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Lecture17HO - *\$*\$:\$:\$ CS440/ECE448 Intro to Articial...

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Lecture 17: More on exact inference in Bayes Nets Prof. Julia Hockenmaier [email protected] http://cs.illinois.edu/fa11/cs440 CS440/ECE448: Intro to Artificial Intelligence 2 CS440/ECE448: Intro AI Intelligence Grade SAT Letter Difficulty !"#\$%& !"#\$() *\$%& +,-. +,+. *\$() +,/ +,0 1\$2 1\$3 4\$" +,5 +,- 4\$6 +,7 +,8 4\$9 +,-- +,+5 :\$%& :\$() +,8 +,7 4\$" 4\$6 4\$9 *\$%&;:\$%& +,< +,7 +,< *\$%&;:\$() +,+. +,/. +,= *\$(); :\$%& +,- +,+0 +,+/ *\$()%;:\$() +,. +,< +,/ *\$%& *\$() +,= +,< 3 CS440/ECE448: Intro AI Intelligence Grade SAT Letter Difficulty What is the probability of getting a strong letter if you are an intelligent student? 1\$2 1\$3 4\$" +,5 +,- 4\$6 +,7 +,8 4\$9 +,-- +,+5 :\$%& :\$() +,8 +,7 4\$" 4\$6 4\$9 *\$%&;:\$%& +,< +,7 +,< *\$%&;:\$() +,+. +,/. +,= *\$(); :\$%& +,- +,+0 +,+/ *\$()%;:\$() +,. +,< +,/ Review: inference in Bayes Nets What is the probability of getting a strong letter if you are an intelligent student? We want to compute the probability of a set of query variables X (= the letter) given an event e (= being intelligent) An event = an assignment of values to a set of evidence variables E (= intelligence) 4 CS440/ECE448: Intro AI P ( X = x | e ) = P ( X = x | e ) P ( e )

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Review: conditional probability P ( Y ) can be computed by marginalization: If we can compute P ( X,Y ) , we can also compute P ( X | Y ) 5 CS440/ECE448: Intro AI P ( X | Y ) = P ( X , Y ) P ( Y ) P ( Y = y ) = P ( X = x , Y = y ) x ! Computing inferences in Bayes Nets What is the probability of getting a strong letter if you are an intelligent student?
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Lecture17HO - *\$*\$:\$:\$ CS440/ECE448 Intro to Articial...

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