CS228 Problem Set #2
1
CS 228, Winter 20112012
Problem Set #2
This assignment is due at 12 noon on Feburary 6. Submissions should be placed
in the ﬁling cabinet labeled CS228 Homework Submission Box located in the lobby
outside Gates 187
.
Suppose we wish to perform exact inference over a chain Markov Random Field given by
X
1

X
2
 ··· 
X
n
. We construct a clique tree of the form
C
1
 ··· 
C
n

1
where
Scope
[
C
i
] =
{
X
i
,X
i
+1
}
, and calibrate it, resulting in a calibrated clique tree
T
over unnormalized factors
F
.
Assume that each variable
X
i
has

V
al
(
X
i
)

=
d
.
a)
[5 points]
Describe how to compute the marginal of a single variable,
P
Φ
(
X
i
) for a given
X
i
using the calibrated clique tree. What is the running time cost of this operation? Does
the result depend on which clique we use to extract the marginal from? Why?
Now, consider the problem of answering a query
P
(
X
1
,X
3
) in our calibrated clique tree. We
cannot extract this marginal from any clique in
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Winter '09
 Dynamic Programming, Computational complexity theory, Markov random field, clique tree

Click to edit the document details