Hidden Markov Models
Hidden Markov models (HMMs), are used for statistical modelling of nonstationary stochastic processes such as speech and time-varying noise. An HMM models the time-variations of the statistics of a random process, with a Markovian chain of state-dependent stationary sub-processes. An HMM is essentially a Bayesian finite state process, with a Markovian prior for modelling the transitions between the states, and a set of state pdfs for the modelling of the random variations of the stochastic process within each state.
This chapter begins with a brief introduction to continuous and finite-state nonstationary models, before concentrating on the theory and applications of hidden Markov models. We study the Baum-Welch method for the maximum likelihood training of the parameters of an HMM, and then consider the use of HMMs and the Viterbi decoding algorithm for the classification and decoding of an unlabelled observation sequence. Finally the application of HMMs in signal enhancement is considered.
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