lOMoARcPSD|54878315
UNIVERSITY EXAMINATIONS
JAN/FEB 2024
COS4852
Machine Learning
Welcome to the COS4852 exam.
Examiner name: Prof E van der Poel
Internal moderator name: Dr P le Roux
External moderator name: Prof JV du Toit
This paper consists of 9 pages – not including this page.
Instructions:
See instruction on first page of the examination paper.
Additional student instructions
1. Students must upload their answer scripts in a single PDF file (answer scripts must not be
password protected or uploaded as “read only” files)
2. Incorrect file format and uncollated answer scripts will not be considered.
3. NO emailed scripts will be accepted.
4. Students are advised to preview submissions (answer scripts) to ensure legibility and that the
correct answer script file has been uploaded.
5. Incorrect answer scripts and/or submissions made on unofficial examinations platforms
(including the invigilator cell phone application) will not be marked and no opportunity will be
granted for resubmission.
6. Mark awarded for incomplete submission will be the student’s final mark. No opportunity for
resubmission will be granted.
7. Mark awarded for illegible scanned submission will be the student’s final mark. No opportunity for
resubmission will be granted.
8. Submissions will only be accepted from registered student accounts.
9. Students who have not utilised invigilation or proctoring tools will be subjected to disciplinary
processes (only include if applicable).
10. Students suspected of dishonest conduct during the examinations will be subjected to
disciplinary processes. UNISA has a zero tolerance for plagiarism and/or any other forms of
academic dishonesty.
11. Students are provided one hour to submit their answer scripts after the official examination
time. Submissions made after the official examination time will be rejected by the examination
regulations and will not be marked.
12. Students experiencing network or load shedding challenges are advised to apply together with
supporting evidence for an Aegrotat within 3 days of the examination session.
13. Students experiencing technical challenges, contact the SCSC 080 000 1870 or email
or refer to URL link for the list of additional contact numbers or
alternatively email your module lecturer. ONLY communication from your myLIfe account will be
considered.
Downloaded by Stephen ()
, lOMoARcPSD|54878315
Instructions:
1. Answer all the questions.
2. Write neatly and legibly. If we cannot read your answer we cannot mark it.
3. Define your variables and notation and show the formulae and each step in
your calculations. Do NOT just write down a final answer where calculations or
algorithms are involved. The final answer only gets one mark. The formulae and
calculations get the bulk of the marks. Answers must be supported by detailed
work.
4. The APPENDIX on p. 8 gives values and functions that you should use in your
calculations.
5. This paper consists of 9 pages.
[TURN PAGE . . . ]
Downloaded by Stephen ()
, lOMoARcPSD|54878315
JAN/FEB 2024
2 COS4852
Question 1: Concept Learning [21]
Let X be an instance space consisting of points in the Euclidian plane with integer
coordinates (x, y), with positive and negative instances as shown in this figure.
y
10 Positive instances:
(5,5)
(-6,4)
(-3,-4)
5 (2,-4)
Negative instances:
(-1,2)
x (-2,0)
-10 -5 5 10 (6,7)
(8,-8)
-5
-10
Let H be the set of hypotheses consisting of porigin-centered donuts. Formally,
the donut hypothesis has the form h ← ha < x2 + y 2 < bi, where a < b and
a, b ∈ Z ( Z is the set of non-negative integers, {0, 1, 2, 3, . . .} ). This can be
shortened to h ← ha, bi.
An example of a donut hypothesis is h ← h3, 4i and is shown in the figure as a
green donut (notice that this hypothesis does not explain the data correctly).
(a) Find the S-boundary set of the given instance space. Write out the hypotheses
in the form given above. Draw the donut(s) representing the S-boundary set
in the given instance space (reproduce the figures above but use your own
donut(s)). Show your assumptions (HINT: the instance space is infinite). (9)
(b) Find the G-boundary set of the given instance space. Write out the hypotheses
in the form given above. Draw the donut(s) representing the G-boundary set
in the given instance space (reproduce the figures above but use your own
donut(s)). (7)
(c) i. What is the most general hypothesis in this instance space? Explain your
answer. (2)
ii. What is the most specific hypothesis in this instance space? Explain your
answer. (2)
iii. Which of these two hypotheses (most general, most specific) is a valid
hypothesis? (1)
[TURN PAGE . . . ]
Downloaded by Stephen ()
, lOMoARcPSD|54878315
JAN/FEB 2024
3 COS4852
Question 2: k -nearest neighbours [19]
Consider the following dataset consisting of 10 instances in (x, y) coordinates,
classified as either Class P or Class N:
P1 : (2.3, 3.1) - Class P
P2 : (5.0, 6.0) - Class P
P3 : (6.0, 3.0) - Class P
P4 : (4.0, 4.0) - Class P
P5 : (6.0, 5.0) - Class P
N1 : (7.0, 7.0) - Class N
N2 : (8.8, 3.2) - Class N
N3 : (9.6, 6.1) - Class N
N4 : (6.2, 8.2) - Class N
N5 : (4.5, 7.9) - Class N
A new instance U of unknown class is at (6, 6).
(a) Use the K NN-algorithm to determine the class of U.
i. First use the Euclidian distance measure (see Appendix on p. 8) and k = 5.
Show all your distance calculations, the ordering of instances, and the
process of selecting the class for the unknown instance U. (7)
ii. Repeat the calculations with the Manhattan distance measure. (7)
iii. Compare your classification results from the two distance measures. (1)
(b) Is k = 5 a good choice in this particular problem? Explain your answer. If
there is a better value for k give the value. Show how you get this value for k ,
and explain why it is better. (4)
[TURN PAGE . . . ]
Downloaded by Stephen ()
UNIVERSITY EXAMINATIONS
JAN/FEB 2024
COS4852
Machine Learning
Welcome to the COS4852 exam.
Examiner name: Prof E van der Poel
Internal moderator name: Dr P le Roux
External moderator name: Prof JV du Toit
This paper consists of 9 pages – not including this page.
Instructions:
See instruction on first page of the examination paper.
Additional student instructions
1. Students must upload their answer scripts in a single PDF file (answer scripts must not be
password protected or uploaded as “read only” files)
2. Incorrect file format and uncollated answer scripts will not be considered.
3. NO emailed scripts will be accepted.
4. Students are advised to preview submissions (answer scripts) to ensure legibility and that the
correct answer script file has been uploaded.
5. Incorrect answer scripts and/or submissions made on unofficial examinations platforms
(including the invigilator cell phone application) will not be marked and no opportunity will be
granted for resubmission.
6. Mark awarded for incomplete submission will be the student’s final mark. No opportunity for
resubmission will be granted.
7. Mark awarded for illegible scanned submission will be the student’s final mark. No opportunity for
resubmission will be granted.
8. Submissions will only be accepted from registered student accounts.
9. Students who have not utilised invigilation or proctoring tools will be subjected to disciplinary
processes (only include if applicable).
10. Students suspected of dishonest conduct during the examinations will be subjected to
disciplinary processes. UNISA has a zero tolerance for plagiarism and/or any other forms of
academic dishonesty.
11. Students are provided one hour to submit their answer scripts after the official examination
time. Submissions made after the official examination time will be rejected by the examination
regulations and will not be marked.
12. Students experiencing network or load shedding challenges are advised to apply together with
supporting evidence for an Aegrotat within 3 days of the examination session.
13. Students experiencing technical challenges, contact the SCSC 080 000 1870 or email
or refer to URL link for the list of additional contact numbers or
alternatively email your module lecturer. ONLY communication from your myLIfe account will be
considered.
Downloaded by Stephen ()
, lOMoARcPSD|54878315
Instructions:
1. Answer all the questions.
2. Write neatly and legibly. If we cannot read your answer we cannot mark it.
3. Define your variables and notation and show the formulae and each step in
your calculations. Do NOT just write down a final answer where calculations or
algorithms are involved. The final answer only gets one mark. The formulae and
calculations get the bulk of the marks. Answers must be supported by detailed
work.
4. The APPENDIX on p. 8 gives values and functions that you should use in your
calculations.
5. This paper consists of 9 pages.
[TURN PAGE . . . ]
Downloaded by Stephen ()
, lOMoARcPSD|54878315
JAN/FEB 2024
2 COS4852
Question 1: Concept Learning [21]
Let X be an instance space consisting of points in the Euclidian plane with integer
coordinates (x, y), with positive and negative instances as shown in this figure.
y
10 Positive instances:
(5,5)
(-6,4)
(-3,-4)
5 (2,-4)
Negative instances:
(-1,2)
x (-2,0)
-10 -5 5 10 (6,7)
(8,-8)
-5
-10
Let H be the set of hypotheses consisting of porigin-centered donuts. Formally,
the donut hypothesis has the form h ← ha < x2 + y 2 < bi, where a < b and
a, b ∈ Z ( Z is the set of non-negative integers, {0, 1, 2, 3, . . .} ). This can be
shortened to h ← ha, bi.
An example of a donut hypothesis is h ← h3, 4i and is shown in the figure as a
green donut (notice that this hypothesis does not explain the data correctly).
(a) Find the S-boundary set of the given instance space. Write out the hypotheses
in the form given above. Draw the donut(s) representing the S-boundary set
in the given instance space (reproduce the figures above but use your own
donut(s)). Show your assumptions (HINT: the instance space is infinite). (9)
(b) Find the G-boundary set of the given instance space. Write out the hypotheses
in the form given above. Draw the donut(s) representing the G-boundary set
in the given instance space (reproduce the figures above but use your own
donut(s)). (7)
(c) i. What is the most general hypothesis in this instance space? Explain your
answer. (2)
ii. What is the most specific hypothesis in this instance space? Explain your
answer. (2)
iii. Which of these two hypotheses (most general, most specific) is a valid
hypothesis? (1)
[TURN PAGE . . . ]
Downloaded by Stephen ()
, lOMoARcPSD|54878315
JAN/FEB 2024
3 COS4852
Question 2: k -nearest neighbours [19]
Consider the following dataset consisting of 10 instances in (x, y) coordinates,
classified as either Class P or Class N:
P1 : (2.3, 3.1) - Class P
P2 : (5.0, 6.0) - Class P
P3 : (6.0, 3.0) - Class P
P4 : (4.0, 4.0) - Class P
P5 : (6.0, 5.0) - Class P
N1 : (7.0, 7.0) - Class N
N2 : (8.8, 3.2) - Class N
N3 : (9.6, 6.1) - Class N
N4 : (6.2, 8.2) - Class N
N5 : (4.5, 7.9) - Class N
A new instance U of unknown class is at (6, 6).
(a) Use the K NN-algorithm to determine the class of U.
i. First use the Euclidian distance measure (see Appendix on p. 8) and k = 5.
Show all your distance calculations, the ordering of instances, and the
process of selecting the class for the unknown instance U. (7)
ii. Repeat the calculations with the Manhattan distance measure. (7)
iii. Compare your classification results from the two distance measures. (1)
(b) Is k = 5 a good choice in this particular problem? Explain your answer. If
there is a better value for k give the value. Show how you get this value for k ,
and explain why it is better. (4)
[TURN PAGE . . . ]
Downloaded by Stephen ()
