1. Draw a graphical model over
C
1
...C
N
, O
1
...O
N
that satisﬁes the conditional inde
pendencies listed above.
2. Implement sumproduct and maxproduct algorithms in MATLAB for this graphical
model.
3. We has made 20 observation of the weather over the last few months (i.e.,
O
1
...O
N
) :
{
R,F,F,H,F,H,H,H,H,H,H,H,H,R,H,H,H,R,H,H
}
Some of the values for the conditional probability table (CPT) are as follows.
P
(
C
1) :
S
M
A
W
0.15
0.6
0.2
0.05
S
M
A
W
S
0.8
0.17
0.02
0.01
M
0.1
0.7
0.19
0.01
A
0.02
0.05
0.7
0.23
W
0.2
0.01
0.04
0.7
Table 1:
P
(
C
t
+1
=
j

C
t
=
i
) for all
t
≥
1 (i:row, j:column)
H
R
F
S
0.4
0.3
0.3
M
0.5
0.45
0.05
A
0.3
0.4
0.3
W
0.0001
0.2499
0.75
Table 2:
P
(
O
t
=
j

C
t
=
i
)
For inference, apply both sum–product and max–product algorithms to the following
problems. Submit all of your codes (zipped as ’hw3BP.zip’) and report the results.
(a) Compute the probability of (
S,M,A,W
) for each of all 20 observations
(e.g.,
∀
t,P
(
C
t
=
M

O
1
...O
N
)). Save the result of (4
×
20) probability matrix as
”gamma.txt”, and draw it into a ﬁgure as ”gamma.png” (xaxis: 20 time steps,
yaxis: probability). Submit the ’gamma.txt’ and ’ ’gamma.png’.
4
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View Full Document(b) Determine the most likely sequence of
C
1
...C
N
that generated this observed
sequence.
5
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 Spring '13
 Dr. Zare
 Dynamic Programming, Probability, Probability theory, Bayesian network, graphical model, Chordal graph

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