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1、AdvancedMachineLearningGraphicalModelsEricXingVisittoAsiaX1SmokingX2Lecture10,August12,2009TuberculosisX3LungCancerX4BronchitisX5TuberculosisXorCancer6XRayResultXDyspnea7X8Reading:EricXing©EricXing@CMU,2006-20091Whatisagraphicalmodel?---examplefrommedicaldiagnosticsòA
2、possibleworldforapatientwithlungproblem:VisittoAsiaXSmokingX12TuberculosisX3LungCancerX4BronchitisX5TuberculosisXorCancer6XRayResultX7DyspneaX8EricXing©EricXing@CMU,2006-200921RecapofBasicProb.ConceptsòRepresentation:whatisthejointprobabilitydist.onmultiplevariables?P
3、(X,X,X,X,X,X,X,X,)12345678ABòHowmanystateconfigurationsintotal?---28CDEòAretheyallneededtoberepresented?FòDowegetanyscientific/medicalinsight?GHòLearning:wheredowegetallthisprobabilities?òMaximal-likelihoodestimation?buthowmanydatadoweneed?òWheredoweputdomainknowledge
4、intermsofplausiblerelationshipsbetweenvariables,andplausiblevaluesoftheprobabilities?òInference:Ifnotallvariablesareobservable,howtocomputetheconditionaldistributionoflatentvariablesgivenevidence?6òComputingp(H
5、A)wouldrequiresummingoverall2configurationsoftheunobserve
6、dvariablesEricXing©EricXing@CMU,2006-20093DependenciesamongvariablesVisittoAsiaXSmokingX12PatientInformationTuberculosisX3LungCancerX4BronchitisX5MedicalDifficultiesTuberculosisXorCancer6XRayResultX7DyspneaX8DiagnosticTestsEricXing©EricXing@CMU,2006-200942Probabilisti
7、cGraphicalModels,con'dßIfXi'sareconditionallyindependent(asdescribedbyaPGM),thejointcanbefactoredtoaproductofsimplerterms,e.g.,VisittoAsiaX1SmokingX2P(X,X,X,X,X,X,X,X)12345678TuberculosisX3LungCancerX4BronchitisX5=P(X)P(X)P(X
8、X)P(X
9、X)P(X
10、X)Tuberculosis12314252XorCance
11、r6P(X
12、X,X)P(X
13、X)P(X
14、X,X)63476856XRayResultX7DyspneaX8ßWhywemayfavoraPGM?°Representationcost:howmanyprobabilitystatementsareneeded?2+2+4+4+4+8+4+8=36,an8-foldreductionfrom28!°Algorithmsforsystematicandefficientinference/learningcomputation•Exploringthegraphstructureand
15、probabilistic(e.g.,Bayesian,Markovian)semantics°Incorporationofdomainknowledgeandcausal(logical)structuresEricXing©EricXing@
