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# sol1 - CSCI 5512 Homework 1 Solutions Professor Arindam...

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CSCI 5512: Homework 1 Solutions Professor: Arindam Banerjee TA: Eric Theriault Spring 2010 Problem 1 Part a Explicitly sum P ( b | j, ¬ m ) = αP ( b ) X e P ( e ) X a P ( a | b,e ) P ( j | a ) P ( ¬ m | a ) = 0 . 0051 Part b P ( B,E | j,m ) = αP ( B,E,j,m ) = αP ( B ) P ( E ) X a P ( a | B,E ) P ( j | a ) P ( m | a ) = αf B ( B ) × f E ( E ) × f ¯ AJM ( B,E ) where f ¯ AJM ( B,E ) = X a f A ( a,B,E ) × f J ( j,a ) × f M ( m,a ) This should be a 2 × 2 matrix of values for all instantiations of B and E . Pointwise multi- plication with f B ( B ) and f E ( E ) yields another 2 × 2 matrix. This should be normalized to ﬁnd α , then take the element that corresponds to b and ¬ e . P ( b, ¬ e | j,m ) = 0 . 2836 1

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Problem 2 The burglary network can be factorized as follows: f B ( B ) = P ( B ) f E ( E ) = P ( E ) f A ( B,E,A ) = P ( A | B,E ) f J ( A,J ) = P ( J | A ) f M ( A,M ) = P ( M | A ) The following are the messages that are passed in the sum-product algorithm: μ f B B = f B ( B ) μ B f A = f B ( B ) μ f E E = f E ( E ) μ E f A = f E ( E ) μ J f J = 1
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sol1 - CSCI 5512 Homework 1 Solutions Professor Arindam...

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