Substate tying with combined parameter training and reduction in tied-mixture HMM design

Two approaches are proposed for the design of tied-mixture hidden Markov models (TMHMM). One approach improves parameter sharing via partial tying of TMHMM states. To facilitate tying at the substate level, the state emission probabilities are constructed in two stages or, equivalently, are viewed as a “mixture of mixtures of Gaussians.” This paradigm allows, and is complemented with, an optimization technique to seek the best complexity-accuracy tradeoff solution, which jointly exploits Gaussian density sharing and substate tying. Another approach to enhance model training is combined training and reduction of model parameters. The procedure starts by training a system with a large universal codebook of Gaussian densities. It then iteratively reduces the size of both the codebook and the mixing coefficient matrix, followed by parameter re-training. The additional cost in design complexity is modest. Experimental results on the ISOLET database and its E-set subset show that substate tying reduces the classification error rate by over 15%, compared to standard Gaussian sharing and whole-state tying. TMHMM design with combined training and reduction of parameters reduces the classification error rate by over 20% compared to conventional TMHMM design. When the two proposed approaches were integrated, 25% error rate reduction over TMHMM with whole-state tying was achieved.