic questions, each a multiple choice question with one correct answer. The diagnostic
question is designed so that each of the incorrect answers highlights a common misconception.
An example of the diagnostic problem is shown in figure 1. When students incorrectly answer
the diagnostic question, it reveals the nature of their misconception and, by understanding these
misconceptions, the platform can offer additional guidance to help resolve them.
1
https://markus.teach.cs.toronto.edu/csc311-2020-09
1
CSC311 Fall 2020 Final Project
Figure 1: An example diagnostic question [1].
In this project, you will build machine learning algorithms to predict whether a student can correctly
answer a specific diagnostic question based on the student’s previous answers to other questions
and other students’ responses. Predicting the correctness of students’ answers to as yet unseen
diagnostic questions helps estimate the student’s ability level in a personalized education platform.
Moreover, these predictions form the groundwork for many advanced customized tasks. For instance, using the predicted correctness, the online platform can automatically recommend a set of
diagnostic questions of appropriate difficulty that fit the student’s background and learning status.
You will begin by applying existing machine learning algorithms you learned in this course. You
will then compare the performances of different algorithms and analyze their advantages and disadvantages. Next, you will modify existing algorithms to predict students’ answers with higher
accuracy. Lastly, you will experiment with your modification and write up a short report with the
results.
You will measure the performance of the learning system in terms of prediction accuracy, although
you are welcome to include other metrics in your report if you believe they provide additional
insight:
Prediction Accuracy = The number of correct predictions
The number of total predictions
3 Data
We subsampled answers of 542 students to 1774 diagnostic questions from the dataset provided by
Eedi2
, an online education platform that is currently being used in many schools [1]. The platform
offers crowd-sourced mathematical diagnostic questions to students from primary to high school
(between 7 and 18 years old). The truncated dataset is provided in the folder /data.
2
https://eedi.com/
2
CSC311 Fall 2020 Final Project
Figure 2: An example sparse matrix [1].
3.1 Primary Data
The primary data, train_data.csv, is the main dataset you will be using to train the learning
algorithms throughout the project. There is also a validation set valid_data.csv that you should
use for model selection and a test set test_data.csv that you should use for reporting the final
performance. All primary data csv files are composed of 3 columns:
• question id: ID of the question answered (starts from 0).
• user id: ID of the student who answered the question (starts from 0).
• is correct: Binary indicator whether the student’s answer was correct (0 is incorrect, 1 is
correct).
We also provide a sparse matrix, sparse_matrix.npz, where each row corresponds to the user id
and each column corresponds to the question id. An illustration of the sparse matrix is shown in
figure 2. The correct answer given a pair of (user id, question id) will have an entry 1 and an
incorrect answer will have an entry 0. Answers with no observation and held-out data (that will
be used for validation and test) will have an entry NaN (np.NaN).
3.2 Question Metadata
We also provide the question metadata, question_meta.csv, which contains the following columns:
• question id: ID of the question answered (starts from 0).
• subject id: The subject of the question covered in an area of mathematics. The text description of each subject is provided in subject_meta.csv.
3.3 Student Metadata
Lastly, we provide the student metadata, student_meta.csv, that is composed of the following
columns:
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CSC311 Fall 2020 Final Project
• user id: ID of the student who answered the question (starts from 0).
• gender: Gender of the student, when available. 1 indicates a female, 2 indicates a male, and
0 indicates unspecified.
• data of birth: Birth date of the student, when available.
• premium pupil: Student’s eligibility for free school meals or pupil premium due to being
financially disadvantaged, when available.
4 Part A
In the first part of the project, you will implement and apply various machine learning algorithms
you studied in the course to predict students’ correctness of a given diagnostic question. Review the
course notes if you don’t recall the details of each algorithm. For this part, you will only be using
the primary data: train_data.csv, sparse_matrix.npz, valid_data.csv, and test_data.csv.
Moreover, you may use the helper functions provided in utils.py to load the dataset and evaluate
your model. You may also use any functions from packages NumPy, Scipy, Pandas, and PyTorch.
Make sure you understand the code instead of using it as a black box.
1. [5pts] k-Nearest Neighbor. In this problem, using the provided code at part_a/knn.py,
you will experiment with k-Nearest Neighbor (kNN) algorithm.
The provided kNN code performs collaborative filtering that uses other students’ answers
to predict whether the specific student can correctly answer some diagnostic questions. In
particular, the starter code implements user-based collaborative filtering: given a user, kNN
finds the closest user that similarly answered other questions and predicts the correctness
based on the closest student’s correctness. The core underlying assumption is that if student
A has the same correct and incorrect answers on other diagnostic questions as student B, A’s
correctness on specific diagnostic questions matches that of student B.
(a) Complete a function main located at knn.py that runs kNN for different values of k ∈
{1, 6, 11, 16, 21, 26}. Plot and report the accuracy on the validation data as a function
of k.
(b) Choose k

