04_07.04_-_Hidden_Markov_Models_2-2_-_9_slides_05-28

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1、NLPIntroductiontoNLPHiddenMarkovModels(cont’d)ObservationLikelihood•GivenmultipleHMMs–e.g.,fordiferentlanguages–Whichoneisthemostlikelytohavegeneratedtheobservationsequence•Naïvesolution–tryallpossiblestatesequencesForwardAlgorithm•Dynamicprogrammingmethod–Compu

2、tingaforwardtrellisthatencodesallpossiblestatepaths.–BasedontheMarkovassumptionthattheprobabilityofbeinginanystateatagiventimepointonlydependsontheprobabilitiesofbeinginallstatesattheprevioustimepointHMMLearning•Supervised–Trainingsequencesarelabeled•Unsupervise

3、d–Trainingsequencesareunlabeled–Knownnumberofstates•Semi-supervised–SometrainingsequencesarelabeledSupervisedHMMLearning•EstimatethestatictransitionprobabilitiesusingMLECount(q=s,q=s)tit+1ja=ijCount(q=s)ti•EstimatetheobservationprobabilitiesusingMLECount(q=s,o=v

4、)ijikb(k)=jCount(q=s)ij•UsesmoothingUnsupervisedHMMTraining•Given:–observationsequences•Goal:–buildtheHMM•UseEM(ExpectationMaximization)methods–forward-backward(Baum-Welch)algorithm–Baum-WelchfindsanapproximatesolutionforP(O

5、µ)OutlineofBaum-Welch•Algorithm–Random

6、lysettheparametersoftheHMM–Untiltheparametersconvergerepeat:•Estep–determinetheprobabilityofthevariousstatesequencesforgeneratingtheobservations•Mstep–reestimatetheparametersbasedontheseprobabilities•Notes–thealgorithmguaranteesthatateachiterationthelikelihoodof

7、thedataP(O

8、µ)increases–itcanbestoppedatanypointandgiveapartialsolution–itconvergestoalocalmaximumNLP