CMPT 310 - Artificial Intelligence Survey
Bonus Assignment
Due date: April 25, 2021 J. Classen
5 bonus marks April 12, 2021
Important Note: Students must work individually on this, and other CMPT 310, assign-
ments. You may not discuss the specific questions in this assignment, nor their solutions
with any other student. You may not provide or use any solution, in whole or in part, to or
by another student.
You are encouraged to discuss the general concepts involved in the questions in the context
of completely different problems. If you are in doubt as to what constitutes acceptable
discussion, please ask!
Cross-Validation
In the lecture we discussed that in order to evaluate a hypothesis generated by a learning
algorithm, it is important to keep the training data and test data separate. It is not surprising
that the learnt model exhibits a low error rate on the set of examples it was trained on. If
it really generalizes well only becomes apparent when being tested on previously unseen
examples, similar as to how a professor knows that an exam will not accurately evaluate
students if they have already seen the exam questions.
When we have N examples in total, a straightforward approach is to split them into a
training set and test set, use the training set to train, and then test using the test set. A
disadvantage of this is that we don’t make full use of all available data: if we use half the
data for the test set, then we are only training on half the data, and we may get a poor
hypothesis. On the other hand, if we reserve only 10% of the data for the test set, then it
may happen that we get a very poor estimate of the actual accuracy.
One approach is to “squeeze” more out of the data and still get an accurate estimate
using a technique called k-fold cross-validation. The idea is that each example serves
double duty as training data and test data. First we split the data into k equal subsets.
We then perform k rounds of learning; on each round 1
k
of the data is held out as a test
set and the remaining examples are used as training data. The average test set score of the
k rounds should then be a better estimate than a single score. Popular values for k are 5
and 10 – enough to give an estimate that is statistically likely to be accurate, at a cost of 5
to 10 times longer computation time. (The extreme is k = N , also known as leave-one-out
cross-validation or LOOCV.)
The neural network for the restaurant scenario whose learning performance is measured
on slide “Neural Networks 27” has four hidden nodes, as shown on slide “Neural Networks
22”. This number was chosen somewhat arbitrarily. In this assignment, we want to use
cross-validation to find the best number of hidden nodes (using a single hidden layer).
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Software
Similar as in Assignment 1, we will use Python 31, and code from the aima-python repository.
However, note that this time we provide you with a ZIP file that contains
• a template Python file abonus.py for your solution and
• (modified) module files learning.py and utils.py from the repository needed to solve
this assignment, as well as
• files restaurant.csv and restaurant numeric.csv with the data for the 12 examples
for the restaurant scenario from the lecture slides for illustration purposes.
There is no need to check out code from the repository through git. Simply extract the
contents of abonus.zip into a separate directory and work on your solution there. Initially,
when running abonus.py, you should see the following output:
Size 1: 0
Size 2: 0
Size 3: 0
Size 4: 0
Size 5: 0
Size 6: 0
Size 7: 0
Size 8: 0
Size 9: 0
Size 10: 0
Size 11: 0
Size 12: 0
Size 13: 0
Size 14: 0
Size 15: 0
Take some time to read and understand the files being provided in abonus.zip. For your
solution, fill in the parts of the template that say “### YOUR CODE HERE ###”. Do not use
any modules or code except from the files provided in the ZIP and the standard Python
3 library. Do not modify anything else. In particular, leave learning.py and utils.py
unchanged (you will be only submitting your modified abonus.py file).
1https://www.python.org/
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Question 1: Generate a Data Set (2 bonus marks)
Implement the function generate restaurant dataset(size) that takes an integer size as
argument, and generates a data set with that many new, random examples for the restaurant
scenario.
Note that the module learning.py already contains code for generating example data
from the “real” restaurant decision tree, which you are free to use for this purpose. The
problem is that the data being generated there contains non-numerical attributes, and so as
a next step, it has to be converted into numerical form so it can be processed by a neural
network. Specifically, convert the data so that
• all Boolean attributes are represented in the obvious fashion, representing ’No’ by 0
and ’Yes’ by 1;
• for the Patrons attribute, use local encoding and represent ’None’ by 0, ’Some’ by
1, and ’Full’ by 2;
• for the Price attribute, use local encoding and represent ’$’ by 0, ’$$’ by 1, and
’$$$’ by 2;
• for the WaitEstimate attribute, use local encoding and represent ’0-10’ by 0, ’10-30’
by 1, ’39-60’ by 2, and ’>60’ by 3;
• for the Type attribute, use distributed encoding, where each value of Burger, French,
Italian and Thai is represented by an attribute of the same name that takes value 1
just in case the restaurant is of that particular type, and where all others are 0.
The output of the function should be an instance of the DataSet class that represents
a set of examples generated from the restaurant decision tree, but using this numerical
representation.
Note: For illustration, the CSV files in the ZIP contain the 12 restaurant examples from
the slides, once in their original representation, and once converted into numeric form. Your
function should not return these examples, but newly created, random ones.
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Question 2: Do Cross-Validation (2 bonus marks)
Next, implement the function
nn cross validation(dataset,hidden units, epochs, k)
whose arguments are a data set, the number of hidden units to be used for the neural
network, the maximal number of epochs to be used during training, and the k parameter,
respectively.
The function should perform one k-fold cross-validation on the given data set, where
in each round, a (new) neural network is trained whose (single) hidden layer consist of a
number of nodes as specified by hidden units, and where the maximal number of epochs
being performed during training is as specified by epochs. The return value should be the
overall error, averaged over all k rounds.
Note: The original aima-python repository version of module learning.py contains
code for doing a cross-validation. Do not use this functionality (it will not work “out of the
box”), but implement your own! However, you may use all other code from the learning.py
module provided in the ZIP file. In particular, you do not have to implement the Back-
propagation algorithm yourself.
Question 3: Run Experiments (1 bonus mark)
Finally, run experiments to determine the optimal network structure. Create a PDF doc-
ument that shows an example run of your program, and briefly explains what the optimal
number of hidden units is according to the results of your experiments. (You are invited to
also include plots or other visual representations of your data, but this is optional and not
required for receiving marks.)
For your experiments, you may use the values for N, k, epochs, and size limit that are
given in the provided template, or higher ones. Note that it will take a certain amount of
time for the program to run all experiments, so while working on your solution, it may be
helpful to set these variables to smaller values, and only increase them again once you are
ready to run the actual experiments.
What to Submit
Your submission should consist of
• a file abonus.py that is the modified template file containing your own implementation
and
• a PDF file called abonus.pdf, containing the example run and your (brief) analysis of
the results.
In particular, there is no need to submit the other Python module files from the ZIP (you
should not modify these for your solution).
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