Hidden markov model with binned duration and its application

Hidden Markov models (HMM) have been widely used in various applications such as speech processing and bioinformatics. However, the standard hidden Markov model requires state occupancy durations to be geometrically distributed, which can be inappropriate in some real-world applications where the distributions on state intervals deviate significantly from the geometric distribution, such as multi-modal distributions and heavy-tailed distributions. The hidden Markov model with duration (HMMD) avoids this limitation by explicitly incorporating the appropriate state duration distribution, at the price of significant computational expense. As a result, the applications of HMMD are still quited limited. In this work, we present a new algorithm - Hidden Markov Model with Binned Duration (HMMBD), whose result shows no loss of accuracy compared to the HMMD decoding performance and a computational expense that only differs from the much simpler and faster HMM decoding by a constant factor. More precisely, we further improve the computational complexity of HMMD from &thetas;( TNN + TND) to &thetas;(TNN + TND*), where TNN stands for the computational complexity of the HMM, D is the max duration value allowed and can be very large and D* generally could be a small constant value.