隐马尔可夫模型_刘秉权

2006112„„„„„3NNSSS,,,21LtqttjS1-t,1,2,L),Sq,Sq|SP(qk2-ti1-tjtL===t1−t())Sq|SP(q),Sq,Sq|SP(qi1-tjtk2-ti1-tjt======L4(MarkovModel)tji,i1-tjta)Sq|SP(q===,Nji,1≤≤ji,a0aji,≥1aN1jji,=∑=5„6M1S2S3S8.01.01.02.06.02.03.03.04.0][==ijaA7=O4233213113133332332131131333333231133310536.1)2.0)(1.0)(3.0)(4.0)(1.0)(8.0)(8.0(1)|()|()|()|()|()|()|()()|,,,,,,,()|(−×==⋅⋅⋅⋅⋅⋅⋅=⋅⋅⋅⋅⋅⋅⋅==aaaaaaaSSPSSPSSPSSPSSPSSPSSPSPMSSSSSSSSPMOP8(HiddenMarkovModel,HMM)„MM„HMM()()9NMHMM1011„„„12HMM),,,,(πλBAMN=),,(πλBA=NMABπ13ijaA=)|(1itjtijSqSqPa===−Nji≤≤,10≥ija11=∑=Njija14jSkv)(kbBj=)|()(jtktjSqvOPkb===Nj≤≤1Mk≤≤10)(≥kbj1)(1=∑=Mkjkb15iππ=)(1iiSqP==πNi≤≤10≥iπ11=∑=Niiπ16),,(πλBA=TOOOO,,,21L=1.iππ=iSq=12.1=t3.iS)(kbjktvO=4.ijajtSq=+15.1+=ttTt3417HMM1TOOOO,,,21L=),,(πλBA=)|(λOP2TOOOO,,,21L=),,(πλBA=TqqqS,,,21L=SO3),,(πλBA=)|(λOP181∑∑==QQQOPQPQOPOP),|()|()|,()|(λλλλTOOOO,,,21L=TqqqQ,,,21L=TTqqqqqqqaaaQP132211)|(−=Lπλ)()()(),|(2121TqqqObObObQOPTL=λ)(TNO)(2TNO19(DynamicProgramming)„(DynamicTime-Wraping)„20HMM21)|,()(21λαitttSqOOOPi==LTt≤≤11.)()(11Obiiiπα=Ni≤≤12.)(])([)(111+=+∑=tjNiijttObaijαα11−≤≤Tt,Nj≤≤13.∑==NiTiOP1)()|(αλ22S1S2S3SNtt+1)(itα)(1jt+α)(])([)(111+=+∑=tjNiijttObaijαα231,3)|,()(21λβitTtttSqOOOPi==++L11−≤≤Tt1.1)(=iTβNi≤≤12.∑=++=NjttjijtjObai111)()()(ββNiTt≤≤−≤≤1,113.∑==NiiOP11)()|(βλ24S1S2SiS3SNtt+1)(itβ)(1jt+β∑=++=NjttjijtjObai111)()()(ββ252ViterbiHMM),|(maxarg*λOQPQQ=)(2TNOViterbi)|,,,,,(max)(2121,,,121λδtitqqqtOOOSqqqPitLLL==−)(])(max[)(11++=tiijtjtObajiδδ)(itϕ26Viterbi)()(11Obiiiπδ=0)(1=iϕNi≤≤1)(])([max)(11tjijtNitObaij−≤≤=δδNjTt≤≤≤≤1,2)(])([maxarg)(11tjijtNitObaij−≤≤=δϕNjTt≤≤≤≤1,2)])([max1*ipTNiδ≤≤=)]([maxarg1*iqTNiTδ≤≤=)(*11*++=tttqqϕ1,...,2,1−−=TTt273HMMTOOOO,,,21L=λiπija)(kbjO)|(λOP28HMM),(ˆ1iiSqδπ=∑∑==+×==1-T1it1-T1j1tit)S,(q)S,(q)S,(q)(ˆttiijiijqqQqqQaδδδ∑∑==×==T1jtT1ktjt)S,(q)v,(O)S,(q)(ˆttjkjjqQvqQkbδδδ⎩⎨⎧≠==yxyxyx01),(δ29EM(Expectation-Maximization)„HMMEM„EM“(E)”“(M)”„“E”“M”„EM30(Baum-Welch)1.iπija)(kbj0λ0=i2.EMEiλ12),(jitξ)(itγME3iπija)(kbj1+iλ3.1+=iiEMiπija)(kbj31(1)HMMti1+tj∑∑==++++++++========NiNjttjijtttjijtttjijtjtitjtittjObaijObaiOPjObaiOPOSqSqPOSqSqPji1111111111)()()()()()()|()()()()|()|,,(),|,(),(βαβαλβαλλλξ3233(2)HMMti∑==Njttjii1),()(ξγ34(3))(S1i1iqiγπ==∑∑====1-T1t1-T1t(i)j)(i,)(ttiijiijqqQqqQaγξ∑∑==×==T1T1kt(j))v,(O(j))(ttttjkjjqQvqQkbγδγ35HMM„„„„„„„„„„DNA/36NLP„(POSTagging)„N-gram„HMM„……