Generalized Discriminative Training for Speech Recognition

In speech recognition, discriminative training has proved to be an effective method to improve recognition accuracy. It has successfully improved systems of different scales and different languages. While discriminative training has been developing for over 20 years, it continues to draw attention to researchers and remains to be one of the most important topics in speech recognition to date. Discriminative training aims to directly minimize the errors made by the generative models. It is often formulated as an optimization problem which involves the reference and the competing hypotheses. The goal of the optimization is to search for the model parameters which can minimize the error on the train set, and the error is often represented by some smoothed error functions. While being an effective method, discriminative training comes with a few drawbacks. First, the optimization problem is difficult to solve due to the complex objective functions. This leads to the need of heuristics and smoothing techniques in the optimization algorithms. Second, discriminative training is much more time consuming compared to the conventional maximum likelihood (ML) approach, since in addition to the reference, discriminative training also considers the competitors. The prolonged training time becomes an even bigger issue when one incorporates both model space and feature space discriminative training. The goal of this thesis is to propose a family of optimization algorithms which are simple and efficient. When tuning and heuristics become necessary, the theories behind the algorithms should explain the meaning of the parameters, and give the users some basic ideas about tuning instead of using a pure empirical approach. Therefore, we reformulate the optimization problem for discriminative training, and propose new optimization algorithms based on Lagrange relaxation. In which, we relax the difficult optimization problems into simpler convex problems. We propose the generalized Baum-Welch (GBW) algorithm for model space discriminative training and the generalized discriminative feature transformation (GDFT) for feature space discriminative training. The GBW algorithm generalizes the Baum-Welch (BW) and the extended Baum-Welch (EBW) algo-