[SOLVED] Coms 573 machine learning problem set 4

1. (15 pts.) Consider the following Bayesian network
Visit to Asia?
(A)
Smoker?
(S)
Tuberculosis?
(T)
Lung Cancer?
(C)
Bronchitis?
(B)
Tuberculosis or Cancer?
(P)
Positive X-Ray?
(X)
Dyspnoea?
(D)
(a) (12 pts.) True or false? Please explain.
i. dsep(T, ∅, B)
ii. dsep(A, {D, C}, B)
iii. dsep(A, P, {X, D})
iv. dsep({A, X}, {P, S}, {C, D})
(b) (3 pts.) Express P(a, s, t, c, p, b, x, d) in factored form (the chain rule for BNs).2. (10 pts.) Give all the DAGs which are independence (d-separation) equivalent to the above
DAG.3. (20 pts.) Jack has three coins C1, C2, and C3 with p1, p2, and p3 as their corresponding
probabilities of landing heads. Jack flips coin C1 twice and then decides, based on the
outcomes, whether to flip coin C2 or C3 next: if the two C1 flips come out the same, Jack
flips coin C2 three times; if the two C1 flips come out different, Jack flips coin C3 three times.Given the outcome of Jack’s last three flips as: tail, head, tail, we want to know whether
his first two flips came out the same. Describe a Bayesian network and a corresponding
probabilistic query that answers this question. (You are NOT required to compute the query.)