ps4 - CS221 Problem Set #4 1 CS 221, Autumn 2007 Problem...

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CS221 Problem Set #4 1 CS 221, Autumn 2007 Problem Set #4 — Bayes Nets and Perception Due by 9:30am on Tuesday, December 4. Please see the course information page on the class website for late homework submission instructions. SCPD students can also fax their solutions to (650) 725-1449 with a Flled out route form 1 as the cover page. We will not accept solutions by email or courier. 1 Written part (80 points) NOTE: These questions require thought, but do not require long answers. Please try to be as concise as possible. 1. [18 points] Inference in Bayesian Networks Consider the following belief network: A B C D F E G (a) [6 points] Consider the query P ( G ) and the elimination ordering A,B,C,D,E,F (where we are eliminating A Frst, not last). Show what the variable elimination algorithm will do on this graph by Flling in the following table: var eliminated factors used factor generated A f 1 ( A ) ,f 2 ( A,B,C ) f 3 ( B,C ) B C D E ± 1 Available from http://scpd.stanford.edu/scpd/students/routing.htm
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CS221 Problem Set #4 2 Note: your generated factors should be written in the form f i ( X 1 ,...,X ) for some set of variables X 1 ,...,X . The Frst row has been Flled out for you. (b) [6 points] Show that the elimination ordering matters to the complexity of the in- ference process. SpeciFcally, assume that all variables have the same domain size m > 2, and Fnd a di±erent elimination ordering for the same query whose complexity is asymptotically di±erent as a function of m . Show the behavior of the algorithm on this ordering in the following table: var eliminated factors used factor generated (c) [6 points] Now, consider the general case. Sketch a simple BN over n random variables where there is one elimination ordering for some query P ( X ) that achieves performance which is linear in n , and another elimination ordering for the same query whose performance is exponential in n . 2.
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ps4 - CS221 Problem Set #4 1 CS 221, Autumn 2007 Problem...

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