A Constrained Line Search Optimization Method for Discriminative Training of HMMs

In this paper, we propose a novel optimization algorithm called constrained line search (CLS) for discriminative training (DT) of Gaussian mixture continuous density hidden Markov model (CDHMM) in speech recognition. The CLS method is formulated under a general framework for optimizing any discriminative objective functions including maximum mutual information (MMI), minimum classification error (MCE), minimum phone error (MPE)/minimum word error (MWE), etc. In this method, discriminative training of HMM is first cast as a constrained optimization problem, where Kullback-Leibler divergence (KLD) between models is explicitly imposed as a constraint during optimization. Based upon the idea of line search, we show that a simple formula of HMM parameters can be found by constraining the KLD between HMM of two successive iterations in an quadratic form. The proposed CLS method can be applied to optimize all model parameters in Gaussian mixture CDHMMs, including means, covariances, and mixture weights. We have investigated the proposed CLS approach on several benchmark speech recognition databases, including TIDIGITS, Resource Management (RM), and Switchboard. Experimental results show that the new CLS optimization method consistently outperforms the conventional EBW method in both recognition performance and convergence behavior.