EXAMINATION
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DEPARTMENT OF COMPUTER SCIENCE
EXAMINATION
CM50263: Artificial INTELLIGENCE
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This exam is an individual assessment.
CM
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Instructions
This exam consists of 16 multiple choice questions and 1 essay question. Some multiple choice questions are worth 3 marks, some are worth 6 marks. The essay question is worth 25 marks. The total amount of marks available is 100. Please note that for the multiple choice questions, there may be more than one correct choice. An example question is below (this question will not count).
Which of the following is an even number? (Mark all choices that could apply)
(a) 0
(b) 1
(c) 2
(d) 3
(e) 10
(f) None of the above.
Notice that there is more than one correct choice in this question and that the question asks you to mark all choices that could apply.
To receive credit for a question, you need to mark all correct choices and none of the incorrect choices. For example, to receive credit on the sample question above, you would need to mark (a), (c), (e), and nothing else. Partial credit is not available.
If the question explicitly asks you to choose only one answer , please do so. In such cases, if you mark more than one choice, you will receive 0 marks for the question.
You must show some working for each question and submit this in a PDF file. Failure to do so will result in receiving 0 marks for each question with no working.
It is to your advantage to answer all questions because it is not possible to get negative marks for a question.
Please enter your answers into the template CSV file provided. At the end of the exam, upload a ZIP file containing two files:
**1. The completed answer sheet. (1 CSV file)
- Your working for all questions, and your submission for the essay question.** (1 PDF file)
Do not forget to enter your candidate number.
CM
Uninformed Search
Consider a search tree with constant branching factor b. We know that the shallowest solution can be found at depth 3, and that the maximum depth of a node is 4. Assume that we have a maximum allowed space complexity of 100, and no limit to our time complexity. What is the maximum value ofbsuch that we can gurantee we will find a solution:
- using a breadth-first search? Select exactly one answer.
(a) 2
(b) 3
(c) 4
(d) 5
(e) 10
(f) 25
(g) 33
(h) 100
[3]
- using a depth-first search? Select exactly one answer.
(a) 2
(b) 3
(c) 4
(d) 5
(e) 10
(f) 25
(g) 33
(h) 100
[3]
Informed Search
Consider the search space below, in which a consistent heuristic is given for each state. The initial state is the leftmost state, and the single goal state is the rightmost state.
- We perform one greedy best-first search, and one A* search. If our Algorithm leaves us with a choice of which state to add to the frontier, we choose one at random. Letabe the total path cost of the path found by the greedy best-first search, andbthe total path cost of the path found by the A* search. What are the possible values ofab?
(a) 0
(b) 1
(c) 2
(d) 3
(e) 4
(f) 5
[6]
- A successor state of a statesis a state that can be reached in one action froms. Let minsuc(s)be defined as the minimum cost of an action from any successor state ofs. Consider the following heuristic on an arbitrary search space:
h(s) =
{
0 ifsor any successor state ofsis a goal state
minsuc(s) otherwise
Which of the following statements are true? Select exactly one answer.
(a) his always an admissible and consistent heuristic.
(b) his sometimes not consistent, but is always an admissible heuristic.
(c) his sometimes not consistent and sometimes not admissible.
(d) his sometimes admissible but never consistent.
(e) his never admissible or consistent.
[6]
Adversarial Search
Consider the minimax game below, where maximizer takes the first turn, followed by minimizer, and then finally maximizer. The utility values of the terminal nodes is given in the circle.
- What is the value of this game? Select exactly one answer.
(a) 2
(b) 3
(c) 4
(d) 5
(e) 7
(f) 8
(g) 9
[3]
- We apply alpha-beta pruning, exploring nodes from left to right. How many terminal nodes can be pruned?
(a) 0
(b) 1
(c) 2
(d) 3
(e) 4
(f) 5
(g) 6
(h) 7
(i) 8
[3]
Propositional Logic
Consider the following knowledge base, consisting of six sentences:
KB ={A 1 =PQ, A 2 =P, A 3 =QR, A 4 =PS, A 5 =R, A 6 =SR}
- Let KB 1 be the knowledge base obtained by removingA 1 from KB , KB 2 the knowledge base obtained by removingA 2 from KB , and so on. From which knowledge bases can the empty clause be derived using resolution?
(a) KB 1
(b) KB 2
(c) KB 3
(d) KB 4
(e) KB 5
(f) KB 6
[6]
Predicate Logic
Consider the Wumpus World below, taken from the Russell and Norvig textbook.
- Consider each of the predicate logic sentences below. Which are true in the Wumpus model above, given the standard interpretation? N.B.Square 2 , 3 refers to the square with the gold in it.
(a) W umpus(Square 2 , 2 )
(b) x(Gold(x)P it(x))
(c) xy(W umpus(x)W umpus(y))
(d) xy(P it(x)(Adjacent(x, y)Breeze(y))
(e) xy(W umpus(y)((Adjacent(x, y)Stench(x))
[6]
Probabilistic Reasoning
- A supermarket recalls a food product that has been contaminated with a bacteria which causes food poisoning. Out of all items of this product, 1% are known to have been contaminated (C). Of those people who have ingested the contaminated product, 80% show symptom X, 50% show symptom Y and 30% show symptom Z. Furthermore, each symptom occasionally appears in people who have not ingested the contaminated product; in this case 5% show symptom X, 10% show symptom Y and 0.1% show symptom Z. The presence of symptoms X, Y and Z are conditionally independent given whether or not the food is contaminated. The Bayes network shown below expresses this information.
