History and Theoretical Basics of Hidden Markov Models

Abstract

The following chapter can be understood as one sort of brief introduction to the history and basics of the Hidden Markov Models. Hidden Markov Models (HMMs) are learnable finite stochastic automates. Nowadays, they are considered as a specific form of dynamic Bayesian networks. Dynamic Bayesian networks are based on the theory of Bayes (Bayes & Price, 1763). A Hidden Markov Model consists of two stochastic processes. The first stochastic process is a Markov chain that is characterized by states and transition probabilities. The states of the chain are externally not visible, therefore “hidden”. The second stochastic process produces emissions observable at each moment, depending on a state-dependent probability distribution. It is important to notice that the denomination “hidden” while defining a Hidden Markov Model is referred to the states of the Markov chain, not to the parameters of the model. The history of the HMMs consists of two parts. On the one hand there is the history of Markov process and Markov chains, and on the other hand there is the history of algorithms needed to develop Hidden Markov Models in order to solve problems in the modern applied sciences by using for example a computer or similar electronic devices.