Generalization of extended baum-welch parameter estimation for discriminative training and decoding

We demonstrate the generalizability of the Extended Baum-Welch (EBW) algorithm not only for HMM parameter estimation but for decoding as well. We show that there can exist a general function associated with the objective function under EBW that reduces to the well-known auxiliary function used in the Baum-Welch algorithm for maximum likelihood estimates. We generalize representation for the updates of model parameters by making use of a differentiable function (such as arithmetic or geometric mean) on the updated and current model parameters and describe their effect on the learning rate during HMM parameter estimation. Improvements on speech recognition tasks are also presented here.