Probablistic Graphical Models, Spring 2007
Homework 1
Due at the beginning of class on 10/08/07
Instructions
There are six questions in this homework. The last question involves 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
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>
.tgz where your userid is your CS or Andrew id, and copy it to /afs/cs/academic/class/10708
f07/hw1/
<
userid
>
.
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for instructions. If you are not a CMU student
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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
[6 pts] Representation
Consider N+1 binary random variables
X
1
...X
N
,Y
that have the following conditional independencies:
∀
i,j
,
X
i
⊥
X
j

Y
1. Suppose you wish to store the joint probability distribution of these N+1 variables as a single table.
How many parameters will you need, to represent this table?
2. Draw a graphical model over these N+1 variables that encodes the conditional independencies above.
How many parameters will you need to completely describe the distribution using this representation?
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 Fall '07
 CarlosGustin
 Probability theory, probability density function, Cecilia, Bayesian network, graphical model, Belief propagation

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