CMU CS 10708 - Homework (2 pages)

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Homework



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Homework

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Pages:
2
School:
Carnegie Mellon University
Course:
Cs 10708 - Probabilistic Graphical Models
Probabilistic Graphical Models Documents

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Probablistic Graphical Models Spring 2007 Homework 2 Due at the beginning of class on 10 17 07 Instructions There are six 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 10708f07 hw2 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 10708 07 instr cs cmu edu 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 class1 Refer to the web page for policies regarding collaboration due dates and extensions 1 20 pts Markov Networks We define the following properties for a set of conditional independencies Strong Union X Y Z X Y Z W In other words additional evidence cannot induce dependence Transitivity For all disjoint X Y Z and variable A X A Z A Y Z X Y Z Intuitively this statement asserts that if X are both correlated with A given Z then they are also correlated with each other given Z 1 Construct a simple BN G such that I G does not satisfy both of the above properties 2 Prove that if I H is the set of independencies of a Markov Network H then I H satisfies the above properties 3 Let Il H X X X NH X NH X X X where NH X is the set of neighbors of X in H be the set of local Markov independencies associated with H and Ip H X Y X X Y X Y H be the set of pairwise Markov independencies associated with H Prove the following assertion about Markov Networks Il H Ip H 1 Please contact Monica Hopes meh cs if you need a copy of a handout 1 2 10 pts Constructing Junction Tree To construct a Junction Tree from a chordal graph H we build an undirected graph whose



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