Which stochastic models allow Baum-Welch training?

Since the introduction of hidden Markov models to the field of automatic speech recognition, a great number of variants to the original model have been proposed. This paper aims to provide a unifying framework for many of these models. By representing model assumptions in the form of a graph, we show that an algorithm similar to Baum´s exists only if a certain graph-theoretical criterion-the chordality-is satisfied. In this case, the equations for the forward calculation and parameter re-estimation can readily be read from the graph´s clique decomposition. As an illustration of the usefulness of this approach, several previously proposed enhancements to HMMs are analyzed and compared based on this graphical method