Hidden Markov Models

Abstract

AbstractAhidden Markov model (HMM)is asystemthat evolves over time withprobabilistic Markov dynamics, and whose states arehidden(unobservable). One of the most studied applications of hidden Markov models is the recognition of patterns in spoken language to identify words. This is the main purpose of speech recognition theory. HMM theory has evolved to include many other fields such as biosciences, computer vision, communications, acoustics, and finance. This chapter presents an introduction to hidden Markov models and is organized as follows. The first section introduces the fundamentals of hidden Markov models. The next section discusses three fundamental problems and their applications: 1. The evaluation problem: given a model and a sequence of observations, how do we compute the probability of the sequence (likelihood of the sequence given the model)? 2. The decoding problem (most probable explanation): given a model and a sequence of observations, what is the optimal, in some meaningful sense, sequence of states that produced the observations? 3. The estimation problem: given a sequence of observations, how do we adjust the model parameters to maximize the probability of getting the sequence?The third section presents an application of hidden Markov models in computational biology.