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A formally unifying approach for a class of discriminative training criteria including Maximum Mutual Information (MMI) and Minimum Classification Error (MCE) criterion is presented, including the optimization methods gradient descent (GD) and extended Baum-Welch (EB) algorithm. Using discriminative criteria, novel approaches to splitting of mixture Gaussian densities and to linear feature transformation are derived. Furthermore, efficient algorithms for the application of discriminative training to speech recognition with both small and large vocabulary are developed. Finally, a novel evaluation method for the stochastic models used in speech recognition is derived using methods related to discriminative training. 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