((Hint : Consider all active trails,
⟨
X
1
⇌
X
2
· · ·
⇌
X
n
⟩
that go through Alarm, make
sure that there still an active trail under the same conditions – i.e. observed variables–
between
X
1
and
X
n
in the marginalized network.)
3
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Figure 3: Burglar Alarm Network
2. Generalize the procedure you used to solve the above into a nodeelimination algorithm.
That is, define an algorithm that transforms the structure of
G
into
G
′
such that one
of the nodes
X
l
of
G
is not in
G
′
and
G
′
is an I–map of the marginal distribution over
the remaining variables as defined by
G
.
(Hint: Consider the relationship between the variables you added edges to in part 1
and the node being marginalized. Now, can you devise a set of generic rules over these
affected variables?
It would be helpful to think about different local configurations
around
X
l
)
4
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 Spring '13
 Dr.ZAre
 Probability theory, pts, 3 pts, 4 pts, graphical model

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