Description
You may complete this homework assignment either individually or in teams up to 2 people.
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Inference in probabilistic graphical models [15 points]: Consider the probabilistic graphical model for a (somewhat facetious/futuristic) medical diagnostic domain1 shown below. This graph could be used to diagnose whether a patient is su ering from a mere common cold (C) and/or the more dangerous Martian Death Flu (M), based on the patient’s symptoms { whether or not the patient has a runny nose (R), whether or not the patient has a headache (H), and whether or not the patient occasionally spontaneously bursts into ames (S) { as well as relevant background information, namely whether or not he or she has previously visited Mars (V ).
V
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M
R H S
The probability tables for this model are shown below:
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P (R j C; M)
P (M j V )
C
M
R = 0
R = 1
P(V )
P(C)
V=0 V=1
C=0 C=1
V
M=0 M=1
0
0
0:95
0:05
0
1:0
0:0
0
1
0:50
0:50
0:9999 0:0001
0:950:05
1
0:001
0:999
1
0
0:10
0:90
1
1
0:02
0:98
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P (C = 1 j R = 1; H = 1; M = 0), i.e., if the patient has a runny nose and a headache but does not have Martian Death Flu, then what’s the probability that they have a common cold?
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P (M = 1 j H = 1; C = 0), i.e., if the patient has a headache but not a common cold, then what’s the probability that they have Martian Death Flu?
There is no code you need to submit. Just submit your derivations, calculations, and nal answers in a PDF (homework7 WPIUSERNAME1.pdf
or homework7 WPIUSERNAME1 WPIUSERNAME2.pdf for teams).
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