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隐Markov模型.ppt

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第四讲隐Markov模型Markov过程与Markov链转移概率：akl=P(πi=l|πi-1=k) 初始概率 SunnyEachurncontaincoloredballsandthereare4distinctcolors. Chooseanurnaccordingtosomerandomprocedure,getaballfromtheurn,andrecord(observe)itscolor. Theballisreplaced. Selectanewurnandrepeattheaboveprocedure. Colorsofselectedballsareobservedbut sequenceofchoosingurnsishidden.HiddenMarkovModels-HMM(1)Circlesindicatestates Arrowsindicateprobabilisticdependenciesbetweenstates Greencirclesarehiddenstates Dependentonlyonthepreviousstate “Thepastisindependentofthefuturegiventhepresent.” Purplenodesareobservedstates DependentonlyontheircorrespondinghiddenstateN:{s1…sN}arethevaluesforthehiddenstates M:{o1…oM}arethevaluesfortheobservations P={pi}aretheinitialstateprobabilities A={aij}arethestatetransitionprobabilities B={bik}aretheobservationstateprobabilities {N,M,P,A,B}AnHMM,λ,isa5-tupleconsistingof Nthenumberofstates Mthenumberofpossibleobservations {1,2,..N}Thestartingstateprobabilities P(q0=Si)=i a11 a22 … a1N a21 a22 … a2N : : : aN1 aN2 … aNN b1(1) b1(2) … b1(M) b2(1) b2(2) … b2(M) : : : bN(1) bN(2) … bN(M)Hiddenstates:the(TRUE)statesofasystemthatmaybedescribedbyaMarkovprocess(e.g.,theweather). Observablestates:thestatesoftheprocessthatare`visible'(e.g.,seaweeddampness).Outputmatrix:containingtheprobabilityofobservingaparticularobservablestategiventhatthehiddenmodelisinaparticularhiddenstate. InitialDistribution:containstheprobabilityofthe(hidden)modelbeinginaparticularhiddenstateattimet=1. Statetransitionmatrix:holdingtheprobabilityofahiddenstategiventheprevioushiddenstate.Computetheprobabilityofagivenobservationsequence Givenanobservationsequence,computethemostlikelyhiddenstatesequence Givenanobservationsequenceandsetofpossiblemodels,whichmodelmostcloselyfitsthedata?HMM应用(1)Computetheprobabilityofagivenobservationsequence Givenanobservationsequence,computethemostlikelyhiddenstatesequence Givenanobservationsequenceandsetofpossiblemodels,whichmodelmostcloselyfitsthedata?HMM的基本算法前向－后向算法Spe