2023-24 Second Semester AI3043 Bayesian Networks
Assignment 2 Exact Inference: Variable Elimination
Due Date: 17/Apr/2024(Wed), before 11:59am, submitted to iSpace
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}
Figure 1: Bayesian network
- Write the chain rule for the joint distribution P (R, L, Q, T, S)
P (R, L, Q, T, S) = P (R) P (L | R) P (Q | R, L) P (T | R, L, Q) P (S | R, L, Q, T)
Note: You must use VE (variable elimination) method to solve these questions below! - What is the probability that there are many tourists?
- What is the probability that the quokkas are happy, given there are lots of quokka selfies being taken and it
is not raining. - Calculate P (r | l
c
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