that has the highest performance on validation data. Report the chosen k

and the final test accuracy.
(c) Implement a function knn_impute_by_item on the same file that performs item-based
collaborative filtering instead of user-based collaborative filtering. Given a question,
kNN finds the closest question that was answered similarly, and predicts the correctness
basted on the closest question’s correctness. State the underlying assumption on itembased collaborative filtering. Repeat part (a) and (b) with item-based collaborative
filtering.
(d) Compare the test performance between user- and item- based collaborative filtering.
State which method performs better.
(e) List at least two potential limitations of kNN for the task you are given.
2. [15pts] Item Response Theory. In this problem, you will implement an Item-Response
Theory (IRT) model to predict students’ correctness to diagnostic questions.
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CSC311 Fall 2020 Final Project
The IRT assigns each student an ability value and each question a difficulty value to formulate
a probability distribution. In the one-parameter IRT model, βj represents the difficulty of
the question j, and θi that represents the i-th students ability. Then, the probability that
the question j is correctly answered by student i is formulated as:
p(cij = 1|θi
, βj ) = exp (θi − βj )
1 + exp (θi − βj )
We provide the starter code in part_a/item_response.py.
(a) Derive the log-likelihood log p(C|θ, β) for all students and questions. Here C is the
sparse matrix. Also, show the derivative of the log-likelihood with respect to θi and βj
(Hint: recall the derivative of the logistic model with respect to the parameters).
(b) Implement missing functions in item_response.py that performs alternating gradient
descent on θ and β to maximize the log-likelihood. Report the hyperparameters you
selected. With your chosen hyperparameters, report the training curve that shows the
training and validation log-likelihoods as a function of iteration.
(c) With the implemented code, report the final validation and test accuracies.
(d) Select five questions j1, j2, j3, j4, and j5. Using the trained θ and β, plot five curves on
the same plot that shows the probability of the correct response p(cij ) as a function of θ
given a question j. Comment on the shape of the curves and briefly describe what these
curves represent.
3. [15pts] Matrix Factorization OR Neural Networks. In this question, please read both
option (i) and option (ii), but you only need to do one of the two.
(i) Option 1: Matrix Factorization. In this problem, you will be implementing matrix
factorization methods. The starter code is located at part_a/matrix_factorization.
(a) Using a function svd_reconstruct that factorizes the sparse matrix using singularvalue decomposition, try out at least 5 different k and select the best k using the
validation set. Report the final validation and test performance with your chosen k.
(b) State one limitation of SVD in the task you are given. (Hint: how are you treating
the missing entries?)
(c) Implement functions als and update_u_z located at the same file that performs
alternating least square method (ALS). Review the details in the course slides. As
a reminder, the objective for ALS is as follows:
min
U,Z
1
2
X
(n,m)∈O

Cnm − u
>
n zm
2
,
where C is the sparse matrix and O = {(n, m) : entry (n, m) of matrix C is observed}.
(d) Learn the representations U and Z using ALS. Tune learning rate and number of
iterations. Report your chosen hyperparameters. Try at least 5 different values of
k and select the best k

that achieves the lowest validation accuracy.
(e) With your chosen k

, plot and report how the training and validation squared-errorlosses change as a function of iteration. Also report final validation accuracy and
test accuracy.
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CSC311 Fall 2020 Final Project
(f) For ALS, you trained the model as a regression problem; your loss function was a
squared-error-loss. How would you modify the loss function if you would like to train
the model as a binary classification problem? Describe your modified loss function.
(ii) Option 2: Neural Networks. In this problem, you will implement neural networks
to predict students’ correctness on a diagnostic question. Specifically, you will design an
autoencoder model. Given a user v ∈ R
Nquestions from a set of users S, our objective is:
min
θ
X
v∈S
kv − f(v; θ)k
2
2
,
where f is the reconstruction of the input v. The network computes the following
function:
f(v; θ) = h(W(2)g(W(1)v + b
(1)) + b
(2)) ∈ R
Nquestions
for some activation functions h and g. In this question, you will be using sigmoid
activation functions for both. Here, W(1) ∈ R
k×Nquestions and W(2) ∈ R
Nquestions×k
,
where k ∈ N is the latent dimension. We provide the starter code written in PyTorch at
part_a/neural_network.
(a) Describe at least three differences between ALS and neural networks.
(b) Implement a class AutoEncoder that performs a forward pass of the autoencoder
following the instructions in the docstring.
(c) Train the autoencoder using latent dimensions of k ∈ {10, 50, 100, 200, 500}. Also,
tune optimization hyperparameters such as learning rate and number of iterations.
Select k

