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2023-24 Second Semester
AI3043 Bayesian Networks
Assignment 3
Due Date: 5/May/2024(Sun), before 10pm, submitted to iSpace
Part A: (40pts)
Question 1: What is a clique tree?
Answer:
Question 2:What properties does a clique tree have?
Answer:
Question 3: Is a clique tree directed or undirected?
Answer:
Question 4: Is a moral graph directed or undirected?
Answer:
Question 5: Discuss the difference between variable elimination method and clique tree method?
Answer:
Part B: (60pts) Consider the following Bayesian networks:
• R: it is raining or not, with binary values r: it is raining and r
c
: it is not raining. val(R) = {r, rc}
• L: there are juicy leaves or not, val(L) = {l, lc}
• Q: the quokkas are happy or unhappy, val(Q) = {q, qc}
• T: there are lots of tourist or not many, val(T) = {t, tc}
• S: people are taking lots of quokka selfies, or not. val(R) = {s, sc}
1. Construct a Clique tree T of this Bayesian network B:
(a) What is the moral graph of this Bayesian network B? Moralized this Bayesian network and triangulated
it if necessary.
(b) Draw a clique tree and assigned each clique with conditional probability distributions specified in
the orginal Bayesian network.
(c) Which clique would you like to chose as the pivot clique when constructing a clique tree.
2. Message collection:
(a) Add directions of message propagation towards your chosen pivot clique on your clique tree.
(b) Write down the message collecting functions from the leave cliques towards the pivot clique explicitly.
(Hint: find functions f1 and f2 associated with the edges.)
3. Message distribution
(a) Write down the message passing functions from pivot clique to the other cliques explicitly. (Hint: find
functions in the opposite directions of f1 and f2.)
4. Before we answer any query, we need to identify a clique which contains the query variable and then find the
message function h (potential) which is the joint distribution of all the variables in the clique.
(a) Suppose the pivot clique contains our query variable, write down the message function h of the pivot
clique.
(b) Normalize the potentials h.
In our next assignment 4, we will use the actually data to answer several specific queries such as those in your
assignment 1 and 2.
1
Figure 1: Bayesian network B
2
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