Solving large margin estimation of HMMS via semidefinite programming
Xinwei Li, Hui Qin Jiang · 2006
In this paper, we propose to use a new optimization method, i.e., semidefinite programming (SDP), to solve large margin estimation (LME) problem of continuous density hidden Markov models (CDHMM’s) in speech recognition. First of all, we introduce a new constraint into the LME to guarantee the boundedness of the margin of CDHMM’s. Secondly, we show that the LME problem under this new constraint can be formulated as a semidefinite programming problem under some relaxation conditions and it can be solved very efficiently by using some fast optimization algorithms specially designed for SDP. The new method is evaluated in a speaker independent E-set speech recognition task on the OGI ISOLET database. Experimental results clearly demonstrate that the large margin estimation via the semidefinite programing (SDP) method can achieve significant word error rate (WER) reduction over the conventional HMM training methods, such as MLE and MCE. It is also shown that the new SDP-based method outperforms the previously proposed optimization methods using gradient descent search.