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: