Markov Model Concepts: The Essence

Abstract

The integrated use of hidden Markov models (HMMs) and Markov chain models can be considered the state-of-the-art for the analysis of sequential data. The former represents a generative model that covers the “appearance” of the underlying data whereas the latter describes restrictions of possible hypotheses sequences. Hidden Markov models describe a two-stage stochastic process with hidden states and observable outputs. The first stage can be interpreted as a probabilistic finite state automaton, which is the basis for the generative modeling as it is described by the second stage. Markov chain models are usually realized as stochastic n-gram models, which describe the probability of the occurrence of entire symbol sequences. For both HMMs and Markov chain models efficient algorithms exist for parameter estimation and for model evaluation. They can be used in an integrated manner for effective segmentation and classification of sequential data. This chapter gives a detailed overview of the theoretical foundations of Markovian models as they are used for handwriting recognition.