C
P(c) = 0. 01
X
P(x|c) = 0. 8
P(x|c) = 0. 05
Y
P(y|c) = 0. 5
P(y|c) = 0. 1
Z
P(z|c) = 0. 3
P(z|c) = 0. 001
Someone ate the recalled food product and developed symptoms X and Y, but not
symptom Z. What is the probability that they ate one of the contaminated items? Choose
the answer which is closest to your calculated value. Select exactly one answer.
(a) 0. 28
(b) 0. 36
(c) 0. 43
(d) 0. 53
(e) 0. 68
[6]
- Consider the following Bayes network where the only independence assumptions between the variables A to F are those enforced by the shape of the network.
D
A B
C
E
F
Which of the following statements are true? Select all that apply.
(a) A is independent of B.
(b) A is conditionally independent of B given E.
(c) A is conditionally independent of F given E.
(d) C is independent of D.
(e) C is conditionally independent of D given A.
(f) C is conditionally independent of D given F.
[6]
Supervised Learning
- You are training ak -nearest neighbours (minimum Euclidean distance) classifier with k= 1on the following labelled dataset:
Class 1:
{[
1
0. 5
]
,
[
2
1
]
,
[
2
0. 5
]}
Class 2:
{[
0. 5
1
]
,
[
1
0. 5
]}
What is the leave-one-out cross validation error of the classifier on the training dataset?
Select exactly one answer.
(a) 1/
(b) 2/
(c) 3/
(d) 4/
(e) 5/
[6]
- An experiment is conducted with a potentially biased coin. Each flip of this coin is independent. Within an individual trial of the experiment the coin is flipped in sequence, and the number of the flip in which the first head appears is recorded. For example, if a trial saw the coin first land tails, and then heads, the value recorded would be 2. The outcome of each trial is a random variable X modelled by a geometric probability distribution, where P(X = x) = (1)x^1 for an unknown parameter (0,1] corresponding to the probability an individual coin flip lands heads. 10 samples are collected for the experiment, and the data obtained is given in Table 1 below.
First head on coin flip 1 2 3 4
Number of samples 3 3 3 1
Table 1: Experiment data
Find the maximum likelihood estimation for . That is, find the value of which
maximises the probability of observing the data.
Choose the answer which is closest to your calculated value. Select exactly one answer.
(a) 0.
(b) 0.
(c) 0.
(d) 0.
(e) 0.
[6]
Markov Decision Processes and Reinforcement Learning
This part is related to the Questions 13,14, and 15. Consider the Markov Decision Process (MDP) given in the figure below. Actions are represented by black dots. The pair of numbers beside each arrow indicate the transition probabilities (the left number) under an action and the rewards (the right number) received when the agent goes to a state. Assume a discount factor of= 0. 95 for questions 13, 14, and 15.
- How many distinct deterministic policies are there in this MDP? Select exactly one answer.
(a) 1
(b) 2
(c) 4
(d) 8
(e) 16
[3]
- What is the value of the optimal policy at state S3? Select exactly one answer.
(a) 5
(b) 40
(c) 80
(d) 100
(e) 120
[3]
- What is the value of the optimal policy at state S0? Select exactly one answer.
(a) 2
(b) 4.
(c) 36.
(d) 72.
(e) 96.
[3]
- We can represent the state visited and reward obtained by a decision process as a probability distribution: P(st+1, rt+1|s 0 , a 0 , r 1 ,… , rt, st, at), (1) where s 0 is the initial state, a 0 is the first action selected, r 1 is the first reward received, stis the state at timet, atis the action selected at timet, and rtis the reward at timet.
Which of the following statements are true? Select all that apply.
(a) A Markov Decision Process (MDP) may have infinite state and action spaces.
(b) Reinforcement learning requires the environment to be an MDP.
(c) There can be more than one optimal policy for an MDP.
(d) There can be more than one optimal value function for an MDP.
(e) Q-learning requires that the values of (1) above are known.
(f) An MDP requires that (1) above is equivalent to P(st+1, rt+1|st, at).
[6]
The essay question: critical evaluation of an AI application
- You were asked to read the following 3 papers in advance of coming to this exam:
- Silver, David, et al. Mastering the game of Go with deep Machine learning 人工智能”> Neural Networks and tree search. nature 529.7587 (2016): 484-489.
- Senior, Andrew W., et al. Improved protein structure prediction using potentials from deep learning. Nature 577.7792 (2020): 706-710.
- Brown, Tom B., et al. Language models are few-shot learners. arXiv preprint arXiv:2005.14165 (2020).
Select one of these papers, indicate its title in your answer and write an essay of about
one page comprising:
- one paragraph summarising the papers contributions and motivations,
- one paragraph giving a high-level overview of the methodology or techniques covered in the paper
- one or two paragraphs giving your critical assessment of the research contributions and AI applications discussed, informed by aspects such as the related work and conclusions. The following marking criteria are applied: The essay is worth 25 marks with an in-principle distribution of 6/6/13 for the three parts. Your essay will be assessed based on the accuracy and clarity of your statements. In addition, your essay will be assessed based on the breadth and depth of your evaluation, and how well you support your arguments. Note: Breadth relates to the variety of issues that you touch upon. Depth relates to how thoughtful and penetrating your comments are. [25]
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