Introduction
Bayesiannetwork,alsoknownasbeliefnetwork,isanextensionofBayesianmethodandiscurrentlyoneofthemosteffectivetheoreticalmodelsinthefieldofuncertainknowledgeexpressionandreasoning.SinceitwasproposedbyPearlin1988,ithasbecomearesearchhotspotinrecentyears.ABayesiannetworkisaDirectedAcyclicGraph(DAG),whichiscomposedofnodesrepresentingvariablesanddirectededgesconnectingthesenodes.Nodesrepresentrandomvariables,andthedirectededgesbetweennodesrepresentthemutualrelationshipbetweennodes(fromtheparentnodetoitschildnodes).Conditionalprobabilityisusedtoexpressthestrengthoftherelationship.Ifthereisnoparentnode,thepriorprobabilityisused.Informationexpression.Thenodevariablecanbeanabstractionofanyproblem,suchas:testvalue,observationphenomenon,opinionconsultation,etc.Itissuitableforexpressingandanalyzinguncertainandprobabilisticevents,appliedtodecision-makingthatconditionallyreliesonmultiplecontrolfactors,andcanmakeinferencesfromincomplete,inaccurateoruncertainknowledgeorinformation.
Matemaattinen määritelmä
Olkoon G=(I,E)Suunnattu syklinen kuva( DAG), jossaI edustaa graafin kaikkia solmuja ja E edustaa suunnattujen yhdistävien rivisegmenttien joukkoa, ja OlkoonX=(X i)i∈Ion satunnainen muuttuja, jota esittää anodi< i>isuunnassaan syklisessä kuvassa,JossolmunXyhteistodennäköisyysjakauma voidaan ilmaista seuraavasti:
SittenX kutsutaan Bayesianne-verkoksisuhteelliseksiohjautuvaan sykliseen kuvaanG, joka edustaa solmua"syy".
Foranyrandomvariable,thejointdistributioncanbeobtainedbymultiplyingtherespectivelocalconditionalprobabilitydistributions:
Accordingtotheaboveformula,wecancombinethejointdistributionofaBayesiannetworkTheprobabilitydistributioniswrittenas:
(Foreach"riippuvainen"muuttujaXjsuhteessa X:ääni)
Thedifferencebetweentheabovetwoexpressionsliesinthepartoftheconditionalprobability.IntheBayesiannetwork,ifthe"dependent"variableisknown,somenodeswillbeconditionallyindependentfromthe"dependent"variable,andonlyrelatedtothe"dependent"variable.Onlythenodeoftheconditionalprobabilityexists.
Ifthenumberofdependenciesofthejointdistributionisveryrare,usingtheBayesianfunctionmethodcansaveconsiderablememorycapacity.Forexample,ifyouwanttostore10variableswhosevaluesareall0or1asaconditionalprobabilitytabletype,anintuitiveideaknowsthatwehavetocalculateatotalofvalues;butifthereisnocorrelationamongthese10variables."Ifthe“dependent”variableismorethanthreeormore,thentheconditionalprobabilitytableoftheBayesiannetworkonlyneedstocalculateatmostonevalue.AnotheradvantageoftheBayesianInternetisthatitiseasierforhumanstoknowwhetherthevariablesareconditionallyindependentordependentandthetypeoflocaldistribution(localdistribution)tofindallrandomvariablesThejointdistribution.
Solutionmethod
TheaboveexampleisaverysimpleBayesiannetworkmodel,butifthemodelisverycomplex,thentheenumerationmethodwillbeusedtosolvetheprobability.Itbecomesverycomplicatedanddifficulttocalculate,sootheralternativemethodsmustbeused.Generallyspeaking,Bayesianprobabilitycanbecalculatedinthefollowingways:
Tarkka päättely
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Luetteloitu perustelumenetelmä (kuten yllä oleva esimerkki)
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Muuttujaeliminointialgoritmi (muuttujan eliminointi)
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Satunnainen päättely (MonteCarlomethod)
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Suoranäytteenottoalgoritmi
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Hylkää näytteenottoalgoritmi
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Samoin painotusalgoritmi
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MarkovchainMonteCarloMarkovchainMonteCarloalgorithm
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Here,taketheMarkovchainMonteCarloalgorithmasanexample,andthetypeofMarkovchainMonteCarloalgorithmTherearemany,soonlyoneofthestepsofGibbssamplingisexplainedhere:First,fixthevariablewithagivenvalue,andthenrandomlygiveaninitialvaluetotheothervariableswithoutagivenvalue,andthenenterthefollowingiterativesteps:
(1)Valitse satunnaisesti yksi muuttujista, joilla ei ole arvoa
(2)Ota uusi arvo ehdollisesta jakelusta ja laske sitten uudelleen
Aftertheiterativeclumps,deletethepreviousnumbersthatarenotyetstable,andyoucanfindtheapproximateconditionalprobabilitydistribution.TheadvantageoftheMarkovchainMonteCarloalgorithmisthatitisveryefficientwhencomputingalargenetwork,butthedisadvantageisthattheextractedsamplesarenotindependent.
WhenthestructureandparametersontheBayesiannetworkareknown,wecanusetheabovemethodstofindtheprobabilityofaspecificsituation,butifthestructureorparametersontheInternetareunknown,wemustItismoredifficulttoestimatethestructureorparametersofthenetworkbasedontheobserveddata.Generallyspeaking,itismoredifficulttoestimatethestructureofthenetworkthantheparametersonthenode.AccordingtotheunderstandingoftheBayesiannetworkstructureandthecompletenessoftheobservations,wecandivideitintothefollowingfoursituations:
Rakenne | Havainnot | Menetelmät |
Tunnettu | Valmis | Maksimitodennäköisyysarviointimenetelmä (MLE) |
Tunnettu | Osa | EMalgoritmi GreedyHill-kiipeilymenetelmä |
Tuntematon | Valmis | Hae koko mallitilasta |
Tuntematon | Osa | Rakennealgoritmi EMalgoritmi Rajallinen supistuminen |
Features
1.Bayesiannetworkitselfisanuncertaincausalassociationmodel.Bayesiannetworkisdifferentfromotherdecisionmodels.Ititselfisaprobabilisticknowledgeexpressionandreasoningmodelthatvisualizesmultipleknowledgediagrams,anditmorecloselycontainsthecausalrelationshipandconditionalcorrelationbetweennetworknodevariables.
2.Bayesiannetworkhasastrongabilitytodealwithuncertainproblems.Bayesiannetworkexpressesthecorrelationbetweenvariousinformationelementswithconditionalprobability,andcanlearnandreasonundertheconditionoflimited,incompleteanduncertaininformation.
3.Bayesiannetworkscaneffectivelyexpressandintegratemulti-sourceinformation.Bayesiannetworkcanincorporatevariousinformationrelatedtofaultdiagnosisandmaintenancedecision-makingintothenetworkstructure,andprocessitinaunifiedmanneraccordingtothenode,whichcaneffectivelyintegrateinformationrelatedtotherelationship.
ForBayesiannetworkreasoningresearch,avarietyofapproximatereasoningalgorithmsareproposed,whicharemainlydividedintotwocategories:simulation-basedmethodsandsearch-basedmethods.Inthefieldoffaultdiagnosis,asfarasourhydropowersimulationisconcerned,theprobabilityoffailureisoftenverysmall,soitisgenerallymoresuitabletousesearchinferencealgorithms.Foranexample,wemustfirstanalyzewhichalgorithmmodeltouse:
a.)Ifthenodereliabilitynetworkofthisexampleisasimpledirectedgraphstructure,anditsnumberofnodesissmall,AdopttheprecisereasoningofBayesiannetwork,whichincludesmulti-treepropagationalgorithm,clumptreepropagationalgorithm,graphreductionalgorithm,selecttheappropriatealgorithmfortheinstanceevent;
b.)IfitistheinstanceThegraphstructureofthedrawnnodeiscomplexandthenumberofnodesislarge.Wecanuseapproximatereasoningalgorithmtostudyit.Forspecificimplementation,itisbesttosimplifythecomplexandhugenetwork,andthenconsideritincombinationwithprecisereasoning.
Indailylife,peopleoftenmakecommonsensereasoning,andthiskindofreasoningisusuallyinaccurate.Forexample,ifyouseeapersonwithdamphaircominginandyouthinkitisrainingoutside,thenyoumaybewrong;ifyouseeamanandawomanwithachildinthepark,youthinktheyareafamily,youmayalsoMadeamistake.Inengineering,wealsoneedtomakescientificandreasonablereasoning.However,theproblemsinengineeringpracticearegenerallymorecomplicated,andtherearemanyuncertainfactors.Thisbringsgreatdifficultiestoaccuratereasoning.Longago,uncertaintyreasoningwasanimportantresearchfieldofartificialintelligence.Althoughmanyresearchersinthefieldofartificialintelligenceintroduceothernon-probabilisticprinciples,theyalsobelievethatitispossibletoconstructanduseprobabilisticmethodsbasedoncommonsensereasoning.Inordertoimprovetheaccuracyofreasoning,peopleintroducedprobabilitytheory.TheBayesianNetwork(BayesianNetwork)firstproposedbyJudeaPearlin1988isessentiallyaprobability-baseduncertaintyreasoningnetwork.Itisagraphicalmodelusedtoexpresstheconnectionprobabilityofasetofvariables,anditprovidesawaytoexpresscausalinformation.Atthattime,itwasmainlyusedtodealwithuncertaininformationinartificialintelligence.Subsequently,itgraduallybecamethemainstreamofinformationtechnologytodealwithuncertainty,andithasbeenimportantlyappliedinmanyintelligentsystemsinthefieldsofcomputerintelligencescience,industrialcontrol,andmedicaldiagnosis.
Bayesiantheoryisanimportanttooltodealwithuncertaininformation.Asamethodofuncertaintyreasoningbasedonprobability,Bayesiannetworkshavebeenimportantapplicationsinintelligentsystemsdealingwithuncertaininformation,andhavebeensuccessfullyusedinmedicaldiagnosis,statisticaldecision-making,expertsystems,learningpredictions,etc.field.ThesesuccessfulapplicationsfullydemonstratethatBayesiannetworktechnologyisapowerfulmethodofuncertaintyreasoning.
Bayesianne-verkkojen sovellustaso
Bayesianne-verkkoja käytetään jatkuvasti laskennallisessa biologiassa ja bioinformatiikan geenisäätelyverkoissa), proteiinirakenteessa, geenin ilmentämisanalyysissä, lääketieteessä, asiakirjojen luokittelussa, tiedonhaussa, päätöksenteossa, fuusiossa, suunnittelussa, suunnittelussa, suunnittelussa.