MARKOV RANDOM FIELDS

Jon Hamaker
Institute for Signal and Information Processing
Mississippi State University, Mississippi State, MS 39762
email: hamaker@isip.msstate.edu

ABSTRACT

The assumptions and processes associated with using Markov chains are familiar to the speech community. These form the framework of most state-of-the-art speech recognition systems today. However, Markov chains are only a specific example of a much broader set of models known as Markov random fields. Rather than being associated with temporal dependencies, such as in Markov chains, Markov random fields are concerned with general spatial dependencies of states in the model. A famous example of this is the Ising Model of ferromagnetism which describes the probability of magnetic polarity at a point based on the polarity at surrounding points. Naturally, this branch of mathematics has found numerous other applications in image processing, and pattern recognition which exploit the spatial framework of the Markov random fields.

In this talk we present a detailed explanation of the mathematical framework used in describing Markov random fields. We will be particularly interested in examining the similarities and differences between the Markov chains common to speech recognition and the generalized Markov random fields. We will draw upon several examples to support and motivate the mathematical explanations.

Additional items of interest: