11 Uncertainty - CSCI 5582 Fall 2006 Artificial I...

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Unformatted text preview: CSCI 5582 Fall 2006 Artificial I ntelligence Lecture 14 Jim Martin CSCI 5582 Fall 2006 Review basics More on independence Break Bayesian Belief Nets CSCI 5582 Fall 2006 Review Joint Distributions Atomic Events I ndependence assumptions CSCI 5582 Fall 2006 Review: Joint Distribution Toothache=True Toothache=False Cavity True 0.04 0.06 Cavity False 0.01 0.89 Each cell represents a conjunction of the variables in the model . CSCI 5582 Fall 2006 Atomic Events The entries in the table represent the probabilities of atomic events Events where the values of all the variables are specified CSCI 5582 Fall 2006 I ndependence Two variables A and B are independent iff P(A| B) = P(A). I n other words, knowing B gives you no information about B. Or P(A^ B)=P(A| B)P(B)=P(A)P(B) I .e. Two coin tosses CSCI 5582 Fall 2006 Mental Exercise With a fair coin which of the following two sequences is more likely? HHHHHTTTTT HTTHHHTHTT CSCI 5582 Fall 2006 Conditional I ndependence Consider the dentist problem with 3 variables: cavity, toothache, catch I f I have a cavity, then the chances that there will be a catch is independent of whether or not I have a toothache as well. I .e. P(Catch| Cavity^ Toothache)= P(Catch| Cavity) CSCI 5582 Fall 2006 Conditional I ndependence Remember that having the joint distribution over N variables allows you to answer all the questions involving those variables. Exploiting conditional independence allows us to represent the complete joint distribution with fewer entries. I .e. Fewer than the 2 N normally needed CSCI 5582 Fall 2006 Conditional I ndependence P(Cavity,Catch,Toothache) = P(Cavity)P(Catch,Toothache| Cavity) = P(Cavity)P(Catch| Cavity)P(Toothache| Cavity) CSCI 5582 Fall 2006 Conditional I ndependence P(Cavity,Catch,Toothache) = P(Catch)P(Cavity,Toothache| Catch) CSCI 5582 Fall 2006...
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11 Uncertainty - CSCI 5582 Fall 2006 Artificial I...

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