King’s College London
This paper is part of an examination of the College counting towards the award
of a degree. Examinations are governed by the College Regulations under the
authority of the Academic Board.
Degree Programmes BSc, MSci, BEng, MEng
Module Code 6CCS3AIN
Module Title Artificial Intelligence Reasoning and Decision
Making
Examination Period January 2020 (Period 1)
Time Allowed Two hours
Rubric ANSWER ALL QUESTIONS. A correct choice will give
marks. However, marks will be deducted for incorrect
choices, but no question can yield a negative overall num-
ber of points. That is each question gives at least 0 points,
regardless of the answers.
The answers to questions need to be clearly made by pen on
the appropriate grid on the answer sheet provided at the
back of the exam paper.
Calculators Calculators may be used. The following models are permit-
ted: Casio fx83 / Casio fx85.
Notes Books, notes or other written material may not be brought
into this examination
PLEASE DO NOT REMOVE THIS PAPER FROM THE
EXAMINATION ROOM
2020 King’s College London
January 2020 6CCS3AIN
How to correctly use your Answer Sheet
-
You must provide the answers to all questions on the answer sheet by
making the appropriate choice selections when ready to commit them.
-
Please make your choice selections on the answer sheet (at the back
of the exam paper) by filling out the corresponding box using a pen.
-
If you find the following ‘Candidate Instructions’ and ‘LEMS answer sheet’
on your desk, please ignore them:
-
Below are examples of how to correctly and incorrectly make your choice
selections on the answer sheet.
Correct Incorrect
-
Only one answer sheet per exam will be provided so make your choice se-
lections carefully.
-
If for any reason you make a mistake making your choice selection, put a
line over the choice boxes of the question item and provide the correction
in writing next to the question item. In the example below, the selections A
and C will be considered instead of B and D.
January 2020 6CCS3AIN
- The random variables Y and Z are non-interacting causes of X. Given the
conditional probability values P (x|y) = 0. 9 and P (x|z) = 0. 3 , what does
the Noisy Or model give as the value of P (x|y, z)?
[4 marks]
A. 0.
B. 0.
C. 0.
D. 0.
E. 0.
Answer
A.
Marking scheme
A. 4
B. -
C. -
D. -
E. -
no negative overall mark
January 2020 6CCS3AIN
- Consider the joint probability table for the three binary variables P , Q and
R:
p ¬ p
q ¬ q q ¬ q
r 0 0 0 0.
¬ r 0 0 0 0.
What is P (p ∧ ¬r)?
[4 marks]
A. 0.
B. 0.
C. 0.
D. 0.
E. None of the above
Answer
A.
Marking scheme
A. 4
B. -
C. -
D. -
E. -
no negative overall mark
January 2020 6CCS3AIN
- Consider the joint probability table for the three binary variables P , Q and
R:
p ¬ p
q ¬ q q ¬ q
r 0 0 0 0.
¬ r 0 0 0 0.
What is P (q|p, r)?
[4 marks]
A. a number in (0, 0 .1]
B. a number in (0. 1 , 0 .2]
C. a number in (0. 2 , 0 .3]
D. a number in (0. 4 , 0 .5]
E. None of the above
Answer
E.
P (q|p, r) = P P ( p, q, r(p, r) ) = (0 + 0 0. 108 .082) > 0. 5
Marking scheme
A. -
B. -
C. -
D. -
E. 4
no negative overall mark
January 2020 6CCS3AIN
- Consider the following normal form game:
L R
U 4 5
4 1
D 5 4
1 4
Identify any Pareto optimal outcomes:
[4 marks]
A. (U, L)
B. (U, R)
C. (D, L)
D. (D, R)
E. There are none
Answer
A, B, C, D.
Marking scheme
A. 1
B. 1
C. 1
D. 1
E. -
no negative overall mark
January 2020 6CCS3AIN
- Consider the following normal form game:
L M R
U 4 1 6
3 1 2
D 5 1 4
2 1 3
Identify any pure strategy Nash equilibria:
[4 marks]
A. (U, L)
B. (U, R)
C. (D, L)
D. (D, R)
E. There are none
Answer
E.
