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 hare been proposed. This paper aims to provide a unifying framework for many of these models, BS 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 HMM's are analyzed and compared based on this graphical method.