# Lecture16HO - CS440/ECE448 Intro to Articial Intelligence...

This preview shows pages 1–5. Sign up to view the full content.

Lecture 16 Exact inference in Bayes Nets Prof. Julia Hockenmaier [email protected] http://cs.illinois.edu/fa11/cs440 CS440/ECE448: Intro to ArtiFcial Intelligence Grades…. Your midterm percentages Your MP percentages 4 CS440/ECE448: Intro AI

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
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
¬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

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
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
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 8

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

This preview shows document pages 1 - 5. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online