Probablistic Graphical Models, Spring 2007
Homework 3
Due at the beginning of class on 11/05/07
Instructions
There are ﬁve questions in this homework. The last question involves some programming which should be
done in MATLAB. Do
not
attach your code to the writeup. Make a tarball of your code and output, name
it
<
userid
>
.tgz where your userid is your CS or Andrew id, and copy it to /afs/cs/academic/class/10708
f07/hw3/
<
userid
>
.
If you are not submitting this from an SCS machine, you might need to authenticate yourself ﬁrst. See
http://www.cs.cmu.edu/
∼
help/afs/cross
realm.html
for instructions. If you are not a CMU student
and don’t have a CS or Andrew id, email your submission to [email protected]
You are allowed to use any of (and only) the material distributed in class for the homeworks. This includes
the slides and the handouts given in the class
1
. Refer to the web page for policies regarding collaboration,
due dates, and extensions.
1
[10 pts] Score Equivalence
Recall the deﬁnition of score equivalence covered in class. A scoring function is called scoreequivalent if
the score of two Iequivalent BNs( ie with set of independencies) is the same. A simple prior, called the
K2 prior, that can be used in the Bayesian score to score BNs is to take a ﬁxed Dirichlet distribution
Dirichlet
(
α,α,.
..,α
) (for this problem, assume
α
is 1) for every parameter.
Show that the Bayesian score with such a K2 prior is not score equivalent.
Hint: construct a data set for which the score of the network
X
→
Y
diﬀers from the score of
X
←
Y
.
2
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 Fall '07
 CarlosGustin
 Probability theory, Bayesian network, jb gjb, hj Wij xi, Harmonium Model

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