Hidden Markov Random Fields

Abstract

A hidden Markov model is a random sequence or field Y(t)= =f(X(t)), where X(t), tin bold Z^d, is a Markov process (d=1)= or a Markov random field with values in a finite set of cardinality N= . The authors address the problem of approximating a general stationary r= andom process or field with such a hidden Markov model; X is supposed t= o be first-order but f and N can be chosen arbitrarily. They prove th= at hidden Markov models are weakly dense among finite-state-space station= ary processes or fields. The issue of modeling is then considered, a non-= parametric estimator is proposed and is proved to be consistent. The meth= odology is illustrated on two examples in speech recognition and texture = modeling, and more applications are given.