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1、Conditionalrandomfield1ConditionalrandomfieldAconditionalrandomfield(CRF)isastatisticalmodellingmethodoftenappliedinpatternrecognition.Morespecificallyitisatypeofdiscriminativeundirectedprobabilisticgraphicalmodel.Itisusedtoencodeknownrelationshipsbetweenobs
2、ervationsandconstructconsistentinterpretations.Itisoftenusedforlabelingorparsingofsequentialdata,suchasnaturallanguagetextorbiologicalsequences[1]andcomputervision[2].Specifically,CRFsfindapplicationsinshallowparsing[3],namedentityrecognition[4]andgenefindin
3、g,amongothertasks,beinganalternativetotherelatedhiddenMarkovmodels.Incomputervision,CRFsareoftenusedforobjectrecognitionandimagesegmentation.DescriptionLafferty,McCallumandPereira(2001)defineaCRFonobservationsandrandomvariablesasfollows:Letbeagraphsuchthat,s
4、othatisindexedbytheverticesof.Thenisaconditionalrandomfieldincase,whenconditionedon,therandomvariablesobeytheMarkovpropertywithrespecttothegraph:,wheremeansthatandareneighborsin.WhatthismeansisthataCRFisanundirectedgraphicalmodelwhosenodescanbedividedintoexa
5、ctlytwodisjointsetsand,theobservedandoutputvariables,respectively;theconditionaldistributionisthenmodeled.InferenceForgeneralgraphs,theproblemofexactinferenceinCRFsisintractable.TheinferenceproblemforaCRFisbasicallythesameasforanMRFandthesameargumentshold.[5
6、]Howeverthereexistspecialcasesforwhichexactinferenceisfeasible:•Ifthegraphisachainoratree,messagepassingalgorithmsyieldexactsolutions.Thealgorithmsusedinthesecasesareanalogoustotheforward-backwardandViterbialgorithmforthecaseofHMMs.•IftheCRFonlycontainspair-
7、wisepotentialsandtheenergyissubmodular,combinatorialmincut/maxflowalgorithmsyieldexactsolutions.Ifexactinferenceisimpossible,severalalgorithmscanbeusedtoobtainapproximatesolutions.Theseinclude:•Loopybeliefpropagation•Alphaexpansion•Meanfieldinference•Linearp
8、rogrammingrelaxationsParameterLearningLearningtheparametersisusuallydonebymaximumlikelihoodlearningfor.Ifallnodeshaveexponentialfamilydistributionsandallnodesareobservedduringtraining,thisoptimi
