An Introduction to Artificial Intelligence Week 8

Course Name: An Introduction to Artificial Intelligence

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These are An Introduction to Artificial Intelligence Answers Week 8


For Question 1 to 3 –

image 30

Q1. Minimum number of values required to store the above Bayes net is

Answer: 12


Q2. Which of the following are true about the above bayesian network?
a. C is conditionally independent of D, given A.
b. C is conditionally independent of D, given E.
c. B is conditionally independent of A, given C.
d. B is conditionally independent of C, given A

Answer: a. C is conditionally independent of D, given A.


These are An Introduction to Artificial Intelligence Answers Week 8


Q3. Given C and D, E is independent of which of the following variables? (Select only one option)
a. A
b. B
c. Both A and B
d. Neither A nor B

Answer: c. Both A and B


Q4. Which of the following statements are true?
a. Bayesian network can be used to find the number of satisfying assignments for any Boolean formula
b. Inference in a Bayesian network always has exponential time complexity, irrespective of structure
c. Inference in a Bayesian network may be polynomial time for certain structures of the network
d. Cut sets can simplify inference in Bayesian networks

Answer: a, c, d


These are An Introduction to Artificial Intelligence Answers Week 8


Q5. Which of the following will always hold?
a. P(a,b) = P(a|b)P(b)
b. P(a,b|c) = P(a|c)P(b|c)
c. 1 = P(a|¬b) + P(a|b)
d. P(a,b|c) = P(b|c)P(a|b,c)

Answer: a, d


Q6. Consider the following Bayesian network along with the conditional probabilities given below. What is the value of P(C | D,E)? Give the answer as a decimal rounded to 2 decimal places (for example, 0.12 for 0.1234)

image 31

P(A) = 0.5, P(B) = 0.4, P(C| A,B) = 0.9, P(C| ¬A,B) = 0.5, P(C| A,¬B) = 0.2, P(C| ¬A,¬B) = 0.1, P(D | C) = 0.8, P(D| ¬C) = 0.2, P(E | C) = 0.1, P(E | ¬C) = 0.4.

Answer: 0.37


These are An Introduction to Artificial Intelligence Answers Week 8


Q7. In the above question, which are the evidence and hidden variables for the computation of P(C | D,E)? Return the answer as evidence variables followed by hidden variables separated by a %, where each group is lexicographically sorted (eg. if evidence is C and D and hidden variable is A, return CD%A).

Answer: DE%AB


Q8. Consider the following joint probability matrix. Each row contains a value for x and each column contains a value for y. What is the value of P(y=2|x=2)? Give the answer as a decimal rounded to 2 decimal places (for example, 0.12 for 0.123)

image 32

Answer: 0.29


These are An Introduction to Artificial Intelligence Answers Week 8


Q9. You toss a fair coin 3 times. Given that you observed at least one head, what is the probability that you observed at least 2 heads? If the answer is expressed as m/n where m and n are coprime, give the answer as m+n.

Answer: 11


Q10. Which of the following statements are correct?
a. There exists a unique Bayesian network for every joint probability distribution.
b. Multiple valid Bayesian networks can be constructed to represent the same joint probability distributions.
c. Two variables in a bayesian network are conditionally independent if and only if they are d-separated.
d. Bayesian network structures are required to be directed acyclic graphs.

Answer: b, d


These are An Introduction to Artificial Intelligence Answers Week 8



These are An Introduction to Artificial Intelligence Answers Week 8

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These are An Introduction to Artificial Intelligence Answers Week 8
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