Hidden Markov models: a guided tour

Hidden Markov modeling is a probabilistic technique for the study of time series. Hidden Markov theory permits modeling with any of the classical probability distributions. The costs of implementation are linear in the length of data. Models can be nested to reflect hierarchical sources of knowledge. These and other desirable features have made hidden Markov methods increasingly attractive for problems in language, speech and signal processing. The basic ideas are introduced by elementary examples in the spirit of the Polya urn models. The main tool in hidden Markov modeling is the Baum-Welch (or forward-backward) algorithm for maximum likelihood estimation of the model parameters. This iterative algorithm is discussed both from an intuitive point of view as an exercise in the art of counting and from a formal point of view via the information-theoretic Q-function. Selected examples drawn from the literature illustrate how the Baum-Welch technique places a rich variety of computational models at the disposal of the researcher