HiddenMarkovModelsDavidMeirBleiNovember1,1999WhatisanHMM?GraphicalModelCirclesindicatestatesArrowsindicateprobabilisticdependenciesbetweenstatesWhatisanHMM?GreencirclesarehiddenstatesDependentonlyonthepreviousstate“Thepastisindependentofthefuturegiventhepresent.”WhatisanHMM?PurplenodesareobservedstatesDependentonlyontheircorrespondinghiddenstateHMMFormalism{S,K,P,A,B}S:{s1…sN}arethevaluesforthehiddenstatesK:{k1…kM}arethevaluesfortheobservationsSSSKKKSKSKHMMFormalism{S,K,P,A,B}P={pi}aretheinitialstateprobabilitiesA={aij}arethestatetransitionprobabilitiesB={bik}putethemostlikelyhiddenstatesequenceGivenanobservationsequenceandsetofpossiblemodels,whichmodelmostcloselyfitsthedata?oTo1otot-1ot+putetheprobabilityoftheobservationsequenceDecodingDecodingoTo1otot-1ot+1x1xt+1xTxtxt-1
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