hw4-v2 - Probablistic Graphical Models Spring 2007 Homework...

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Homework 4 Due at the beginning of class on 11/26/07 Instructions There are four 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/hw4/ < 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 [20 pts]Importance Sampling sampler is defined w ( x ) = P ( x ) / Q ( x ) where P is the distribution we want to sample from and Q is a proposal distribu- tion. 1. Why is computing the probability of a complete instantiation of the variables in a Markov Random Field com- putationally intractable? 2. Given a chordal graph, describe how to compute the likelihood weighting for an importance sampler( Hint:What is the relationship between chordal graphs and junction trees? ) 3. Given a non-chordal graph, describe how to compute the likelihood weighting for an importance sampler. 4. Briefly comment on why it is not useful to use importance sampling for approximate inference on MRFs. 2 [20 pts] BP in sigmoid networks Consider a three-layer sigmoid network ( X 1 ,... X n , Y 1 ,..., Y n , Z 1 ... Z n ). All the variables are binary; the variables X 1 ,... X n in the top layer are all independent of each other; the variables in the second and third layers depend on the variables in their previous layer CPT: P ( y j | x 1 ... x n ) = sigmoid ( i w 1 i , j x i + w 1 0 , j ) P ( z j | y 1 ... y n ) = sigmoid ( i w 2 i , j y i + w 2 0 , j ) where sigmoid ( x ) = 1 / ( 1 + exp t ) . 1
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This note was uploaded on 05/25/2008 for the course MACHINE LE 10708 taught by Professor Carlosgustin during the Fall '07 term at Carnegie Mellon.

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hw4-v2 - Probablistic Graphical Models Spring 2007 Homework...

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