Non-uniform Kernel Allocation Based Parsimonious HMM

In conventional Gaussian mixture based Hidden Markov Model (HMM), all states are usually modeled with a uniform, fixed number of Gaussian kernels. In this paper, we propose to allocate kernels nonuniformly to construct a more parsimonious HMM. Different number of Gaussian kernels are allocated to states in a non-uniform and parsimonious way so as to optimize the Minimum Description Length (MDL) criterion, which is a combination of data likelihood and model complexity penalty. By using the likelihoods obtained in Baum-Welch training, we develop an effcient backward kernel pruning algorithm, and it is shown to be optimal under two mild assumptions. Two databases, Resource Management and Microsoft Mandarin Speech Toolbox, are used to test the proposed parsimonious modeling algorithm. The new parsimonious models improve the baseline word recognition error rate by 11.1% and 5.7%, relatively. Or at the same performance level, a 35-50% model compressions can be obtained.