The discrimination technique for estimating parameters of Gaussian mixtures that is based on the Extended Baum-Welch transformations (EBW) has had significant impact on the speech recognition community. \ud In this paper we introduce a general definition of a family of EBW transformations that can be associated with a weighted sum of updated and initial models. We compute a gradient steepness measurement for a family of EBW transformations that are applied to functions of Gaussian mixtures and demonstrate the growth property of these transformations. We consider EBW transformations of discriminative functions in which EBW controlled parameters are adapted to a gradient steepness measurement or to the likelihood of the data given the model. We present experimental results that show that adapted EBW transformations can significantly speed up estimating parameters of Gaussian mixtures and give better decoding results
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