the coupled nodes are given by b t c u2061 i u2211 m 1 m i c u2062 u2062 w i m c u2062 n u2061 o t c u03bc i m c u i m c eq 5 are the mean and covariance matrix of the ith state of a coupled node and mth component of the associated mixture node in the cth channel is the number of mixtures corresponding to the ith state of a coupled node in the cth stream and the weight p u2061 p t c m q t c i is the component of the mixture node in the cth stream at time t the constructed hmm must be trained to identify words maximum likelihood ml training of the dynamic bayesian networks in general and of the coupled hmms in particular is well understood any discrete time and space dynamical system governed by a hidden markov chain emits a sequence of observable outputs with one output observation for each state in a trajectory of such states from the observable sequence of outputs the most likely dynamical system can be calculated the result is a model for the underlying process alternatively given a sequence of outputs the most likely sequence of states can be determined in speech recognition tasks a database of words along with separate training set for each word can be generated unfortunately the iterative maximum likelihood estimation of the.