Berkeley COMPSCI 188 - Lecture 16: Bayes’ Nets III - D2873725

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Berkeley COMPSCI 188 - Lecture 16: Bayes’ Nets III

School name University of California, Berkeley

Course Compsci 188- Introduction to Artificial Intelligence

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CS 188: Artificial Intelligence Spring 2006TodayReachability (the Bayes’ Ball)ExampleSlide 6SummaryInferenceReminder: Alarm NetworkAtomic InferenceSlide 11Slide 12Slide 13Inference by EnumerationSlide 15Evaluation TreeVariable Elimination: IdeaBasic ObjectsBasic OperationsSlide 20Slide 21Slide 22General Variable EliminationSlide 24Slide 25CS 188: Artificial IntelligenceSpring 2006Lecture 16: Bayes’ Nets III3/16/2006Dan Klein – UC BerkeleyTodayLast time:Bayes netsConditional independenceToday:More conditional independenceInference to answer queriesReachability (the Bayes’ Ball)Correct algorithm:Start at source nodeTry to reach target by searchStates: node, along with previous arcSuccessor function:Unobserved nodes:To any childTo any parent if coming from a child (or start)Observed nodes:From parent to parentIf you can’t reach a node, it’s conditionally independent of the start nodeSX XSSX XSExampleRTBDLT’YesYesExampleVariables:R: RainingT: TrafficD: Roof dripsS: I’m sadQuestions:TSDRYesSummaryBayes nets compactly encode joint distributionsGuaranteed independencies of distributions can be deduced from BN graph structureThe Bayes’ ball algorithm (aka d-separation)A Bayes net may have other independencies that are not detectable until you inspect its specific distributionInferenceInference: calculating some statistic from a joint probability distributionExamples:Posterior marginal probability:Most likely explanation:RTBDLT’Reminder: Alarm NetworkAtomic InferenceGiven unlimited time, inference in BNs is easyRecipe:State the marginal probabilities you wantFigure out ALL the atomic probabilities you needCalculate and combine themExample:ExampleWhere did we use the BN structure?We didn’t!ExampleExampleNormalizeInference by EnumerationAtomic inference is extremely slow!Slightly clever way to save work:Move the sums as far right as possibleExample:ExampleEvaluation TreeView the nested sums as a computation tree:Still repeated work: calculate P(m | a) P(j | a) twice, etc.Variable Elimination: IdeaLots of redundant work in the computation tree!We can save time if we cache all partial resultsThis is the basic idea behind variable eliminationBasic ObjectsTrack objects called factorsInitial factors are local CPTsDuring elimination, create new factorsAnatomy of a factor:Variables introducedVariables summed outArgument variables, always non-evidence variables4 numbers, one for each value of D and EBasic OperationsFirst basic operation: join factorsCombining two factors:Just like a database joinBuild a factor over the union of the domainsExample:Basic OperationsSecond basic operation: marginalizationTake a factor and sum out a variableShrinks a factor to a smaller oneA projection operationExample:ExampleExampleGeneral Variable EliminationQuery:Start with initial factors:Local CPTs (but instantiated by evidence)While there are still hidden variables (not Q or evidence):Pick a hidden variable HJoin all factors mentioning HProject out HJoin all remaining factors and normalizeExampleChoose AExampleChoose

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