that has the highest validation accuracy.
(d) With your chosen k

, plot and report how the training and validation objectives
changes as a function of epoch. Also, report the final test accuracy.
(e) Modify a function train so that the objective adds the L2 regularization. The
objective is as follows:
min
θ
X
v∈S
kv − f(v; θ)k
2
2 +
λ
2
(kW(1)k
2
F + kW(2)k
2
F
)
You may use a method get_weight_norm to obtain the regularization term. Using
the k and other hyperparameters selected from part (d), tune the regularization
penalty λ ∈ {0.001, 0.01, 0.1, 1}. With your chosen λ, report the final validation and
test accuracy. Does your model perform better with the regularization penalty?
4. [15pts] Ensemble. In this problem, you will be implementing bagging ensemble to improve the stability and accuracy of your base models. Select and train 3 base models with
bootstrapping the training set. You may use the same or different base models. Your implementation should be completed in part_a/ensemble.py. To predict the correctness, generate
3 predictions by using the base model and average the predicted correctness. Report the final
validation and test accuracy. Explain the ensemble process you implemented. Do you obtain
better performance using the ensemble? Why or why not?
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CSC311 Fall 2020 Final Project
5 Part B
In the second part of the project, you will modify one of the algorithms you implemented in part A to
hopefully predict students’ answers to the diagnostic question with higher accuracy. In particular,
consider the results obtained in part A, reason about what factors are limiting the performance of
one of the methods (e.g. overfitting? underfitting? optimization difficulties?) and come up with
a proposed modification to the algorithm which could help address this problem. Rigorously test
the performance of your modified algorithm, and write up a report summarizing your results as
described below.
You will not be graded on how well the algorithm performs (i.e. its accuracy); rather, your grade
will be based on the quality of your analysis. Try to be creative! You may also optionally use the
provided metadata (question_meta.csv and student_meta.csv) to improve the accuracy of the
model. At last, you are free to use any third-party ideas or code as long as it is publicly available.
You must properly provide references to any work that is not your own in the write-up.
The length of your report for part B should be 3-4 pages. Don’t be afraid to keep the text short
and to include large illustrative figures. The guidelines and marking schemes are as follows:
1. [15pts] Formal Description: Precisely define the way in which you are extending the
algorithm. You should provide equations and possibly an algorithm box. Describe way your
proposed method should be expected to perform better. For instance, are you intending it to
improve the optimization, reduce overfitting, etc.?
2. [10pts] Figure or Diagram: that shows the overall model or idea. The idea is to make
your report more accessible, especially to readers who are starting by skimming your report.
3. [15pts] Comparison or Demonstration: Include:
• A comparison of the accuracies obtained by your model to those from baseline models.
Include a table or a plot for an illustrative comparison.
• Based on the argument you gave for why your extension should help, design and carry
out an experiment to test your hypothesis. E.g., consider how you would disentangle
whether the benefits are due to optimization or regularization.
4. [15pts] Limitations: of your approach.
• Describe some settings in which we’d expect your approach to perform poorly, or where
all existing models fail.
• Try to guess or explain why these limitations are the way they are.
• Give some examples of possible extensions, ways to address these limitations, or open
problems.
6 Optional: Competition
Optionally, you will take part in a competition where you will submit the predictions of your model
on a private test dataset. We will be using a platform called Kaggle3
, which is a popular online
community of data scientists and machine learning practitioners to solve data science challenges.
3
https://www.kaggle.com/
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CSC311 Fall 2020 Final Project
You will first form a team on Kaggle and submit your prediction as a csv file on the project website,
which can be found here:
https://www.kaggle.com/t/51c62bffb0f348008333b29ab4385b23
Your submission should be a csv file with two columns id and is correct. You should use the
provided functions load_private_test_csv to load the dataset and save_private_test_csv to
save the predictions as a csv file both located at utils.py. Once you save the csv file, you
can directly upload it to the competition page. After the submission, you can find your model’s
performance on the public leaderboard, which displays an accuracy of your predictions on 70% of
private data. The full leaderboard that uses all private data will be released after the competition.
You are not required to use your model from Part B for this part.
Performance on the competition will not affect your grade, not even as extra credit. The top 3 teams
with the highest performance on all private data will receive a special gift from the instructors.
7 Friendly Advice
• Read carefully! Make sure you are following the guidelines. Read this document carefully
to understand the dataset, what you are asked to implement and demonstrate, etc. Ask
questions on Piazza and visit office hours if you are unsure of any requirements.
• Be honest! You are not being marked on how good the results are. It doesn’t matter if
your method is better or worse than the ones you compare to. What matters is that you
clearly describe the problem, your method, what you did, and what the results were. Just be
scientific.
• Be careful! Don’t do things like test on your training data, set hyperparameters using test
accuracy, compare unfairly against other methods, include plots with unlabeled axes, use
undefined symbols in equations, etc. Do sensible crosschecks like running your algorithms
several times to understand the between-run variability, performing gradient checking, etc.
References
[1] Wang, Zichao, et al. Diagnostic Questions: The NeurIPS 2020 Education Challenge. arXiv
preprint arXiv:2007.12061 (2020)
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