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

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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/

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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.

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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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