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Unformatted text preview: 1 Introduction to Probabilistic Graphical Models December 26, 2006 Problem set 4  Solutions Lecturer: Eran Segal 1. (a) This can be done by summing out the variables that we wish to remove and incorpo rating their effects into the leak noise parameter. The important thing to see here is that the summing out can be done efficiently. P ( F i = f i , D 1 , ..., D ‘ ) = X D ‘ +1 ,...,D k P ( F i = f i , D 1 . . . D k ) = X D ‘ +1 ,...,D k P ( F i = f i  D 1 ...D k ) · P ( D 1 . . . D k ) = X D ‘ +1 ,...,D k P ( F i = f i  D 1 ...D k ) · k Y i =1 P ( D i ) = X D ‘ +1 ,...,D k (1 λ ) k Y j =1 (1 λ j ) d j · k Y i =1 P ( D i ) = (1 λ ) ‘ Y j =1 (1 λ j ) d j P ( D j ) X D ‘ +1 ,...,D k k Y i = ‘ +1 (1 λ i ) d i · P ( D i ) For each D i where i > ‘ the term in parentheses can be simplified as follows: (1 λ i ) P ( D i = 1) + P ( D i = 0) = 1 λ i P ( D i = 1) And so the entire term in parentheses can be written as: k Y i = ‘ +1 (1 λ i P ( D i = 1)) We will denote this term as A ....
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This note was uploaded on 02/05/2010 for the course CS CS229 taught by Professor Eransegal during the Fall '07 term at École Normale Supérieure.
 Fall '07
 EranSegal

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