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9th Annual Conference of the International-Speech-Communication-Association (INTERSPEECH 2008)

作者： Liu, Peng Soong, Frank Microsoft Res Asia Beijing 100080 Peoples R China

ISBN: (纸本)9781615673780

In this paper, we reformulate the optimization in discriminative training (DT) of HMMs as an ellipsoid constrained quadratic programming (ECQP) problem, where a second order of the nonlinear space is adopted. We show that the unique optimal solution of ECQP can be obtained by an efficient line search and no relaxation is needed as in a general quadratically constrained quadratic programming (QCQP). Moreover, a subspace combination condition is introduced to further simplify it under certain cases. The concrete ECQP form of DT of HMMs is given based on a locality constraint and reasonable assumptions, and the algorithm can be conducted to update Gaussians jointly or separately in either sequential or batch mode. Under the perspective of ECQP, relationships between various popular DT optimization algorithms are discussed. Experimental results on two recognition tasks show that ECQP considerably outperforms other popular algorithms in terms of final recognition accuracy and convergence speed in iterations.

关键词： discriminative training ellipsoid constrained quadratic programming hidden Markov model

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A quadratic Optimization Approach to Discriminative Training of CDHMMs

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IEEE SIGNAL PROCESSING LETTERS 2009年第1-3期16卷 149-152页

作者： Liu, Peng Soong, Frank Microsoft Res Asia Beijing 100190 Peoples R China

In this letter, we reformulate the discriminative training (DT) of continuous density hidden Markov models (CDHMMs) as an ellipsoid constrained quadratic programming (ECQP) problem, and we solve it by a line search algorithm. The ellipsoid constraint intrinsically arises from the step-size control in each iteration of DT optimization, which leads to an efficient solution without relaxing the objective function to be convex, as in a general quadratic programming problem. Moreover, the problem can be equivalently converted to a lower-dimensional one under some conditions, which helps further to simplify the solution. We show that under a Kullback-Leibler divergence (KLD) constraint, DT of CDHMM parameters such as Gaussian means and variances can be efficiently solved by the proposed algorithm, with only mild assumptions adopted. Experimental results on two tasks show that the ECQP approach considerably outperforms other popular algorithms in terms of both final recognition accuracy and convergence speed.

关键词： Discriminative training ellipsoid constrained quadratic programming hidden Markov model

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