Lecture16HO - CS440/ECE448: Intro to Articial Intelligence!...

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Lecture 16 Exact inference in Bayes Nets Prof. Julia Hockenmaier juliahmr@illinois.edu http://cs.illinois.edu/fa11/cs440 CS440/ECE448: Intro to ArtiFcial Intelligence Grades…. Your midterm percentages Your MP percentages 4 CS440/ECE448: Intro AI
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Your Quiz totals 5 CS440/ECE448: Intro AI Your current and predicted fnal grades Probability review 7 CS440/ECE448: Intro AI ¬Square Atomic events Boolean random variable Square 8 CS440/ECE448: Intro AI Square red yellow blue Categorical random variable Color
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¬Square Complex events 9 CS440/ECE448: Intro AI Square Joint probability P(A,B) P(A ! B) = P(A, B) If A and B are boolean variables: P(A,B) = P(A B) 10 CS440/ECE448: Intro AI B A A ˬ B Conditional probability P(A|B) Defnition: Product rule P(A,B) = P(A | B)P(B) 11 CS440/ECE448: Intro AI P(A | B) = P(A,B) P(B) B A A ˬ B The Full joint distribution From the full joint distribution, we can obtain: Conditional distributions P(Fun? | Weather) Marginal distributions P(Weather) 12 CS440/ECE448: Intro AI Weather Sunny Cloudy Rainy Snowy Fun? Yes 0.25 0.15 0.05 0.13 No 0.05 0.1 0.25 0.02
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Independence Random variables X and Y are independent ( X ˵ Y) if P(X,Y) = P(X) ! P(Y) NB.: Since X and Y are R.V.s (not individual events), P(X,Y) = P(X) " P(Y) is an abbreviation for: ˲ x ˲ y P(X=x,Y=y) =P(X=x) " P(Y=y) X and Y are conditionally independent given Z ( X ˵ Y | Z) if P(X,Y | Z) = P(X | Z ) ! P(Y | Z) 13 CS440/ECE448: Intro AI Conditional Independence X and Y are conditionally independent given Z ( X ˵ Y | Z) if
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Lecture16HO - CS440/ECE448: Intro to Articial Intelligence!...

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