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COMP 4211: Machine Learning

Programming Assignment 1

1 Objective
The objective of this programming assignment is twofold:
1. To acquire a better understanding of supervised learning methods by using a public-domain
software package called scikit-learn.
2. To evaluate the performance of several supervised learning methods by conducting empirical study on three data sets.
The assignment consists of the following tasks:
1. To learn to use the linear regression model for regression.
2. To learn to use the logistic regression model for classification.
3. To learn to use the single-hidden-layer neural network model for classification.
4. To conduct empirical study using different supervised learning methods.
5. To write up a report.
Each of these tasks will be elaborated in the following subsections.
2.1 Regression Method
Linear regression is a basic model for regression which is expressed in the form f(x; w) =
w0 + w1x1 + · · · + wdxd, where w denotes the parameters to be learned from data. Note that
this basic model has no hyperparameter to set.
1
2.2 Classification Methods
2.2.1 Logistic Regression
Learning of the logistic regression model should use a gradient-descent algorithm by minimizing
the cross-entropy loss.1
It requires that the step size parameter η be specified. Try out a
few values (<1) and choose one that leads to stable convergence. You may also decrease η
gradually during the learning process to enhance convergence. A common criterion used for
early stopping is when the improvement between iterations does not exceed a small threshold
or when the number of iterations has reached a prespecified maximum.
2.2.2 Single-hidden-layer Neural Networks
Neural network classifiers generalize logistic regression by introducing one or more hidden layers.
The learning algorithm for them is similar to that for logistic regression as described above.
For the single-hidden-layer neural network model, the number of hidden units H should be
determined using cross validation. The generalization performance of the model is estimated
for each candidate value of H ∈ {1, 2, . . . , 10}. This is done by randomly sampling 80% of the
training instances to train a classifier and then validating it on the remaining 20%. Five such
random data splits are performed and the average over these five trials is used to estimate the
generalization performance. The value H∗
that gives the best performance among the 10 choices
of H can then be found. Subsequently, a neural network classifier with H∗ hidden units in a
single layer is trained from scratch using all the training instances available. In addition, if you
wish, you may learn to use the more powerful model selection submodule in scikit-learn
to facilitate performing grid search for hyperparameter tuning. Since the solution found may
depend on the initial weight values chosen randomly, you may repeat each setting multiple times
and report the average classification accuracy.
2.3 Empirical Study
You will use three binary classification and regression data sets which are available as a ZIP
file (datasets.zip). The following table shows the number of features, number of training
examples, and number of test examples for each data set.
Data set #features #train #test
fifa 36 13191 4397
finance 26 2754 918
orbits 12 9642 3215
When you load each .npz data file, you will find six NumPy arrays.
train X classification train Y regression train Y
test X classification test Y regression test Y
1For simplicity, you are not required to add regularization terms to the loss functions though you may do it if
you wish.
2
Each row of X stores the features of one example and the corresponding row of Y stores its class
label (0 or 1) for classification, and regression label (0 to 1) for regression. As is always the
case, the label files for the test sets should not be used for training but only for measuring the
accuracy on the test data.
For each of the three data sets, you will evaluate the following methods with respect to the
regression and classification accuracy on the training set and the test set separately:2
• Linear regression
• Logistic regression
• Neural network with H∗ hidden units (H∗ determined by cross validation)
You are expected to also report the time required by each method to complete the task, excluding
the time needed for loading the data files. For the linear regression model, you are required to
compute the squared error (f(x; w) − y)
2
for each data point in the test set and then plot
the distribution of the squared error values as a histogram. For the logistic regression model,
you are required to visualize the classification results to depict the performance on both the
training and test sets. For the neural network model, you should report the performance of each
value of H ∈ {1, 2, . . . , 10} in the cross validation procedure for determining the best value H∗
.
Furthermore, you should keep in mind to report the best (i.e., lowest) loss of the neural network
model on both the training and test sets before the model is overfitted. For reporting the results
of the neural network model, you are required to visualize not only the classification results on
the training set and test set after training the model, but also the change in performance on the
training set and validation set during training the model.
Your programs should be written in such a way that the TA can run them easily to verify the
results reported by you.
2.4 Report Writing
In your report, you are expected to present the parameter settings and the experiment results.
Besides reporting the accuracy (for both training and test data) in numbers, graphical aids
should also be used to analyze the performance of different methods visually. Note that you may
not score high if you fail to provide analysis and visualization of your experiment results. Some
utilities in scikit-learn such as auc and confusion matrix are recommended for reporting
the experiment results. For the time required by each method to complete the task, you report
it in seconds.
3 Some Programming Tips
As is always the case, good programming practices should be applied when coding your program.
Below are some common ones but they are by no means complete:
• Using functions to structure program clearly
2You may also try to use single-hidden-layer neural networks for the regression tasks but it is not required for
this assignment. Please note that the squared loss should be used for regression tasks.
3
• Using meaningful variable and function names to improve readability
• Using indentation
• Using consistent styles
• Including concise but informative comments
For scikit-learn in particular, you are recommended to take full advantage of the built-in
classes which can keep your program both short and efficient. Proper use of implementation
tricks often leads to speedup by orders of magnitude. Please be careful to choose the built-in
4 Assignment Submission
Assignment submission should only be done electronically using the Course Assignment Submission System (CASS):
https://cssystem.cse.ust.hk/UGuides/cass/student.html
There should be two files in your submission with the following naming convention required:
1. Report (with filename report): preferably in PDF format.
2. Source code and a README file (with filename code): all necessary code for running
your program as well as a brief user guide for the TA to run the programs easily to
verify your results, all compressed into a single ZIP or RAR file. The data should not be
submitted to keep the file size small.
When multiple versions with the same filename are submitted, only the latest version according
to the timestamp will be used for grading. Files not adhering to the naming convention above
will be ignored.
This programming assignment will be counted towards 12% of your final course grade. Note that
the plus sign (+) in the table below indicates that reporting without providing the corresponding
code will get zero point. The maximum scores for different tasks are as follows:
4
(60)
Report
(+40)
Empirical study on linear regression
– Build the linear regression model 2
– Compute the R2
score of the linear regression model on
both the training and test sets 3 +2
– Depict a histogram of the squared errors of the data points
in the test set of the linear regression model 10 +3
Empirical study on logistic regression
descent optimization algorithm, and present the model settings 5 +2
– Compute the accuracy of the logistic regression model on
both the training and test sets 5 +3
– Record and visualize the experiment results of the logistic
regression model on both the training and test sets 10 +3
Empirical study on neural network model
descent optimization algorithm, and present the model settings 5 +2
– Report the parameter tuning results of the neural network
model using cross validation 5 +4
– Compute the best (i.e., lowest) loss of the neural network model
on both the training and test sets before the model is overfitted 5 +3
– Record and visualize the experiment results of the neural
network model, including performance change over time 10 +3
Writing report
– Present the computing environment for this assignment +2
– Present the time required by each method to complete the task +3
– Compare and analyze the performance of all the regression
and classification methods involved +10
Late submission will be accepted but with penalty. The late penalty is deduction of one point
(out of a maximum of 100 points) for every minute late after 11:59pm. Being late for a fraction of
a minute is considered a full minute. For example, two points will be deducted if the submission
time is 00:00:34. Machine Learning Programming Assignment 1