classification - Basic Hidden Markov Model, Viterbi algorithm -


i new hidden markov models , trying wrap head around pretty basic part of theory.

i use hmm classifier, so, given time series of data have 2 classes: background , signal.

how emission probabilities estimated each class? viterbi algorithm need template of background , signal estimate prob(data|state)? or have missed point?

to classification viterbi need know model parameters.
background , signal 2 hidden states. model parameters , observed data want use viterbi calculate sequence of hidden states.

to quote hmmlearn documentation:

the hmm generative probabilistic model, in sequence of observable x variables generated sequence of internal hidden states z. hidden states not observed directly. transitions between hidden states assumed have form of (first-order) markov chain. can specified start probability vector π , transition probability matrix a. emission probability of observable can distribution parameters θ conditioned on current hidden state. hmm determined π, , θ

.

there 3 fundamental problems hmms:

given model parameters , observed data, estimate optimal sequence of hidden states. given model parameters , observed data, calculate likelihood of data. given observed data, estimate model parameters.

the first , second problem can solved dynamic programming algorithms known viterbi algorithm , forward-backward algorithm, respectively. last 1 can solved iterative expectation-maximization (em) algorithm, known baum-welch algorithm.


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