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School of Computer Science
The University of Adelaide
Artificial Intelligence
Assignment 3
Semester 1, 2020
Due 11.59 pm, Monday 8 June 2020
Your task is to perform exact inference on a PGM and also manually conduct approximate
inference and compare the results. You only need to deal with one (small) network, but you
will need to compute the exact inference and also compute approximate inference manually
(i.e. generate random numbers, use these to generate samples, count the samples, etc). You
should submit a 2-3 page report of your working and findings.
More details are as below.
There is no need to code, but you will need to work through the algorithm(s) manually on
paper. The network below shows the conditional probability relationships between variables
S (Sick), P (Pub), H (Headache), L (Lecture) and D(Doctor) which capture conditional
probabilities relating whether or not a student has a Headache to whether they are Sick,
whether they went to the Pub last night, whether they go to the 9am Lecture or not and
whether they visit a Doctor.
Figure 1: A Bayes Net representing the conditional relationships between illness, lecture
attendance, pub and doctor visits.
The queries you must solve are:
P(Sick|Lecture=true, Doctor=true)
P(Sick|Doctor=false)
P(Pub|Lecture=false)
P(Pub|Lecture=false,Doctor=true)
You must produce exact results for the first two, and both exact and approximate results (by
sampling) for the third and fourth queries. You will need to conduct manual sampling by any
method you choose to generate the approximate results. For the exact results: Undergrads
can choose any exact inference method; Postgrads will be eligible for full marks only if the
exact results are generated using variable elimination.
To “implement" your manual sampling procedure you will need generate a set of random
samples. For example, for the first query you will need to generate 3 random true/false values
(for Sick, Headache and Pub) for each sample1
. You can do this by tossing a coin, but since
you'll have to generate 3 values for each sample, this could get dull and time-consuming.
Instead I suggest you visit a website such as https://www.random.org/integers/, generate a
list of integers between 0 and 100, and treat values greater than 50 as true and less than or
equal to 50 as false. For the first query, if you decide to generate 20 samples, you'll need 60
random values (3 per sample). For the second query you'll need 80 (4 per sample).
Submission and Assessment
You should submit a pdf report of maximum 2-3 pages via MyUni (Assigments). The report
should briefly describe the algorithm you have chosen to implement, provide your exact
working for each query and a table showing the results for each (hand-written equations and
tables will not be marked). I recommend you tabulate results for 10 samples and for 20
samples and compare these to the exact results. Marks will be allocated according to the
following rubric:
 Exact results and corresponding working: 30 marks
 Approximate inference results (with working): 40 marks
 Report coherence including description of approximate inference algorithm used: 30
marks
As noted above, Postgraduates are expected to use variable elimination to generate their
exact results. If a postgrad chooses not to use variable elimination they can achieve up to
15/30 on that component. Full marks will be awarded for complete and correct results, and a
coherent description of the sampling method used. If you present results in your report that
are inconsistent with the sampling method you have attempted, and you do not acknowledge
this in your report, you will automatically be given zero marks for the Assignment and referred