Marking scheme
A. -
B. -
C -
D. -
E. 4
no negative overall mark
January 2020 6CCS3AIN
- Given the Bayesian network:
P
Q
R S T
Which variables are in the Markov blanket of S?
[2 marks]
A. P
B. Q
C. R
D. T
E. S
Answer
C, D.
Marking scheme
A. -
B. -
C. 1
D. 1
E. -
no negative overall mark
January 2020 6CCS3AIN
- Given the probability distribution P(U, V, W, X, Y ), and the query P (w|x, y),
which of the following are hidden variables:
[2 marks]
A. U
B. V
C. W
D. X
E. Y
Answer
A, B.
Marking scheme
A. 1
B. 1
C. -
D. -
E. -
no negative overall mark
January 2020 6CCS3AIN
- A variable X has values x 1 ,... , xn, and there is a probability distribution
P(X) over X. P(X) is such that:
[4 marks]
A. The maximum possible value of any P (xi) is 1.
B. There is at least one P (xi) with value 1.
C. If x 1 = 1, x 2 = 0, n = 2, then E[X] = P (X = x 1 )
D. For any P (xi) and P (xj ), P (xi) + P (xj ) = 1.
E. P (xi) cannot have the value 0.
Answer
A, C.
Marking scheme
A. 2
B. -
C. 2
D. -
E. -
no negative overall mark
January 2020 6CCS3AIN
- Use prior sampling to create an estimate of P (a, ¬b, c, ¬d) based on three
sampled events from the following network and its associated probabilities.
A B
C
D
P (a) = 0. 5
P (b) = 0. 4
P (c | a, b) = 0. 11
P (c | a, ¬b) = 0. 51
P (c | ¬a, b) = 0. 41
P (c | ¬a, ¬b) = 0. 61
P (d | c) = 0. 8
When generating sampled events, use the following list of random numbers
picked from a uniform distribution between 0 and 1:
1 2 3 4 5 6 7 8 9 10 11 12
random number 0 0 0 0 0 0 0 0 0 0 0 0.
[4 marks]
A. The first sample returns the event a, ¬b, c, ¬d.
B. The second sample returns the event a, ¬b, c, ¬d.
C. The third sample returns the event a, ¬b, c, ¬d.
D. It is impossible that any sample returns the event a, ¬b, c, ¬d.
E. None of the above.
Answer
E.
First sample:
- Since 0. 23 < P r(a), we have that A = T rue.
- Since 0. 5 ≥ P r(b), we have that B = F alse.
- Since 0. 5 < P r(c | a, ¬b), we have that C = T rue.
- Since 0. 2 < P r(d | c), we have that D = T rue.
- Hence, the first sample returns the event a, ¬b, c, d.
January 2020 6CCS3AIN
Second sample:
1. Since 0. 2 < P r(a), we have that A = T rue.
2. Since 0. 42 ≥ P r(b), we have that B = F alse.
3. Since 0. 3 < P r(c | a, ¬b), we have that C = T rue.
4. Since 0. 2 < P r(d | c), we have that D = T rue.
5. Hence, the first sample returns the event a, ¬b, c, d.
Third sample:
1. Since 0. 1 < P r(a), we have that A = T rue.
2. Since 0. 1 < P r(b), we have that B = T rue. This means we can the
sample will be a, b, C, D, so regardless of what C and D are, it will not
be the event a, ¬b, c, ¬d.
Marking scheme
A. -
B. -
C. -
D. -
E. 4
no negative overall mark
January 2020 6CCS3AIN
B. -
C. -
D. -
E. 4
no negative overall mark
January 2020 6CCS3AIN
- Consider n binary random variables X 1 , X 2 ,... Xn. Which of the following
statements are correct.
[4 marks]
A. There are distributions such that it is required to store Ω(2n) different
values.
B. There are cases where the joint distribution can be stored in o(n) space.
C. Assume n is even and you are promised that all Xi for i ≤ n/ 2 are
independent and identically distributed random variables. Then the joint
probability distribution P (X 1 , X 2 ,... , Xn) can always be stored using
O(n) space.
D. There always exists i, j such that Xi and Xj have the same distribution.
E. None of the above
Answer
A, B.
Marking scheme
A. 2
B. 2
C. -
D. -
E. -
no negative overall mark
