an introduction to conditional random fields

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1、AnIntroductiontoConditionalRandomFieldsCharlesSuttonUniversityofEdinburghcsutton@inf.ed.ac.ukAndrewMcCallumUniversityofMassachusettsAmherstmccallum@cs.umass.edu17November2010AbstractOftenwewishtopredictalargenumberofvariablesthatdependoneachotheraswellasonotherobservedvariables.Structuredpredic

2、-tionmethodsareessentiallyacombinationofclassicationandgraph-icalmodeling,combiningtheabilityofgraphicalmodelstocompactlymodelmultivariatedatawiththeabilityofclassicationmethodstoperformpredictionusinglargesetsofinputfeatures.Thistutorialde-scribesconditionalrandomelds,apopularprobabilisticm

3、ethodforstructuredprediction.CRFshaveseenwideapplicationinnaturallan-guageprocessing,computervision,andbioinformatics.WedescribemethodsforinferenceandparameterestimationforCRFs,includingarXiv:1011.4088v1[stat.ML]17Nov2010practicalissuesforimplementinglargescaleCRFs.Wedonotassumepreviousknowledg

4、eofgraphicalmodeling,sothistutorialisintendedtobeusefultopractitionersinawidevarietyofelds.Contents1Introduction12Modeling52.1GraphicalModeling62.2GenerativeversusDiscriminativeModels102.3Linear-chainCRFs182.4GeneralCRFs212.5ApplicationsofCRFs232.6FeatureEngineering242.7NotesonTerminology263In

5、ference273.1Linear-ChainCRFs283.2InferenceinGraphicalModels323.3ImplementationConcerns404ParameterEstimation43i4.1MaximumLikelihood444.2StochasticGradientMethods524.3Parallelism544.4ApproximateTraining544.5ImplementationConcerns615RelatedWorkandFutureDirections635.1RelatedWork635.2FrontierAreas

6、701IntroductionFundamentaltomanyapplicationsistheabilitytopredictmultiplevariablesthatdependoneachother.Suchapplicationsareasdiverseasclassifyingregionsofanimage[60],estimatingthescoreinagameofGo[111],segmentinggenesinastrandofDNA[5],andextractingsyntaxfromnatural-languagetext[123].Insuchapplic

7、ations,wewishtopredictavectory=fy0;y1;:::;yTgofrandomvariablesgivenanobservedfeaturevectorx.Arelativelysimpleexamplefromnatural-languageprocessingispart-of-speechtagging,inwhicheachvariableysisthepart-of-speechtagofthewordatpositi